@inproceedings{2091,
abstract = {We present a novel multi-scale representation and acquisition method for the animation of high-resolution facial geometry and wrinkles. We first acquire a static scan of the face including reflectance data at the highest possible quality. We then augment a traditional marker-based facial motion-capture system by two synchronized video cameras to track expression wrinkles. The resulting model consists of high-resolution geometry, motion-capture data, and expression wrinkles in 2D parametric form. This combination represents the facial shape and its salient features at multiple scales. During motion synthesis the motion-capture data deforms the high-resolution geometry using a linear shell-based mesh-deformation method. The wrinkle geometry is added to the facial base mesh using nonlinear energy optimization. We present the results of our approach for performance replay as well as for wrinkle editing. },
author = {Bernd Bickel and Botsch, Mario and Angst, Roland and Matusik, Wojciech and Otaduy, Miguel A and Pfister, Hanspeter and Groß, Markus S},
publisher = {ACM},
title = {{Multi scale capture of facial geometry and motion}},
doi = {doi:10.1145/1275808.1276419},
year = {2007},
}
@article{2093,
abstract = {We present a novel multi-scale representation and acquisition method for the animation of high-resolution facial geometry and wrinkles. We first acquire a static scan of the face including reflectance data at the highest possible quality. We then augment a traditional marker-based facial motion-capture system by two synchronized video cameras to track expression wrinkles. The resulting model consists of high-resolution geometry, motion-capture data, and expression wrinkles in 2D parametric form. This combination represents the facial shape and its salient features at multiple scales. During motion synthesis the motion-capture data deforms the high-resolution geometry using a linear shell-based mesh-deformation method. The wrinkle geometry is added to the facial base mesh using nonlinear energy optimization. We present the results of our approach for performance replay as well as for wrinkle editing. },
author = {Bernd Bickel and Botsch, Mario and Angst, Roland and Matusik, Wojciech and Otaduy, Miguel A and Pfister, Hanspeter and Groß, Markus S},
journal = {ACM Transactions on Graphics},
number = {3},
publisher = {ACM},
title = {{Multi scale capture of facial geometry and motion}},
doi = {10.1145/1276377.1276419},
volume = {26},
year = {2007},
}
@article{2118,
abstract = {We extend to infinite dimensions an explicit formula of Chill, Fašangová, Metafune, and Pallara for the optimal angle of analyticity of analytic Ornstein-Uhlenbeck semigroups. The main ingredient is an abstract representation of the Ornstein-Uhlenbeck operator in divergence form. },
author = {Jan Maas and van Neerven, Jan M},
journal = {Archiv der Mathematik},
number = {3},
pages = {226 -- 236},
publisher = {Birkhäuser},
title = {{On analytic Ornstein-Uhlenbeck semigroups in infinite dimensions}},
doi = {10.1007/s00013-007-2082-x},
volume = {89},
year = {2007},
}
@article{221,
author = {De La Bretèche, Régis and Browning, Timothy D},
journal = {Michigan Mathematical Journal},
number = {1},
pages = {51 -- 80},
publisher = {Project Euclid},
title = {{On Manin's conjecture for singular del Pezzo surfaces of degree four, I}},
doi = {10.1307/mmj/1177681985},
volume = {55},
year = {2007},
}
@article{222,
abstract = {Acknowledgements. The authors are grateful to Ulrich Derenthal and Brendan Hassett for several useful conversations relating to universal torsors for singular del Pezzo surfaces. Special thanks are due to Roger Heath–Brown whose ideas led us to the proof of Lemma 6. The paper was finalised while the first author was at the École Normale Supérieure, and the second author was at Oxford University supported by EPSRC grant number GR/R93155/01. The hospitality and financial support of these institutions is gratefully acknowledged. Finally, the authors would like to thank the anonymous referee for his careful reading of the manuscript and numerous useful suggestions.},
author = {de la Bretèche, Régis and Timothy Browning},
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
number = {3},
pages = {579 -- 605},
publisher = {Unknown},
title = {{On Manin's conjecture for singular del Pezzo surfaces of degree four, II}},
doi = {10.1017/S0305004107000205},
volume = {143},
year = {2007},
}
@article{223,
abstract = {Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B → ∞. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.},
author = {Timothy Browning},
journal = {Monatshefte fur Mathematik},
number = {1},
pages = {13 -- 38},
publisher = {Springer},
title = {{Density of integer solutions to diagonal quadratic forms}},
doi = {10.1007/s00605-007-0457-5},
volume = {152},
year = {2007},
}
@article{7753,
abstract = {In many species, females show reduced expression of a trait that is under sexual selection in males, and this expression is thought to be maintained through genetic associations with the male phenotype. However, there is also the potential for the female trait to convey an advantage in intrasexual conflicts over resources. We tested this hypothesis in a feral population of Soay sheep, in which males and females have a polymorphism for horn development, producing either full (normal horned), reduced (scurred) or no (polled, females only) horns. During the lambing period, females who possessed horns were more likely to initiate and win aggressive interactions, independent of age, weight and birthing status. The occurrence of aggression was also context dependent, decreasing over the lambing period and associated with local density. Our results demonstrate that a trait that confers benefits to males during intrasexual competition for mates may also be used by females in intrasexual competition over resources: males use weaponry to gain mates, whereas females use weaponry to gain food.},
author = {Robinson, Matthew Richard and Kruuk, Loeske E.B},
issn = {1744-9561},
journal = {Biology Letters},
number = {6},
pages = {651--654},
publisher = {The Royal Society},
title = {{Function of weaponry in females: The use of horns in intrasexual competition for resources in female Soay sheep}},
doi = {10.1098/rsbl.2007.0278},
volume = {3},
year = {2007},
}
@unpublished{6321,
abstract = {These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.},
author = {Browning, Timothy D},
booktitle = {arXiv},
title = {{The Manin conjecture in dimension 2}},
year = {2007},
}
@inbook{6323,
abstract = {This paper surveys recent progress towards the Manin conjecture for (singular and non-singular) del Pezzo surfaces. To illustrate some of the techniques available, an upper bound of the expected order of magnitude is established for a singular del Pezzo surface of degree four.},
author = {Browning, Timothy D},
booktitle = {A Tribute to Gauss and Dirichlet},
pages = {39--56},
publisher = {American Mathematical Society},
title = {{An overview of Manin's conjecture for del Pezzo surfaces}},
volume = {7},
year = {2007},
}
@article{128,
abstract = {A 671 nm diode laser with a mode-hop-free tuning range of 40 GHz is described. This long tuning range is achieved by simultaneously ramping the external cavity length with the laser injection current. The laser output pointing remains fixed, independent of its frequency because of the cover slip cavity design. This system is simple, economical, robust, and easy to use for spectroscopy, as we demonstrate with lithium vapor and lithium atom beam experiments. },
author = {Carr, Adra and Serchest, Yancey and Waitukaitis, Scott R and Perreault, John and Lonij, Vincent and Cronin, Alexander},
journal = {Review of Scientific Instruments},
number = {10},
publisher = {American Institute of Physics},
title = {{Cover slip external cavity diode laser}},
doi = {10.1063/1.2801006},
volume = {78},
year = {2007},
}
@inbook{167,
abstract = {This book contains research articles on Diophantine Geometry, written by participants of a research program held at the Ennio De Giorgi Mathematical Research Center in Pisa, Italy, during the period April – July 2005. The authors are eminent experts in the field. Several subfields of the main topic are presented; the volume thus is particularly useful to get a broad overview of recent research developments.},
author = {Browning, Timothy D and Heath Brown, Roger},
booktitle = {Diophantine Geometry},
editor = {Zannier, Umberto},
pages = {93 -- 100},
publisher = {Edizioni della Normale},
title = {{Simultaneous equal sums of three powers}},
volume = {4},
year = {2007},
}
@article{1035,
abstract = {We explore the rich internal structure of Cs2 Feshbach molecules. Pure ultracold molecular samples are prepared in a CO2 -laser trap, and a multitude of weakly bound states is populated by elaborate magnetic-field ramping techniques. Our methods use different Feshbach resonances as input ports and various internal level crossings for controlled state transfer. We populate higher partial-wave states of up to eight units of rotational angular momentum (l -wave states). We investigate the molecular structure by measurements of the magnetic moments for various states. Avoided level crossings between different molecular states are characterized through the changes in magnetic moment and by a Landau-Zener tunneling method. Based on microwave spectroscopy, we present a precise measurement of the magnetic-field-dependent binding energy of the weakly bound s -wave state that is responsible for the large background scattering length of Cs. This state is of particular interest because of its quantum-halo character.},
author = {Mark, Michael and Ferlaino, Francesca and Knoop, Steven and Danzl, Johann G and Kraemer, Tobias and Chin, Cheng and Nägerl, Hanns and Grimm, Rudolf},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = {4},
publisher = {American Physical Society},
title = {{Spectroscopy of ultracold trapped cesium Feshbach molecules}},
doi = {10.1103/PhysRevA.76.042514},
volume = {76},
year = {2007},
}
@article{9149,
abstract = {The interaction of tidal currents with sea-floor topography results in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in the mixing of the abyssal ocean, and hence in controlling the large-scale ocean circulation.
As part of on-going work aimed at providing a theory for the vertical distribution of wave breaking over sea-floor topography, in this paper we investigate the instability of internal tides in a very simple linear model that helps us to relate the formation of unstable regions to simple features in the sea-floor topography. For two-dimensional tides over one-dimensional topography we find that the formation of overturning instabilities is closely linked to the singularities in the topography shape and that it is possible to have stable waves at the sea floor and unstable waves in the ocean interior above.
