TY - JOUR
AB - The function of protein and RNA molecules depends on complex epistatic interactions between sites. Therefore, the deleterious effect of a mutation can be suppressed by a compensatory second-site substitution. In relating a list of 86 pathogenic mutations in human IRNAs encoded by mitochondrial genes to the sequences of their mammalian orthologs, we noted that 52 pathogenic mutations were present in normal tRNAs of one or several nonhuman mammals. We found at least five mechanisms of compensation for 32 pathogenic mutations that destroyed a Watson-Crick pair in one of the four tRNA stems: restoration of the affected Watson-Crick interaction (25 cases), strengthening of another pair (4 cases), creation of a new pair (8 cases), changes of multiple interactions in the affected stem (11 cases) and changes involving the interaction between the loop and stem structures (3 cases). A pathogenic mutation and its compensating substitution are fixed in a lineage in rapid succession, and often a compensatory interaction evolves convergently in different clades. At least 10%, and perhaps as many as 50%, of all nucleotide substitutions in evolving mammalian (RNAs participate in such interactions, indicating that the evolution of tRNAs proceeds along highly epistatic fitness ridges.
AU - Kern, Andrew D
AU - Fyodor Kondrashov
ID - 889
IS - 11
JF - Nature Genetics
TI - Mechanisms and convergence of compensatory evolution in mammalian mitochondrial tRNAs
VL - 36
ER -
TY - JOUR
AB - New alleles become fixed owing to random drift of nearly neutral mutations or to positive selection of substantially advantageous mutations. After decades of debate, the fraction of fixations driven by selection remains uncertain. Within 9,390 genes, we analysed 28,196 codons at which rat and mouse differ from each other at two nucleotide sites and 1,982 codons with three differences. At codons where rat-mouse divergence involved two non-synonymous substitutions, both of them occurred in the same lineage, either rat or mouse, in 64% of cases; however, independent substitutions would occur in the same lineage with a probability of only 50%. All three non-synonymous substitutions occurred in the same lineage for 46% of codons, instead of the 25% expected. Furthermore, comparison of 12 pairs of prokaryotic genomes also shows clumping of multiple non-synonymous substitutions in the same lineage. This pattern cannot be explained by correlated mutation or episodes of relaxed negative selection, but instead indicates that positive selection acts at many sites of rapid, successive amino acid replacement.
AU - Bazykin, Georgii A
AU - Fyodor Kondrashov
AU - Ogurtsov, Aleksey Yu
AU - Sunyaev, Shamil R
AU - Kondrashov, Alexey S
ID - 898
IS - 6991
JF - Nature
TI - Positive selection at sites of multiple amino acid replacements since rat-mouse divergence
VL - 429
ER -
TY - JOUR
AB - We compare the functional spectrum of protein evolution in two separate animal lineages with respect to two hypotheses: (1) rates of divergence are distributed similarly among functional classes within both lineages, indicating that selective pressure on the proteome is largely independent of organismic-level biological requirements; and (2) rates of divergence are distributed differently among functional classes within each lineage, indicating species-specific selective regimes impact genome-wide substitutional patterns. Integrating comparative genome sequence with data from tissue-specific expressed-sequence-tag (EST) libraries and detailed database annotations, we find a functional genomic signature of rapid evolution and selective constraint shared between mammalian and nematode lineages despite their extensive morphological and ecological differences and distant common ancestry. In both phyla, we find evidence of accelerated evolution among components of molecular systems involved in coevolutionary change. In mammals, lineage-specific fast evolving genes include those involved in reproduction, immunity, and possibly, maternal-fetal conflict. Likelihood ratio tests provide evidence for positive selection in these rapidly evolving functional categories in mammals. In contrast, slowly evolving genes, in terms of amino acid or insertion/deletion (indel) change, in both phyla are involved in core molecular processes such as transcription, translation, and protein transport. Thus, strong purifying selection appears to act on the same core cellular processes in both mammalian and nematode lineages, whereas positive and/or relaxed selection acts on different biological processes in each lineage.
AU - Castillo-Davis, Cristian I
AU - Fyodor Kondrashov
AU - Hartl, Daniel L
AU - Kulathinal, Rob J
ID - 902
IS - 5
JF - Genome Research
TI - The functional genomic distribution of protein divergence in two animal phyla: Coevolution, genomic conflict, and constraint
VL - 14
ER -
TY - JOUR
AB - 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.
AU - Tamas Hausel
AU - Hunsicker, Eugénie
AU - Mazzeo, Rafe R
ID - 1456
IS - 3
JF - Duke Mathematical Journal
TI - Hodge cohomology of gravitational instantons
VL - 122
ER -
TY - JOUR
AB - The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and Atiyah and Bott asserts that its rational cohomology ring is generated by the universal classes, that is, by the Kunneth components of the Chern classes of the universal bundle.
