TY - JOUR
AB - We introduce propagation models (PMs), a formalism able to express several kinds of equations that describe the behavior of biochemical reaction networks. Furthermore, we introduce the propagation abstract data type (PADT), which separates concerns regarding different numerical algorithms for the transient analysis of biochemical reaction networks from concerns regarding their implementation, thus allowing for portable and efficient solutions. The state of a propagation abstract data type is given by a vector that assigns mass values to a set of nodes, and its (next) operator propagates mass values through this set of nodes. We propose an approximate implementation of the (next) operator, based on threshold abstraction, which propagates only "significant" mass values and thus achieves a compromise between efficiency and accuracy. Finally, we give three use cases for propagation models: the chemical master equation (CME), the reaction rate equation (RRE), and a hybrid method that combines these two equations. These three applications use propagation models in order to propagate probabilities and/or expected values and variances of the model's variables.
AU - Henzinger, Thomas A
AU - Mateescu, Maria
ID - 2302
IS - 2
JF - IEEE ACM Transactions on Computational Biology and Bioinformatics
TI - The propagation approach for computing biochemical reaction networks
VL - 10
ER -
TY - JOUR
AB - The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses.
AU - Ebersberger, Ingo
AU - De Matos Simoes, Ricardo
AU - Kupczok, Anne
AU - Gube, Matthias
AU - Kothe, Erika
AU - Voigt, Kerstin
AU - Von Haeseler, Arndt
ID - 2411
IS - 5
JF - Molecular Biology and Evolution
TI - A consistent phylogenetic backbone for the fungi
VL - 29
ER -
TY - JOUR
AB - We show that bosons interacting via pair potentials with negative scattering length form bound states for a suitable number of particles. In other words, the absence of many-particle bound states of any kind implies the non-negativity of the scattering length of the interaction potential.
AU - Seiringer, Robert
ID - 2318
IS - 3
JF - Journal of Spectral Theory
TI - Absence of bound states implies non-negativity of the scattering length
VL - 2
ER -
TY - CONF
AB - We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning vertices from where the objective can be ensured with probability 1. We study for the first time the average case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average case running time is linear (as compared to the worst case linear number of iterations and quadratic time complexity). Second, for the average case analysis over all MDPs we show that the expected number of iterations is constant and the average case running time is linear (again as compared to the worst case linear number of iterations and quadratic time complexity). Finally we also show that given that all MDPs are equally likely, the probability that the classical algorithm requires more than constant number of iterations is exponentially small.
AU - Chatterjee, Krishnendu
AU - Joglekar, Manas
AU - Shah, Nisarg
ID - 2715
TI - Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives
VL - 18
ER -
TY - CONF
AB - We study the problem of maximum marginal prediction (MMP) in probabilistic graphical models, a task that occurs, for example, as the Bayes optimal decision rule under a Hamming loss. MMP is typically performed as a two-stage procedure: one estimates each variable's marginal probability and then forms a prediction from the states of maximal probability. In this work we propose a simple yet effective technique for accelerating MMP when inference is sampling-based: instead of the above two-stage procedure we directly estimate the posterior probability of each decision variable. This allows us to identify the point of time when we are sufficiently certain about any individual decision. Whenever this is the case, we dynamically prune the variables we are confident about from the underlying factor graph. Consequently, at any time only samples of variables whose decision is still uncertain need to be created. Experiments in two prototypical scenarios, multi-label classification and image inpainting, show that adaptive sampling can drastically accelerate MMP without sacrificing prediction accuracy.
AU - Lampert, Christoph
ID - 2825
TI - Dynamic pruning of factor graphs for maximum marginal prediction
VL - 1
ER -
TY - JOUR
AB - We study evolutionary game theory in a setting where individuals learn from each other. We extend the traditional approach by assuming that a population contains individuals with different learning abilities. In particular, we explore the situation where individuals have different search spaces, when attempting to learn the strategies of others. The search space of an individual specifies the set of strategies learnable by that individual. The search space is genetically given and does not change under social evolutionary dynamics. We introduce a general framework and study a specific example in the context of direct reciprocity. For this example, we obtain the counter intuitive result that cooperation can only evolve for intermediate benefit-to-cost ratios, while small and large benefit-to-cost ratios favor defection. Our paper is a step toward making a connection between computational learning theory and evolutionary game dynamics.
