Distinct nonuniform cable properties optimize rapid and efficient activation of fast-spiking GABAergic interneurons - Norenberg, Anja; Hua Hu; Vida, Imre; Bartos, Marlene; Peter Jonas (PNAS)
Fast-spiking, parvalbumin-expressing basket cells (BCs) play a key role in feedforward and feedback inhibition in the hippocampus. However, the dendritic mechanisms underlying rapid interneuron recruitment have remained unclear. To quantitatively address this question, we developed detailed passive cable models of BCs in the dentate gyrus based on dual somatic or somatodendritic recordings and complete morphologic reconstructions. Both specific membrane capacitance and axial resistivity were comparable to those of pyramidal neurons, but the average somatodendritic specific membrane resistance (R(m)) was substantially lower in BCs. Furthermore, R(m) was markedly nonuniform, being lowest in soma and proximal dendrites, intermediate in distal dendrites, and highest in the axon. Thus, the somatodendritic gradient of R(m) was the reverse of that in pyramidal neurons. Further computational analysis revealed that these unique cable properties accelerate the time course of synaptic potentials at the soma in response to fast inputs, while boosting the efficacy of slow distal inputs. These properties will facilitate both rapid phasic and efficient tonic activation of BCs in hippocampal microcircuits.

Beyond TARPs: The growing list of auxiliary AMPAR subunits - Guzmán, José; Jonas, Peter M (Neuron)
A recent paper by von Engelhardt et al. identifies a novel auxiliary subunit of native AMPARs, termedCKAMP44. Unlike other auxiliary subunits, CKAMP44 accelerates desensitization and prolongs recovery from desensitization. CKAMP44 is highly expressed in hippocampal dentate gyrus granule cells and decreases the paired-pulse ratio at perforant path input synapses. Thus, both principal and auxiliary AMPAR subunits control the time course of signaling at glutamatergic synapses.

GABA release at terminals of CCK-interneurons: Synchrony, asynchrony and modulation by cannabinoid receptors (commentary on Ali & Todorova) - Jonas, Peter M; Hefft, Stefan (The European Journal of Neuroscience)

Solving the chemical master equation using sliding windows - Wolf, Verena; Goel, Rushil; Mateescu, Maria; Henzinger, Thomas A (BMC Systems Biology)
Background The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases computationally expensive or even infeasible as the number of reachable states can be very large or infinite. We introduce the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a "window" into the state space. In subsequent steps, the window follows the direction in which the probability mass moves, until the time period of interest has elapsed. We construct the window based on a deterministic approximation of the future behavior of the system by estimating upper and lower bounds on the populations of the chemical species. Results In order to show the effectiveness of our approach, we apply it to several examples previously described in the literature. The experimental results show that the proposed method speeds up the analysis considerably, compared to a global analysis, while still providing high accuracy. Conclusions The sliding window method is a novel approach to address the performance problems of numerical algorithms for the solution of the chemical master equation. The method efficiently approximates the probability distributions at the time points of interest for a variety of chemically reacting systems, including systems for which no upper bound on the population sizes of the chemical species is known a priori.

Hybrid numerical solution of the chemical master equation - Henzinger, Thomas A; Mateescu, Maria; Mikeev, Linar; Wolf, Verena
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe net- works of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the construction of a stochastic hybrid model in which certain discrete random variables of the original Markov chain are approximated by continuous deterministic variables. We compute the solution of the stochastic hybrid model using a numerical algorithm that discretizes time and in each step performs a mutual update of the transient prob- ability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We im- plemented the algorithm and we demonstrate its usefulness and efficiency on several case studies from systems biology.

Invariant and type inference for matrices - Henzinger, Thomas A; Hottelier, Thibaud; Kovács, Laura; Voronkov, Andrei
We present a loop property generation method for loops iterating over multi-dimensional arrays. When used on matrices, our method is able to infer their shapes (also called types), such as upper-triangular, diagonal, etc. To gen- erate loop properties, we first transform a nested loop iterating over a multi- dimensional array into an equivalent collection of unnested loops. Then, we in- fer quantified loop invariants for each unnested loop using a generalization of a recurrence-based invariant generation technique. These loop invariants give us conditions on matrices from which we can derive matrix types automatically us- ing theorem provers. Invariant generation is implemented in the software package Aligator and types are derived by theorem provers and SMT solvers, including Vampire and Z3. When run on the Java matrix package JAMA, our tool was able to infer automatically all matrix types describing the matrix shapes guaranteed by JAMA’s API.