For three-dimensional tides over two-dimensional topography there is in addition an effect of geometric focusing of wave energy into localized regions of high wave amplitude, and we investigate this focusing effect in simple examples. Overall, we find that the distribution of unstable wave breaking regions can be highly non-uniform even for very simple idealized topography shapes.},
author = {BÜHLER, OLIVER and MULLER, Caroline J},
issn = {0022-1120},
journal = {Journal of Fluid Mechanics},
keywords = {Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics},
pages = {1--28},
publisher = {Cambridge University Press},
title = {{Instability and focusing of internal tides in the deep ocean}},
doi = {10.1017/s0022112007007410},
volume = {588},
year = {2007},
}
@unpublished{3742,
abstract = {Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes. Finding these models requires us to solve an inverse problem: given experimentally measured expectation values, what are the parameters of the underlying Hamiltonian? This problem sits at the intersection of statistical physics and machine learning, and we suggest that more efficient solutions are possible by merging ideas from the two fields. We use a combination of recent coordinate descent algorithms with an adaptation of the histogram Monte Carlo method, and implement these techniques to take advantage of the sparseness found in data on real neurons. The resulting algorithm learns the parameters of an Ising model describing a network of forty neurons within a few minutes. This opens the possibility of analyzing much larger data sets now emerging, and thus testing hypotheses about the collective behaviors of these networks.},
author = {Broderick,Tamara and Dudik,Miroslav and Gasper Tkacik and Schapire,Robert E and Bialek, William S},
booktitle = {ArXiv},
publisher = {ArXiv},
title = {{Faster solutions of the inverse pairwise Ising problem}},
volume = {q-bio.QM},
year = {2007},
}
@article{4234,
abstract = {We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two sources of multiplicative noise. The stationary probability distributions have two characteristic power-law scales. Numerical simulations show that noise suppresses the explosion of the growth rate which occurs in the deterministic counterpart. Instead, in different parameter regimes populations will grow with "anomalous" stochastic rates and (i) stabilise at "random carrying capacities", or (ii) go extinct in random times. Using logistic fits to reconstruct the simulated data, we find that even highly significant estimations do not recover or reflect information about the deterministic part of the process. Therefore, the logistic interpretation is not biologically meaningful. These results have implications for distinct model-aided calculations in biological situations because these kinds of estimations could lead to spurious conclusions. (c) 2006 Elsevier B.V. All rights reserved.},
author = {de Vladar, Harold and Pen, I.},
journal = {Physica A},
pages = {477 -- 485},
publisher = {Elsevier},
title = {{Determinism, noise, and spurious estimations in a generalised model of population growth}},
doi = {10.1016/j.physa.2006.06.025},
volume = {373},
year = {2007},
}
@article{3411,
abstract = {Mechanical single-molecule techniques offer exciting possibilities to investigate protein folding and stability in native environments at submolecular resolution. By applying a free-energy reconstruction procedure developed by Hummer and Szabo, which is based on a statistical theorem introduced by Jarzynski, we determined the unfolding free energy of the membrane proteins bacteriorhodopsin (BR), halorhodopsin, and the sodium-proton antiporter NhaA. The calculated energies ranged from 290.5kcal/mol for BR to 485.5kcal/mol for NhaA. For the remarkably stable BR, the equilibrium unfolding free energy was independent of pulling rate and temperature ranging between 18 and 42°C. Our experiments also revealed heterogeneous energetic properties in individual transmembrane helices. In halorhodopsin, the stabilization of a short helical segment yielded a characteristic signature in the energy profile. In NhaA, a pronounced peak was observed at a functionally important site in the protein. Since a large variety of single- and multispan membrane proteins can be tackled in mechanical unfolding experiments, our approach provides a basis for systematically elucidating energetic properties of membrane proteins with the resolution of individual secondary-structure elements.},
author = {Preiner, Johannes and Harald Janovjak and Rankl, Christian and Knaus, Helene and Cisneros, David A and Kedrov, Alexej and Kienberger, Ferry and Mueller, Daniel J and Hinterdorfer, Peter},
journal = {Biophysical Journal},
number = {3},
pages = {930 -- 937},
publisher = {Biophysical Society},
title = {{Free energy of membrane protein unfolding derived from single-molecule force measurements}},
doi = {10.1529/biophysj.106.096982},
volume = {93},
year = {2007},
}
@article{3427,
abstract = {We present a general theoretical framework to discuss mechanisms of morphogen transport and gradient formation in a cell layer. Trafficking events on the cellular scale lead to transport on larger scales. We discuss in particular the case of transcytosis where morphogens undergo repeated rounds of internalization into cells and recycling. Based on a description on the cellular scale, we derive effective nonlinear transport equations in one and two dimensions which are valid on larger scales. We derive analytic expressions for the concentration dependence of the effective diffusion coefficient and the effective degradation rate. We discuss the effects of a directional bias on morphogen transport and those of the coupling of the morphogen and receptor kinetics. Furthermore, we discuss general properties of cellular transport processes such as the robustness of gradients and relate our results to recent experiments on the morphogen Decapentaplegic (Dpp) that acts in the wing disk of the fruit fly Drosophila.
© 2007 The American Physical Society},
author = {Bollenbach, Mark Tobias and Kruse, Karsten and Pantazis, Periklis and Gonzalez Gaitan, Marcos and Julicher, Frank},
journal = {Physical Review E Statistical Nonlinear and Soft Matter Physics},
number = {1},
publisher = {American Institute of Physics},
title = {{Morphogen transport in epithelia}},
doi = {10.1103/PhysRevE.75.011901},
volume = {75},
year = {2007},
}
@inproceedings{3561,
abstract = {The main result of this paper is an extension of de Silva's Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we prove that i + 1 points in the sample span an i-simplex in the restricted Delaunay triangulation iff every subset of the i + 1 points has a weak witness.},
author = {Attali, Dominique and Herbert Edelsbrunner and Mileyko, Yuriy},
pages = {143 -- 150},
publisher = {ACM},
title = {{Weak witnesses for Delaunay triangulations of submanifolds}},
doi = {10.1145/1236246.1236267},
year = {2007},
}
@article{9524,
abstract = {Cytosine methylation is the most common covalent modification of DNA in eukaryotes. DNA methylation has an important role in many aspects of biology, including development and disease. Methylation can be detected using bisulfite conversion, methylation-sensitive restriction enzymes, methyl-binding proteins and anti-methylcytosine antibodies. Combining these techniques with DNA microarrays and high-throughput sequencing has made the mapping of DNA methylation feasible on a genome-wide scale. Here we discuss recent developments and future directions for identifying and mapping methylation, in an effort to help colleagues to identify the approaches that best serve their research interests.},
author = {ZILBERMAN, Daniel and Henikoff, Steven},
issn = {1477-9129},
journal = {Development},
number = {22},
pages = {3959--3965},
publisher = {The Company of Biologists},
title = {{Genome-wide analysis of DNA methylation patterns}},
doi = {10.1242/dev.001131},
volume = {134},
year = {2007},
}
@article{9487,
abstract = {Cytosine DNA methylation is considered to be a stable epigenetic mark, but active demethylation has been observed in both plants and animals. In Arabidopsis thaliana, DNA glycosylases of the DEMETER (DME) family remove methylcytosines from DNA. Demethylation by DME is necessary for genomic imprinting, and demethylation by a related protein, REPRESSOR OF SILENCING1, prevents gene silencing in a transgenic background. However, the extent and function of demethylation by DEMETER-LIKE (DML) proteins in WT plants is not known. Using genome-tiling microarrays, we mapped DNA methylation in mutant and WT plants and identified 179 loci actively demethylated by DML enzymes. Mutations in DML genes lead to locus-specific DNA hypermethylation. Reintroducing WT DML genes restores most loci to the normal pattern of methylation, although at some loci, hypermethylated epialleles persist. Of loci demethylated by DML enzymes, >80% are near or overlap genes. Genic demethylation by DML enzymes primarily occurs at the 5′ and 3′ ends, a pattern opposite to the overall distribution of WT DNA methylation. Our results show that demethylation by DML DNA glycosylases edits the patterns of DNA methylation within the Arabidopsis genome to protect genes from potentially deleterious methylation.},
author = {Penterman, Jon and ZILBERMAN, Daniel and Huh, Jin Hoe and Ballinger, Tracy and Henikoff, Steven and Fischer, Robert L.},
issn = {1091-6490},
journal = {Proceedings of the National Academy of Sciences},
number = {16},
pages = {6752--6757},
publisher = {National Academy of Sciences},
title = {{DNA demethylation in the Arabidopsis genome}},
doi = {10.1073/pnas.0701861104},
volume = {104},
year = {2007},
}
@inproceedings{2333,
author = {Lieb, Élliott H and Robert Seiringer and Solovej, Jan P},
pages = {239 -- 248},
publisher = {American Mathematical Society},
title = {{Ground-state energy of a dilute Fermi gas}},
doi = {10.1090/conm/412},
volume = {412},
year = {2006},
}
@inproceedings{2334,
author = {Robert Seiringer and Lieb, Élliott H and Yngvason, Jakob},
editor = {Zambrini, Jean-Claude},
publisher = {World Scientific Publishing},
title = {{One-dimensional behavior of dilute, trapped Bose gases in traps}},
doi = {10.1007/s00220-003-0993-3},
year = {2006},
}
@misc{2363,
abstract = { We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state. },
author = {Lieb, Élliott H and Robert Seiringer},
booktitle = {Communications in Mathematical Physics},
number = {2},
pages = {505 -- 537},
publisher = {Springer},
title = {{Derivation of the Gross-Pitaevskii equation for rotating Bose gases}},
doi = {10.1007/s00220-006-1524-9},
volume = {264},
year = {2006},
}
@article{2364,
abstract = {We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation.},
author = {Robert Seiringer},
journal = {Reviews in Mathematical Physics},
number = {3},
pages = {233 -- 253},
publisher = {World Scientific Publishing},
title = {{A correlation estimate for quantum many-body systems at positive temperature}},
doi = {10.1142/S0129055X06002632},
volume = {18},
year = {2006},
}
@article{2365,
abstract = {We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller.},
author = {Robert Seiringer},
journal = {Communications in Mathematical Physics},
number = {3},
pages = {729 -- 757},
publisher = {Springer},
title = {{The thermodynamic pressure of a dilute fermi gas}},
doi = {10.1007/s00220-005-1433-3},
volume = {261},
year = {2006},
}
@article{2366,
abstract = {Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.},
author = {Frank, Rupert L and Laptev, Ari and Lieb, Élliott H and Robert Seiringer},
journal = {Letters in Mathematical Physics},
number = {3},
pages = {309 -- 316},
publisher = {Springer},
title = {{Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials}},
doi = {10.1007/s11005-006-0095-1},
volume = {77},
year = {2006},
}
@inbook{2369,
abstract = {One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results.},
author = {Aizenman, Michael and Lieb, Élliott H and Robert Seiringer and Solovej, Jan P and Yngvason, Jakob},
booktitle = {Mathematical Physics of Quantum Mechanics},
editor = {Asch, Joachim and Joye, Alain},
pages = {199 -- 215},
publisher = {Springer},
title = {{Bose-Einstein condensation as a quantum phase transition in an optical lattice}},
doi = {10.1007/b11573432},
volume = {690},
year = {2006},
}
@unpublished{573,
abstract = {Mitchison and Jozsa recently suggested that the "chained-Zeno" counterfactual computation protocol recently proposed by Hosten et al. is counterfactual for only one output of the computer. This claim was based on the existing abstract algebraic definition of counterfactual computation, and indeed according to this definition, their argument is correct. However, a more general definition (physically adequate) for counterfactual computation is implicitly assumed by Hosten et. al. Here we explain in detail why the protocol is counterfactual and how the "history tracking" method of the existing description inadequately represents the physics underlying the protocol. Consequently, we propose a modified definition of counterfactual computation. Finally, we comment on one of the most interesting aspects of the error-correcting protocol. },
author = {Hosten, Onur and Rakher, Matthew and Barreiro, Julio and Peters, Nicholas and Kwiat, Paul},
pages = {12},
publisher = {ArXiv},
title = {{Counterfactual computation revisited}},
year = {2006},
}
@unpublished{574,
abstract = {Vaidman, in a recent article adopts the method of 'quantum weak measurements in pre- and postselected ensembles' to ascertain whether or not the chained-Zeno counterfactual computation scheme proposed by Hosten et al. is counterfactual; which has been the topic of a debate on the definition of counterfactuality. We disagree with his conclusion, which brings up some interesting aspects of quantum weak measurements and some concerns about the way they are interpreted. },
author = {Hosten, Onur and Kwiat, Paul},
pages = {2},
publisher = {ArXiv},
title = {{Weak measurements and counterfactual computation}},
year = {2006},
}
@article{6151,
author = {Salecker, Iris and Häusser, Michael and de Bono, Mario},
issn = {1469-221X},
journal = {EMBO reports},
number = {6},
pages = {585--589},
publisher = {Wiley},
title = {{On the axonal road to circuit function and behaviour: Workshop on the assembly and function of neuronal circuits}},
doi = {10.1038/sj.embor.7400713},
volume = {7},
year = {2006},
}
@article{1461,
abstract = {This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial L 2 harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of L 2 harmonic forms on complete hyperkähler manifolds of linear growth.},
author = {Tamas Hausel and Swartz, Edward},
journal = {Proceedings of the American Mathematical Society},
number = {8},
pages = {2403 -- 2409},
publisher = {American Mathematical Society},
