TY - JOUR
AB - The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs, and written for non-experts in algebraic topology.
AU - Bendich, Paul
AU - Cabello, Sergio
AU - Edelsbrunner, Herbert
ID - 3310
IS - 11
JF - Pattern Recognition Letters
TI - A point calculus for interlevel set homology
VL - 33
ER -
TY - JOUR
AB - We introduce two-level discounted and mean-payoff games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted or mean-payoff game and the lower level game is a (undiscounted) reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. For both discounted and mean-payoff two-level games, we show the existence of pure memoryless optimal strategies for both players and an ordered field property. We show that if there is only one player (Markov decision processes), then the values can be computed in polynomial time. It follows that whether the value of a player is equal to a given rational constant in two-level discounted or mean-payoff games can be decided in NP ∩ coNP. We also give an alternate strategy improvement algorithm to compute the value. © 2012 World Scientific Publishing Company.
AU - Chatterjee, Krishnendu
AU - Majumdar, Ritankar
ID - 3314
IS - 3
JF - International Journal of Foundations of Computer Science
TI - Discounting and averaging in games across time scales
VL - 23
ER -
TY - JOUR
AB - The physical distance between presynaptic Ca2+ channels and the Ca2+ sensors that trigger exocytosis of neurotransmitter-containing vesicles is a key determinant of the signalling properties of synapses in the nervous system. Recent functional analysis indicates that in some fast central synapses, transmitter release is triggered by a small number of Ca2+ channels that are coupled to Ca2+ sensors at the nanometre scale. Molecular analysis suggests that this tight coupling is generated by protein–protein interactions involving Ca2+ channels, Ca2+ sensors and various other synaptic proteins. Nanodomain coupling has several functional advantages, as it increases the efficacy, speed and energy efficiency of synaptic transmission.
AU - Eggermann, Emmanuel
AU - Bucurenciu, Iancu
AU - Goswami, Sarit
AU - Jonas, Peter M
ID - 3317
IS - 1
JF - Nature Reviews Neuroscience
TI - Nanodomain coupling between Ca(2+) channels and sensors of exocytosis at fast mammalian synapses
VL - 13
ER -
TY - JOUR
AB - Computing the topology of an algebraic plane curve C means computing a combinatorial graph that is isotopic to C and thus represents its topology in R2. We prove that, for a polynomial of degree n with integer coefficients bounded by 2ρ, the topology of the induced curve can be computed with bit operations ( indicates that we omit logarithmic factors). Our analysis improves the previous best known complexity bounds by a factor of n2. The improvement is based on new techniques to compute and refine isolating intervals for the real roots of polynomials, and on the consequent amortized analysis of the critical fibers of the algebraic curve.
AU - Kerber, Michael
AU - Sagraloff, Michael
ID - 3331
IS - 3
JF - Journal of Symbolic Computation
TI - A worst case bound for topology computation of algebraic curves
VL - 47
ER -
TY - CONF
AB - We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with \omega-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity gameswith respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition function is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).
AU - Chatterjee, Krishnendu
ID - 3341
TI - Robustness of structurally equivalent concurrent parity games
VL - 7213
ER -
TY - CONF
AB - Many infinite state systems can be seen as well-structured transition systems (WSTS), i.e., systems equipped with a well-quasi-ordering on states that is also a simulation relation. WSTS are an attractive target for formal analysis because there exist generic algorithms that decide interesting verification problems for this class. Among the most popular algorithms are acceleration-based forward analyses for computing the covering set. Termination of these algorithms can only be guaranteed for flattable WSTS. Yet, many WSTS of practical interest are not flattable and the question whether any given WSTS is flattable is itself undecidable. We therefore propose an analysis that computes the covering set and captures the essence of acceleration-based algorithms, but sacrifices precision for guaranteed termination. Our analysis is an abstract interpretation whose abstract domain builds on the ideal completion of the well-quasi-ordered state space, and a widening operator that mimics acceleration and controls the loss of precision of the analysis. We present instances of our framework for various classes of WSTS. Our experience with a prototype implementation indicates that, despite the inherent precision loss, our analysis often computes the precise covering set of the analyzed system.