This paper studies the larger, non-compact moduli space of Higgs bundles, as introduced by Hitchin and Simpson, with values in the canonical bundle K. This is diffeomorphic to the space of all connections of central constant curvature, whether unitary or not. The main result of the paper is that, in the rank 2 case, the rational cohomology ring of this space is again generated by universal classes.
The spaces of Higgs bundles with values in K(n) for n > 0 turn out to be essential to the story. Indeed, we show that their direct limit has the homotopy type of the classifying space of the gauge group, and hence has cohomology generated by universal classes. 2000 Mathematics Subject Classification 14H60 (primary), 14D20, 14H81, 32Q55, 58D27 (secondary).
AU - Tamas Hausel
AU - Thaddeus, Michael
ID - 1464
IS - 3
JF - Proceedings of the London Mathematical Society
TI - Generators for the cohomology ring of the moduli space of rank 2 higgs bundles
VL - 88
ER -
TY - JOUR
AB - The simultaneous multiple volume (SMV) approach in navigator-gated MRI allows the use of the whole motion range or the entire scan time for the reconstruction of final images by simultaneously acquiring different image volumes at different motion states. The motion tolerance range for each volume is kept small, thus SMV substantially increases the scan efficiency of navigator methods while maintaining the effectiveness of motion suppression. This article reports a general implementation of the SMV approach using a multiprocessor scheduling algorithm. Each motion state is regarded as a processor and each volume is regarded as a job. An efficient scheduling that completes all jobs in minimal time is maintained even when the motion pattern changes. Initial experiments demonstrated that SMV significantly increased the scan efficiency of navigatorgated MRI.
AU - Vladimir Kolmogorov
AU - Nguyen, Thành D
AU - Nuval, Anthony
AU - Spincemaille, Pascal
AU - Prince, Martin R
AU - Zabih, Ramin
AU - Wang, Yusu
ID - 3172
IS - 2
JF - Magnetic Resonance in Medicine
TI - Multiprocessor scheduling implementation of the simultaneous multiple volume SMV navigator method
VL - 52
ER -
TY - JOUR
AB - In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.
AU - Vladimir Kolmogorov
AU - Zabih, Ramin
ID - 3173
IS - 2
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - What energy functions can be minimized via graph cuts?
VL - 26
ER -
TY - CONF
AB - Feature space clustering is a popular approach to image segmentation, in which a feature vector of local properties (such as intensity, texture or motion) is computed at each pixel. The feature space is then clustered, and each pixel is labeled with the cluster that contains its feature vector. A major limitation of this approach is that feature space clusters generally lack spatial coherence (i.e., they do not correspond to a compact grouping of pixels). In this paper, we propose a segmentation algorithm that operates simultaneously in feature space and in image space. We define an energy function over both a set of clusters and a labeling of pixels with clusters. In our framework, a pixel is labeled with a single cluster (rather than, for example, a distribution over clusters). Our energy function penalizes clusters that are a poor fit to the data in feature space, and also penalizes clusters whose pixels lack spatial coherence. The energy function can be efficiently minimized using graph cuts. Our algorithm can incorporate both parametric and non-parametric clustering methods. It can be applied to many optimization-based clustering methods, including k-means and k-medians, and can handle models which are very close in feature space. Preliminary results are presented on segmenting real and synthetic images, using both parametric and non-parametric clustering.
AU - Zabih, Ramin
AU - Vladimir Kolmogorov
ID - 3177
TI - Spatially coherent clustering using graph cuts
VL - 2
ER -
TY - JOUR
AB - Minimum cut/maximum flow algorithms on graphs have emerged as an increasingly useful tool for exactor approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push -relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.
AU - Boykov, Yuri
AU - Vladimir Kolmogorov
ID - 3178
IS - 9
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision
VL - 26
ER -
TY - CONF
AB - The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently, an approach based on optimization by graph-cut has been developed which successfully combines both types of information. In this paper we extend the graph-cut approach in three respects. First, we have developed a more powerful, iterative version of the optimisation. Secondly, the power of the iterative algorithm is used to simplify substantially the user interaction needed for a given quality of result. Thirdly, a robust algorithm for "border matting" has been developed to estimate simultaneously the alpha-matte around an object boundary and the colours of foreground pixels. We show that for moderately difficult examples the proposed method outperforms competitive tools.
AU - Rother, Carsten
AU - Vladimir Kolmogorov
AU - Blake, Andrew
ID - 3179
IS - 3
TI - "GrabCut" - Interactive foreground extraction using iterated graph cuts
VL - 23
ER -
TY - CONF
AB - A new technique for proving the adaptive indistinguishability of two systems, each composed of some component systems, is presented, using only the fact that corresponding component systems are non-adaptively indistinguishable. The main tool is the definition of a special monotone condition for a random system F, relative to another random system G, whose probability of occurring for a given distinguisher D is closely related to the distinguishing advantage ε of D for F and G, namely it is lower and upper bounded by ε and (1+ln1), respectively.
A concrete instantiation of this result shows that the cascade of two random permutations (with the second one inverted) is indistinguishable from a uniform random permutation by adaptive distinguishers which may query the system from both sides, assuming the components’ security only against non-adaptive one-sided distinguishers.
