@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{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},
}