AU - Zufferey, Damien
AU - Wies, Thomas
AU - Henzinger, Thomas A
ID - 3251
TI - Ideal abstractions for well structured transition systems
VL - 7148
ER -
TY - JOUR
AB - Spontaneous release of glutamate is important for maintaining synaptic strength and controlling spike timing in the brain. Mechanisms regulating spontaneous exocytosis remain poorly understood. Extracellular calcium concentration ([Ca2+]o) regulates Ca2+ entry through voltage-activated calcium channels (VACCs) and consequently is a pivotal determinant of action potential-evoked vesicle fusion. Extracellular Ca 2+ also enhances spontaneous release, but via unknown mechanisms. Here we report that external Ca2+ triggers spontaneous glutamate release more weakly than evoked release in mouse neocortical neurons. Blockade of VACCs has no effect on the spontaneous release rate or its dependence on [Ca2+]o. Intracellular [Ca2+] slowly increases in a minority of neurons following increases in [Ca2+]o. Furthermore, the enhancement of spontaneous release by extracellular calcium is insensitive to chelation of intracellular calcium by BAPTA. Activation of the calcium-sensing receptor (CaSR), a G-protein-coupled receptor present in nerve terminals, by several specific agonists increased spontaneous glutamate release. The frequency of spontaneous synaptic transmission was decreased in CaSR mutant neurons. The concentration-effect relationship for extracellular calcium regulation of spontaneous release was well described by a combination of CaSR-dependent and CaSR-independent mechanisms. Overall these results indicate that extracellular Ca2+ does not trigger spontaneous glutamate release by simply increasing calcium influx but stimulates CaSR and thereby promotes resting spontaneous glutamate release.
AU - Vyleta, Nicholas
AU - Smith, Stephen
ID - 469
IS - 12
JF - European Journal of Neuroscience
TI - Spontaneous glutamate release is independent of calcium influx and tonically activated by the calcium-sensing receptor
VL - 31
ER -
TY - JOUR
AB - BioSig is an open source software library for biomedical signal processing. The aim of the BioSig project is to foster research in biomedical signal processing by providing free and open source software tools for many different application areas. Some of the areas where BioSig can be employed are neuroinformatics, brain-computer interfaces, neurophysiology, psychology, cardiovascular systems, and sleep research. Moreover, the analysis of biosignals such as the electroencephalogram (EEG), electrocorticogram (ECoG), electrocardiogram (ECG), electrooculogram (EOG), electromyogram (EMG), or respiration signals is a very relevant element of the BioSig project. Specifically, BioSig provides solutions for data acquisition, artifact processing, quality control, feature extraction, classification, modeling, and data visualization, to name a few. In this paper, we highlight several methods to help students and researchers to work more efficiently with biomedical signals.
AU - Schlögl, Alois
AU - Vidaurre, Carmen
AU - Sander, Tilmann
ID - 490
JF - Computational Intelligence and Neuroscience
TI - BioSig: The free and open source software library for biomedical signal processing
VL - 2011
ER -
TY - JOUR
AB - In their search for antigens, lymphocytes continuously shuttle among blood vessels, lymph vessels, and lymphatic tissues. Chemokines mediate entry of lymphocytes into lymphatic tissues, and sphingosine 1-phosphate (S1P) promotes localization of lymphocytes to the vasculature. Both signals are sensed through G protein-coupled receptors (GPCRs). Most GPCRs undergo ligand-dependent homologous receptor desensitization, a process that decreases their signaling output after previous exposure to high ligand concentration. Such desensitization can explain why lymphocytes do not take an intermediate position between two signals but rather oscillate between them. The desensitization of S1P receptor 1 (S1PR1) is mediated by GPCR kinase 2 (GRK2). Deletion of GRK2 in lymphocytes compromises desensitization by high vascular S1P concentrations, thereby reducing responsiveness to the chemokine signal and trapping the cells in the vascular compartment. The desensitization kinetics of S1PR1 allows lymphocytes to dynamically shuttle between vasculature and lymphatic tissue, although the positional information in both compartments is static.