title = {{Intersection forms of toric hyperkähler varieties}},
doi = {10.1090/S0002-9939-06-08248-7},
volume = {134},
year = {2006},
}
@article{1462,
abstract = {A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hubert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on ℂ2 (recovering results of Nakajima-Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced.},
author = {Tamas Hausel},
journal = {PNAS},
number = {16},
pages = {6120 -- 6124},
publisher = {National Academy of Sciences},
title = {{Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform}},
doi = {10.1073/pnas.0601337103},
volume = {103},
year = {2006},
}
@article{1033,
abstract = {Systems of three interacting particles are notorious for their complex physical behaviour. A landmark theoretical result in few-body quantum physics is Efimov\'s prediction1,2 of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov\'s problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics3-8. However, the observation of Efimov quantum states has remained an elusive goal3,5. Here we report the observation of an Efimov resonance in an ultracold gas of caesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss9,10 when the strength of the two-body interaction is varied. We also detect a minimum 9,11,12 in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems7. While Feshbach resonances13,14 have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter15 to the world of few-body quantum phenomena.},
author = {Kraemer, Tobias and Mark, Michael and Waldburger, Philipp and Danzl, Johann G and Chin, Cheng and Engeser, Bastian and Lange, Adam and Pilch, Karl and Jaakkola, Antti and Nägerl, Hanns and Grimm, Rudolf},
journal = {Nature},
number = {7082},
pages = {315 -- 318},
publisher = {Nature Publishing Group},
title = {{Evidence for Efimov quantum states in an ultracold gas of caesium atoms}},
doi = {10.1038/nature04626},
volume = {440},
year = {2006},
}
@inproceedings{1034,
abstract = {Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov\'s prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction [1, 2]. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov\'s scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms [3]. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems.},
author = {Nägerl, Hanns and Kraemer, Tobias and Mark, Michael and Waldburger, Philipp and Danzl, Johann G and Engeser, Bastian and Lange, Adam and Pilch, Karl and Jaakkola, Antti and Chin, Cheng and Grimm, Rudolf},
pages = {269 -- 277},
publisher = {AIP},
title = {{Experimental evidence for Efimov quantum states}},
doi = {10.1063/1.2400657},
volume = {869},
year = {2006},
}
@article{3755,
abstract = {A primitive example of adaptation in gene expression is the balance between the rate of synthesis and degradation of cellular RNA, which allows rapid responses to environmental signals. Here, we investigate how multidrug efflux pump systems mediate the dynamics of a simple drug-inducible system in response to a steady level of inducer. Using fluorescence correlation spectroscopy, we measured in real time within a single bacterium the transcription activity at the RNA level of the acrAB-TolC multidrug efflux pump system. When cells are exposed to constant level of anhydrotetracycline inducer and are adsorbed onto a poly-L-lysine-coated surface, we found that the acrAB-TolC promoter is steadily active. We also monitored the activity of the tet promoter to characterize the effect of this efflux system on the dynamics of drug-inducible transcription. We found that the transcriptional response of the tet promoter to a steady level of aTc rises and then falls back to its preinduction level. The rate of RNA degradation was constant throughout the transcriptional pulse, indicating that the modulation of intracellular inducer concentration alone can produce this pulsating response. Single-cell experiments together with numerical simulations suggest that such pulsating response in drug-inducible genetic systems is a property emerging from the dependence of drug-inducible transcription on multidrug efflux systems.},
author = {Le,Thuc T. and Emonet,Thierry and Harlepp, Sébastien and Calin Guet and Cluzel,Philippe},
journal = {Biophysical Journal},
number = {9},
pages = {3315 -- 3321},
publisher = {Biophysical Society},
title = {{Dynamical determinants of drug-inducible gene expression in a single bacterium}},
doi = {10.1529/biophysj.105.073353},
volume = {90},
year = {2006},
}
@article{3813,
abstract = {Hyperpolarization-activated channels (Ih or HCN channels) are widely expressed in principal neurons in the central nervous system. However, Ih in inhibitory GABAergic interneurons is less well characterized. We examined the functional properties of Ih in fast-spiking basket cells (BCs) of the dentate gyrus, using hippocampal slices from 17- to 21-day-old rats. Bath application of the Ih channel blocker ZD 7288 at a concentration of 30 microm induced a hyperpolarization of 5.7 +/- 1.5 mV, an increase in input resistance and a correlated increase in apparent membrane time constant. ZD 7288 blocked a hyperpolarization-activated current in a concentration-dependent manner (IC50, 1.4 microm). The effects of ZD 7288 were mimicked by external Cs+. The reversal potential of Ih was -27.4 mV, corresponding to a Na+ to K+ permeability ratio (PNa/PK) of 0.36. The midpoint potential of the activation curve of Ih was -83.9 mV, and the activation time constant at -120 mV was 190 ms. Single-cell expression analysis using reverse transcription followed by quantitative polymerase chain reaction revealed that BCs coexpress HCN1 and HCN2 subunit mRNA, suggesting the formation of heteromeric HCN1/2 channels. ZD 7288 increased the current threshold for evoking antidromic action potentials by extracellular stimulation, consistent with the expression of Ih in BC axons. Finally, ZD 7288 decreased the frequency of miniature inhibitory postsynaptic currents (mIPSCs) in hippocampal granule cells, the main target cells of BCs, to 70 +/- 4% of the control value. In contrast, the amplitude of mIPSCs was unchanged, consistent with the presence of Ih in inhibitory terminals. In conclusion, our results suggest that Ih channels are expressed in the somatodendritic region, axon and presynaptic elements of fast-spiking BCs in the hippocampus.},
author = {Aponte, Yexica and Lien, Cheng-Chang and Reisinger, Ellen and Peter Jonas},
journal = {Journal of Physiology},
number = {Pt 1},
pages = {229 -- 43},
publisher = {Wiley-Blackwell},
title = {{Hyperpolarization-activated cation channels in fast-spiking interneurons of rat hippocampus}},
doi = {10.1113/jphysiol.2005.104042},
volume = {574},
year = {2006},
}
@article{4173,
abstract = {Background: Zebrafish (D. rerio) has become a powerful and widely used model system for the analysis of vertebrate embryogenesis and organ development. While genetic methods are readily available in zebrafish, protocols for two dimensional (2D) gel electrophoresis and proteomics have yet to be developed. Results: As a prerequisite to carry out proteomic experiments with early zebrafish embryos, we developed a method to efficiently remove the yolk from large batches of embryos. This method enabled high resolution 2D gel electrophoresis and improved Western blotting considerably. Here, we provide detailed protocols for proteomics in zebrafish from sample preparation to mass spectrometry (MS), including a comparison of databases for MS identification of zebrafish proteins. Conclusion: The provided protocols for proteomic analysis of early embryos enable research to be taken in novel directions in embryogenesis.},
author = {Link, Vinzenz and Shevchenko, Andrej and Heisenberg, Carl-Philipp J},
journal = {BMC Developmental Biology},
pages = {1 -- 9},
publisher = {BioMed Central},
title = {{Proteomics of early zebrafish embryos}},
doi = {10.1186/1471-213X-6-1},
volume = {6},
year = {2006},
}
@article{3009,
author = {Paciorek, Tomasz and Friml, Jirí},
journal = {Journal of Cell Science},
number = {7},
pages = {1199 -- 1202},
publisher = {Company of Biologists},
title = {{Auxin signaling}},
doi = {10.1242/jcs.02910},
volume = {119},
year = {2006},
}
@unpublished{3431,
abstract = {Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the retina, and show that pairwise interactions account for observed higher-order correlations. By first finding a representative ensemble for observed networks we can create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses.},
author = {Gasper Tkacik and Schneidman, E. and Berry, M. J. and Bialek, William S},
booktitle = {ArXiv},
pages = {1 -- 4},
publisher = {ArXiv},
title = {{Ising models for networks of real neurons}},
year = {2006},
}
@article{3695,
abstract = {We give an analytical and geometrical treatment of what it means to separate a Gaussian kernel along arbitrary axes in Ropfn, and we present a separation scheme that allows us to efficiently implement anisotropic Gaussian convolution filters for data of arbitrary dimensionality. Based on our previous analysis we show that this scheme is optimal with regard to the number of memory accesses and interpolation operations needed. The proposed method relies on nonorthogonal convolution axes and works completely in image space. Thus, it avoids the need for a fast Fourier transform (FFT)-subroutine. Depending on the accuracy and speed requirements, different interpolation schemes and methods to implement the one-dimensional Gaussian (finite impulse response and infinite impulse response) can be integrated. Special emphasis is put on analyzing the performance and accuracy of the new method. In particular, we show that without any special optimization of the source code, it can perform anisotropic Gaussian filtering faster than methods relying on the FFT.},
author = {Christoph Lampert and Wirjadi,Oliver},
journal = {IEEE Transactions on Image Processing (TIP)},
number = {11},
pages = {3501 -- 3513},
publisher = {IEEE},
title = {{An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter}},
doi = { 10.1109/TIP.2006.877501 },
volume = {15},
year = {2006},
}
@book{2335,
abstract = {This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.},
author = {Lieb, Élliott H and Robert Seiringer and Solovej, Jan P and Yngvason, Jakob},
booktitle = {The mathematics of the Bose gas and its condensation},
publisher = {Birkhäuser},
title = {{The mathematics of the Bose gas and its condensation}},
volume = {34},
year = {2005},
}
@inbook{2336,
abstract = {
Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, ρ, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4–5 decades ago, and to explore new regimes not treated before. For systems with repulsive (i.e. positive) interaction potentials the experimental low temperature state and the ground state are effectively synonymous — and this fact is used in all modeling. In such cases, the leading term in the energy/particle is 2πħ2 aρ/m where a is the scattering length of the two-body potential. Owing to the delicate and peculiar nature of bosonic correlations (such as the strange N 7/5 law for charged bosons), four decades of research failed to establish this plausible formula rigorously. The only previous lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct asymptotic formula has been obtained by us and this work will be presented. The reason behind the mathematical difficulties will be emphasized. A different formula, postulated as late as 1971 by Schick, holds in two dimensions and this, too, will be shown to be correct. With the aid of the methodology developed to prove the lower bound for the homogeneous gas, several other problems have been successfully addressed. One is the proof by us that the Gross-Pitaevskii equation correctly describes the ground state in the ‘traps’ actually used in the experiments. For this system it is also possible to prove complete Bose condensation and superfluidity as we have shown. On the frontier of experimental developments is the possibility that a dilute gas in an elongated trap will behave like a one-dimensional system; we have proved this mathematically. Another topic is a proof that Foldy’s 1961 theory of a high density Bose gas of charged particles correctly describes its ground state energy; using this we can also prove the N 7/5 formula for the ground state energy of the two-component charged Bose gas proposed by Dyson in 1967. All of this is quite recent work and it is hoped that the mathematical methodology might be useful, ultimately, to solve more complex problems connected with these interesting systems.},
author = {Lieb, Élliott H and Robert Seiringer and Solovej, Jan P and Yngvason, Jakob},
booktitle = {Perspectives in Analysis},
editor = {Benedicks, Michael and Jones, Peter W and Smirnov, Stanislav and Winckler, Björn},
pages = {97 -- 183},
publisher = {Springer},
title = {{The quantum-mechanical many-body problem: The Bose gas}},
doi = {10.1007/3-540-30434-7_9},
volume = {27},
year = {2005},
}
@article{2359,
abstract = {The validity of substituting a c-number z for the k = 0 mode operator a0 is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities such as the pressure or ground state energy, but also the value of |z|2 that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry-breaking term. This point had previously been elusive.},
author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob},
journal = {Physical Review Letters},
number = {8},
publisher = {American Physical Society},
title = {{Justification of c-number substitutions in bosonic hamiltonians}},
doi = {10.1103/PhysRevLett.94.080401},
volume = {94},
year = {2005},
}
@article{2361,
abstract = {The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(Ï±lnÏ±) of a density matrix Ï±123 on the product of three Hilbert spaces satisfies S[Ï±123]- S[Ï±12]≤S[Ï±23]-S[Ï±2]. We strengthen this to S[Ï±123]-S[Ï±12] ≤αnα(S[Ï±23α]-S[Ï±2α]), where the nα are weights and the Ï±23α are partitions of Ï±23. Correspondingly, there is a strengthening of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.},
author = {Lieb, Élliott H and Robert Seiringer},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = {6},
publisher = {American Physical Society},
title = {{Stronger subadditivity of entropy}},
doi = {10.1103/PhysRevA.71.062329},
volume = {71},
year = {2005},
}
@article{2362,
abstract = {Recent developments in the physics of low-density trapped gases make it worthwhile to verify old, well-known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the ground-state energy of a dilute gas of N fermions interacting with a short-range, positive potential of scattering length a. For spin-12 fermions, this is E∼E0+(22m)2πNa, where E0 is the energy of the noninteracting system and is the density. A similar formula holds in two dimensions (2D), with a replaced by ln(a2). Obviously this 2D energy is not the expectation value of a density-independent pseudopotential.},
