The complexity of request-response games - Chatterjee, Krishnendu; Henzinger, Thomas A; Horn, Florian
We consider two-player graph games whose objectives are request-response condition, i.e conjunctions of conditions of the form "if a state with property Rq is visited, then later a state with property Rp is visited". The winner of such games can be decided in EXPTIME and the problem is known to be NP-hard. In this paper, we close this gap by showing that this problem is, in fact, EXPTIME-complete. We show that the problem becomes PSPACE-complete if we only consider games played on DAGs, and NP-complete or PTIME-complete if there is only one player (depending on whether he wants to enforce or spoil the request-response condition). We also present near-optimal bounds on the memory needed to design winning strategies for each player, in each case.

Scheduling large jobs by abstraction refinement - Henzinger, Thomas A; Singh, Vasu; Wies, Thomas; Zufferey, Damien
The static scheduling problem often arises as a fundamental problem in real-time systems and grid computing. We consider the problem of statically scheduling a large job expressed as a task graph on a large number of computing nodes, such as a data center. This paper solves the large-scale static scheduling problem using abstraction refinement, a technique commonly used in formal verification to efficiently solve computationally hard problems. A scheduler based on abstraction refinement first attempts to solve the scheduling problem with abstract representations of the job and the computing resources. As abstract representations are generally small, the scheduling can be done reasonably fast. If the obtained schedule does not meet specified quality conditions (like data center utilization or schedule makespan) then the scheduler refines the job and data center abstractions and, again solves the scheduling problem. We develop different schedulers based on abstraction refinement. We implemented these schedulers and used them to schedule task graphs from various computing domains on simulated data centers with realistic topologies. We compared the speed of scheduling and the quality of the produced schedules with our abstraction refinement schedulers against a baseline scheduler that does not use any abstraction. We conclude that abstraction refinement techniques give a significant speed-up compared to traditional static scheduling heuristics, at a reasonable cost in the quality of the produced schedules. We further used our static schedulers in an actual system that we deployed on Amazon EC2 and compared it against the Hadoop dynamic scheduler for large MapReduce jobs. Our experiments indicate that there is great potential for static scheduling techniques.

From boolean to quantitative synthesis - Cerny, Pavol; Henzinger, Thomas A
Motivated by improvements in constraint-solving technology and by the increase of routinely available computational power, partial-program synthesis is emerging as an effective approach for increasing programmer productivity. The goal of the approach is to allow the programmer to specify a part of her intent imperatively (that is, give a partial program) and a part of her intent declaratively, by specifying which conditions need to be achieved or maintained. The task of the synthesizer is to construct a program that satisfies the specification. As an example, consider a partial program where threads access shared data without using any synchronization mechanism, and a declarative specification that excludes data races and deadlocks. The task of the synthesizer is then to place locks into the program code in order for the program to meet the specification. In this paper, we argue that quantitative objectives are needed in partial-program synthesis in order to produce higher-quality programs, while enabling simpler specifications. Returning to the example, the synthesizer could construct a naive solution that uses one global lock for shared data. This can be prevented either by constraining the solution space further (which is error-prone and partly defeats the point of synthesis), or by optimizing a quantitative objective that models performance. Other quantitative notions useful in synthesis include fault tolerance, robustness, resource (memory, power) consumption, and information flow.

Growth kinetics of asymmetric Bi2S3 nanocrystals: Size distribution focusing in nanorods - Ibáñez, Maria; Guardia, Pablo; Shavel, Alexey; Cadavid, Doris; Arbiol, Jordi; Morante, Joan; Cabot, Andreu (Journal of Physical Chemistry C)
The growth kinetics of colloidal Bi2S3 nanorods was investigated. After nucleation, the length distribution of the growing Bi 2S3 nanorods narrows with the reaction time until a bimodal length distribution appears. From this critical reaction time on, the smallest nanorods of the ensemble dissolve, feeding with monomer the growth of the largest ones. A comprehensive characterization of the size-distribution evolution of Bi2S3 nanorods is used here to illustrate the dependences of the anisotropic growth rates of cylindrical nanoparticles on the nanoparticle dimensions and the monomer concentration in solution. With this goal in mind, a diffusion-reaction model is presented to explain the origin of the experimentally obtained length distribution focusing mechanism. The model is able to reproduce the decrease of the growth rate in the nanorod axial direction with both its thickness and length. On the other hand, low lateral reaction rates prevent the nanorod thickness distribution to be focused. In both crystallographic growth directions, a concentration-dependent critical thickness exists, which discriminates between nanorods with positive growth rates and those dissolving in the reaction solution.