As applications we provide some results in various fields as almost k-wise independent probability spaces, decorrelation theory and computational indistinguishability (i.e., pseudo-randomness).
AU - Maurer, Ueli M
AU - Krzysztof Pietrzak
ID - 3208
TI - Composition of random systems: When two weak make one strong
VL - 2951
ER -
TY - JOUR
AB - The folding and stability of transmembrane proteins is a fundamental and unsolved biological problem. Here, single bacteriorhodopsin molecules were mechanically unfolded from native purple membranes using atomic force microscopy and force spectroscopy. The energy landscape of individual transmembrane α helices and polypeptide loops was mapped by monitoring the pulling speed dependence of the unfolding forces and applying Monte Carlo simulations. Single helices formed independently stable units stabilized by a single potential barrier. Mechanical unfolding of the helices was triggered by 3.9–7.7 Å extension, while natural unfolding rates were of the order of 10−3 s−1. Besides acting as individually stable units, helices associated pairwise, establishing a collective potential barrier. The unfolding pathways of individual proteins reflect distinct pulling speed-dependent unfolding routes in their energy landscapes. These observations support the two-stage model of membrane protein folding in which α helices insert into the membrane as stable units and then assemble into the functional protein.
AU - Harald Janovjak
AU - Struckmeier, Jens
AU - Hubain, Maurice
AU - Kessler, Max
AU - Kedrov, Alexej
AU - Mueller, Daniel J
ID - 3419
IS - 5
JF - Structure
TI - Probing the energy landscape of the membrane protein bacteriorhodopsin
VL - 12
ER -
TY - JOUR
AB - Single-molecule force-spectroscopy was employed to unfold and refold single sodium-proton antiporters (NhaA) of Escherichia coli from membrane patches. Although transmembrane α-helices and extracellular polypeptide loops exhibited sufficient stability to individually establish potential barriers against unfolding, two helices predominantly unfolded pairwise, thereby acting as one structural unit. Many of the potential barriers were detected unfolding NhaA either from the C-terminal or the N-terminal end. It was found that some molecular interactions stabilizing secondary structural elements were directional, while others were not. Additionally, some interactions appeared to occur between the secondary structural elements. After unfolding ten of the 12 helices, the extracted polypeptide was allowed to refold back into the membrane. After five seconds, the refolded polypeptide established all secondary structure elements of the native protein. One helical pair showed a characteristic spring like “snap in” into its folded conformation, while the refolding process of other helices was not detected in particular. Additionally, individual helices required characteristic periods of time to fold. Correlating these results with the primary structure of NhaA allowed us to obtain the first insights into how potential barriers establish and determine the folding kinetics of the secondary structure elements.
AU - Kedrov, Alexej
AU - Ziegler, Christine
AU - Harald Janovjak
AU - Kühlbrandt, Werner
AU - Mueller, Daniel J
ID - 3420
IS - 5
JF - Journal of Molecular Biology
TI - Controlled unfolding and refolding of a single sodium/proton antiporter using atomic force microscopy
VL - 340
ER -
TY - CHAP
AU - Herbert Edelsbrunner
ID - 3574
T2 - Handbook of Discrete and Computational Geometry
TI - Biological applications of computational topology
ER -
TY - CHAP
AB - The Jacobi set of two Morse functions defined on a common - manifold is the set of critical points of the restrictions of one func- tion to the level sets of the other function. Equivalently, it is the set of points where the gradients of the functions are parallel. For a generic pair of Morse functions, the Jacobi set is a smoothly embed- ded 1-manifold. We give a polynomial-time algorithm that com- putes the piecewise linear analog of the Jacobi set for functions specified at the vertices of a triangulation, and we generalize all results to more than two but at most Morse functions.
AU - Herbert Edelsbrunner
AU - Harer, John
ID - 3575
T2 - Foundations of Computational Mathematics
TI - Jacobi sets of multiple Morse functions
VL - 312
ER -
TY - CHAP
AU - Ulrich, Florian
AU - Heisenberg, Carl-Philipp
ED - Korzh, Vladimir
ED - Gong, Zhiyuan
ID - 3587
T2 - Fish development and genetics : the zebrafish and medaka models
TI - Gastrulation in zebrafish
VL - 2
ER -
TY - GEN
AB - Genome sizes vary enormously. This variation in DNA content correlates with effective population size, suggesting that deleterious additions to the genome can accumulate in small populations. On this view, the increased complexity of biological functions associated with large genomes partly reflects evolutionary degeneration.
AU - Charlesworth, Brian
AU - Nicholas Barton
ID - 3595
IS - 6
T2 - Current Biology
TI - Genome size: Does bigger mean worse?