author = {Lieb, Élliott H and Robert Seiringer and Solovej, Jan P},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = {5},
publisher = {American Physical Society},
title = {{Ground state energy of the low density Fermi gas}},
doi = {10.1103/PhysRevA.71.053605},
volume = {71},
year = {2005},
}
@article{2867,
abstract = {The plant hormone auxin elicits many specific context-dependent developmental responses. Auxin promotes degradation of Aux/IAA proteins that prevent transcription factors of the auxin response factor (ARF) family from regulating auxin-responsive target genes. Aux/IAAs and ARFs are represented by large gene families in Arabidopsis. Here we show that stabilization of BDL/IAA12 or its sister protein IAA13 prevents MP/ARF5-dependent embryonic root formation whereas stabilized SHY2/IAA3 interferes with seedling growth. Although both bdl and shy2-2 proteins inhibited MP/ARF5-dependent reporter gene activation, shy2-2 was much less efficient than bdl to interfere with embryonic root initiation when expressed from the BDL promoter. Similarly, MP was much more efficient than ARF16 in this process. When expressed from the SHY2 promoter, both shy2-2 and bdl inhibited cell elongation and auxin-induced gene expression in the seedling hypocotyl. By contrast, gravitropism and auxin-induced gene expression in the root, which were promoted by functionally redundant NPH4/ARF7 and ARF19 proteins, were inhibited by shy2-2, but not by bdl protein. Our results suggest that auxin signals are converted into specific responses by matching pairs of coexpressed ARF and Aux/IAA proteins.},
author = {Weijers, Dolf and Eva Benková and Jäger, Katja E and Schlereth, Alexandra and Hamann, Thorsten and Kientz, Marika and Wilmoth, Jill C and Reed, Jason W and Jürgens, Gerd},
journal = {EMBO Journal},
number = {10},
pages = {1874 -- 1885},
publisher = {Wiley-Blackwell},
title = {{Developmental specificity of auxin response by pairs of ARF and Aux/IAA transcriptional regulators}},
doi = {10.1038/sj.emboj.7600659},
volume = {24},
year = {2005},
}
@article{8028,
abstract = {Transmission of signals within the brain is essential for cognitive function, but it is not clear how neural circuits support reliable and accurate signal propagation over a sufficiently large dynamic range. Two modes of propagation have been studied: synfire chains, in which synchronous activity travels through feedforward layers of a neuronal network, and the propagation of fluctuations in firing rate across these layers. In both cases, a sufficient amount of noise, which was added to previous models from an external source, had to be included to support stable propagation. Sparse, randomly connected networks of spiking model neurons can generate chaotic patterns of activity. We investigate whether this activity, which is a more realistic noise source, is sufficient to allow for signal transmission. We find that, for rate-coded signals but not for synfire chains, such networks support robust and accurate signal reproduction through up to six layers if appropriate adjustments are made in synaptic strengths. We investigate the factors affecting transmission and show that multiple signals can propagate simultaneously along different pathways. Using this feature, we show how different types of logic gates can arise within the architecture of the random network through the strengthening of specific synapses.},
author = {Vogels, Tim P and Abbott, L. F.},
issn = {0270-6474},
journal = {Journal of Neuroscience},
number = {46},
pages = {10786--10795},
publisher = {Society for Neuroscience},
title = {{Signal propagation and logic gating in networks of integrate-and-fire neurons}},
doi = {10.1523/jneurosci.3508-05.2005},
volume = {25},
year = {2005},
}
@article{212,
abstract = {For any n ≧ 2, let F ∈ ℤ [ x 1, … , xn ] be a form of degree d≧ 2, which produces a geometrically irreducible hypersurface in ℙn–1. This paper is concerned with the number N(F;B) of rational points on F = 0 which have height at most B. For any ε > 0 we establish the estimate N(F; B) = O(B n− 2+ ε ), whenever either n ≦ 5 or the hypersurface is not a union of lines. Here the implied constant depends at most upon d, n and ε.},
author = {Timothy Browning and Heath-Brown, Roger},
journal = {Journal fur die Reine und Angewandte Mathematik},
number = {584},
pages = {83 -- 115},
publisher = {Walter de Gruyter and Co },
title = {{Counting rational points on hypersurfaces}},
doi = {https://doi.org/10.1515/crll.2005.2005.584.83},
year = {2005},
}
@article{214,
abstract = {Given an absolutely irreducible ternary form F, the purpose of this paper is to produce better upper bounds for the number of integer solutions to the equation F=0, that are restricted to lie in very lopsided boxes. As an application of the main result, a new paucity estimate is obtained for equal sums of two like powers.},
author = {Timothy Browning and Heath-Brown, Roger},
journal = {Mathematische Zeitschrift},
number = {2},
pages = {233 -- 247},
publisher = {Unknown},
title = {{Plane curves in boxes and equal sums of two powers}},
doi = {10.1007/s00209-004-0719-z},
volume = {251},
year = {2005},
}
@inbook{1444,
abstract = {The paper surveys the mirror symmetry conjectures of Hausel-Thaddeus and Hausel-Rodriguez-Villegas concerning the equality of certain Hodge numbers of SL(n, ℂ) vs. PGL(n, ℂ) flat connections and character varieties for curves, respectively. Several new results and conjectures and their relations to works of Hitchin, Gothen, Garsia-Haiman and Earl-Kirwan are explained. These use the representation theory of finite groups of Lie-type via the arithmetic of character varieties and lead to an unexpected conjecture for a Hard Lefschetz theorem for their cohomology.},
author = {Tamas Hausel},
booktitle = {Geometric Methods in Algebra and Number Theory},
pages = {193 -- 217},
publisher = {Springer},
title = {{Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve}},
doi = {10.1007/0-8176-4417-2_9},
volume = {235},
year = {2005},
}
@article{1447,
abstract = {Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper we will give two proofs that the injectivity part of the Hard Lefschetz theorem survives for toric hyperkähler varieties. We explain how this implies the g-inequalities for rationally representable matroids. We show how the geometrical intuition in the first proof, coupled with results of Chari [3], leads to a proof of the g-inequalities for general matroid complexes, which is a recent result of Swartz [20]. The geometrical idea in the second proof will show that a pure O-sequence should satisfy the g-inequalities, thus showing that our result is in fact a consequence of a long-standing conjecture of Stanley.},
author = {Tamas Hausel},
journal = {Open Mathematics},
number = {1},
pages = {26 -- 38},
publisher = {Central European Science Journals},
title = {{Quaternionic geometry of matroids}},
doi = {10.2478/BF02475653},
volume = {3},
year = {2005},
}
@article{1463,
abstract = {We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkähler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohomology rings of a hyperpolygon space.},
author = {Tamas Hausel and Proudfoot, Nicholas J},
journal = {Topology},
number = {1},
pages = {231 -- 248},
publisher = {Elsevier},
title = {{Abelianization for hyperkähler quotients}},
doi = {10.1016/j.top.2004.04.002},
volume = {44},
year = {2005},
}
@article{3721,
abstract = {Recent advances in atomic force microscopy allowed globular and membrane proteins to be mechanically unfolded on a single-molecule level. Presented is an extension to the existing force spectroscopy experiments. While unfolding single bacteriorhodopsins from native purple membranes, small oscillation amplitudes (6–9nm) were supplied to the vertical displacement of the cantilever at a frequency of 3kHz. The phase and amplitude response of the cantilever-protein system was converted to reveal the elastic (conservative) and viscous (dissipative) contributions to the unfolding process. The elastic response (stiffness) of the extended parts of the protein were in the range of a few tens pN/nm and could be well described by the derivative of the wormlike chain model. Discrete events in the viscous response coincided with the unfolding of single secondary structure elements and were in the range of 1μNs/m. In addition, these force modulation spectroscopy experiments revealed novel mechanical unfolding intermediates of bacteriorhodopsin. We found that kinks result in a loss of unfolding cooperativity in transmembrane helices. Reconstructing force-distance spectra by the integration of amplitude-distance spectra verified their position, offering a novel approach to detect intermediates during the forced unfolding of single proteins.},
author = {Harald Janovjak and Mueller, Daniel J and Humphris, Andrew D},
journal = {Biophysical Journal},
number = {2},
pages = {1423 -- 1431},
publisher = {Biophysical Society},
title = {{Molecular force modulation spectroscopy revealing the dynamic response of single bacteriorhodopsins}},
doi = {10.1529/biophysj.104.052746},
volume = {88},
year = {2005},
}
@article{3741,
abstract = {In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial assumptions about the structure of data. Here, we reformulate the clustering problem from an information theoretic perspective that avoids many of these assumptions. In particular, our formulation obviates the need for defining a cluster "prototype," does not require an a priori similarity metric, is invariant to changes in the representation of the data, and naturally captures nonlinear relations. We apply this approach to different domains and find that it consistently produces clusters that are more coherent than those extracted by existing algorithms. Finally, our approach provides a way of clustering based on collective notions of similarity rather than the traditional pairwise measures.},
author = {Slonim,N. and Atwal,G. and Gasper Tkacik and Bialek, William S},
journal = {PNAS},
number = {51},
pages = {18297 -- 18302},
publisher = {National Academy of Sciences},
title = {{Information-based clustering}},
doi = {10.1073/pnas.0507432102},
volume = {102},
year = {2005},
}
@unpublished{3746,
abstract = {We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained with manageable computational effort. The same methods allow estimation of higher order, multi-information terms. These ideas are illustrated by analyses of gene expression, financial markets, and consumer preferences. In each case, information theoretic measures correlate with independent, intuitive measures of the underlying structures in the system.},
author = {Slonim,Noam and Atwal,Gurinder S and Gasper Tkacik and Bialek, William S},
booktitle = {ArXiv},
pages = {1 -- 11},
publisher = {ArXiv},
title = {{Estimating mutual information and multi-information in large networks}},
year = {2005},
}
@article{4252,
abstract = {Empirical studies of quantitative genetic variation have revealed robust patterns that are observed both across traits and across species. However, these patterns have no compelling explanation, and some of the observations even appear to be mutually incompatible. We review and extend a major class of theoretical models, ‘mutation–selection models’, that have been proposed to explain quantitative genetic variation. We also briefly review an alternative class of ‘balancing selection models’. We consider to what extent the models are compatible with the general observations, and argue that a key issue is understanding and modelling pleiotropy. We discuss some},
author = {Johnson, Toby and Nicholas Barton},
journal = {Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences},
number = {1459},
pages = {1411 -- 1425},
publisher = {Royal Society, The},
title = {{Theoretical models of selection and mutationon quantitative traits}},
doi = {10.1098/rstb.2005.1667},
volume = {360},
year = {2005},
}
@article{3416,
abstract = {In the last decade atomic force microscopy has been used to measure the mechanical stability of single proteins. These force spectroscopy experiments have shown that many water-soluble and membrane proteins unfold via one or more intermediates. Recently, Li and co-workers found a linear correlation between the unfolding force of the native state and the intermediate in fibronectin, which they suggested indicated the presence of a molecular memory or multiple unfolding pathways (1). Here, we apply two independent methods in combination with Monte Carlo simulations to analyze the unfolding of α-helices E and D of bacteriorhodopsin (BR). We show that correlation analysis of unfolding forces is very sensitive to errors in force calibration of the instrument. In contrast, a comparison of relative forces provides a robust measure for the stability of unfolding intermediates. The proposed approach detects three energetically different states of α-helices E and D in trimeric BR. These states are not observed for monomeric BR and indicate that substantial information is hidden in forced unfolding experiments of single proteins.},
author = {Harald Janovjak and Sapra, Tanuj K and Mueller, Daniel J},
journal = {Biophysical Journal},
number = {5},
pages = {37 -- 39},
publisher = {Biophysical Society},
title = {{Complex stability of single proteins explored by forced unfolding experiments}},
doi = {10.1529/biophysj.105.059774},
volume = {88},
year = {2005},
}
@article{3426,
abstract = {We discuss the formation of graded morphogen profiles in a cell layer by nonlinear transport phenomena, important for patterning developing organisms. We focus on a process termed transcytosis, where morphogen transport results from the binding of ligands to receptors on the cell surface, incorporation into the cell, and subsequent externalization. Starting from a microscopic model, we derive effective transport equations. We show that, in contrast to morphogen transport by extracellular diffusion, transcytosis leads to robust ligand profiles which are insensitive to the rate of ligand production.},
author = {Bollenbach, Mark Tobias and Kruse, Karsten and Pantazis, Periklis and González Gaitán, Marcos and Jülicher, Frank},
journal = {Physical Review Letters},
number = {1},
publisher = {American Physical Society},
title = {{Robust formation of morphogen gradients}},
doi = {10.1103/PhysRevLett.94.018103},
volume = {94},
year = {2005},
}
@article{9514,
abstract = {Background:
DNA methylation occurs at preferred sites in eukaryotes. In Arabidopsis, DNA cytosine methylation is maintained by three subfamilies of methyltransferases with distinct substrate specificities and different modes of action. Targeting of cytosine methylation at selected loci has been found to sometimes involve histone H3 methylation and small interfering (si)RNAs. However, the relationship between different cytosine methylation pathways and their preferred targets is not known.