Determinizing discounted-sum automata - Boker, Udi; Henzinger, Thomas A
A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, which values a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by lambda^i, where the discount factor lambda is a fixed rational number greater than 1. Discounted summation is a common and useful measuring scheme, especially for infinite sequences, which reflects the assumption that earlier weights are more important than later weights. Determinizing automata is often essential, for example, in formal verification, where there are polynomial algorithms for comparing two deterministic NDAs, while the equivalence problem for NDAs is not known to be decidable. Unfortunately, however, discounted-sum automata are, in general, not determinizable: it is currently known that for every rational discount factor 1 < lambda < 2, there is an NDA with lambda (denoted lambda-NDA) that cannot be determinized. We provide positive news, showing that every NDA with an integral factor is determinizable. We also complete the picture by proving that the integers characterize exactly the discount factors that guarantee determinizability: we show that for every non-integral rational factor lambda, there is a nondeterminizable lambda-NDA. Finally, we prove that the class of NDAs with integral discount factors enjoys closure under the algebraic operations min, max, addition, and subtraction, which is not the case for general NDAs nor for deterministic NDAs. This shows that for integral discount factors, the class of NDAs forms an attractive specification formalism in quantitative formal verification. All our results hold equally for automata over finite words and for automata over infinite words.

The complexity of quantitative information flow problems - Cerny, Pavol; Chatterjee, Krishnendu; Henzinger, Thomas A
In this paper, we investigate the computational complexity of quantitative information flow (QIF) problems. Information-theoretic quantitative relaxations of noninterference (based on Shannon entropy)have been introduced to enable more fine-grained reasoning about programs in situations where limited information flow is acceptable. The QIF bounding problem asks whether the information flow in a given program is bounded by a constant $d$. Our first result is that the QIF bounding problem is PSPACE-complete. The QIF memoryless synthesis problem asks whether it is possible to resolve nondeterministic choices in a given partial program in such a way that in the resulting deterministic program, the quantitative information flow is bounded by a given constant $d$. Our second result is that the QIF memoryless synthesis problem is also EXPTIME-complete. The QIF memoryless synthesis problem generalizes to QIF general synthesis problem which does not impose the memoryless requirement (that is, by allowing the synthesized program to have more variables then the original partial program). Our third result is that the QIF general synthesis problem is EXPTIME-hard.

Dynamic reactive modules - Fisher, Jasmin; Henzinger, Thomas A; Nickovic, Dejan; Piterman, Nir; Singh, Anmol; Vardi, Moshe
State-transition systems communicating by shared variables have been the underlying model of choice for applications of model checking. Such formalisms, however, have difficulty with modeling process creation or death and communication reconfigurability. Here, we introduce “dynamic reactive modules” (DRM), a state-transition modeling formalism that supports dynamic reconfiguration and creation/death of processes. The resulting formalism supports two types of variables, data variables and reference variables. Reference variables enable changing the connectivity between processes and referring to instances of processes. We show how this new formalism supports parallel composition and refinement through trace containment. DRM provide a natural language for modeling (and ultimately reasoning about) biological systems and multiple threads communicating through shared variables.

The decidability frontier for probabilistic automata on infinite words - Chatterjee, Krishnendu; Henzinger, Thomas A; Tracol, Mathieu
We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, Büchi, coBüchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present a complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words.

Approximation of event probabilities in noisy cellular processes - Didier, Frédéric; Henzinger, Thomas A; Mateescu, Maria; Wolf, Verena (Theoretical Computer Science)
Molecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Discrete-state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computationally expensive. We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required.

