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 -