VL - 14
ER -
TY - JOUR
AB - We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(Δz̄) =inline imagewhere n is the number of loci contributing to the trait variance, VA(1)=VA is the additive genetic variance, and VA(k) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*A), is closely related to var(Δz̄); (V*A) (1 –F)inline imageThus, epistasis inflates the expected additive variance above VA(1 –F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*AA)). This is not true in general with diploidy, because dominance alone can reduce (V*A) below VA(1 –F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(Δz̄)=inline image=1 (2F) kVA(k) and (V*A) = (1 –F)inline imagek(2F)k-1VA(k) With dominance (and even without epistasis), var(Δz̄)and (V*A) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*A)(1 –F) VA+ 4FVAA+2FVD+2FCAD, where CAD is a sum of two terms describing covariances between additive effects and dominance and additive × dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase VA, we question the evolutionary importance of such increases.
AU - Nicholas Barton
AU - Turelli, Michael
ID - 3614
IS - 10
JF - Evolution; International Journal of Organic Evolution
TI - Effects of allele frequency changes on variance components under a general model of epistasis
VL - 58
ER -
TY - JOUR
AB - We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., ρ2ij > 3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.
AU - Turelli, Michael
AU - Nicholas Barton
ID - 3615
IS - 2
JF - Genetics
TI - Polygenic variation maintained by balancing selection: pleiotropy, sex-dependent allelic effects and GxE interactions
VL - 166
ER -
TY - GEN
AU - Nicholas Barton
ID - 3616
IS - 15
T2 - Current Biology
TI - Speciation: Why, how, where and when?
VL - 14
ER -
TY - JOUR
AB - The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns > 3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.
AU - Nicholas Barton
AU - Etheridge, Alison M
ID - 3617
IS - 2
JF - Genetics
TI - The effect of selection on genealogies
VL - 166
ER -
TY - CONF
AB - Capturing images of documents using handheld digital cameras has a variety of applications in academia, research, knowledge management, retail, and office settings. The ultimate goal of such systems is to achieve image quality comparable to that currently achieved with flatbed scanners even for curved, warped, or curled pages. This can be achieved by high-accuracy 3D modeling of the page surface, followed by a "flattening" of the surface. A number of previous systems have either assumed only perspective distortions, or used techniques like structured lighting, shading, or side-imaging for obtaining 3D shape. This paper describes a system for handheld camera-based document capture using general purpose stereo vision methods followed by a new document dewarping technique. Examples of shape modeling and dewarping of book images is shown.
AU - Ulges, Adrian
AU - Christoph Lampert
AU - Breuel,Thomas M
ID - 3688
TI - Document capture using stereo vision
ER -
TY - JOUR
AB - The operation of neuronal networks crucially depends on a fast time course of signaling in inhibitory interneurons. Synapses that excite interneurons generate fast currents, owing to the expression of glutamate receptors of specific subunit composition. Interneurons generate brief action potentials in response to transient synaptic activation and discharge repetitively at very high frequencies during sustained stimulation. The ability to generate short-duration action potentials at high frequencies depends on the expression of specific voltage-gated K+ channels. Factors facilitating fast action potential initiation following synaptic excitation include depolarized interneuron resting potential, subthreshold conductances and active dendrites. Finally, GABA release at interneuron output synapses is rapid and highly synchronized, leading to a faster inhibition in postsynaptic interneurons than in principal cells. Thus, the expression of distinct transmitter receptors and voltage-gated ion channels ensures that interneurons operate with high speed and temporal precision.
AU - Peter Jonas
AU - Bischofberger, Josef
AU - Fricker, Desdemona
AU - Miles, Richard
ID - 3805
IS - 1
JF - Trends in Neurosciences
TI - Interneuron Diversity series: Fast in, fast out--temporal and spatial signal processing in hippocampal interneurons
VL - 27
ER -
TY - JOUR
AB - The time course of Mg(2+) block and unblock of NMDA receptors (NMDARs) determines the extent they are activated by depolarization. Here, we directly measure the rate of NMDAR channel opening in response to depolarizations at different times after brief (1 ms) and sustained (4.6 s) applications of glutamate to nucleated patches from neocortical pyramidal neurons. The kinetics of Mg(2+) unblock were found to be non-instantaneous and complex, consisting of a prominent fast component (time constant approximately 100 micros) and slower components (time constants 4 and approximately 300 ms), the relative amplitudes of which depended on the timing of the depolarizing pulse. Fitting a kinetic model to these data indicated that Mg(2+) not only blocks the NMDAR channel, but reduces both the open probability and affinity for glutamate, while enhancing desensitization. These effects slow the rate of NMDAR channel opening in response to depolarization in a time-dependent manner such that the slower components of Mg(2+) unblock are enhanced during depolarizations at later times after glutamate application. One physiological consequence of this is that brief depolarizations occurring earlier in time after glutamate application are better able to open NMDAR channels. This finding has important implications for spike-timing-dependent synaptic plasticity (STDP), where the precise (millisecond) timing of action potentials relative to synaptic inputs determines the magnitude and sign of changes in synaptic strength. Indeed, we find that STDP timing curves of NMDAR channel activation elicited by realistic dendritic action potential waveforms are narrower than expected assuming instantaneous Mg(2+) unblock, indicating that slow Mg(2+) unblock of NMDAR channels makes the STDP timing window more precise.