From boolean to quantitative notions of correctness - Henzinger, Thomas A
Classical formalizations of systems and properties are boolean: given a system and a property, the property is either true or false of the system. Correspondingly, classical methods for system analysis determine the truth value of a property, preferably giving a proof if the property is true, and a counterexample if the property is false; classical methods for system synthesis construct a system for which a property is true; classical methods for system transformation, composition, and abstraction aim to preserve the truth of properties. The boolean view is prevalent even if the system, the property, or both refer to numerical quantities, such as the times or probabilities of events. For example, a timed automaton either satisfies or violates a formula of a real-time logic; a stochastic process either satisfies or violates a formula of a probabilistic logic. The classical black-and-white view partitions the world into "correct" and "incorrect" systems, offering few nuances. In reality, of several systems that satisfy a property in the boolean sense, often some are more desirable than others, and of the many systems that violate a property, usually some are less objectionable than others. For instance, among the systems that satisfy the response property that every request be granted, we may prefer systems that grant requests quickly (the quicker, the better), or we may prefer systems that issue few unnecessary grants (the fewer, the better); and among the systems that violate the response property, we may prefer systems that serve many initial requests (the more, the better), or we may prefer systems that serve many requests in the long run (the greater the fraction of served to unserved requests, the better). Formally, while a boolean notion of correctness is given by a preorder on systems and properties, a quantitative notion of correctness is defined by a directed metric on systems and properties, where the distance between a system and a property provides a measure of "fit" or "desirability." There are many ways how such distances can be defined. In a linear-time framework, one assigns numerical values to individual behaviors before assigning values to systems and properties, which are sets of behaviors. For example, the value of a single behavior may be a discounted value, which is largely determined by a prefix of the behavior, e.g., by the number of requests that are granted before the first request that is not granted; or a limit value, which is independent of any finite prefix. A limit value may be an average, such as the average response time over an infinite sequence of requests and grants, or a supremum, such as the worst-case response time. Similarly, the value of a set of behaviors may be an extremum or an average across the values of all behaviors in the set: in this way one can measure the worst of all possible average-case response times, or the average of all possible worst-case response times, etc. Accordingly, the distance between two sets of behaviors may be defined as the worst or average difference between the values of corresponding behaviors. In summary, we propagate replacing boolean specifications for the correctness of systems with quantitative measures for the desirability of systems. In quantitative analysis, the aim is to compute the distance between a system and a property (or between two systems, or two properties); in quantitative synthesis, the objective is to construct a system that has minimal distance from a given property. Multiple quantitative measures can be prioritized (e.g., combined lexicographically into a single measure) or studied along the Pareto curve. Quantitative transformations, compositions, and abstractions of systems are useful if they allow us to bound the induced change in distance from a property. We present some initial results in some of these directions. We also give some potential applications, which not only generalize tradiditional correctness concerns in the functional, timed, and probabilistic domains, but also capture such system measures as resource use, performance, cost, reliability, and robustness.

Fast adaptive uniformization of the chemical master equation - Didier, Frédéric; Henzinger, Thomas A; Mateescu, Maria; Wolf, Verena (IET Systems Biology)
Within systems biology there is an increasing interest in the stochastic behavior of biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous-time Markov chain (CTMC). The uniformization technique is an efficient method to compute probability distributions of a CTMC if the number of states is manageable. However, the size of a CTMC that represents a biochemical reaction network is usually far beyond what is feasible. In this paper we present an on-the-fly variant of uniformization, where we improve the original algorithm at the cost of a small approximation error. By means of several examples, we show that our approach is particularly well-suited for biochemical reaction networks.

Aligators for arrays - Henzinger, Thomas A; Hottelier, Thibaud; Kovács, Laura; Rybalchenko, Andrey
This paper presents Aligators, a tool for the generation of universally quantified array invariants. Aligators leverages recurrence solving and algebraic techniques to carry out inductive reasoning over array content. The Aligators’ loop extraction module allows treatment of multi-path loops by exploiting their commutativity and serializability properties. Our experience in applying Aligators on a collection of loops from open source software projects indicates the applicability of recurrence and algebraic solving techniques for reasoning about arrays.

SABRE: A tool for the stochastic analysis of biochemical reaction networks - Didier, Frédéric; Henzinger, Thomas A; Mateescu, Maria; Wolf, Verena
The importance of stochasticity within biological systems has been shown repeatedly during the last years and has raised the need for efficient stochastic tools. We present SABRE, a tool for stochastic analysis of biochemical reaction networks. SABRE implements fast adaptive uniformization (FAU), a direct numerical approximation algorithm for computing transient solutions of biochemical reaction networks. Biochemical reactions networks represent biological systems studied at a molecular level and these reactions can be modeled as transitions of a Markov chain. SABRE accepts as input the formalism of guarded commands, which it interprets either as continuous-time or as discrete-time Markov chains. Besides operating in a stochastic mode, SABRE may also perform a deterministic analysis by directly computing a mean-field approximation of the system under study. We illustrate the different functionalities of SABRE by means of biological case studies.