AU - Eichner, Alexander
AU - Sixt, Michael K
ID - 491
IS - 198
JF - Science Signaling
TI - Setting the clock for recirculating lymphocytes
VL - 4
ER -
TY - JOUR
AB - Cancer stem cells or cancer initiating cells are believed to contribute to cancer recurrence after therapy. MicroRNAs (miRNAs) are short RNA molecules with fundamental roles in gene regulation. The role of miRNAs in cancer stem cells is only poorly understood. Here, we report miRNA expression profiles of glioblastoma stem cell-containing CD133 + cell populations. We find that miR-9, miR-9 * (referred to as miR-9/9 *), miR-17 and miR-106b are highly abundant in CD133 + cells. Furthermore, inhibition of miR-9/9 * or miR-17 leads to reduced neurosphere formation and stimulates cell differentiation. Calmodulin-binding transcription activator 1 (CAMTA1) is a putative transcription factor, which induces the expression of the anti-proliferative cardiac hormone natriuretic peptide A (NPPA). We identify CAMTA1 as an miR-9/9 * and miR-17 target. CAMTA1 expression leads to reduced neurosphere formation and tumour growth in nude mice, suggesting that CAMTA1 can function as tumour suppressor. Consistently, CAMTA1 and NPPA expression correlate with patient survival. Our findings could provide a basis for novel strategies of glioblastoma therapy.
AU - Schraivogel, Daniel
AU - Weinmann, Lasse
AU - Beier, Dagmar
AU - Tabatabai, Ghazaleh
AU - Eichner, Alexander
AU - Zhu, Jia
AU - Anton, Martina
AU - Sixt, Michael K
AU - Weller, Michael
AU - Beier, Christoph
AU - Meister, Gunter
ID - 518
IS - 20
JF - EMBO Journal
TI - CAMTA1 is a novel tumour suppressor regulated by miR-9/9 * in glioblastoma stem cells
VL - 30
ER -
TY - JOUR
AB - Software transactional memories (STM) are described in the literature with assumptions of sequentially consistent program execution and atomicity of high level operations like read, write, and abort. However, in a realistic setting, processors use relaxed memory models to optimize hardware performance. Moreover, the atomicity of operations depends on the underlying hardware. This paper presents the first approach to verify STMs under relaxed memory models with atomicity of 32 bit loads and stores, and read-modify-write operations. We describe RML, a simple language for expressing concurrent programs. We develop a semantics of RML parametrized by a relaxed memory model. We then present our tool, FOIL, which takes as input the RML description of an STM algorithm restricted to two threads and two variables, and the description of a memory model, and automatically determines the locations of fences, which if inserted, ensure the correctness of the restricted STM algorithm under the given memory model. We use FOIL to verify DSTM, TL2, and McRT STM under the memory models of sequential consistency, total store order, partial store order, and relaxed memory order for two threads and two variables. Finally, we extend the verification results for DSTM and TL2 to an arbitrary number of threads and variables by manually proving that the structural properties of STMs are satisfied at the hardware level of atomicity under the considered relaxed memory models.