AU - Kampa, Bjorn M
AU - Clements, John
AU - Peter Jonas
AU - Stuart, Greg J
ID - 3807
IS - Pt 2
JF - Journal of Physiology
TI - Kinetics of Mg(2+) unblock of NMDA receptors: implications for spike-timing dependent synaptic plasticity
VL - 556
ER -
TY - JOUR
AB - Neural stem cells in various regions of the vertebrate brain continuously generate neurons throughout life. In the mammalian hippocampus, a region important for spatial and episodic memory, thousands of new granule cells are produced per day, with the exact number depending on environmental conditions and physical exercise. The survival of these neurons is improved by learning and conversely learning may be promoted by neurogenesis. Although it has been suggested that newly generated neurons may have specific properties to facilitate learning, the cellular and synaptic mechanisms of plasticity in these neurons are largely unknown. Here we show that young granule cells in the adult hippocampus differ substantially from mature granule cells in both active and passive membrane properties. In young neurons, T-type Ca2+ channels can generate isolated Ca2+ spikes and boost fast Na+ action potentials, contributing to the induction of synaptic plasticity. Associative long-term potentiation can be induced more easily in young neurons than in mature neurons under identical conditions. Thus, newly generated neurons express unique mechanisms to facilitate synaptic plasticity, which may be important for the formation of new memories.
AU - Schmidt-Hieber, Christoph
AU - Peter Jonas
AU - Bischofberger, Josef
ID - 3809
IS - 6988
JF - Nature
TI - Enhanced synaptic plasticity in newly generated granule cells of the adult hippocampus
VL - 429
ER -
TY - JOUR
AB - Voltage-gated potassium (Kv) channels control action potential repolarization, interspike membrane potential, and action potential frequency in excitable cells. It is thought that the combinatorial association between distinct alpha and beta subunits determines whether Kv channels function as non-inactivating delayed rectifiers or as rapidly inactivating A-type channels. We show that membrane lipids can convert A-type channels into delayed rectifiers and vice versa. Phosphoinositides remove N-type inactivation from A-type channels by immobilizing the inactivation domains. Conversely, arachidonic acid and its amide anandamide endow delayed rectifiers with rapid voltage-dependent inactivation. The bidirectional control of Kv channel gating by lipids may provide a mechanism for the dynamic regulation of electrical signaling in the nervous system.
AU - Oliver, Dominik
AU - Lien, Cheng-Chang
AU - Soom, Malle
AU - Baukrowitz, Thomas
AU - Peter Jonas
AU - Fakler, Bernd
ID - 3810
IS - 5668
JF - Science
TI - Functional conversion between A-type and delayed rectifier K+ channels by membrane lipids
VL - 304
ER -
TY - CONF
AB - We study infinite stochastic games played by n-players on a finite graph with goals given by sets of infinite traces. The games are stochastic (each player simultaneously and independently chooses an action at each round, and the next state is determined by a probability distribution depending on the current state and the chosen actions), infinite (the game continues for an infinite number of rounds), nonzero sum (the players' goals are not necessarily conflicting), and undiscounted. We show that if each player has a reachability objective, that is, if the goal for each player i is to visit some subset R-i of the states, then there exists an epsilon-Nash equilibrium in memoryless strategies, for every epsilon > 0. However, exact Nash equilibria need not exist. We study the complexity of finding such Nash equilibria, and show that the payoff of some epsilon-Nash equilibrium in memoryless strategies can be epsilon-approximated in NP. We study the important subclass of n-player turn-based probabilistic games, where at each state at most one player has a nontrivial choice of moves. For turn-based probabilistic games, we show the existence of epsilon-Nash equilibria in pure strategies for games where the objective of player i is a Borel set B-i of infinite traces. However, exact Nash equilibria may not exist. For the special case of omega-regular objectives, we show exact Nash equilibria exist, and can be computed in NP when the omega-regular objectives are expressed as parity objectives.
AU - Krishnendu Chatterjee
AU - Majumdar, Ritankar S
AU - Jurdziński, Marcin
ID - 3894
TI - On Nash equilibria in stochastic games
VL - 3210
ER -
TY - CONF
AB - In 2-player non-zero-sum games, Nash equilibria capture the options for rational behavior if each player attempts to maximize her payoff. In contrast to classical game theory, we consider lexicographic objectives: first, each player tries to maximize her own payoff, and then, the player tries to minimize the opponent's payoff. Such objectives arise naturally in the verification of systems with multiple components. There, instead of proving that each component satisfies its specification no matter how the other components behave, it often suffices to prove that each component satisfies its specification provided that the other components satisfy their specifications. We say that a Nash equilibrium is secure if it is an equilibrium with respect to the lexicographic objectives of both players. We prove that in graph games with Borel objectives, which include the games that arise in verification, there may be several Nash equilibria, but there is always a unique maximal payoff profile of secure equilibria. We show how this equilibrium can be computed in the case of omega-regular objectives, and we characterize the memory requirements of strategies that achieve the equilibrium.
