TY - JOUR
AB - Eukaryotic chromatin is separated into functional domains differentiated by posttranslational histone modifications, histone variants, and DNA methylation1–6. Methylation is associated with repression of transcriptional initiation in plants and animals, and is frequently found in transposable elements. Proper methylation patterns are critical for eukaryotic development4,5, and aberrant methylation-induced silencing of tumor suppressor genes is a common feature of human cancer7. In contrast to methylation, the histone variant H2A.Z is preferentially deposited by the Swr1 ATPase complex near 5′ ends of genes where it promotes transcriptional competence8–20. How DNA methylation and H2A.Z influence transcription remains largely unknown. Here we show that in the plant Arabidopsis thaliana, regions of DNA methylation are quantitatively deficient in H2A.Z. Exclusion of H2A.Z is seen at sites of DNA methylation in the bodies of actively transcribed genes and in methylated transposons. Mutation of the MET1 DNA methyltransferase, which causes both losses and gains of DNA methylation4,5, engenders opposite changes in H2A.Z deposition, while mutation of the PIE1 subunit of the Swr1 complex that deposits H2A.Z17 leads to genome-wide hypermethylation. Our findings indicate that DNA methylation can influence chromatin structure and effect gene silencing by excluding H2A.Z, and that H2A.Z protects genes from DNA methylation.
AU - ZILBERMAN, Daniel
AU - Coleman-Derr, Devin
AU - Ballinger, Tracy
AU - Henikoff, Steven
ID - 9457
IS - 7218
JF - Nature
KW - Multidisciplinary
SN - 0028-0836
TI - Histone H2A.Z and DNA methylation are mutually antagonistic chromatin marks
VL - 456
ER -
TY - JOUR
AB - It was recently shown by Hansen that the Wigner-Yanase entropy is, for general states of quantum systems, not subadditive with respect to decomposition into two subsystems, although this property is known to hold for pure states. We investigate the question whether the weaker property of subadditivity for pure states with respect to decomposition into more than two subsystems holds. This property would have interesting applications in quantum chemistry. We show, however, that it does not hold in general, and provide a counterexample.
AU - Robert Seiringer
ID - 2367
IS - 3
JF - Letters in Mathematical Physics
TI - On the failure of subadditivity of the Wigner-Yanase entropy
VL - 80
ER -
TY - JOUR
AB - After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α0.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2370
IS - 3
JF - Reports on Mathematical Physics
TI - Bose-Einstein condensation and spontaneous symmetry breaking
VL - 59
ER -
TY - JOUR
AB - We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zα = 2/π.
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2371
IS - 2
JF - Communications in Mathematical Physics
TI - Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value
VL - 275
ER -
TY - JOUR
AB - The increasing interest in the Müller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock (HF) functional, but with a modified exchange term in which the square of the density matrix γ(x, x′) is replaced by the square of γ1 2 (x, x′). After an extensive introductory discussion of density-matrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing γ 's have unique densities ρ(r), which is a physically desirable property often absent in HF theory. We show that minimizers exist if N≤Z, and derive various properties of the minimal energy and the corresponding minimizers. We also give a precise statement about the equation for the orbitals of γ, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Siedentop, Heinz K
ID - 2372
IS - 5
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Müller's exchange-correlation energy in density-matrix-functional theory
VL - 76
ER -
TY - JOUR
AB - For the BCS equation with local two-body interaction λV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as γ"0. We derive necessary and sufficient conditions onV(x) for the existence of a nontrivial solution for all values of γ>0.
AU - Frank, Rupert L
AU - Hainzl, Christian
AU - Naboko, Serguei N
AU - Robert Seiringer
ID - 2373
IS - 4
JF - Journal of Geometric Analysis
TI - The critical temperature for the BCS equation at weak coupling
VL - 17
ER -
TY - JOUR
AB - We give a Cwikel-Lieb-Rozenblum type bound on the number of bound states of Schrödinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2375
IS - 2-3
JF - Letters in Mathematical Physics
TI - Number of bound states of Schrödinger operators with matrix-valued potentials
VL - 82
ER -
TY - CHAP
AU - László Erdös
ED - Gesztesy, Fritz
ED - Deift, Percy
ED - Galvez, Percy
ED - Perry, Peter
ED - Schlag, Wilhelm
ID - 2705
T2 - Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry Simon's 60th Birthday
TI - Recent developments in quantum mechanics with magnetic fields
VL - 76
ER -
TY - JOUR
AB - In quantum information science, the phase of a wave function plays an important role in encoding information. Although most experiments in this field rely on dynamic effects to manipulate this information, an alternative approach is to use geometric phase, which has been argued to have potential fault tolerance. We demonstrated the controlled accumulation of a geometric phase, Berry's phase, in a superconducting qubit; we manipulated the qubit geometrically by means of microwave radiation and observed the accumulated phase in an interference experiment. We found excellent agreement with Berry's predictions and also observed a geometry-dependent contribution to dephasing.