The robustness of level sets - Bendich, Paul; Edelsbrunner, Herbert; Morozov, Dmitriy; Patel, Amit
We define the robustness of a level set homology class of a function f:XR as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case X=R3 has ramifications in medical imaging and scientific visualization.

Persistent homology under non-uniform error - Bendich, Paul; Edelsbrunner, Herbert; Kerber, Michael; Patel, Amit
Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classes. Prior work has shown that the homology and robustness information can be read off the extended persistence diagram of the function. This paper extends these results to a non-uniform error model in which perturbations vary in their magnitude across the domain.

STM imaging of electronic waves on the surface of Bi2Te3 Topologically protected surface states and hexagonal warping effects - Alpichshev, Zhanybek; Analytis, James; Chu, Jiunhaw; Fisher, Ian; Chen, Yulin; Shen, Zhixun; Fang, Aiping; Kapitulnik, Aharon (Physical Review Letters)
Scanning tunneling spectroscopy studies on high-quality Bi2Te3 crystals exhibit perfect correspondence to angle-resolved photoemission spectroscopy data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear, dispersing with a wave vector that may result from a hexagonal warping term.

Polygonal reconstruction from approximate offsets - Berberich, Eric; Halperin, Dan; Kerber, Michael; Pogalnikova, Roza
Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape with a disk of fixed radius? If it does, we also seek a preferably simple solution shape P;P’s offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give a decision algorithm for fixed radius in O(nlogn) time that handles any polygonal shape. For convex shapes, the complexity drops to O(n), which is also the time required to compute a solution shape P with at most one more vertex than a vertex-minimal one.

Energy parity games - Chatterjee, Krishnendu; Doyen, Laurent
Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resource-constrained omega-regular specifications, energy parity games provide one of the simplest model of games with combined qualitative and quantitative objective. Our main results are as follows: (a) exponential memory is sufficient and may be necessary for winning strategies in energy parity games; (b) the problem of deciding the winner in energy parity games can be solved in NP ∩ coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games. We also show that the problem of deciding the winner in energy parity games is polynomially equivalent to the problem of deciding the winner in mean-payoff parity games, which can thus be solved in NP ∩ coNP. As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.

Discounting in games across time scales - Chatterjee, Krishnendu; Majumdar, Ritankar
We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. We show the existence of pure memoryless optimal strategies for both players and an ordered field property for such games. 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 games can be decided in NP intersected coNP. We also give an alternate strategy improvement algorithm to compute the value.

Mean-payoff automaton expressions - Chatterjee, Krishnendu; Doyen, Laurent; Edelsbrunner, Herbert; Henzinger, Thomas A; Rannou, Philippe
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions.

Obliging games - Chatterjee, Krishnendu; Horn, Florian; Löding, Christof
Graph games of infinite length provide a natural model for open reactive systems: one player (Eve) represents the controller and the other player (Adam) represents the environment. The evolution of the system depends on the decisions of both players. The specification for the system is usually given as an ω-regular language L over paths and Eve’s goal is to ensure that the play belongs to L irrespective of Adam’s behaviour. The classical notion of winning strategies fails to capture several interesting scenarios. For example, strong fairness (Streett) conditions are specified by a number of request-grant pairs and require every pair that is requested infinitely often to be granted infinitely often: Eve might win just by preventing Adam from making any new request, but a “better” strategy would allow Adam to make as many requests as possible and still ensure fairness. To address such questions, we introduce the notion of obliging games, where Eve has to ensure a strong condition Φ, while always allowing Adam to satisfy a weak condition Ψ. We present a linear time reduction of obliging games with two Muller conditions Φ and Ψ to classical Muller games. We consider obliging Streett games and show they are co-NP complete, and show a natural quantitative optimisation problem for obliging Streett games is in FNP. We also show how obliging games can provide new and interesting semantics for multi-player games.

Qualitative analysis of partially-observable Markov Decision Processes - Chatterjee, Krishnendu; Doyen, Laurent; Henzinger, Thomas A
We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with parity objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider qualitative analysis problems: given a POMDP with a parity objective, decide whether there exists an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis problem for POMDPs with parity objectives and its subclasses: safety, reachability, Büchi, and coBüchi objectives. We establish several upper and lower bounds that were not known in the literature. Second, we give optimal bounds (matching upper and lower bounds) for the memory required by pure and randomized observation-based strategies for each class of objectives.

Randomness for free - Chatterjee, Krishnendu; Doyen, Laurent; Gimbert, Hugo; Henzinger, Thomas A
We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (players interact simultaneously); and (b) turn-based (players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. We present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function (probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.