Results:
We used a microarray-based profiling method to explore the involvement of Arabidopsis CMT3 and DRM DNA methyltransferases, a histone H3 lysine-9 methyltransferase (KYP) and an Argonaute-related siRNA silencing component (AGO4) in methylating target loci. We found that KYP targets are also CMT3 targets, suggesting that histone methylation maintains CNG methylation genome-wide. CMT3 and KYP targets show similar proximal distributions that correspond to the overall distribution of transposable elements of all types, whereas DRM targets are distributed more distally along the chromosome. We find an inverse relationship between element size and loss of methylation in ago4 and drm mutants.
Conclusion:
We conclude that the targets of both DNA methylation and histone H3K9 methylation pathways are transposable elements genome-wide, irrespective of element type and position. Our findings also suggest that RNA-directed DNA methylation is required to silence isolated elements that may be too small to be maintained in a silent state by a chromatin-based mechanism alone. Thus, parallel pathways would be needed to maintain silencing of transposable elements.},
author = {Tran, Robert K. and ZILBERMAN, Daniel and de Bustos, Cecilia and Ditt, Renata F. and Henikoff, Jorja G. and Lindroth, Anders M. and Delrow, Jeffrey and Boyle, Tom and Kwong, Samson and Bryson, Terri D. and Jacobsen, Steven E. and Henikoff, Steven},
issn = {1465-6906},
journal = {Genome Biology},
number = {11},
publisher = {Springer Nature},
title = {{Chromatin and siRNA pathways cooperate to maintain DNA methylation of small transposable elements in Arabidopsis}},
doi = {10.1186/gb-2005-6-11-r90},
volume = {6},
year = {2005},
}
@article{9491,
abstract = {Cytosine DNA methylation in vertebrates is widespread, but methylation in plants is found almost exclusively at transposable elements and repetitive DNA [1]. Within regions of methylation, methylcytosines are typically found in CG, CNG, and asymmetric contexts. CG sites are maintained by a plant homolog of mammalian Dnmt1 acting on hemi-methylated DNA after replication. Methylation of CNG and asymmetric sites appears to be maintained at each cell cycle by other mechanisms. We report a new type of DNA methylation in Arabidopsis, dense CG methylation clusters found at scattered sites throughout the genome. These clusters lack non-CG methylation and are preferentially found in genes, although they are relatively deficient toward the 5′ end. CG methylation clusters are present in lines derived from different accessions and in mutants that eliminate de novo methylation, indicating that CG methylation clusters are stably maintained at specific sites. Because 5-methylcytosine is mutagenic, the appearance of CG methylation clusters over evolutionary time predicts a genome-wide deficiency of CG dinucleotides and an excess of C(A/T)G trinucleotides within transcribed regions. This is exactly what we find, implying that CG methylation clusters have contributed profoundly to plant gene evolution. We suggest that CG methylation clusters silence cryptic promoters that arise sporadically within transcription units.},
author = {Tran, Robert K. and Henikoff, Jorja G. and ZILBERMAN, Daniel and Ditt, Renata F. and Jacobsen, Steven E. and Henikoff, Steven},
issn = {1879-0445},
journal = {Current Biology},
number = {2},
pages = {154--159},
publisher = {Elsevier},
title = {{DNA methylation profiling identifies CG methylation clusters in Arabidopsis genes}},
doi = {10.1016/j.cub.2005.01.008},
volume = {15},
year = {2005},
}
@article{2355,
abstract = {The BMV conjecture for traces, which states that Tr exp(A - λB) is the Laplace transform of a positive measure, is shown to be equivalent to two other statements: (i) The polynomial λ → Tr(A + λB) p has only non-negative coefficients for all A, B ≥ 0, p ∈ ℕ and (ii) λ → Tr(A + λB)-p is the Laplace transform of a positive measure for A, B ≥ 0, p > 0.},
author = {Lieb, Élliott H and Robert Seiringer},
journal = {Journal of Statistical Physics},
number = {1-2},
pages = {185 -- 190},
publisher = {Springer},
title = {{ Equivalent forms of the Bessis-Moussa-Villani conjecture}},
doi = {10.1023/B:JOSS.0000019811.15510.27},
volume = {115},
year = {2004},
}
@article{2356,
abstract = {Recent experimental and theoretical work has shown that there are conditions in which a trapped, low-density Bose gas behaves like the one-dimensional delta-function Bose gas solved years ago by Lieb and Liniger. This is an intrinsically quantum-mechanical phenomenon because it is not necessary to have a trap width that is the size of an atom - as might have been supposed - but it suffices merely to have a trap width such that the energy gap for motion in the transverse direction is large compared to the energy associated with the motion along the trap. Up to now the theoretical arguments have been based on variational - perturbative ideas or numerical investigations. In contrast, this paper gives a rigorous proof of the one-dimensional behavior as far as the ground state energy and particle density are concerned. There are four parameters involved: the particle number, N, transverse and longitudinal dimensions of the trap, r and L, and the scattering length a of the interaction potential. Our main result is that if r/L → 0 and N → ∞ the ground state energy and density can be obtained by minimizing a one-dimensional density functional involving the Lieb-Liniger energy density with coupling constant ∼ a/r 2. This density functional simplifies in various limiting cases and we identify five asymptotic parameter regions altogether. Three of these, corresponding to the weak coupling regime, can also be obtained as limits of a three-dimensional Gross-Pitaevskii theory. We also show that Bose-Einstein condensation in the ground state persists in a part of this regime. In the strong coupling regime the longitudinal motion of the particles is strongly correlated. The Gross-Pitaevskii description is not valid in this regime and new mathematical methods come into play.},
author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob},
journal = {Communications in Mathematical Physics},
number = {2},
pages = {347 -- 393},
publisher = {Springer},
title = {{One-dimensional behavior of dilute, trapped Bose gases}},
doi = {10.1007/s00220-003-0993-3},
volume = {244},
year = {2004},
}
@article{2360,
abstract = {An optical lattice model developed that is similar to the Bose-Hubbard model to describe the transition between Bose-Einstein condensation (BEC) and a Mott insulator state was analyzed. It was found that the system was a hard core lattice gas at half of the maximum density and the optical lattice was modeled by a periodic potential of strength λ. It was also observed that the interparticle interaction was essential for this transition that occurred even in the ground state. The results show that all the essential features could be proved rigorously such as the existence of BEC for small λ and its suppression for a large λ.},
author = {Aizenman, Michael and Lieb, Élliott H and Robert Seiringer and Solovej, Jan P and Yngvason, Jakob},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = {2},
pages = {023612 -- 1--0236121--2},
publisher = {American Physical Society},
title = {{Bose-Einstein quantum phase transition in an optical lattice model}},
doi = {10.1103/PhysRevA.70.023612},
volume = {70},
year = {2004},
}
@article{1456,
abstract = {We study the space of L2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including asymptotically locally Euclidean manifolds, the (known types of) gravitational instantons, and also Poincaré metrics on ℚ-rank 1 ends of locally symmetric spaces and on the complements of smooth divisors in Kähler manifolds. The answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold. The L2 signature formula implied by our result is closely related to the one proved by Dai and more generally by Vaillant and identifies Dai's τ-invariant directly in terms of intersection cohomology of differing perversities. This work is also closely related to a recent paper of Carron and the forthcoming paper of Cheeger and Dai. We apply our results to a number of examples, gravitational instantons among them, arising in predictions about L2 harmonic forms in duality theories in string theory.},
author = {Tamas Hausel and Hunsicker, Eugénie and Mazzeo, Rafe R},
journal = {Duke Mathematical Journal},
number = {3},
pages = {485 -- 548},
publisher = {Duke University Press},
title = {{Hodge cohomology of gravitational instantons}},
doi = {10.1215/S0012-7094-04-12233-X},
volume = {122},
year = {2004},
}
@article{1464,
abstract = {The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and Atiyah and Bott asserts that its rational cohomology ring is generated by the universal classes, that is, by the Kunneth components of the Chern classes of the universal bundle.
This paper studies the larger, non-compact moduli space of Higgs bundles, as introduced by Hitchin and Simpson, with values in the canonical bundle K. This is diffeomorphic to the space of all connections of central constant curvature, whether unitary or not. The main result of the paper is that, in the rank 2 case, the rational cohomology ring of this space is again generated by universal classes.
