Zero-Reachability in Probabilistic Multi-Counter Automata

We study the qualitative and quantitative zero-reachability problem in probabilistic multi-counter systems. We identify the undecidable variants of the problems, and then we concentrate on the remaining two cases. In the first case, when we are interested in the probability of all runs that visit zero in some counter, we show that the qualitative zero-reachability is decidable in time which is polynomial in the size of a given pMC and doubly exponential in the number of counters. Further, we show that the probability of all zero-reaching runs can be effectively approximated up to an arbitrarily small given error epsilon > 0 in time which is polynomial in log(epsilon), exponential in the size of a given pMC, and doubly exponential in the number of counters. In the second case, we are interested in the probability of all runs that visit zero in some counter different from the last counter. Here we show that the qualitative zero-reachability is decidable and SquareRootSum-hard, and the probability of all zero-reaching runs can be effectively approximated up to an arbitrarily small given error epsilon > 0 (these result applies to pMC satisfying a suitable technical condition that can be verified in polynomial time). The proof techniques invented in the second case allow to construct counterexamples for some classical results about ergodicity in stochastic Petri nets.Comment: 20 page

Micromagnetic understanding of stochastic resonance driven by spin-transfertorque

In this paper, we employ micromagnetic simulations to study non-adiabatic stochastic resonance (NASR) excited by spin-transfer torque in a super-paramagnetic free layer nanomagnet of a nanoscale spin valve. We find that NASR dynamics involves thermally activated transitions among two static states and a single dynamic state of the nanomagnet and can be well understood in the framework of Markov chain rate theory. Our simulations show that a direct voltage generated by the spin valve at the NASR frequency is at least one order of magnitude greater than the dc voltage generated off the NASR frequency. Our computations also reproduce the main experimentally observed features of NASR such as the resonance frequency, the temperature dependence and the current bias dependence of the resonance amplitude. We propose a simple design of a microwave signal detector based on NASR driven by spin transfer torque.Comment: 25 pages 8 figures, accepted for pubblication on Phys. Rev.

Link Prediction Based on Local Random Walk

The problem of missing link prediction in complex networks has attracted much attention recently. Two difficulties in link prediction are the sparsity and huge size of the target networks. Therefore, the design of an efficient and effective method is of both theoretical interests and practical significance. In this Letter, we proposed a method based on local random walk, which can give competitively good prediction or even better prediction than other random-walk-based methods while has a lower computational complexity.Comment: 6 pages, 2 figure

Quantitative multi-objective verification for probabilistic systems

We present a verification framework for analysing multiple quantitative objectives of systems that exhibit both nondeterministic and stochastic behaviour. These systems are modelled as probabilistic automata, enriched with cost or reward structures that capture, for example, energy usage or performance metrics. Quantitative properties of these models are expressed in a specification language that incorporates probabilistic safety and liveness properties, expected total cost or reward, and supports multiple objectives of these types. We propose and implement an efficient verification framework for such properties and then present two distinct applications of it: firstly, controller synthesis subject to multiple quantitative objectives; and, secondly, quantitative compositional verification. The practical applicability of both approaches is illustrated with experimental results from several large case studies

Long-Range Navigation on Complex Networks using L\'evy Random Walks

We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by L\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary probability distribution, the occupation probability, the mean first passage time, and the average time to reach a node on the network. We found that the long-range navigation using the L\'evy random walk strategy, compared with the normal random walk strategy, is more efficient at reducing the time to cover the network. The dynamical effect of using the L\'evy walk strategy is to transform a large-world network into a small world. Our exact results provide a general framework that connects two important fields: L\'evy navigation strategies and dynamics on complex networks.Comment: 6 pages, 3 figure

An Inverse Method for Policy-Iteration Based Algorithms

We present an extension of two policy-iteration based algorithms on weighted graphs (viz., Markov Decision Problems and Max-Plus Algebras). This extension allows us to solve the following inverse problem: considering the weights of the graph to be unknown constants or parameters, we suppose that a reference instantiation of those weights is given, and we aim at computing a constraint on the parameters under which an optimal policy for the reference instantiation is still optimal. The original algorithm is thus guaranteed to behave well around the reference instantiation, which provides us with some criteria of robustness. We present an application of both methods to simple examples. A prototype implementation has been done

