Using Strategy Improvement to Stay Alive

We design a novel algorithm for solving Mean-Payoff Games (MPGs). Besides solving an MPG in the usual sense, our algorithm computes more information about the game, information that is important with respect to applications. The weights of the edges of an MPG can be thought of as a gained/consumed energy -- depending on the sign. For each vertex, our algorithm computes the minimum amount of initial energy that is sufficient for player Max to ensure that in a play starting from the vertex, the energy level never goes below zero. Our algorithm is not the first algorithm that computes the minimum sufficient initial energies, but according to our experimental study it is the fastest algorithm that computes them. The reason is that it utilizes the strategy improvement technique which is very efficient in practice

Critical slowing down in polynomial time algorithms

Combinatorial optimization algorithms which compute exact ground state configurations in disordered magnets are seen to exhibit critical slowing down at zero temperature phase transitions. Using arguments based on the physical picture of the model, including vanishing stiffness on scales beyond the correlation length and the ground state degeneracy, the number of operations carried out by one such algorithm, the push-relabel algorithm for the random field Ising model, can be estimated. Some scaling can also be predicted for the 2D spin glass.Comment: 4 pp., 3 fig

Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

Anomalous electrical and frictionless flow conductance in complex networks

We study transport properties such as electrical and frictionless flow conductance on scale-free and Erdos-Renyi networks. We consider the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G, with a power-law tail distribution \Phi_{SF}(G) \sim G^{g_G}, where g_G = 2\lambda - 1, where \lambda is the decay exponent for the scale-free network degree distribution. We confirm our predictions by simulations of scale-free networks solving the Kirchhoff equations for the conductance between a pair of nodes. The power-law tail in \Phi_{SF}(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erdos-Renyi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical 'transport backbone' picture we suggest that the conductances of scale-free and Erdos-Renyi networks can be approximated by ck_Ak_B/(k_A+k_B) for any pair of nodes A and B with degrees k_A and k_B. Thus, a single quantity c, which depends on the average degree of the network, characterizes transport on both scale-free and Erdos-Renyi networks. We determine that c tends to 1 for increasing , and it is larger for scale-free networks. We compare the electrical results with a model for frictionless transport, where conductance is defined as the number of link-independent paths between A and B, and find that a similar picture holds. The effects of distance on the value of conductance are considered for both models, and some differences emerge. Finally, we use a recent data set for the AS (autonomous system) level of the Internet and confirm that our results are valid in this real-world example.Comment: 8 pages, 11 figure

Innovative Approach to Learning in the Disciplines of the «Circle of MSC»

Настоящая статья посвящена вопросам и проблемам инновационного подхода к обучению по дисциплинам «круга МСС».This article is devoted to the issues and problems of an innovative approach to teaching in the disciplines of the «circle of MSС»

Simulation of the Zero Temperature Behavior of a 3-Dimensional Elastic Medium

We have performed numerical simulation of a 3-dimensional elastic medium, with scalar displacements, subject to quenched disorder. We applied an efficient combinatorial optimization algorithm to generate exact ground states for an interface representation. Our results indicate that this Bragg glass is characterized by power law divergences in the structure factor $S(k)\sim A k^{-3}$. We have found numerically consistent values of the coefficient $A$ for two lattice discretizations of the medium, supporting universality for $A$ in the isotropic systems considered here. We also examine the response of the ground state to the change in boundary conditions that corresponds to introducing a single dislocation loop encircling the system. Our results indicate that the domain walls formed by this change are highly convoluted, with a fractal dimension $d_f=2.60(5)$. We also discuss the implications of the domain wall energetics for the stability of the Bragg glass phase. As in other disordered systems, perturbations of relative strength $\delta$ introduce a new length scale $L^* \sim \delta^{-1/\zeta}$ beyond which the perturbed ground state becomes uncorrelated with the reference (unperturbed) ground state. We have performed scaling analysis of the response of the ground state to the perturbations and obtain $\zeta = 0.385(40)$. This value is consistent with the scaling relation $\zeta=d_f/2- \theta$, where $\theta$ characterizes the scaling of the energy fluctuations of low energy excitations.Comment: 20 pages, 13 figure

Variations on the Stochastic Shortest Path Problem

In this invited contribution, we revisit the stochastic shortest path problem, and show how recent results allow one to improve over the classical solutions: we present algorithms to synthesize strategies with multiple guarantees on the distribution of the length of paths reaching a given target, rather than simply minimizing its expected value. The concepts and algorithms that we propose here are applications of more general results that have been obtained recently for Markov decision processes and that are described in a series of recent papers.Comment: Invited paper for VMCAI 201

Cognitive Information Processing

Contains reports on three research projects.Center for Advanced Television StudiesAmerican Broadcasting CompanyAmpex CorporationColumbia Broadcasting Systems (until 5/86)Harris Corporation (until 5/86)Home Box OfficeKodak (from 1/87)Public Broadcasting ServiceNational Broadcasting CompanyRCA CorporationTektronixZenith (from 5/86)3M Company (until 5/86)International Business Machines, Inc.Defense Advanced Research Agency (Contract N00014-85-K-0213

Neural networks impedance control of robots interacting with environments

In this paper, neural networks impedance control is proposed for robot-environment interaction. Iterative learning control is developed to make the robot dynamics follow a given target impedance model. To cope with the problem of unknown robot dynamics, neural networks are employed such that neither the robot structure nor the physical parameters are required for the control design. The stability and performance of the resulted closed-loop system are discussed through rigorous analysis and extensive remarks. The validity and feasibility of the proposed method are verified through simulation studies

Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations

Exact ground states of three-dimensional random field Ising magnets (RFIM) with Gaussian distribution of the disorder are calculated using graph-theoretical algorithms. Systems for different strengths h of the random fields and sizes up to N=96^3 are considered. By numerically differentiating the bond-energy with respect to h a specific-heat like quantity is obtained, which does not appear to diverge at the critical point but rather exhibits a cusp. We also consider the effect of a small uniform magnetic field, which allows us to calculate the T=0 susceptibility. From a finite-size scaling analysis, we obtain the critical exponents \nu=1.32(7), \alpha=-0.63(7), \eta=0.50(3) and find that the critical strength of the random field is h_c=2.28(1). We discuss the significance of the result that \alpha appears to be strongly negative.Comment: 9 pages, 9 figures, 1 table, revtex revised version, slightly extende