The spaces of Higgs bundles with values in K(n) for n > 0 turn out to be essential to the story. Indeed, we show that their direct limit has the homotopy type of the classifying space of the gauge group, and hence has cohomology generated by universal classes. 2000 Mathematics Subject Classification 14H60 (primary), 14D20, 14H81, 32Q55, 58D27 (secondary). },
author = {Tamas Hausel and Thaddeus, Michael},
journal = {Proceedings of the London Mathematical Society},
number = {3},
pages = {632 -- 658},
publisher = {Oxford University Press},
title = {{Generators for the cohomology ring of the moduli space of rank 2 higgs bundles}},
doi = {10.1112/S0024611503014618},
volume = {88},
year = {2004},
}
@article{3807,
abstract = {The time course of Mg(2+) block and unblock of NMDA receptors (NMDARs) determines the extent they are activated by depolarization. Here, we directly measure the rate of NMDAR channel opening in response to depolarizations at different times after brief (1 ms) and sustained (4.6 s) applications of glutamate to nucleated patches from neocortical pyramidal neurons. The kinetics of Mg(2+) unblock were found to be non-instantaneous and complex, consisting of a prominent fast component (time constant approximately 100 micros) and slower components (time constants 4 and approximately 300 ms), the relative amplitudes of which depended on the timing of the depolarizing pulse. Fitting a kinetic model to these data indicated that Mg(2+) not only blocks the NMDAR channel, but reduces both the open probability and affinity for glutamate, while enhancing desensitization. These effects slow the rate of NMDAR channel opening in response to depolarization in a time-dependent manner such that the slower components of Mg(2+) unblock are enhanced during depolarizations at later times after glutamate application. One physiological consequence of this is that brief depolarizations occurring earlier in time after glutamate application are better able to open NMDAR channels. This finding has important implications for spike-timing-dependent synaptic plasticity (STDP), where the precise (millisecond) timing of action potentials relative to synaptic inputs determines the magnitude and sign of changes in synaptic strength. Indeed, we find that STDP timing curves of NMDAR channel activation elicited by realistic dendritic action potential waveforms are narrower than expected assuming instantaneous Mg(2+) unblock, indicating that slow Mg(2+) unblock of NMDAR channels makes the STDP timing window more precise.},
author = {Kampa, Bjorn M and Clements, John and Peter Jonas and Stuart, Greg J},
journal = {Journal of Physiology},
number = {Pt 2},
pages = {337 -- 45},
publisher = {Wiley-Blackwell},
title = {{Kinetics of Mg(2+) unblock of NMDA receptors: implications for spike-timing dependent synaptic plasticity}},
doi = {10.1113/jphysiol.2003.058842 },
volume = {556},
year = {2004},
}
@article{9517,
abstract = {Multicellular eukaryotes produce small RNA molecules (approximately 21–24 nucleotides) of two general types, microRNA (miRNA) and short interfering RNA (siRNA). They collectively function as sequence-specific guides to silence or regulate genes, transposons, and viruses and to modify chromatin and genome structure. Formation or activity of small RNAs requires factors belonging to gene families that encode DICER (or DICER-LIKE [DCL]) and ARGONAUTE proteins and, in the case of some siRNAs, RNA-dependent RNA polymerase (RDR) proteins. Unlike many animals, plants encode multiple DCL and RDR proteins. Using a series of insertion mutants of Arabidopsis thaliana, unique functions for three DCL proteins in miRNA (DCL1), endogenous siRNA (DCL3), and viral siRNA (DCL2) biogenesis were identified. One RDR protein (RDR2) was required for all endogenous siRNAs analyzed. The loss of endogenous siRNA in dcl3 and rdr2 mutants was associated with loss of heterochromatic marks and increased transcript accumulation at some loci. Defects in siRNA-generation activity in response to turnip crinkle virus in dcl2 mutant plants correlated with increased virus susceptibility. We conclude that proliferation and diversification of DCL and RDR genes during evolution of plants contributed to specialization of small RNA-directed pathways for development, chromatin structure, and defense.},
author = {Xie, Zhixin and Johansen, Lisa K. and Gustafson, Adam M. and Kasschau, Kristin D. and Lellis, Andrew D. and ZILBERMAN, Daniel and Jacobsen, Steven E. and Carrington, James C.},
issn = {1545-7885},
journal = {PLoS Biology},
number = {5},
pages = {0642--0652},
publisher = {Public Library of Science},
title = {{Genetic and functional diversification of small RNA pathways in plants}},
doi = {10.1371/journal.pbio.0020104},
volume = {2},
year = {2004},
}
@article{9511,
abstract = {Recent progress in understanding the silencing of transposable elements in the model plant Arabidopsis has revealed an interplay between DNA methylation, histone methylation and small interfering RNAs. DNA and histone methylation are not always sufficient to maintain silencing, and RNA-based reinforcement can be needed to maintain as well as initiate it.},
author = {ZILBERMAN, Daniel and Henikoff, Steven},
issn = {1465-6906},
journal = {Genome Biology},
number = {12},
publisher = {Springer Nature},
title = {{Silencing of transposons in plant genomes: kick them when they're down}},
doi = {10.1186/gb-2004-5-12-249},
volume = {5},
year = {2004},
}
@article{9493,
abstract = {In a number of organisms, transgenes containing transcribed inverted repeats (IRs) that produce hairpin RNA can trigger RNA-mediated silencing, which is associated with 21-24 nucleotide small interfering RNAs (siRNAs). In plants, IR-driven RNA silencing also causes extensive cytosine methylation of homologous DNA in both the transgene "trigger" and any other homologous DNA sequences--"targets". Endogenous genomic sequences, including transposable elements and repeated elements, are also subject to RNA-mediated silencing. The RNA silencing gene ARGONAUTE4 (AGO4) is required for maintenance of DNA methylation at several endogenous loci and for the establishment of methylation at the FWA gene. Here, we show that mutation of AGO4 substantially reduces the maintenance of DNA methylation triggered by IR transgenes, but AGO4 loss-of-function does not block the initiation of DNA methylation by IRs. AGO4 primarily affects non-CG methylation of the target sequences, while the IR trigger sequences lose methylation in all sequence contexts. Finally, we find that AGO4 and the DRM methyltransferase genes are required for maintenance of siRNAs at a subset of endogenous sequences, but AGO4 is not required for the accumulation of IR-induced siRNAs or a number of endogenous siRNAs, suggesting that AGO4 may function downstream of siRNA production.},
author = {ZILBERMAN, Daniel and Cao, Xiaofeng and Johansen, Lisa K. and Xie, Zhixin and Carrington, James C. and Jacobsen, Steven E.},
issn = {1879-0445},
journal = {Current Biology},
number = {13},
pages = {1214--1220},
publisher = {Elsevier},
title = {{Role of Arabidopsis ARGONAUTE4 in RNA-directed DNA methylation triggered by inverted repeats}},
doi = {10.1016/j.cub.2004.06.055},
volume = {14},
year = {2004},
}
@inproceedings{2337,
author = {Lieb, Élliott H and Robert Seiringer},
editor = {Karpeshina, Yulia and Weikard, Rudi and Zeng, Yanni},
pages = {239 -- 250},
publisher = {American Mathematical Society},
title = {{Bose-Einstein condensation of dilute gases in traps }},
doi = {10.1090/conm/327/05818},
volume = {327},
year = {2003},
}
@article{2354,
abstract = {We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the Gross-Pitaevskii (GP) limit of a dilute gas. Analysing both the absolute and the bosonic ground states of the system, we show, in particular, their different behaviour for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.},
author = {Robert Seiringer},
journal = {Journal of Physics A: Mathematical and Theoretical},
number = {37},
pages = {9755 -- 9778},
publisher = {IOP Publishing Ltd.},
title = {{Ground state asymptotics of a dilute, rotating gas}},
doi = {10.1088/0305-4470/36/37/312},
volume = {36},
year = {2003},
}
@article{2357,
abstract = {The classic Poincaré inequality bounds the L q-norm of a function f in a bounded domain Ω ⊂ ℝ n in terms of some L p-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Τ from Ω and concentrate our attention on Λ = Ω \ Τ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it might have a very bad constant. This is so even if the volume of Τ is arbitrarily small. A Poincaré inequality does hold, however, if one makes the additional assumption that f has a finite L p gradient norm on the whole of Ω, not just on Λ. The important point is that the Poincaré inequality thus obtained bounds the L q-norm of f in terms of the L p gradient norm on Λ (not Ω) plus an additional term that goes to zero as the volume of Τ goes to zero. This error term depends on Τ only through its volume. Apart from this additive error term, the constant in the inequality remains that of the 'nice' domain Ω. In the second generalization we are given a vector field A and replace ∇ by ∇ + iA(x) (geometrically, a connection on a U(1) bundle). Unlike the A = 0 case, the infimum of ∥(∇ + iA)f∥ p over all f with a given ∥f∥ q is in general not zero. This permits an improvement of the inequality by the addition of a term whose sharp value we derive. We describe some open problems that arise from these generalizations.},
author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob},
journal = {Annals of Mathematics},
number = {3},
pages = {1067 -- 1080},
publisher = {Princeton University Press},
title = {{Poincaré inequalities in punctured domains}},
doi = {10.4007/annals.2003.158.1067 },
volume = {158},
year = {2003},
}
@article{2358,
abstract = {A study was conducted on the one-dimensional (1D) bosons in three-dimensional (3D) traps. A rigorous analysis was carried out on the parameter regions in which various types of 1D or 3D behavior occurred in the ground state. The four parameter regions include density, transverse, longitudinal dimensions and scattering length.},
author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob},
journal = {Physical Review Letters},
number = {15},
pages = {1504011 -- 1504014},
publisher = {American Physical Society},
title = {{One-dimensional Bosons in three-dimensional traps}},
doi = {10.1103/PhysRevLett.91.150401},
volume = {91},
year = {2003},
}
@article{1457,
abstract = {Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Stromdnger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equal. This provides significant evidence in support of SYZ. Moreover, the examples are of great interest in their own right: they are spaces of flat SLr-connections on a smooth curve. The mirror is the corresponding space for the Langlands dual group PGLr. These examples therefore throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.},
author = {Tamas Hausel and Thaddeus, Michael},
journal = {Inventiones Mathematicae},
number = {1},
pages = {197 -- 229},
publisher = {Springer},
title = {{Mirror symmetry, langlands duality, and the Hitchin system}},
doi = {10.1007/s00222-003-0286-7},
volume = {153},
year = {2003},
}
@article{1458,
abstract = {The moduli space of stable bundles of rank $2$ and degree $1$ on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the noncompact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance.},
author = {Tamas Hausel and Thaddeus, Michael},
journal = {Journal of the American Mathematical Society},
number = {2},
pages = {303 -- 329},
publisher = {American Mathematical Society},
title = {{Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles}},
doi = {10.1090/S0894-0347-02-00417-4},
volume = {16},
year = {2003},
}
@article{1459,
abstract = {In this paper we explicitly calculate the analogue of the 't Hooft SU (2) Yang-Mills instantons on Gibbons-Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi-Hanson, or Ak ALE gravitational instantons and the multi-Taub-NUT spaces, or Ak ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU (2) magnetic monopole solutions of the Bogomolny equations on flat ℝ3.},
author = {Etesi, Gábor and Tamas Hausel},
journal = {Communications in Mathematical Physics},
number = {2},
pages = {275 -- 288},
publisher = {Springer},
title = {{On Yang-Mills instantons over multi-centered gravitational instantons}},
doi = {10.1007/s00220-003-0806-8},
volume = {235},
year = {2003},
}
@article{166,
abstract = {For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.},
author = {Browning, Timothy D and Swarbick Jones, M},
journal = {Proceedings of the Bonn session in analytic number theory and diophantine equations},
publisher = {Mathematisches Institut der Universität Bonn},
title = {{Counting rational points on del Pezzo surfaces of degree 5}},
volume = {360},
year = {2003},
}
@article{3725,