AU - Krishnendu Chatterjee
AU - Thomas Henzinger
AU - Jurdziński, Marcin
ID - 3895
TI - Games with secure equilibria
ER -
TY - JOUR
AU - Timothy Browning
ID - 205
IS - 3
JF - Acta Arithmetica
TI - Counting rational points on cubic and quartic surfaces
VL - 108
ER -
TY - JOUR
AB - Let T ⊂ ℙ 4 be a non-singular threefold of degree at least four. Then we show that the number of points in T(ℚ), with height at most B, is o(B 3) or B → ∞.
AU - Timothy Browning
ID - 206
IS - 1
JF - Quarterly Journal of Mathematics
TI - A note on the distribution of rational points on threefolds
VL - 54
ER -
TY - JOUR
AU - Browning, Timothy D
ID - 207
IS - 3
JF - Mathematical Proceedings of the Cambridge Philosophical Society
TI - Sums of four biquadrates
VL - 134
ER -
TY - JOUR
AB - For any ε > 0 and any diagonal quadratic form Q ∈ ℤ[x 1, x 2, x 3, x 4] with a square-free discriminant of modulus Δ Q ≠ 0, we establish the uniform estimate ≪ε B 3/2+ε + B 2+ε/Δ Q 1/6 for the number of rational points of height at most B lying in the projective surface Q = 0.
AU - Timothy Browning
ID - 208
IS - 1
JF - Quarterly Journal of Mathematics
TI - Counting rational points on diagonal quadratic surfaces
VL - 54
ER -
TY - CONF
AU - Lieb, Élliott H
AU - Robert Seiringer
ED - Karpeshina, Yulia
ED - Weikard, Rudi
ED - Zeng, Yanni
ID - 2337
TI - Bose-Einstein condensation of dilute gases in traps
VL - 327
ER -
TY - JOUR
AB - We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the Gross-Pitaevskii (GP) limit of a dilute gas. Analysing both the absolute and the bosonic ground states of the system, we show, in particular, their different behaviour for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.
AU - Robert Seiringer
ID - 2354
IS - 37
JF - Journal of Physics A: Mathematical and Theoretical
TI - Ground state asymptotics of a dilute, rotating gas
VL - 36
ER -
TY - JOUR
AB - The classic Poincaré inequality bounds the L q-norm of a function f in a bounded domain Ω ⊂ ℝ n in terms of some L p-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Τ from Ω and concentrate our attention on Λ = Ω \ Τ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it might have a very bad constant. This is so even if the volume of Τ is arbitrarily small. A Poincaré inequality does hold, however, if one makes the additional assumption that f has a finite L p gradient norm on the whole of Ω, not just on Λ. The important point is that the Poincaré inequality thus obtained bounds the L q-norm of f in terms of the L p gradient norm on Λ (not Ω) plus an additional term that goes to zero as the volume of Τ goes to zero. This error term depends on Τ only through its volume. Apart from this additive error term, the constant in the inequality remains that of the 'nice' domain Ω. In the second generalization we are given a vector field A and replace ∇ by ∇ + iA(x) (geometrically, a connection on a U(1) bundle). Unlike the A = 0 case, the infimum of ∥(∇ + iA)f∥ p over all f with a given ∥f∥ q is in general not zero. This permits an improvement of the inequality by the addition of a term whose sharp value we derive. We describe some open problems that arise from these generalizations.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2357
IS - 3
JF - Annals of Mathematics
TI - Poincaré inequalities in punctured domains
VL - 158
ER -
TY - JOUR
AB - A study was conducted on the one-dimensional (1D) bosons in three-dimensional (3D) traps. A rigorous analysis was carried out on the parameter regions in which various types of 1D or 3D behavior occurred in the ground state. The four parameter regions include density, transverse, longitudinal dimensions and scattering length.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2358
IS - 15
JF - Physical Review Letters
TI - One-dimensional Bosons in three-dimensional traps
VL - 91
ER -
TY - THES
AU - Uli Wagner
ID - 2414
TI - On k-Sets and Their Applications
ER -
TY - CONF
AB - We prove a lower bound of 0.3288(4 n) for the rectilinear crossing number cr̄(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadrilaterals in any set of n points in general position in the Euclidean plane. As we see it, the main contribution of this paper is not so much the concrete numerical improvement over earlier bounds, as the novel method of proof, which is not based on bounding cr̄(Kn) for some small n.
AU - Uli Wagner
ID - 2422
TI - On the rectilinear crossing number of complete graphs
ER -
TY - CONF
AB - A finite set N ⊃ Rd is a weak ε-net for an n-point set X ⊃ Rd (with respect to convex sets) if N intersects every convex set K with |K ∩ X| ≥ εn. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al. [7], that every point set X in Rd admits a weak ε-net of cardinality O(ε-d polylog(1/ε)). Moreover, for a number of special point sets (e.g., for points on the moment curve), our method gives substantially better bounds. The construction yields an algorithm to construct such weak ε-nets in time O(n ln(1/ε)). We also prove, by a different method, a near-linear upper bound for points uniformly distributed on the (d - 1)-dimensional sphere.
