@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}, } @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{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{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{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}, } @misc{3509, abstract = {Methods, apparatus and computer program products can generate light weight but highly realistic and accurate colored models of three-dimensional colored objects. The colored model may be generated from a second plurality of points that define a coarse digital representation of the surface and at least one texture map containing information derived from a first plurality of colored points that define a fine digital representation of the surface. This derivation is achieved by mapping points within the texture map to the fine digital representation of the three-dimensional surface. Colored scan data may be used to construct the fine digital representation as a triangulated surface (i.e., triangulation) using a wrapping operation.}, author = {Williams, Steven and Edelsbrunner, Herbert and Fu, Ping}, title = {{Methods, apparatus and computer program products for modeling three-dimensional colored objects}}, 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{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}, } @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 and Seiringer, Robert and Solovej, Jan and Yngvason, Jakob}, isbn = {978-3-7643-7336-8}, pages = {VIII, 203}, publisher = {Birkhäuser Verlag}, title = {{The Mathematics of the Bose gas and its Condensation}}, doi = {10.1007/b137508}, 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(ϱlnϱ) of a density matrix ϱ123 on the product of three Hilbert spaces satisfies S[ϱ123]- S[ϱ12]≤S[ϱ23]-S[ϱ2]. We strengthen this to S[ϱ123]-S[ϱ12] ≤αnα(S[ϱ23α]-S[ϱ2α]), where the nα are weights and the ϱ23α are partitions of ϱ23. 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}, }