QUASY: quantitative synthesis tool - Chatterjee, Krishnendu; Henzinger, Thomas A; Jobstmann, Barbara; Singh, Rohit
We present the tool Quasy, a quantitative synthesis tool. Quasy takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. The user can choose between a system that satisfies and optimizes the specifications (a) under all possible environment behaviors or (b) under the most-likely environment behaviors given as a probability distribution on the possible input sequences. Quasy solves these two quantitative synthesis problems by reduction to instances of 2-player games and Markov Decision Processes (MDPs) with quantitative winning objectives. Quasy can also be seen as a game solver for quantitative games. Most notable, it can solve lexicographic mean-payoff games with 2 players, MDPs with mean-payoff objectives, and ergodic MDPs with mean-payoff parity objectives.

Quantitative synthesis for concurrent programs - Cerny, Pavol; Chatterjee, Krishnendu; Henzinger, Thomas A; Radhakrishna, Arjun; Singh, Rohit
We present an algorithmic method for the quantitative, performance-aware synthesis of concurrent programs. The input consists of a nondeterministic partial program and of a parametric performance model. The nondeterminism allows the programmer to omit which (if any) synchronization construct is used at a particular program location. The performance model, specified as a weighted automaton, can capture system architectures by assigning different costs to actions such as locking, context switching, and memory and cache accesses. The quantitative synthesis problem is to automatically resolve the nondeterminism of the partial program so that both correctness is guaranteed and performance is optimal. As is standard for shared memory concurrency, correctness is formalized "specification free", in particular as race freedom or deadlock freedom. For worst-case (average-case) performance, we show that the problem can be reduced to 2-player graph games (with probabilistic transitions) with quantitative objectives. While we show, using game-theoretic methods, that the synthesis problem is Nexp-complete, we present an algorithmic method and an implementation that works efficiently for concurrent programs and performance models of practical interest. We have implemented a prototype tool and used it to synthesize finite-state concurrent programs that exhibit different programming patterns, for several performance models representing different architectures.

An output sensitive algorithm for persistent homology - Chen, Chao; Kerber, Michael
In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ>0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0,1), the running time is O(C(1-δ)ΓR(n)log n), where C(1-δ)Γ is the number of homology classes with persistence at least (1-δ)Γ, n is the total number of simplices, and R(n) is the complexity of computing the rank of an n x n matrix with O(n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O(C(1-δ)Γn2.376) algorithm, a O(C(1-δ)Γn2.28) Las-Vegas algorithm, or a O(C(1-δ)Γn2+ε) Monte-Carlo algorithm for an arbitrary ε>0.

Enveloping cell layer differentiation at the surface of zebrafish germ layer tissue explants - Krens, Gabriel; Möllmert, Stephanie; Heisenberg, Carl-Philipp J (PNAS)
Tissue surface tension (TST) is an important mechanical property influencing cell sorting and tissue envelopment. The study by Manning et al. (1) reported on a mathematical model describing TST on the basis of the balance between adhesive and tensile properties of the constituent cells. The model predicts that, in high-adhesion cell aggregates, surface cells will be stretched to maintain the same area of cell–cell contact as interior bulk cells, resulting in an elongated and flattened cell shape. The authors (1) observed flat and elongated cells at the surface of high-adhesion zebrafish germ-layer explants, which they argue are undifferentiated stretched germ-layer progenitor cells, and they use this observation as a validation of their model.

The multiple faces of RIM - Pernia-Andrade, Alejandro; Jonas, Peter M (Neuron)
Rab3 interacting molecules (RIMs) are highly enriched in the active zones of presynaptic terminals. It is generally thought that they operate as effectors of the small G protein Rab3. Three recent papers, by Han et al. (this issue of Neuron), Deng et al. (this issue of Neuron), and Kaeser et al. (a recent issue of Cell), shed new light on the functional role of RIM in presynaptic terminals. First, RIM tethers Ca2+ channels to active zones. Second, RIM contributes to priming of synaptic vesicles by interacting with another presynaptic protein, Munc13.