AU - Leek, Peter J
AU - Johannes Fink
AU - Blais, Alexandre
AU - Bianchetti, R
AU - Göppl, M
AU - Gambetta, Jay M
AU - Schuster, David I
AU - Frunzio, Luigi
AU - Schoelkopf, Robert J
AU - Wallraff, Andreas
ID - 1762
IS - 5858
JF - Science
TI - Observation of Berry's phase in a solid-state qubit
VL - 318
ER -
TY - CONF
AB - 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.
AU - Bernd Bickel
AU - Botsch, Mario
AU - Angst, Roland
AU - Matusik, Wojciech
AU - Otaduy, Miguel A
AU - Pfister, Hanspeter
AU - Groß, Markus S
ID - 2091
TI - Multi scale capture of facial geometry and motion
ER -
TY - JOUR
AB - 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.
AU - Bernd Bickel
AU - Botsch, Mario
AU - Angst, Roland
AU - Matusik, Wojciech
AU - Otaduy, Miguel A
AU - Pfister, Hanspeter
AU - Groß, Markus S
ID - 2093
IS - 3
JF - ACM Transactions on Graphics
TI - Multi scale capture of facial geometry and motion
VL - 26
ER -
TY - JOUR
AB - 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.
AU - Jan Maas
AU - van Neerven, Jan M
ID - 2118
IS - 3
JF - Archiv der Mathematik
TI - On analytic Ornstein-Uhlenbeck semigroups in infinite dimensions
VL - 89
ER -
TY - JOUR
AU - De La Bretèche, Régis
AU - Browning, Timothy D
ID - 221
IS - 1
JF - Michigan Mathematical Journal
TI - On Manin's conjecture for singular del Pezzo surfaces of degree four, I
VL - 55
ER -
TY - JOUR
AB - 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.
AU - de la Bretèche, Régis
AU - Timothy Browning
ID - 222
IS - 3
JF - Mathematical Proceedings of the Cambridge Philosophical Society
TI - On Manin's conjecture for singular del Pezzo surfaces of degree four, II
VL - 143
ER -
TY - JOUR
AB - 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.
AU - Timothy Browning
ID - 223
IS - 1
JF - Monatshefte fur Mathematik
TI - Density of integer solutions to diagonal quadratic forms
VL - 152
ER -
TY - JOUR
AB - 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.
AU - Robinson, Matthew Richard
AU - Kruuk, Loeske E.B
ID - 7753
IS - 6
JF - Biology Letters
SN - 1744-9561
TI - Function of weaponry in females: The use of horns in intrasexual competition for resources in female Soay sheep
VL - 3
ER -
TY - GEN
AB - These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.
AU - Browning, Timothy D
ID - 6321
T2 - arXiv
TI - The Manin conjecture in dimension 2
ER -
TY - CHAP
AB - 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.
AU - Browning, Timothy D
ID - 6323
T2 - A Tribute to Gauss and Dirichlet
TI - An overview of Manin's conjecture for del Pezzo surfaces
VL - 7
ER -
TY - JOUR
AB - 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.
AU - Carr, Adra
AU - Serchest, Yancey
AU - Waitukaitis, Scott R
AU - Perreault, John
AU - Lonij, Vincent
AU - Cronin, Alexander
ID - 128
IS - 10
JF - Review of Scientific Instruments
TI - Cover slip external cavity diode laser
VL - 78
ER -
TY - CHAP
AB - 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.
AU - Browning, Timothy D
AU - Heath Brown, Roger
ED - Zannier, Umberto
ID - 167
T2 - Diophantine Geometry
TI - Simultaneous equal sums of three powers
VL - 4
ER -
TY - JOUR
AB - 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.
