758 research outputs found
Optimal Location of Sources in Transportation Networks
We consider the problem of optimizing the locations of source nodes in
transportation networks. A reduction of the fraction of surplus nodes induces a
glassy transition. In contrast to most constraint satisfaction problems
involving discrete variables, our problem involves continuous variables which
lead to cavity fields in the form of functions. The one-step replica symmetry
breaking (1RSB) solution involves solving a stable distribution of functionals,
which is in general infeasible. In this paper, we obtain small closed sets of
functional cavity fields and demonstrate how functional recursions are
converted to simple recursions of probabilities, which make the 1RSB solution
feasible. The physical results in the replica symmetric (RS) and the 1RSB
frameworks are thus derived and the stability of the RS and 1RSB solutions are
examined.Comment: 38 pages, 18 figure
Computational core and fixed-point organisation in Boolean networks
In this paper, we analyse large random Boolean networks in terms of a
constraint satisfaction problem. We first develop an algorithmic scheme which
allows to prune simple logical cascades and under-determined variables,
returning thereby the computational core of the network. Second we apply the
cavity method to analyse number and organisation of fixed points. We find in
particular a phase transition between an easy and a complex regulatory phase,
the latter one being characterised by the existence of an exponential number of
macroscopically separated fixed-point clusters. The different techniques
developed are reinterpreted as algorithms for the analysis of single Boolean
networks, and they are applied to analysis and in silico experiments on the
gene-regulatory networks of baker's yeast (saccaromices cerevisiae) and the
segment-polarity genes of the fruit-fly drosophila melanogaster.Comment: 29 pages, 18 figures, version accepted for publication in JSTA
Message Passing for Optimization and Control of Power Grid: Model of Distribution System with Redundancy
We use a power grid model with generators and consumption units to
optimize the grid and its control. Each consumer demand is drawn from a
predefined finite-size-support distribution, thus simulating the instantaneous
load fluctuations. Each generator has a maximum power capability. A generator
is not overloaded if the sum of the loads of consumers connected to a generator
does not exceed its maximum production. In the standard grid each consumer is
connected only to its designated generator, while we consider a more general
organization of the grid allowing each consumer to select one generator
depending on the load from a pre-defined consumer-dependent and sufficiently
small set of generators which can all serve the load. The model grid is
interconnected in a graph with loops, drawn from an ensemble of random
bipartite graphs, while each allowed configuration of loaded links represent a
set of graph covering trees. Losses, the reactive character of the grid and the
transmission-level connections between generators (and many other details
relevant to realistic power grid) are ignored in this proof-of-principles
study. We focus on the asymptotic limit and we show that the interconnects
allow significant expansion of the parameter domains for which the probability
of a generator overload is asymptotically zero. Our construction explores the
formal relation between the problem of grid optimization and the modern theory
of sparse graphical models. We also design heuristic algorithms that achieve
the asymptotically optimal selection of loaded links. We conclude discussing
the ability of this approach to include other effects, such as a more realistic
modeling of the power grid and related optimization and control algorithms.Comment: 10 page
Inference in particle tracking experiments by passing messages between images
Methods to extract information from the tracking of mobile objects/particles
have broad interest in biological and physical sciences. Techniques based on
simple criteria of proximity in time-consecutive snapshots are useful to
identify the trajectories of the particles. However, they become problematic as
the motility and/or the density of the particles increases due to uncertainties
on the trajectories that particles followed during the images' acquisition
time. Here, we report an efficient method for learning parameters of the
dynamics of the particles from their positions in time-consecutive images. Our
algorithm belongs to the class of message-passing algorithms, known in computer
science, information theory and statistical physics as Belief Propagation (BP).
The algorithm is distributed, thus allowing parallel implementation suitable
for computations on multiple machines without significant inter-machine
overhead. We test our method on the model example of particle tracking in
turbulent flows, which is particularly challenging due to the strong transport
that those flows produce. Our numerical experiments show that the BP algorithm
compares in quality with exact Markov Chain Monte-Carlo algorithms, yet BP is
far superior in speed. We also suggest and analyze a random-distance model that
provides theoretical justification for BP accuracy. Methods developed here
systematically formulate the problem of particle tracking and provide fast and
reliable tools for its extensive range of applications.Comment: 18 pages, 9 figure
Optimization hardness as transient chaos in an analog approach to constraint satisfaction
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization
problems, as an efficient (that is, polynomial-time) solution to k-SAT (for
) implies efficient solutions to a large number of hard optimization
problems [2,3]. Here we propose a mapping of k-SAT into a deterministic
continuous-time dynamical system with a unique correspondence between its
attractors and the k-SAT solution clusters. We show that beyond a constraint
density threshold, the analog trajectories become transiently chaotic [4-7],
and the boundaries between the basins of attraction [8] of the solution
clusters become fractal [7-9], signaling the appearance of optimization
hardness [10]. Analytical arguments and simulations indicate that the system
always finds solutions for satisfiable formulae even in the frozen regimes of
random 3-SAT [11] and of locked occupation problems [12] (considered among the
hardest algorithmic benchmarks); a property partly due to the system's
hyperbolic [4,13] character. The system finds solutions in polynomial
continuous-time, however, at the expense of exponential fluctuations in its
energy function.Comment: 27 pages, 14 figure
Bootstrap methods for the empirical study of decision-making and information flows in social systems
Abstract: We characterize the statistical bootstrap for the estimation of information theoretic quantities from data, with particular reference to its use in the study of large-scale social phenomena. Our methods allow one to preserve, approximately, the underlying axiomatic relationships of information theoryâin particular, consistency under arbitrary coarse-grainingâthat motivate use of these quantities in the first place, while providing reliability comparable to the state of the art for Bayesian estimators. We show how information-theoretic quantities allow for rigorous empirical study of the decision-making capacities of rational agents, and the time-asymmetric flows of information in distributed systems. We provide illustrative examples by reference to ongoing collaborative work on the semantic structure of the British Criminal Court system and the conflict dynamics of the contemporary Afghanistan insurgency
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