Consequences of different null models on the tree shape bias of supertree methods - Kupczok, Anne (Systematic Biology)
Supertree methods are widely applied and give rise to new conclusions about phylogenies (e.g., Bininda-Emonds et al. 2007). Although several desiderata for supertree methods exist (Wilkinson, Thorley, et al. 2004), only few of them have been studied in greater detail, examples include shape bias (Wilkinson et al. 2005) or pareto properties (Wilkinson et al. 2007). Here I look more closely at two matrix representation methods, matrix representation with compatibility (MRC) and matrix representation with parsimony (MRP). Different null models of random data are studied and the resulting tree shapes are investigated. Thereby I consider unrooted trees and a bias in tree shape is determined by a tree balance measure. The measure for unrooted trees is a modification of a tree balance measure for rooted trees. I observe that depending on the underlying null model of random data, the methods may resolve conflict in favor of more balanced tree shapes. The analyses refer only to trees with the same taxon set, also known as the consensus setting (e.g., Wilkinson et al. 2007), but I will be able to draw conclusions on how to deal with missing data.

Cells on the move in Philadelphia - Sixt, Michael K; Parent, Carole (Molecular Biology and Evolution)
The Minisymposium “Cell Migration and Motility” was attended by approximately 500 visitors and covered a broad range of questions in the field using diverse model systems. Topics comprised actin dynamics, cell polarity, force transduction, signal transduction, bar- rier transmigration, and chemotactic guidance.

Inclusive fitness theory and eusociality - Abbot, Patrick; Abe, Jun; Alcock, John; Alizon, Samuel; Alpedrinha, Joao; Andersson, Malte; Andre, Jean; Van Baalen, Minus; Balloux, Francois; Balshine, Sigal; Barton, Nicholas H; Beukeboom, Leo; et al. (Nature)
Nowak et al.1 argue that inclusive fitness theory has been of little value in explaining the natural world, and that it has led to negligible progress in explaining the evolution of eusociality. However, we believe that their arguments are based upon a misunderstanding of evolutionary theory and a misrepresentation of the empirical literature. We will focus our comments on three general issues.

Measuring the complete force field of an optical trap - Jahnel, Marcus; Behrndt, Martin; Jannasch, Anita; Schaeffer, Erik; Grill, Stephan (Optics Letters)
The use of optical traps to measure or apply forces on the molecular level requires a precise knowledge of the trapping force field. Close to the trap center, this field is typically approximated as linear in the displacement of the trapped microsphere. However, applications demanding high forces at low laser intensities can probe the light-microsphere interaction beyond the linear regime. Here, we measured the full nonlinear force and displacement response of an optical trap in two dimensions using a dual-beam optical trap setup with back-focal-plane photodetection. We observed a substantial stiffening of the trap beyond the linear regime that depends on microsphere size, in agreement with Mie theory calculations. Surprisingly, we found that the linear detection range for forces exceeds the one for displacement by far. Our approach allows for a complete calibration of an optical trap.

Information transmission in genetic regulatory networks a review - Tkacik, Gasper; Walczak, Aleksandra (Journal of Physics: Condensed Matter)
Genetic regulatory networks enable cells to respond to changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits has deepened our understanding of what kinds of computations genetic regulatory networks can perform, and with what reliability. These advances have motivated researchers to look for connections between the architecture and function of genetic regulatory networks. Transmitting information between a network's inputs and outputs has been proposed as one such possible measure of function, relevant in certain biological contexts. Here we summarize recent developments in the application of information theory to gene regulatory networks. We first review basic concepts in information theory necessary for understanding recent work. We then discuss the functional complexity of gene regulation, which arises from the molecular nature of the regulatory interactions. We end by reviewing some experiments that support the view that genetic networks responsible for early development of multicellular organisms might be maximizing transmitted 'positional information'.

The statistical mechanics of a polygenic character under stabilizing selection mutation and drift - de Vladar, Harold; Barton, Nicholas H (Journal of the Royal Society Interface)
By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as five loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.