AU - Chatterjee, Krishnendu
AU - Zufferey, Damien
AU - Nowak, Martin
ID - 2848
JF - Journal of Theoretical Biology
TI - Evolutionary game dynamics in populations with different learners
VL - 301
ER -
TY - JOUR
AU - Edelsbrunner, Herbert
AU - Strelkova, Nataliya
ID - 2849
IS - 6
JF - Russian Mathematical Surveys
TI - On the configuration space of Steiner minimal trees
VL - 67
ER -
TY - CONF
AB - Formal verification aims to improve the quality of hardware and software by detecting errors before they do harm. At the basis of formal verification lies the logical notion of correctness, which purports to capture whether or not a circuit or program behaves as desired. We suggest that the boolean partition into correct and incorrect systems falls short of the practical need to assess the behavior of hardware and software in a more nuanced fashion against multiple criteria.
AU - Henzinger, Thomas A
ID - 2888
T2 - Conference proceedings MODELS 2012
TI - Quantitative reactive models
VL - 7590
ER -
TY - CONF
AB - Systems are often specified using multiple requirements on their behavior. In practice, these requirements can be contradictory. The classical approach to specification, verification, and synthesis demands more detailed specifications that resolve any contradictions in the requirements. These detailed specifications are usually large, cumbersome, and hard to maintain or modify. In contrast, quantitative frameworks allow the formalization of the intuitive idea that what is desired is an implementation that comes "closest" to satisfying the mutually incompatible requirements, according to a measure of fit that can be defined by the requirements engineer. One flexible framework for quantifying how "well" an implementation satisfies a specification is offered by simulation distances that are parameterized by an error model. We introduce this framework, study its properties, and provide an algorithmic solution for the following quantitative synthesis question: given two (or more) behavioral requirements specified by possibly incompatible finite-state machines, and an error model, find the finite-state implementation that minimizes the maximal simulation distance to the given requirements. Furthermore, we generalize the framework to handle infinite alphabets (for example, realvalued domains). We also demonstrate how quantitative specifications based on simulation distances might lead to smaller and easier to modify specifications. Finally, we illustrate our approach using case studies on error correcting codes and scheduler synthesis.
AU - Cerny, Pavol
AU - Gopi, Sivakanth
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
AU - Totla, Nishant
ID - 2890
T2 - Proceedings of the tenth ACM international conference on Embedded software
TI - Synthesis from incompatible specifications
ER -
TY - CONF
AB - Quantitative automata are nondeterministic finite automata with edge weights. They value a
run by some function from the sequence of visited weights to the reals, and value a word by its
minimal/maximal run. They generalize boolean automata, and have gained much attention in
recent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and
limit-average automata, cannot be determinized. Yet, the quantitative setting provides the potential
of approximate determinization. We define approximate determinization with respect to
a distance function, and investigate this potential.
We show that sum automata cannot be determinized approximately with respect to any
distance function. However, restricting to nonnegative weights allows for approximate determinization
with respect to some distance functions.
Discounted-sum automata allow for approximate determinization, as the influence of a word’s
suffix is decaying. However, the naive approach, of unfolding the automaton computations up
to a sufficient level, is shown to be doubly exponential in the discount factor. We provide an
alternative construction that is singly exponential in the discount factor, in the precision, and
in the number of states. We prove matching lower bounds, showing exponential dependency on
each of these three parameters.
Average and limit-average automata are shown to prohibit approximate determinization with
respect to any distance function, and this is the case even for two weights, 0 and 1.
AU - Boker, Udi
AU - Henzinger, Thomas A
ID - 2891
T2 - Leibniz International Proceedings in Informatics
TI - Approximate determinization of quantitative automata
VL - 18
ER -
TY - JOUR
AB - We present an algorithm for simplifying linear cartographic objects and results obtained with a computer program implementing this algorithm.
AU - Edelsbrunner, Herbert
AU - Musin, Oleg
AU - Ukhalov, Alexey
AU - Yakimova, Olga
AU - Alexeev, Vladislav
AU - Bogaevskaya, Victoriya
AU - Gorohov, Andrey
AU - Preobrazhenskaya, Margarita
ID - 2902
IS - 6
JF - Modeling and Analysis of Information Systems
TI - Fractal and computational geometry for generalizing cartographic objects
VL - 19
ER -
TY - CONF
AB - In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. In this paper, we introduce a single topology that enjoys this theorem for all thresholds decomposing a real-valued image into foreground and background. This topology is easy to construct and it generalizes to n-dimensional images.
AU - Edelsbrunner, Herbert
AU - Symonova, Olga
ID - 2903
TI - The adaptive topology of a digital image
ER -
TY - JOUR
AB - Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences.