AU - Matoušek, Jiří
AU - Uli Wagner
ID - 2423
TI - New constructions of weak epsilon-nets
ER -
TY - CONF
AB - We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some (potentially very high-dimensional) Euclidean space ℝd. We assume that M is known to us only through a finite sample P ⊂ M, as it is often the case in applications. The adaptive neighborhood graph is a geometric graph on P. Its complexity is at most min{2O(k)(n, n2}, where n = |P| and k = dim M, as opposed to the n⌈d/2⌉ complexity of the Delaunay triangulation, which is often used to model manifolds. We show that we can provably correctly infer the connectivity of M and the dimension of M from the adaptive neighborhood graph provided a certain standard sampling condition is fulfilled. The running time of the dimension detection algorithm is d2O(k7 log k) for each connected component of M. If the dimension is considered constant, this is a constant-time operation, and the adaptive neighborhood graph is of linear size. Moreover, the exponential dependence of the constants is only on the intrinsic dimension k, not on the ambient dimension d. This is of particular interest if the co-dimension is high, i.e., if k is much smaller than d, as is the case in many applications. The adaptive neighborhood graph also allows us to approximate the geodesic distances between the points in P.
AU - Giesen, Joachim
AU - Uli Wagner
ID - 2424
TI - Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
ER -
TY - JOUR
AB - Male dimorphism is not genetically determined, but is induced by environmental conditions particularly decreasing temperature and density.
AU - Cremer, Sylvia
AU - Heinze, Jürgen
ID - 3917
IS - 15
JF - Blick in die Wissenschaft
TI - Zwischen Hochzeitsflug und Brudermord: reproduktive Taktiken bei Ameisenmännchen
VL - 12
ER -
TY - JOUR
AB - Unlike most social insects, many Cardiocondyla ant species have two male morphs: wingless (ergatoid) males, who remain in the natal nest, and winged males who disperse but, strangely, before leaving may also mate within the nest. Whereas ergatoid males are highly intolerant of each other and fight among themselves, they tend to tolerate their winged counterparts. This is despite the fact that these winged males, like ergatoid males, represent mating competition. Why should ergatoid males tolerate their winged rivals? We developed a mathematical model to address this question. Our model focuses on a number of factors likely toinfluence whether ergatoid males are tolerant of winged males: ergatoid male–winged male relatedness, number of virgin queens, number of winged males, and the number of ejaculates a winged male has (winged males are sperm limited, whereas ergatoid males have lifelong spermatogenesis). Surprisingly, we found that increasing the number of virgin queens favors a kill strategy, whereas an increase in the other factors favors a let-live strategy; these predictions appear true for C. obscurior and for a number of other Cardiocondyla species. Two further aspects, unequal insemination success and multiple mating in queens, were also incorporated into the model and predictions made about their effects on toleration of winged males. The model is applicable more generally in species that have dimorphic males, such as some other ants, bees, and fig wasps.
AU - Anderson, Carl
AU - Cremer, Sylvia
AU - Heinze, Jürgen
ID - 3921
IS - 1
JF - Behavioral Ecology
TI - Live and let die: Why fighter males of the ant Cardiocondyla kill each other but tolerate their winged rivals
VL - 14
ER -
TY - JOUR
AB - Dispersal is advantageous, but, at the same time, it implies high costs and risks. Due to these counteracting selection pressures, many species evolved dispersal polymorphisms, which, in ants, are typically restricted to the female sex (queens). Male polymorphism is presently only known from a few genera, such as Cardiocondyla, in which winged dispersing males coexist with wingless fighter males that mate exclusively inside their maternal nests. We studied the developmental mechanisms underlying these alternative male morphs and found that, first, male dimorphism is not genetically determined, but is induced by environmental conditions (decreasing temperature and density). Second, male morph is not yet fixed at the egg stage, but it differentiates during larval development. This flexible developmental pattern of male morphs allows Cardiocondyla ant colonies to react quickly to changes in their environment. Under good conditions, they invest exclusively in philopatric wingless males. But, when environmental conditions turn bad, colonies start to produce winged dispersal males, even though these males require a many times higher investment by the colony than their much smaller wingless counterparts. Cardiocondyla ants share this potential of optimal resource allocation with other colonial animals and some seed dimorphic plants.
AU - Cremer, Sylvia
AU - Heinze, Jürgen
ID - 3922
IS - 3
JF - Current Biology
TI - Stress grows wings: Environmental induction of winged dispersal males in Cardiocondyla ants
VL - 13
ER -
TY - CHAP
AB - We give analytic inclusion-exclusion formulas for the area and perimeter derivatives of a union of finitely many disks in the plane.