AU - Mark, Michael
AU - Ferlaino, Francesca
AU - Knoop, Steven
AU - Danzl, Johann G
AU - Kraemer, Tobias
AU - Chin, Cheng
AU - Nägerl, Hanns
AU - Grimm, Rudolf
ID - 1035
IS - 4
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Spectroscopy of ultracold trapped cesium Feshbach molecules
VL - 76
ER -
TY - JOUR
AB - 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.
AU - BÜHLER, OLIVER
AU - MULLER, Caroline J
ID - 9149
JF - Journal of Fluid Mechanics
KW - Mechanical Engineering
KW - Mechanics of Materials
KW - Condensed Matter Physics
SN - 0022-1120
TI - Instability and focusing of internal tides in the deep ocean
VL - 588
ER -
TY - GEN
AB - 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.
AU - Broderick,Tamara
AU - Dudik,Miroslav
AU - Gasper Tkacik
AU - Schapire,Robert E
AU - Bialek, William S
ID - 3742
T2 - ArXiv
TI - Faster solutions of the inverse pairwise Ising problem
VL - q-bio.QM
ER -
TY - JOUR
AB - 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.
AU - de Vladar, Harold
AU - Pen, I.
ID - 4234
JF - Physica A
TI - Determinism, noise, and spurious estimations in a generalised model of population growth
VL - 373
ER -
TY - JOUR
AB - 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.
AU - Preiner, Johannes
AU - Harald Janovjak
AU - Rankl, Christian
AU - Knaus, Helene
AU - Cisneros, David A
AU - Kedrov, Alexej
AU - Kienberger, Ferry
AU - Mueller, Daniel J
AU - Hinterdorfer, Peter
ID - 3411
IS - 3
JF - Biophysical Journal
TI - Free energy of membrane protein unfolding derived from single-molecule force measurements
VL - 93
ER -
TY - JOUR
AB - 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
AU - Bollenbach, Mark Tobias
AU - Kruse, Karsten
AU - Pantazis, Periklis
AU - Gonzalez Gaitan, Marcos
AU - Julicher, Frank
ID - 3427
IS - 1
JF - Physical Review E Statistical Nonlinear and Soft Matter Physics
TI - Morphogen transport in epithelia
VL - 75
ER -
TY - CONF
AB - 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.
AU - Attali, Dominique
AU - Herbert Edelsbrunner
AU - Mileyko, Yuriy
ID - 3561
TI - Weak witnesses for Delaunay triangulations of submanifolds
ER -
TY - JOUR
AB - 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.
AU - ZILBERMAN, Daniel
AU - Henikoff, Steven
ID - 9524
IS - 22
JF - Development
SN - 0950-1991
TI - Genome-wide analysis of DNA methylation patterns
VL - 134
ER -
TY - CONF
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2333
TI - Ground-state energy of a dilute Fermi gas
VL - 412
ER -
TY - CONF
AU - Robert Seiringer
AU - Lieb, Élliott H
AU - Yngvason, Jakob
ED - Zambrini, Jean-Claude
ID - 2334
TI - One-dimensional behavior of dilute, trapped Bose gases in traps
ER -
TY - GEN
AB - 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.
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2363
IS - 2
T2 - Communications in Mathematical Physics
TI - Derivation of the Gross-Pitaevskii equation for rotating Bose gases
VL - 264
ER -
TY - JOUR
AB - 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.
AU - Robert Seiringer
ID - 2364
IS - 3
JF - Reviews in Mathematical Physics
TI - A correlation estimate for quantum many-body systems at positive temperature
VL - 18
ER -
TY - JOUR
AB - 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.
AU - Robert Seiringer
ID - 2365
IS - 3
JF - Communications in Mathematical Physics
TI - The thermodynamic pressure of a dilute fermi gas
VL - 261
ER -
TY - JOUR
AB - 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.
AU - Frank, Rupert L
AU - Laptev, Ari
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2366
IS - 3
JF - Letters in Mathematical Physics
TI - Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
VL - 77
ER -
TY - CHAP
AB - 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.
AU - Aizenman, Michael
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ED - Asch, Joachim
ED - Joye, Alain
ID - 2369
T2 - Mathematical Physics of Quantum Mechanics
TI - Bose-Einstein condensation as a quantum phase transition in an optical lattice
VL - 690
ER -
TY - GEN
AB - 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.
