TY - CONF
AB - We define the Morse-Smale complex of a Morse function over a 3-manifold as the overlay of the descending and as- cending manifolds of all critical points. In the generic case, its 3-dimensional cells are shaped like crystals and are sepa- rated by quadrangular faces. In this paper, we give a combi- natorial algorithm for constructing such complexes for piece- wise linear data.
AU - Herbert Edelsbrunner
AU - Harer, John
AU - Natarajan, Vijay
AU - Pascucci, Valerio
ID - 3556
TI - Morse-Smale complexes for piecewise linear 3-manifolds
ER -
TY - CHAP
AB - Given a finite point set in R, the surface reconstruction problem asks for a surface that passes through many but not necessarily all points. We describe an unambigu- ous definition of such a surface in geometric and topological terms, and sketch a fast algorithm for constructing it. Our solution overcomes past limitations to special point distributions and heuristic design decisions.
AU - Herbert Edelsbrunner
ID - 3573
T2 - Discrete & Computational Geometry
TI - Surface reconstruction by wrapping finite sets in space
ER -
TY - JOUR
AB - We develop fast algorithms for computing the linking number of a simplicial complex within a filtration.We give experimental results in applying our work toward the detection of non-trivial tangling in biomolecules, modeled as alpha complexes.
AU - Edelsbrunner, Herbert
AU - Zomorodian, Afra
ID - 3584
IS - 2
JF - Homology, Homotopy and Applications
TI - Computing linking numbers of a filtration
VL - 5
ER -
TY - JOUR
AB - Temporal logics such as Computation Tree Logic (CTL) and Linear Temporal Logic (LTL) have become popular for specifying temporal properties over a wide variety of planning and verification problems. In this paper we work towards building a generalized framework for automated reasoning based on temporal logics. We present a powerful extension of CTL with first-order quantification over the set of reachable states for reasoning about extremal properties of weighted labeled transition systems in general. The proposed logic, which we call Weighted Quantified Computation Tree Logic (WQCTL), captures the essential elements common to the domain of planning and verification problems and can thereby be used as an effective specification language in both domains. We show that in spite of the rich, expressive power of the logic, we are able to evaluate WQCTL formulas in time polynomial in the size of the state space times the length of the formula. Wepresent experimental results on the WQCTL verifier.
AU - Krishnendu Chatterjee
AU - Dasgupta, Pallab
AU - Chakrabarti, Partha P
ID - 3593
IS - 2
JF - Journal of Automated Reasoning
TI - A branching time temporal framework for quantitative reasoning
VL - 30
ER -
TY - JOUR
AB - There are several analyses in evolutionary ecology which assume that a family of offspring has come from only two parents. Here, we present a simple test for detecting when a batch involves two or more subfamilies. It is based on the fact that the mixing of families generates associations amongst unlinked marker loci. We also present simulations illustrating the power of our method for varying numbers of loci, alleles per locus and genotyped individuals.
AU - Vines, Timothy H
AU - Nicholas Barton
ID - 3618
IS - 7
JF - Molecular Ecology
TI - A new approach to detecting mixed families
VL - 12
ER -
TY - JOUR
AB - What is the chance that some part of a stretch of genome will survive? In a population of constant size, and with no selection, the probability of survival of some part of a stretch of map length y<1 approaches View the MathML source for View the MathML source. Thus, the whole genome is certain to be lost, but the rate of loss is extremely slow. This solution extends to give the whole distribution of surviving block sizes as a function of time. We show that the expected number of blocks at time t is 1+yt and give expressions for the moments of the number of blocks and the total amount of genome that survives for a given time. The solution is based on a branching process and assumes complete interference between crossovers, so that each descendant carries only a single block of ancestral material. We consider cases where most individuals carry multiple blocks, either because there are multiple crossovers in a long genetic map, or because enough time has passed that most individuals in the population are related to each other. For species such as ours, which have a long genetic map, the genome of any individual which leaves descendants (∼80% of the population for a Poisson offspring number with mean two) is likely to persist for an extremely long time, in the form of a few short blocks of genome.
AU - Baird, Stuart J
AU - Nicholas Barton
AU - Etheridge, Alison M
ID - 3619
IS - 4
JF - Theoretical Population Biology
TI - The distribution of surviving blocks of an ancestral genome
VL - 64
ER -
TY - JOUR
AB - Stable hybrid zones in which ecologically divergent taxa give rise to a range of recombinants are natural laboratories in which the genetic basis of adaptation and reproductive isolation can be unraveled. One such hybrid zone is formed by the fire-bellied toads Bombina bombina and B. variegata (Anura: Discoglossidae). Adaptations to permanent and ephemeral breeding habitats, respectively, have shaped numerous phenotypic differences between the taxa. All of these are, in principle, candidates for a genetic dissection via QTL mapping. We present here a linkage map of 28 codominant and 10 dominant markers in the Bombina genome. In an F2 cross, markers that were mainly microsatellites, SSCPs or allozymes were mapped to 20 linkage groups. Among the 40 isolated CA microsatellites, we noted a preponderance of compound and frequently interleaved CA-TA repeats as well as a striking polarity at the 5′ end of the repeats.