abstract = {The combination of high-resolution atomic force microscopy (AFM) imaging and single-molecule force-spectroscopy was employed to unfold single bacteriorhodopsins (BR) from native purple membrane patches at various physiologically relevant temperatures. The unfolding spectra reveal detailed insight into the stability of individual structural elements of BR against mechanical unfolding. Intermittent states in the unfolding process are associated with the stepwise unfolding of alpha-helices, whereas other states are associated with the unfolding of polypeptide loops connecting the alpha-helices. It was found that the unfolding forces of the secondary structures considerably decreased upon increasing the temperature from 8 to 52°C. Associated with this effect, the probability of individual unfolding pathways of BR was significantly influenced by the temperature. At lower temperatures, transmembrane alpha-helices and extracellular polypeptide loops exhibited sufficient stability to individually establish potential barriers against unfolding, whereas they predominantly unfolded collectively at elevated temperatures. This suggests that increasing the temperature decreases the mechanical stability of secondary structural elements and changes molecular interactions between secondary structures, thereby forcing them to act as grouped structures.},
author = {Harald Janovjak and Kessler, Max and Oesterhelt, Dieter and Gaub, Hermann and Mueller, Daniel J},
journal = {EMBO Journal},
number = {19},
pages = {5220 -- 5229},
publisher = {Wiley-Blackwell},
title = {{Unfolding pathways of native bacteriorhodopsin depend on temperature}},
doi = {10.1093/emboj/cdg509},
volume = {22},
year = {2003},
}
@article{3752,
abstract = {We use the lac operon in Escherichia coli as a prototype system to illustrate the current state, applicability, and limitations of modeling the dynamics of cellular networks. We integrate three different levels of description (molecular, cellular, and that of cell population) into a single model, which seems to capture many experimental aspects of the system.},
author = {Vilar,Jose M and Calin Guet and Leibler, Stanislas},
journal = {Journal of Cell Biology},
number = {3},
pages = {471 -- 476},
publisher = {Rockefeller University Press},
title = {{Modeling network dynamics: the lac operon, a case study}},
doi = {10.1083/jcb.200301125},
volume = {161},
year = {2003},
}
@article{9495,
abstract = {RNA interference is a conserved process in which double-stranded RNA is processed into 21–25 nucleotide siRNAs that trigger posttranscriptional gene silencing. In addition, plants display a phenomenon termed RNA-directed DNA methylation (RdDM) in which DNA with sequence identity to silenced RNA is de novo methylated at its cytosine residues. This methylation is not only at canonical CpG sites but also at cytosines in CpNpG and asymmetric sequence contexts. In this report, we study the role of the DRM and CMT3 DNA methyltransferase genes in the initiation and maintenance of RdDM. Neither drm nor cmt3 mutants affected the maintenance of preestablished RNA-directed CpG methylation. However, drm mutants showed a nearly complete loss of asymmetric methylation and a partial loss of CpNpG methylation. The remaining asymmetric and CpNpG methylation was dependent on the activity of CMT3, showing that DRM and CMT3 act redundantly to maintain non-CpG methylation. These DNA methyltransferases appear to act downstream of siRNAs, since drm1 drm2 cmt3 triple mutants show a lack of non-CpG methylation but elevated levels of siRNAs. Finally, we demonstrate that DRM activity is required for the initial establishment of RdDM in all sequence contexts including CpG, CpNpG, and asymmetric sites.},
author = {Cao, Xiaofeng and Aufsatz, Werner and ZILBERMAN, Daniel and Mette, M.Florian and Huang, Michael S. and Matzke, Marjori and Jacobsen, Steven E.},
issn = {1879-0445},
journal = {Current Biology},
number = {24},
pages = {2212--2217},
publisher = {Elsevier},
title = {{Role of the DRM and CMT3 methyltransferases in RNA-directed DNA methylation}},
doi = {10.1016/j.cub.2003.11.052},
volume = {13},
year = {2003},
}
@article{2349,
abstract = {The Bose-Einstein condensation (BEC) of the ground state of bosonic atoms in a trap was discussed. The BEC was proved for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schrodinger equation. The BEC was 100% into the state which minimized the Gross-Pitaevskii energy functional. The analysis also included rigorous proof of BEC in a physically realistic, continuum model.},
author = {Lieb, Élliott H and Robert Seiringer},
journal = {Physical Review Letters},
number = {17},
pages = {1704091 -- 1704094},
publisher = {American Physical Society},
title = {{Proof of Bose-Einstein condensation for dilute trapped gases}},
doi = {10.1103/PhysRevLett.88.170409},
volume = {88},
year = {2002},
}
@article{2350,
abstract = {Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge Z and in presence of the quantized radiation field. We consider the case of small coupling constant α, but fixed Zα and ultraviolet cut-off Λ. We prove that after renormalizing the mass the binding energy has, to leading order in α, a finite limit as Λ goes to infinity; i.e., the cut-off can be removed. The expression for the ground state energy shift thus obtained agrees with Bethe's formula for small values of Zα, but shows a different behavior for bigger values.},
author = {Hainzl, Christian and Robert Seiringer},
journal = {Advances in Theoretical and Mathematical Physics},
number = {5},
pages = {847 -- 871},
publisher = {International Press},
title = {{Mass renormalization and energy level shift in non-relativistic QED}},
volume = {6},
year = {2002},
}
@article{2351,
abstract = {We study the Gross-Pitaevskii functional for a rotating two-dimensional Bose gas in a trap. We prove that there is a breaking of the rotational symmetry in the ground state; more precisely, for any value of the angular velocity and for large enough values of the interaction strength, the ground state of the functional is not an eigenfunction of the angular momentum. This has interesting consequences on the Bose gas with spin; in particular, the ground state energy depends non-trivially on the number of spin components, and the different components do not have the same wave function. For the special case of a harmonic trap potential, we give explicit upper and lower bounds on the critical coupling constant for symmetry breaking.},
author = {Robert Seiringer},
journal = {Communications in Mathematical Physics},
number = {3},
pages = {491 -- 509},
publisher = {Springer},
title = {{Gross-Pitaevskii theory of the rotating Bose gas}},
doi = {10.1007/s00220-002-0695-2},
volume = {229},
year = {2002},
}
@article{2352,
abstract = {We present a generalization of the Fefferman-de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions V on ℝn going to zero at infinity. This generalized decomposition can be used to extend previous results on N-body quantum systems with Coulomb interaction to a more general class of interactions. As an example of such an application, we derive the high density asymptotics of the ground state energy of jellium with Yukawa interaction in the thermodynamic limit, using a correlation estimate by Graf and Solovej.},
author = {Hainzl, Christian and Robert Seiringer},
journal = {Letters in Mathematical Physics},
number = {1},
pages = {75 -- 84},
publisher = {Springer},
title = {{General decomposition of radial functions on ℝn and applications to N-body quantum systems}},
doi = {10.1023/A:1020204818938},
volume = {61},
year = {2002},
}
@article{2353,
abstract = {A commonly used theoretical definition of superfluidity in the ground state of a Bose gas is based on the response of the system to an imposed velocity field or, equivalently, to twisted boundary conditions in a box. We are able to carry out this program in the case of a dilute interacting Bose gas in a trap, and we prove that a gas with repulsive interactions is 100% superfluid in the dilute limit in which the Gross-Pitaevskii equation is exact. This is the first example in an experimentally realistic continuum model in which superfluidity is rigorously verified.},
author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob},
journal = {Physical Review B - Condensed Matter and Materials Physics},
number = {13},
publisher = {American Physical Society},
title = {{Superfluidity in dilute trapped Bose gases}},
doi = {10.1103/PhysRevB.66.134529},
volume = {66},
year = {2002},
}
@article{2617,
abstract = {Synapses exhibit different short-term plasticity patterns and this behaviour influences information processing in neuronal networks. We tested how the short-term plasticity of excitatory postsynaptic currents (EPSCs) depends on the postsynaptic cell type, identified by axonal arborizations and molecular markers in the hippocampal CA1 area. Three distinct types of short-term synaptic behaviour (facilitating, depressing and combined facilitating-depressing) were defined by fitting a dynamic neurotransmission model to the data. Approximately 75 % of the oriens-lacunosum-moleculare (O-LM) interneurones received facilitating EPSCs, but in three of 12 O-LM cells EPSCs also showed significant depression. Over 90 % of the O-LM cells were immunopositive for somatostatin and mGluR1α and all tested cells were decorated by strongly mGluR7a positive axon terminals. Responses in eight of 12 basket cells were described well with a model involving only depression, but the other cells displayed combined facilitating-depressing EPSCs. No apparent difference was found between the plasticity of EPSCs in cholecystokinin- or parvalbumin-containing basket cells. In oriens-bistratified cells (O-Bi), two of nine cells showed facilitating EPSCs, another two depressing, and the remaining five cells combined facilitating-depressing EPSCs. Seven of 10 cells tested for somatostatin were immunopositive, but mGluR1α was detectable only in two of 11 tested cells. Furthermore, most O-Bi cells projected to the CA3 area and the subiculum, as well as outside the hippocampal formation. Postsynaptic responses to action potentials recorded in vivo from a CA1 place cell were modelled, and revealed great differences between and within cell types. Our results demonstrate that the short-term plasticity of EPSCs is cell type dependent, but with significant heterogeneity within all three interneurone populations.},
author = {Losonczy, Attila and Zhang, Limei and Ryuichi Shigemoto and Somogyi, Péter and Nusser, Zoltán},
journal = {Journal of Physiology},
number = {1},
pages = {193 -- 210},
publisher = {Wiley-Blackwell},
title = {{Cell type dependence and variability in the short-term plasticity of EPSCs in identified mouse hippocampal interneurones}},
doi = {10.1113/jphysiol.2002.020024},
volume = {542},
year = {2002},
}
@article{1451,
abstract = {Extending work of Bielawski-Dancer 3 and Konno 14, we develop a theory of toric hyperkähler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawrence toric varieties, meaning GIT quotients of even-dimensional affine spaces by symplectic torus actions. A toric hyperkähler variety is a complete intersection in a Lawrence toric variety. Both varieties are non-compact, and they share the same cohomology ring, namely, the Stanley-Reisner ring of a matroid modulo a linear system of parameters. Familiar applications of toric geometry to combinatorics, including the Hard Lefschetz Theorem and the volume polynomials of Khovanskii-Pukhlikov 11, are extended to the hyperkähler setting. When the matroid is graphic, our construction gives the toric quiver varieties, in the sense of Nakajima 17.},
author = {Tamas Hausel and Sturmfels, Bernd},
journal = {Documenta Mathematica},
number = {1},
pages = {495 -- 534},
publisher = {Deutsche Mathematiker Vereinigung},
title = {{Toric hyperkähler varieties}},
volume = {7},
year = {2002},
}
@article{3799,
abstract = {GABAergic interneurones are diverse in their morphological and functional properties. Perisomatic inhibitory cells show fast spiking during sustained current injection, whereas dendritic inhibitory cells fire action potentials with lower frequency. We examined functional and molecular properties of K(+) channels in interneurones with horizontal dendrites in stratum oriens-alveus (OA) of the hippocampal CA1 region, which mainly comprise somatostatin-positive dendritic inhibitory cells. Voltage-gated K(+) currents in nucleated patches isolated from OA interneurones consisted of three major components: a fast delayed rectifier K(+) current component that was highly sensitive to external 4-aminopyridine (4-AP) and tetraethylammonium (TEA) (half-maximal inhibitory concentrations < 0.1 mM for both blockers), a slow delayed rectifier K(+) current component that was sensitive to high concentrations of TEA, but insensitive to 4-AP, and a rapidly inactivating A-type K(+) current component that was blocked by high concentrations of 4-AP, but resistant to TEA. The relative contributions of these components to the macroscopic K(+) current were estimated as 57 +/- 5, 25 +/- 6, and 19 +/- 2 %, respectively. Dendrotoxin, a selective blocker of Kv1 channels had only minimal effects on K(+) currents in nucleated patches. Coapplication of the membrane-permeant cAMP analogue 8-(4-chlorophenylthio)-adenosine 3':5'-cyclic monophosphate (cpt-cAMP) and the phosphodiesterase blocker isobutyl-methylxanthine (IBMX) resulted in a selective inhibition of the fast delayed rectifier K(+) current component. This inhibition was absent in the presence of the protein kinase A (PKA) inhibitor H-89, implying the involvement of PKA-mediated phosphorylation. Single-cell reverse transcription-polymerase chain reaction (RT-PCR) analysis revealed a high abundance of Kv3.2 mRNA in OA interneurones, whereas the expression level of Kv3.1 mRNA was markedly lower. Similarly, RT-PCR analysis showed a high abundance of Kv4.3 mRNA, whereas Kv4.2 mRNA was undetectable. This suggests that the fast delayed rectifier K(+) current and the A-type K(+) current component are mediated predominantly by homomeric Kv3.2 and Kv4.3 channels. Selective modulation of Kv3.2 channels in OA interneurones by cAMP is likely to be an important factor regulating the activity of dendritic inhibitory cells in principal neurone-interneurone microcircuits.},