AU - Hosten, Onur
AU - Rakher, Matthew
AU - Barreiro, Julio
AU - Peters, Nicholas
AU - Kwiat, Paul
ID - 573
TI - Counterfactual computation revisited
ER -
TY - GEN
AB - 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.
AU - Hosten, Onur
AU - Kwiat, Paul
ID - 574
TI - Weak measurements and counterfactual computation
ER -
TY - JOUR
AU - Salecker, Iris
AU - Häusser, Michael
AU - de Bono, Mario
ID - 6151
IS - 6
JF - EMBO reports
SN - 1469-221X
TI - On the axonal road to circuit function and behaviour: Workshop on the assembly and function of neuronal circuits
VL - 7
ER -
TY - JOUR
AB - 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.
AU - Tamas Hausel
AU - Swartz, Edward
ID - 1461
IS - 8
JF - Proceedings of the American Mathematical Society
TI - Intersection forms of toric hyperkähler varieties
VL - 134
ER -
TY - JOUR
AB - 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.
AU - Tamas Hausel
ID - 1462
IS - 16
JF - PNAS
TI - Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform
VL - 103
ER -
TY - JOUR
AB - 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.
AU - Kraemer, Tobias
AU - Mark, Michael
AU - Waldburger, Philipp
AU - Danzl, Johann G
AU - Chin, Cheng
AU - Engeser, Bastian
AU - Lange, Adam
AU - Pilch, Karl
AU - Jaakkola, Antti
AU - Nägerl, Hanns
AU - Grimm, Rudolf
ID - 1033
IS - 7082
JF - Nature
TI - Evidence for Efimov quantum states in an ultracold gas of caesium atoms
VL - 440
ER -
TY - CONF
AB - 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.
AU - Nägerl, Hanns
AU - Kraemer, Tobias
AU - Mark, Michael
AU - Waldburger, Philipp
AU - Danzl, Johann G
AU - Engeser, Bastian
AU - Lange, Adam
AU - Pilch, Karl
AU - Jaakkola, Antti
AU - Chin, Cheng
AU - Grimm, Rudolf
ID - 1034
TI - Experimental evidence for Efimov quantum states
VL - 869
ER -
TY - JOUR
AB - 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.
AU - Le,Thuc T.
AU - Emonet,Thierry
AU - Harlepp, Sébastien
AU - Calin Guet
AU - Cluzel,Philippe
ID - 3755
IS - 9
JF - Biophysical Journal
TI - Dynamical determinants of drug-inducible gene expression in a single bacterium
VL - 90
ER -
TY - JOUR
AB - 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.
AU - Aponte, Yexica
AU - Lien, Cheng-Chang
AU - Reisinger, Ellen
AU - Peter Jonas
ID - 3813
IS - Pt 1
JF - Journal of Physiology
TI - Hyperpolarization-activated cation channels in fast-spiking interneurons of rat hippocampus
VL - 574
ER -
TY - JOUR
AB - 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.
AU - Link, Vinzenz
AU - Shevchenko, Andrej
AU - Heisenberg, Carl-Philipp J
ID - 4173
JF - BMC Developmental Biology
TI - Proteomics of early zebrafish embryos
VL - 6
ER -
TY - JOUR
AU - Paciorek, Tomasz
AU - Friml, Jirí
ID - 3009
IS - 7
JF - Journal of Cell Science
TI - Auxin signaling
VL - 119
ER -
TY - GEN
AB - 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.
AU - Gasper Tkacik
AU - Schneidman, E.
AU - Berry, M. J.
AU - Bialek, William S
ID - 3431
T2 - ArXiv
TI - Ising models for networks of real neurons
ER -
TY - JOUR
AB - 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.
AU - Christoph Lampert
AU - Wirjadi,Oliver
ID - 3695
IS - 11
JF - IEEE Transactions on Image Processing (TIP)
TI - An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter
VL - 15
ER -
TY - BOOK
AB - 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.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ID - 2335
T2 - The mathematics of the Bose gas and its condensation
TI - The mathematics of the Bose gas and its condensation
VL - 34
ER -
TY - CHAP
AB -
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.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ED - Benedicks, Michael
ED - Jones, Peter W
ED - Smirnov, Stanislav
ED - Winckler, Björn
ID - 2336
T2 - Perspectives in Analysis
TI - The quantum-mechanical many-body problem: The Bose gas
VL - 27
ER -