AU - Nürnberger, Beate
AU - Hofman, Sebastian
AU - Förg-Brey, Bqruni
AU - Praetzel, Gabriele
AU - Maclean, Alan W
AU - Szymura, Jacek M
AU - Abbott, Catherine M
AU - Nicholas Barton
ID - 3620
IS - 2
JF - Heredity
TI - A linkage map for the hybridising toads Bombina bombina and B. variegata (Anura: Discoglossidae)
VL - 91
ER -
TY - THES
AU - Christoph Lampert
ID - 3678
T2 - Bonner Mathematische Schriften
TI - The Neumann operator in strictly pseudoconvex domains with weighted Bergman metric
VL - 356
ER -
TY - JOUR
AB - The combination of high-resolution atomic force microscopy (AFM) imaging and single-molecule force-spectroscopy was employed to unfold single bacteriorhodopsins (BR) from native purple membrane patches at various physiologically relevant temperatures. The unfolding spectra reveal detailed insight into the stability of individual structural elements of BR against mechanical unfolding. Intermittent states in the unfolding process are associated with the stepwise unfolding of alpha-helices, whereas other states are associated with the unfolding of polypeptide loops connecting the alpha-helices. It was found that the unfolding forces of the secondary structures considerably decreased upon increasing the temperature from 8 to 52°C. Associated with this effect, the probability of individual unfolding pathways of BR was significantly influenced by the temperature. At lower temperatures, transmembrane alpha-helices and extracellular polypeptide loops exhibited sufficient stability to individually establish potential barriers against unfolding, whereas they predominantly unfolded collectively at elevated temperatures. This suggests that increasing the temperature decreases the mechanical stability of secondary structural elements and changes molecular interactions between secondary structures, thereby forcing them to act as grouped structures.
AU - Harald Janovjak
AU - Kessler, Max
AU - Oesterhelt, Dieter
AU - Gaub, Hermann
AU - Mueller, Daniel J
ID - 3725
IS - 19
JF - EMBO Journal
TI - Unfolding pathways of native bacteriorhodopsin depend on temperature
VL - 22
ER -
TY - JOUR
AB - We use the lac operon in Escherichia coli as a prototype system to illustrate the current state, applicability, and limitations of modeling the dynamics of cellular networks. We integrate three different levels of description (molecular, cellular, and that of cell population) into a single model, which seems to capture many experimental aspects of the system.
AU - Vilar,Jose M
AU - Calin Guet
AU - Leibler, Stanislas
ID - 3752
IS - 3
JF - Journal of Cell Biology
TI - Modeling network dynamics: the lac operon, a case study
VL - 161
ER -
TY - JOUR
AU - Bauer, Wolfgang
AU - Kleine-Berkenbusch, Marco
AU - Bollenbach, Tobias
ID - 3797
IS - 4
JF - Revista Mexicana De Fisica
TI - Breaking atomic nuclei into little pieces: evidence for a phase transition
VL - 49
ER -
TY - JOUR
AB - Kv3 channels are thought to be essential for the fast-spiking (FS) phenotype in GABAergic interneurons, but how these channels confer the ability to generate action potentials (APs) at high frequency is unknown. To address this question, we developed a fast dynamic-clamp system (approximately 50 kHz) that allowed us to add a Kv3 model conductance to CA1 oriens alveus (OA) interneurons in hippocampal slices. Selective pharmacological block of Kv3 channels by 0.3 mm 4-aminopyridine or 1 mm tetraethylammonium ions led to a marked broadening of APs during trains of short stimuli and a reduction in AP frequency during 1 sec stimuli. The addition of artificial Kv3 conductance restored the original AP pattern. Subtraction of Kv3 conductance by dynamic clamp mimicked the effects of the blockers. Application of artificial Kv3 conductance also led to FS in OA interneurons after complete K+ channel block and even induced FS in hippocampal pyramidal neurons in the absence of blockers. Adding artificial Kv3 conductance with altered deactivation kinetics revealed a nonmonotonic relationship between mean AP frequency and deactivation rate, with a maximum slightly above the original value. Insertion of artificial Kv3 conductance with either lowered activation threshold or inactivation also led to a reduction in the mean AP frequency. However, the mechanisms were distinct. Shifting the activation threshold induced adaptation, whereas adding inactivation caused frequency-dependent AP broadening. In conclusion, Kv3 channels are necessary for the FS phenotype of OA interneurons, and several of their gating properties appear to be optimized for high-frequency repetitive activity.