AU - Guerraoui, Rachid
AU - Henzinger, Thomas A
AU - Singh, Vasu
ID - 531
IS - 3
JF - Formal Methods in System Design
TI - Verification of STM on relaxed memory models
VL - 39
ER -
TY - GEN
AB - Computing the winning set for Büchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is ̃O(n·m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the ̃O(n·m) boundary by presenting a new technique that reduces the running time to O(n2). This bound also leads to O(n2) time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of O(n·m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n3)), and (3) in Markov decision processes (improving for m > n4/3 an earlier bound of O(min(m1.5, m·n2/3)). We also show that the same technique can be used to compute the maximal end-component decomposition of a graph in time O(n2), which is an improvement over earlier bounds for m > n4/3. Finally, we show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. This is the first dynamic algorithm for this problem.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
ID - 5379
SN - 2664-1690
TI - An O(n2) time algorithm for alternating Büchi games
ER -
TY - GEN
AB - We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. We study concurrent games with ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). We study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms,that are obtained by characterization of the winning sets as μ-calculus formulas, are considerably more involved than those for turn-based games.
AU - Chatterjee, Krishnendu
ID - 5380
SN - 2664-1690
TI - Bounded rationality in concurrent parity games
ER -
TY - GEN
AB - In two-player finite-state stochastic games of partial obser- vation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distri- bution over the successor states. The game is played for infinitely many rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1) or pos- itively (i.e., with positive probability), no matter the strategy of the second player.
We classify such games according to the information and to the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two- sided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization.
Our main results for pure strategies are as follows: (1) For one-sided games with player 2 perfect observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strate- gies are not sufficient, and present an exponential upper bound on mem- ory both for almost-sure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete and present symbolic algo- rithms that avoid the explicit exponential construction. (2) For one-sided games with player 1 perfect observation we show that non-elementary memory is both necessary and sufficient for both almost-sure and posi- tive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least non-elementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence re- sult exhibit serious flaws in previous results in the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 5381
SN - 2664-1690
TI - Partial-observation stochastic games: How to win when belief fails
ER -
TY - GEN
AB - We consider two-player stochastic games played on a finite state space for an infinite num- ber of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with ω-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity games with respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition func- tion is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).
AU - Chatterjee, Krishnendu
ID - 5382
SN - 2664-1690
TI - Robustness of structurally equivalent concurrent parity games
ER -
TY - GEN
AB - We present a new decidable logic called TREX for expressing constraints about imperative tree data structures. In particular, TREX supports a transitive closure operator that can express reachability constraints, which often appear in data structure invariants. We show that our logic is closed under weakest precondition computation, which enables its use for automated software verification. We further show that satisfiability of formulas in TREX is decidable in NP. The low complexity makes it an attractive alternative to more expensive logics such as monadic second-order logic (MSOL) over trees, which have been traditionally used for reasoning about tree data structures.
AU - Wies, Thomas
AU - Muñiz, Marco
AU - Kuncak, Viktor
ID - 5383
SN - 2664-1690
TI - On an efficient decision procedure for imperative tree data structures
ER -
TY - GEN
AB - We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with positive probability; (ii) the almost decision problem asks whether there is a word that is accepted with probability 1; and (iii) the limit decision problem asks whether for every ε > 0 there is a word that is accepted with probability at least 1 − ε. We unify and generalize several decidability results for probabilistic automata over infinite words, and identify a robust (closed under union and intersection) subclass of probabilistic automata for which all the qualitative decision problems are decidable for parity conditions. We also show that if the input words are restricted to lasso shape words, then the positive and almost problems are decidable for all probabilistic automata with parity conditions.
AU - Chatterjee, Krishnendu
AU - Tracol, Mathieu
ID - 5384
SN - 2664-1690
TI - Decidable problems for probabilistic automata on infinite words
ER -
TY - GEN
AB - There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with “controlled-accumulation”, allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.
AU - Boker, Udi
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Kupferman, Orna
ID - 5385
SN - 2664-1690
TI - Temporal specifications with accumulative values
ER -
TY - GEN
AB - We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.
AU - Chen, Chao
AU - Freedman, Daniel
AU - Lampert, Christoph
ID - 5386
SN - 2664-1690
TI - Enforcing topological constraints in random field image segmentation
ER -
TY - GEN
AB - We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 5387
SN - 2664-1690
TI - Energy and mean-payoff parity Markov decision processes
ER -