AU - Cheng, Ho-Lun
AU - Herbert Edelsbrunner
ID - 3991
T2 - Computer Science in Perspective: Essays Dedicated to Thomas Ottmann
TI - Area and perimeter derivatives of a union of disks
VL - 2598
ER -
TY - JOUR
AB - Computing the volume occupied by individual atoms in macromolecular structures has been the subject of research for several decades. This interest has grown in the recent years, because weighted volumes are widely used in implicit solvent models. Applications of the latter in molecular mechanics simulations require that the derivatives of these weighted volumes be known. In this article, we give a formula for the volume derivative of a molecule modeled as a space-filling diagram made up of balls in motion. The formula is given in terms of the weights, radii, and distances between the centers as well as the sizes of the facets of the power diagram restricted to the space-filling diagram. Special attention is given to the detection and treatment of singularities as well as discontinuities of the derivative.
AU - Herbert Edelsbrunner
AU - Koehl, Patrice
ID - 3992
IS - 5
JF - PNAS
TI - The weighted-volume derivative of a space-filling diagram
VL - 100
ER -
TY - JOUR
AB - We present algorithms for constructing a hierarchy of increasingly coarse Morse-Smale complexes that decompose a piecewise linear 2-manifold. While these complexes are defined only in the smooth category, we extend the construction to the piecewise linearcategory by ensuring structural integrity and simulating differentiability. We then simplify Morse-Smale complexes by canceling pairs of critical points in order of increasing persistence.
AU - Herbert Edelsbrunner
AU - Harer, John
AU - Zomorodian, Afra
ID - 3993
IS - 1
JF - Discrete & Computational Geometry
TI - Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds
VL - 30
ER -
TY - JOUR
AB - The body defined by a finite collection of disks is a subset of the plane bounded by a tangent continuous curve, which we call the skin. We give analytic formulas for the area, the perimeter, the area derivative, and the perimeter derivative of the body. Given the filtrations of the Delaunay triangulation and the Voronoi diagram of the disks, all formulas can be evaluated in time proportional to the number of disks.
AU - Cheng, Ho-Lun
AU - Herbert Edelsbrunner
ID - 3994
IS - 2
JF - Computational Geometry: Theory and Applications
TI - Area, perimeter and derivatives of a skin curve
VL - 26
ER -
TY - CONF
AB - We combine topological and geometric methods to construct a multi-resolution data structure for functions over two-dimensional domains. Starting with the Morse-Smale complex, we construct a topological hierarchy by progressively canceling critical points in pairs. Concurrently, we create a geometric hierarchy by adapting the geometry to the changes in topology. The data structure supports mesh traversal operations similarly to traditional multi-resolution representations.
AU - Bremer, Peer-Timo
AU - Herbert Edelsbrunner
AU - Hamann, Bernd
AU - Pascucci, Valerio
ID - 3997
TI - A multi-resolution data structure for two-dimensional Morse-Smale functions
ER -
TY - CONF
AB - We introduce relaxed scheduling as a paradigm for mesh maintenance and demonstrate its applicability to triangulating a skin surface in R-3.
AU - Herbert Edelsbrunner
AU - Üngör, Alper
ID - 3999
TI - Relaxed scheduling in dynamic skin triangulation
VL - 2866
ER -
TY - JOUR
AB - During vertebrate gastrulation, highly coordinated cellular rearrangements lead to the formation of the three germ layers, ectoderm, mesoderm and endoderm. In zebrafish, silberblick (slb)/wnt11 regulates normal gastrulation movements by activating a signalling pathway similar to the Frizzled-signalling pathway, which establishes epithelial planar cell polarity (PCP) in Drosophila. However, the cellular mechanisms by which slb/wnt11 functions during zebrafish gastrulation are still unclear. Using high-resolution two-photon confocal imaging followed by computer-assisted reconstruction and motion analysis, we have analysed the movement and morphology of individual cells in three dimensions during the course of gastrulation. We show that in slb-mutant embryos, hypoblast cells within the forming germ ring have slower, less directed migratory movements at the onset of gastrulation. These aberrant cell movements are accompanied by defects in the orientation of cellular processes along the individual movement directions of these cells. We conclude that slb/wnt11-mediated orientation of cellular processes plays a role in facilitating and stabilising movements of hypoblast cells in the germ ring, thereby pointing at a novel function of the slb/wnt11 signalling pathway for the regulation of migratory cell movements at early stages of gastrulation.
AU - Ulrich, Florian
AU - Concha, Miguel L
AU - Heid, Paul J
AU - Voss, Ed
AU - Witzel, Sabine
AU - Roehl, Henry
AU - Tada, Masazumi
AU - Wilson, Stephen W
AU - Adams, Richard J
AU - Soll, David R
AU - Heisenberg, Carl-Philipp
ID - 4146
IS - 22
JF - Development
TI - Slb/Wnt11 controls hypoblast cell migration and morphogenesis at the onset of zebrafish gastrulation
VL - 130
ER -