AU - Lien, Cheng-Chang
AU - Peter Jonas
ID - 3804
IS - 6
JF - Journal of Neuroscience
TI - Kv3 potassium conductance is necessary and kinetically optimized for high-frequency action potential generation in hippocampal interneurons
VL - 23
ER -
TY - JOUR
AB - To probe exocytosis at a cortical glutamatergic synapse, we made capacitance measurements in whole-cell recorded hippocampal mossy fiber terminals. Evaluation of different methods by using a morphology-based equivalent electrical model revealed that quantitative capacitance measurements are possible in this presynaptic structure. Voltage pulses leading to presynaptic Ca2+ inflow evoked large capacitance signals that showed saturation with increasing pulse duration. The mean peak capacitance increase was 100 fF, corresponding to a pool of approximately 1,400 releasable vesicles. Thus hippocampal mossy fiber synapses have a vesicular "maxipool." Large pool size and rapid vesicle recycling may underlie the uniquely large extent of activity-dependent plasticity in this synapse.
AU - Hallermann, Stefan
AU - Pawlu, Christian
AU - Peter Jonas
AU - Heckmann, Manfred
ID - 3806
IS - 15
JF - PNAS
TI - A large pool of releasable vesicles in a cortical glutamatergic synapse
VL - 100
ER -
TY - CONF
AB - Many verification, planning, and control problems can be modeled as games played on state-transition graphs by one or two players whose conflicting goals are to form a path in the graph. The focus here is on simple stochastic parity games, that is, two-player games with turn-based probabilistic transitions and omega-regular objectives formalized as parity (Rabin chain) winning conditions. An efficient translation from simple stochastic parity games to nonstochastic parity games is given. As many algorithms are known for solving the latter, the translation yields efficient algorithms for computing the states of a simple stochastic parity game from which a player can win with probability 1. An important special case of simple stochastic parity games are the Markov decision processes with Buchi objectives. For this special case a first provably subquadratic algorithm is given for computing the states from which the single player has a strategy to achieve a Buchi objective with probability 1. For game graphs with m edges the algorithm works in time O(mrootm). Interestingly, a similar technique sheds light on the question of the computational complexity of solving simple Buchi games and yields the first provably subquadratic algorithm, with a running time of O(n(2)/log n) for game graphs with n vertices and O(n) edges.
AU - Krishnendu Chatterjee
AU - Jurdziński, Marcin
AU - Thomas Henzinger
ID - 3897
TI - Simple stochastic parity games
VL - 2803
ER -
TY - CONF
AB - We study the problem of determining stack boundedness and the exact maximum stack size for three classes of interrupt-driven programs. Interrupt-driven programs axe used in many real-time applications that require responsive interrupt handling. In order to ensure responsiveness, programmers often enable interrupt processing in the body of lower-priority interrupt handlers. In such programs a programming error can allow interrupt handlers to be interrupted in cyclic fashion to lead to an unbounded stack, causing the system to crash. For a restricted class of interrupt-driven programs, we show that there is a polynomial-time procedure to check stack boundedness, while determining the exact maximum stack size is PSPACE-complete. For a larger class of programs, the two problems are both PSPACE-complete, and for the largest class of programs we consider, the two problems are PSPACE-hard and can be solved in exponential time.
AU - Krishnendu Chatterjee
AU - Ma, Di
AU - Majumdar, Ritankar S
AU - Zhao, Tian
AU - Thomas Henzinger
AU - Palsberg, Jens
ID - 3898
TI - Stack size analysis for interrupt-driven programs
VL - 2694
ER -
TY - JOUR
AB - Let k⩾5 be an integer, and let x⩾1 be an arbitrary real number. We derive a bound[Formula presented] for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way.
AU - Timothy Browning
ID - 204
IS - 2
JF - Journal of Number Theory
TI - Equal Sums of Two kth Powers
VL - 96
ER -
TY - CHAP
AU - Lieb, Élliott H
AU - Solovej, Jan P
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2338
T2 - Current Developments in Mathematics, 2001
TI - The ground state of the Bose gas
ER -
TY - CONF
AU - Robert Seiringer
ED - Weder, Richardo
ED - Exner, Pavel
ED - Grébert, Benoit
ID - 2339
TI - Symmetry breaking in a model of a rotating Bose gas
VL - 307
ER -
TY - JOUR
AB - The Bose-Einstein condensation (BEC) of the ground state of bosonic atoms in a trap was discussed. The BEC was proved for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schrodinger equation. The BEC was 100% into the state which minimized the Gross-Pitaevskii energy functional. The analysis also included rigorous proof of BEC in a physically realistic, continuum model.
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2349
IS - 17
JF - Physical Review Letters
TI - Proof of Bose-Einstein condensation for dilute trapped gases
VL - 88
ER -
TY - JOUR
AB - Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge Z and in presence of the quantized radiation field. We consider the case of small coupling constant α, but fixed Zα and ultraviolet cut-off Λ. We prove that after renormalizing the mass the binding energy has, to leading order in α, a finite limit as Λ goes to infinity; i.e., the cut-off can be removed. The expression for the ground state energy shift thus obtained agrees with Bethe's formula for small values of Zα, but shows a different behavior for bigger values.
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2350
IS - 5
JF - Advances in Theoretical and Mathematical Physics
TI - Mass renormalization and energy level shift in non-relativistic QED
VL - 6
ER -