Typical properties of optimal growth in the Von Neumann expanding model for large random economies

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$. This model provides an elementary description of the growth of a production economy in the long run. The system turns from a contracting to an expanding phase as $N$ increases beyond $P$. The solution is characterized by a universal behavior, independent of the parameters of the disorder statistics. Associating technological innovation to an increase of $N$, we find that while such an increase has a large positive impact on long term growth when $N\ll P$, its effect on technologically advanced economies ($N\gg P$) is very weak.Comment: 8 pages, 1 figur

A point process framework for modeling electrical stimulation of the auditory nerve

Model-based studies of auditory nerve responses to electrical stimulation can provide insight into the functioning of cochlear implants. Ideally, these studies can identify limitations in sound processing strategies and lead to improved methods for providing sound information to cochlear implant users. To accomplish this, models must accurately describe auditory nerve spiking while avoiding excessive complexity that would preclude large-scale simulations of populations of auditory nerve fibers and obscure insight into the mechanisms that influence neural encoding of sound information. In this spirit, we develop a point process model of the auditory nerve that provides a compact and accurate description of neural responses to electric stimulation. Inspired by the framework of generalized linear models, the proposed model consists of a cascade of linear and nonlinear stages. We show how each of these stages can be associated with biophysical mechanisms and related to models of neuronal dynamics. Moreover, we derive a semi-analytical procedure that uniquely determines each parameter in the model on the basis of fundamental statistics from recordings of single fiber responses to electric stimulation, including threshold, relative spread, jitter, and chronaxie. The model also accounts for refractory and summation effects that influence the responses of auditory nerve fibers to high pulse rate stimulation. Throughout, we compare model predictions to published physiological data and explain differences in auditory nerve responses to high and low pulse rate stimulation. We close by performing an ideal observer analysis of simulated spike trains in response to sinusoidally amplitude modulated stimuli and find that carrier pulse rate does not affect modulation detection thresholds.Comment: 1 title page, 27 manuscript pages, 14 figures, 1 table, 1 appendi

Maximum principle and mutation thresholds for four-letter sequence evolution

A four-state mutation-selection model for the evolution of populations of DNA-sequences is investigated with particular interest in the phenomenon of error thresholds. The mutation model considered is the Kimura 3ST mutation scheme, fitness functions, which determine the selection process, come from the permutation-invariant class. Error thresholds can be found for various fitness functions, the phase diagrams are more interesting than for equivalent two-state models. Results for (small) finite sequence lengths are compared with those for infinite sequence length, obtained via a maximum principle that is equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 figure

Projected single-spin flip dynamics in the Ising Model

We study transition matrices for projected dynamics in the energy-magnetization space, magnetization space and energy space. Several single spin flip dynamics are considered such as the Glauber and Metropolis canonical ensemble dynamics and the Metropolis dynamics for three multicanonical ensembles: the flat energy-magnetization histogram, the flat energy histogram and the flat magnetization histogram. From the numerical diagonalization of the matrices for the projected dynamics we obtain the sub-dominant eigenvalue and the largest relaxation times for systems of varying size. Although, the projected dynamics is an approximation to the full state space dynamics comparison with some available results, obtained by other authors, shows that projection in the magnetization space is a reasonably accurate method to study the scaling of relaxation times with system size. The transition matrices for arbitrary single-spin flip dynamics are obtained from a single Monte-Carlo estimate of the infinite temperature transition-matrix, for each system size, which makes the method an efficient tool to evaluate the relative performance of any arbitrary local spin-flip dynamics. We also present new results for appropriately defined average tunnelling times of magnetization and compute their finite-size scaling exponents that we compare with results of energy tunnelling exponents available for the flat energy histogram multicanonical ensemble.Comment: 23 pages and 6 figure