author = {Lien, Cheng-Chang and Martina, Marco and Schultz, Jobst H and Ehmke, Heimo and Peter Jonas},
journal = {Journal of Physiology},
number = {Pt 2},
pages = {405 -- 419},
publisher = {Wiley-Blackwell},
title = {{Gating, modulation and subunit composition of voltage-gated K(+) channels in dendritic inhibitory interneurones of rat hippocampus}},
doi = { 10.1113/jphysiol.2001.013066},
volume = {538},
year = {2002},
}
@article{3919,
abstract = {Hamilton's concept of local mate competition (LMC) is the standard model to explain female-biased sex ratios in solitary Hymenoptera. In social Hymenoptera, however, LMC has remained controversial, mainly because manipulation of sex allocation by workers in response to relatedness asymmetries is an additional powerful mechanism of female bias. Furthermore, the predominant mating systems in the social insects are thought to make LMC unlikely. Nevertheless, several species exist in which dispersal of males is limited and mating occurs in the nest. Some of these species, such as the ant Cardiocondyla obscurior, have evolved dimorphic males, with one morph being specialized for dispersal and the other for fighting with nest-mate males over access to females. Such life history, combining sociality and alternative reproductive tactics in males, provides a unique opportunity to test the power of LMC as a selective force leading to female-biased sex ratios in social Hymenoptera. We show that, in concordance with LMC predictions, an experimental increase in queen number leads to a shift in sex allocation in favour of non-dispersing males, but does not influence the proportion of disperser males. Furthermore, we can assign this change in sex allocation at the colony level to the queens and rule out worker manipulation.},
author = {Cremer, Sylvia and Heinze, Jürgen},
journal = {Proceedings of the Royal Society of London Series B Biological Sciences},
number = {1489},
pages = {417 -- 422},
publisher = {Royal Society, The},
title = {{Adaptive production of fighter males: queens of the ant Cardiocondyla adjust the sex ratio under local mate competition}},
doi = {10.1098/rspb.2001.1892},
volume = {269},
year = {2002},
}
@article{3621,
abstract = {In 1991, Barton and Turelli developed recursions to describe the evolution of multilocus systems under arbitrary forms of selection. This article generalizes their approach to allow for arbitrary modes of inheritance, including diploidy, polyploidy, sex linkage, cytoplasmic inheritance, and genomic imprinting. The framework is also extended to allow for other deterministic evolutionary forces, including migration and mutation. Exact recursions that fully describe the state of the population are presented; these are implemented in a computer algebra package (available on the Web at http://helios.bto.ed.ac.uk/evolgen). Despite the generality of our framework, it can describe evolutionary dynamics exactly by just two equations. These recursions can be further simplified using a "quasi-linkage equilibrium" (QLE) approximation. We illustrate the methods by finding the effect of natural selection, sexual selection, mutation, and migration on the genetic composition of a population.},
author = {Kirkpatrick, Mark and Johnson, Toby and Nicholas Barton},
journal = {Genetics},
number = {4},
pages = {1727 -- 1750},
publisher = {Genetics Society of America},
title = {{General models of multilocus evolution}},
volume = {161},
year = {2002},
}
@inproceedings{2340,
abstract = {
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in external potentials and interacting via repulsive short range forces are usually described by means of the Gross-Pitaevskii energy functional. In joint work with Elliott H. Lieb and Jakob Yngvason its status as an approximation for the quantum mechanical many-body ground state problem has recently been rigorously clarified. We present a summary of this work, for both the two-and three-dimensional case.
},
author = {Robert Seiringer},
editor = {Demuth, Michael and Schultze, Bert-Wolfgang},
pages = {307 -- 314},
publisher = {Birkhäuser},
title = {{Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state energy formula}},
doi = {10.1007/978-3-0348-8231-6},
volume = {126},
year = {2001},
}
@article{2341,
abstract = {We study the ground state properties of an atom with nuclear charge Z and N bosonic "electrons" in the presence of a homogeneous magnetic field B. We investigate the mean field limit N→∞ with N / Z fixed, and identify three different asymptotic regions, according to B≪Z2,B∼Z2,andB≫Z2 . In Region 1 standard Hartree theory is applicable. Region 3 is described by a one-dimensional functional, which is identical to the so-called Hyper-Strong functional introduced by Lieb, Solovej and Yngvason for atoms with fermionic electrons in the region B≫Z3 ; i.e., for very strong magnetic fields the ground state properties of atoms are independent of statistics. For Region 2 we introduce a general magnetic Hartree functional, which is studied in detail. It is shown that in the special case of an atom it can be restricted to the subspace of zero angular momentum parallel to the magnetic field, which simplifies the theory considerably. The functional reproduces the energy and the one-particle reduced density matrix for the full N-particle ground state to leading order in N, and it implies the description of the other regions as limiting cases.},
author = {Baumgartner, Bernhard and Robert Seiringer},
journal = {Annales Henri Poincare},
number = {1},
pages = {41 -- 76},
publisher = {Birkhäuser},
title = {{Atoms with bosonic "electrons" in strong magnetic fields}},
doi = {10.1007/PL00001032},
volume = {2},
year = {2001},
}
@article{2345,
abstract = {We give upper bounds for the number of spin-1/2 particles that can be bound to a nucleus of charge Z in the presence of a magnetic field B, including the spin-field coupling. We use Lieb's strategy, which is known to yield Nc < 2Z + 1 for magnetic fields that go to zero at infinity, ignoring the spin-field interaction. For particles with fermionic statistics in a homogeneous magnetic field our upper bound has an additional term of the order of Z × min {(B/Z3)2/5, 1 + | 1n(B/Z3)|2}.},
author = {Robert Seiringer},
journal = {Journal of Physics A: Mathematical and General},
number = {9},
pages = {1943 -- 1948},
publisher = {IOP Publishing Ltd.},
title = {{On the maximal ionization of atoms in strong magnetic fields}},
doi = {10.1088/0305-4470/34/9/311},
volume = {34},
year = {2001},
}
@article{2346,
abstract = {By means of a generalization of the Fefferman - de la Llave decomposition we derive a general lower bound on the interaction energy of one-dimensional quantum systems. We apply this result to a specific class of lowest Landau band wave functions.},
author = {Hainzl, Christian and Robert Seiringer},
journal = {Letters in Mathematical Physics},
number = {2},
pages = {133 -- 142},
publisher = {Springer},
title = {{Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics}},
doi = {10.1023/A:1010951905548},
volume = {55},
year = {2001},
}
@article{2347,
abstract = {We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number N is large but ρ̄a2 is small, where ρ̄ is the average particle density and a the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a Gross-Pitaevskii (GP) energy functional with a coupling constant g ∼ 1/| 1n(ρ̄a2)|. In contrast to the 3D case the coupling constant depends on N through the mean density. The GP energy per particle depends only on Ng. In 2D this parameter is typically so large that the gradient term in the GP energy functional is negligible and the simpler description by a Thomas-Fermi type functional is adequate.},
author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {17 -- 31},
publisher = {Springer},
title = {{A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas}},
doi = {10.1007/s002200100533},
volume = {224},
year = {2001},
}
@article{2348,
abstract = {This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to ∞ with the magnetic field B satisfying B ≫ Z4/3 all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy.},
author = {Hainzl, Christian and Robert Seiringer},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {229 -- 248},
publisher = {Springer},
title = {{A discrete density matrix theory for atoms in strong magnetic fields}},
doi = {10.1007/s002200100373},
volume = {217},
year = {2001},
}
@article{2736,
abstract = {We consider the time evolution of N bosonic particles interacting via a mean field Coulomb potential. Suppose the initial state is a product wavefunction. We show that at any finite time the correlation functions factorize in the limit N → ∞. Furthermore, the limiting one particle density matrix satisfies the nonlinear Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy for the correlation functions and a new apriori estimate for the many-body Schrödinger equations.},
author = {László Erdös and Yau, Horng-Tzer},
journal = {Advances in Theoretical and Mathematical Physics},
number = {6},
pages = {1169 -- 1205},
publisher = {International Press},
title = {{Derivation of the nonlinear Schrödinger equation from a many body Coulomb system}},
volume = {5},
year = {2001},
}
@article{1452,
abstract = {In this Note we present pairs of hyperkähler orbifolds which satisfy two different versions of mirror symmetry. On the one hand, we show that their Hodge numbers (or more precisely, stringy E-polynomials) are equal. On the other hand, we show that they satisfy the prescription of Strominger, Yau, and Zaslow (which in the present case goes back to Bershadsky, Johansen, Sadov and Vafa): that a Calabi-Yau and its mirror should fiber over the same real manifold, with special Lagrangian fibers which are tori dual to each other. Our examples arise as moduli spaces of local systems on a curve with structure group SL(n); the mirror is the corresponding space with structure group PGL(n). The special Lagrangian tori come from an algebraically completely integrable Hamiltonian system: the Hitchin system.},
author = {Tamas Hausel and Thaddeus, Michael},
journal = {Comptes Rendus de l'Academie des Sciences - Series I: Mathematics},
number = {4},
pages = {313 -- 318},
publisher = {Elsevier},
title = {{Examples of mirror partners arising from integrable systems}},
doi = {10.1016/S0764-4442(01)02057-2},
volume = {333},
year = {2001},
}
@article{1453,
abstract = {In this Letter we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L2 harmonic 2-form, while at an inner point we recover the Pope-Yuille instanton constructed as a projection of the Levi-Civitá connection onto the positive su(2)+ ⊂ so(4) subalgebra. Our method imitates the Jackiw-Nohl-Rebbi construction originally designed for flat R4. That is we find a one-parameter family of harmonic functions on the Taub-NUT space with a point singularity, rescale the metric and project the obtained Levi-Civitá connection onto the other negative su(2)- ⊂ so(4) part. Our solutions will possess the full U(2) symmetry, and thus provide more solutions to the recently proposed U(2) symmetric ansatz of Kim and Yoon.},
author = {Etesi, Gábor and Tamas Hausel},
journal = {Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics},
number = {1-2},
pages = {189 -- 199},
publisher = {Elsevier},
title = {{Geometric construction of new Yang-Mills instantons over Taub-NUT space}},
doi = {10.1016/S0370-2693(01)00821-8},
volume = {514},
year = {2001},
}
@article{1454,
abstract = {We address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L2 harmonic 2-forms on the space. Gibbons found a non-topological L2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energy. We imitate his construction in the case of the Euclidean Schwarzschild manifold and find a non-topological self-dual L2 harmonic 2-form on it. We show how this gives rise to Abelian instantons and identify them with SU(2)-instantons of Pontryagin number 2n2 found by Charap and Duff in 1977. Using results of Dodziuk and Hitchin we also calculate the full L2 harmonic space for the Euclidean Schwarzschild manifold.},
author = {Etesi, Gábor and Tamas Hausel},
journal = {Journal of Geometry and Physics},
number = {1-2},
pages = {126 -- 136},
publisher = {Elsevier},
title = {{Geometric interpretation of Schwarzschild instantons}},
doi = {10.1016/S0393-0440(00)00040-1},
volume = {37},
year = {2001},
}