AU - Pausinger, Florian
ID - 2904
IS - 3
JF - Journal de Theorie des Nombres des Bordeaux
SN - 2118-8572
TI - Weak multipliers for generalized van der Corput sequences
VL - 24
ER -
TY - JOUR
AU - Edelsbrunner, Herbert
AU - Strelkova, Nataliya
ID - 2912
IS - 6
JF - Uspekhi Mat. Nauk
TI - Configuration space for shortest networks
VL - 67
ER -
TY - CONF
AU - Kroemer, Oliver
AU - Lampert, Christoph
AU - Peters, Jan
ID - 2915
TI - Multi-modal learning for dynamic tactile sensing
ER -
TY - GEN
AB - This paper addresses the problem of approximate MAP-MRF inference in general graphical models. Following [36], we consider a family of linear programming relaxations of the problem where each relaxation is specified by a set of nested pairs of factors for which the marginalization constraint needs to be enforced. We develop a generalization of the TRW-S algorithm [9] for this problem, where we use a decomposition into junction chains, monotonic w.r.t. some ordering on the nodes. This generalizes the monotonic chains in [9] in a natural way. We also show how to deal with nested factors in an efficient way. Experiments show an improvement over min-sum diffusion, MPLP and subgradient ascent algorithms on a number of computer vision and natural language processing problems.
AU - Kolmogorov, Vladimir
AU - Schoenemann, Thomas
ID - 2928
T2 - arXiv
TI - Generalized sequential tree-reweighted message passing
ER -
TY - CONF
AB - In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively.
In particular we generalize the known Min-Max-Theorem for submodular and bisubmodular functions. This theorem asserts that the minimum of the (bi)submodular function can be found by solving a maximization problem over a (bi)submodular polyhedron. We define a k-submodular polyhedron, prove a Min-Max-Theorem for k-submodular functions, and give a greedy algorithm to construct the vertices of the polyhedron.
AU - Huber, Anna
AU - Kolmogorov, Vladimir
ID - 2930
TI - Towards minimizing k-submodular functions
VL - 7422
ER -
TY - JOUR
AB - In this paper, we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from images of different instances of the same object category. We formulate this matching task as an energy minimization problem by defining an elaborate objective function of the appearance and the spatial arrangement of the features. Optimization of this energy is an instance of graph matching, which is in general an NP-hard problem. We describe a novel graph matching optimization technique, which we refer to as dual decomposition (DD), and demonstrate on a variety of examples that this method outperforms existing graph matching algorithms. In the majority of our examples, DD is able to find the global minimum within a minute. The ability to globally optimize the objective allows us to accurately learn the parameters of our matching model from training examples. We show on several matching tasks that our learned model yields results superior to those of state-of-the-art methods.
AU - Torresani, Lorenzo
AU - Kolmogorov, Vladimir
AU - Rother, Carsten
ID - 2931
IS - 2
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - A dual decomposition approach to feature correspondence
VL - 35
ER -
TY - CONF
AB - The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a quantitative measure for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intu- itively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, and that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.
AU - Cerny, Pavol
AU - Chmelik, Martin
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
ID - 2916
T2 - Electronic Proceedings in Theoretical Computer Science
TI - Interface Simulation Distances
VL - 96
ER -
TY - JOUR
AB - The search for extra-terrestrial intelligence (SETI) has been performed principally as a one-way survey, listening of radio frequencies across the Milky Way and other galaxies. However, scientists have engaged in an active messaging only rarely. This suggests the simple rationale that if other civilizations exist and take a similar approach to ours, namely listening but not broadcasting, the result is a silent universe. A simple game theoretical model, the prisoner's dilemma, explains this situation: each player (civilization) can passively search (defect), or actively search and broadcast (cooperate). In order to maximize the payoff (or, equivalently, minimize the risks) the best strategy is not to broadcast. In fact, the active search has been opposed on the basis that it might be dangerous to expose ourselves. However, most of these ideas have not been based on objective arguments, and ignore accounting of the possible gains and losses. Thus, the question stands: should we perform an active search? I develop a game-theoretical framework where civilizations can be of different types, and explicitly apply it to a situation where societies are either interested in establishing a two-way communication or belligerent and in urge to exploit ours. The framework gives a quantitative solution (a mixed-strategy), which is how frequent we should perform the active SETI. This frequency is roughly proportional to the inverse of the risk, and can be extremely small. However, given the immense amount of stars being scanned, it supports active SETI. The model is compared with simulations, and the possible actions are evaluated through the San Marino scale, measuring the risks of messaging.
AU - Vladar, Harold
ID - 2917
IS - 1
JF - International Journal of Astrobiology
TI - The game of active search for extra terrestrial intelligence Breaking the Great Silence
VL - 12
ER -