5,518 research outputs found
Metric characterization of cluster dynamics on the Sierpinski gasket
We develop and implement an algorithm for the quantitative characterization
of cluster dynamics occurring on cellular automata defined on an arbitrary
structure. As a prototype for such systems we focus on the Ising model on a
finite Sierpsinski Gasket, which is known to possess a complex thermodynamic
behavior. Our algorithm requires the projection of evolving configurations into
an appropriate partition space, where an information-based metrics (Rohlin
distance) can be naturally defined and worked out in order to detect the
changing and the stable components of clusters. The analysis highlights the
existence of different temperature regimes according to the size and the rate
of change of clusters. Such regimes are, in turn, related to the correlation
length and the emerging "critical" fluctuations, in agreement with previous
thermodynamic analysis, hence providing a non-trivial geometric description of
the peculiar critical-like behavior exhibited by the system. Moreover, at high
temperatures, we highlight the existence of different time scales controlling
the evolution towards chaos.Comment: 20 pages, 8 figure
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Secure state estimation against sensor attacks in the presence of noise
We consider the problem of estimating the state of a noisy linear dynamical system when an unknown subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm, and derive (optimal) bounds on the achievable state estimation error given an upper bound on the number of attacked sensors. The proposed state estimator involves Kalman filters operating over subsets of sensors to search for a sensor subset which is reliable for state estimation. To further improve the subset search time, we propose Satisfiability Modulo Theory-based techniques to exploit the combinatorial nature of searching over sensor subsets. Finally, as a result of independent interest, we give a coding theoretic view of attack detection and state estimation against sensor attacks in a noiseless dynamical system
Learning and Testing Variable Partitions
Let be a multivariate function from a product set to an
Abelian group . A -partition of with cost is a partition of
the set of variables into non-empty subsets such that is -close to
for some with
respect to a given error metric. We study algorithms for agnostically learning
partitions and testing -partitionability over various groups and error
metrics given query access to . In particular we show that
Given a function that has a -partition of cost , a partition
of cost can be learned in time
for any .
In contrast, for and learning a partition of cost is NP-hard.
When is real-valued and the error metric is the 2-norm, a
2-partition of cost can be learned in time
.
When is -valued and the error metric is Hamming
weight, -partitionability is testable with one-sided error and
non-adaptive queries. We also show that even
two-sided testers require queries when .
This work was motivated by reinforcement learning control tasks in which the
set of control variables can be partitioned. The partitioning reduces the task
into multiple lower-dimensional ones that are relatively easier to learn. Our
second algorithm empirically increases the scores attained over previous
heuristic partitioning methods applied in this context.Comment: Innovations in Theoretical Computer Science (ITCS) 202
Covariate assisted screening and estimation
Consider a linear model , where and .
The vector is unknown but is sparse in the sense that most of its
coordinates are . The main interest is to separate its nonzero coordinates
from the zero ones (i.e., variable selection). Motivated by examples in
long-memory time series (Fan and Yao [Nonlinear Time Series: Nonparametric and
Parametric Methods (2003) Springer]) and the change-point problem (Bhattacharya
[In Change-Point Problems (South Hadley, MA, 1992) (1994) 28-56 IMS]), we are
primarily interested in the case where the Gram matrix is nonsparse but
sparsifiable by a finite order linear filter. We focus on the regime where
signals are both rare and weak so that successful variable selection is very
challenging but is still possible. We approach this problem by a new procedure
called the covariate assisted screening and estimation (CASE). CASE first uses
a linear filtering to reduce the original setting to a new regression model
where the corresponding Gram (covariance) matrix is sparse. The new covariance
matrix induces a sparse graph, which guides us to conduct multivariate
screening without visiting all the submodels. By interacting with the signal
sparsity, the graph enables us to decompose the original problem into many
separated small-size subproblems (if only we know where they are!). Linear
filtering also induces a so-called problem of information leakage, which can be
overcome by the newly introduced patching technique. Together, these give rise
to CASE, which is a two-stage screen and clean [Fan and Song Ann. Statist. 38
(2010) 3567-3604; Wasserman and Roeder Ann. Statist. 37 (2009) 2178-2201]
procedure, where we first identify candidates of these submodels by patching
and screening, and then re-examine each candidate to remove false positives.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1243 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Properties of interaction networks underlying the minority game
The minority game is a well-known agent-based model with no explicit interaction among its agents. However, it is known that they interact through the global magnitudes of the model and through their strategies. In this work we have attempted to formalize the implicit interactions among minority game agents as if they were links on a complex network. We have defined the link between two agents by quantifying the similarity between them. This link definition is based on the information of the instance of the game (the set of strategies assigned to each agent at the beginning) without any dynamic information on the game and brings about a static, unweighed and undirected network. We have analyzed the structure of the resulting network for different parameters, such as the number of agents ( N ) and the agent's capacity to process information ( m ) , always taking into account games with two strategies per agent. In the region of crowd effects of the model, the resulting networks structure is a small-world network, whereas in the region where the behavior of the minority game is the same as in a game of random decisions, networks become a random network of Erdos-Renyi. The transition between these two types of networks is slow, without any peculiar feature of the network in the region of the coordination among agents. Finally, we have studied the resulting static networks for the full strategy minority game model, a maximal instance of the minority game in which all possible agents take part in the game. We have explicitly calculated the degree distribution of the full strategy minority game network and, on the basis of this analytical result, we have estimated the degree distribution of the minority game network, which is in accordance with computational results.Fil: Caridi, Délida Inés. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Exploring the effect of sex on empirical fitness landscapes
The nature of epistasis has important consequences for the evolutionary significance of sex and recombination. Recent efforts to find negative epistasis as a source of negative linkage disequilibrium and associated long-term advantage to sex have yielded little support. Sign epistasis, where the sign of the fitness effects of alleles varies across genetic backgrounds, is responsible for the ruggedness of the fitness landscape, with several unexplored implications for the evolution of sex. Here, we describe fitness landscapes for two sets of strains of the asexual fungus Aspergillus niger involving all combinations of five mutations. We find that 30% of the single-mutation fitness effects are positive despite their negative effect in the wild-type strain and that several local fitness maxima and minima are present. We then compare adaptation of sexual and asexual populations on these empirical fitness landscapes by using simulations. The results show a general disadvantage of sex on these rugged landscapes, caused by the breakdown by recombination of genotypes on fitness peaks. Sex facilitates movement to the global peak only for some parameter values on one landscape, indicating its dependence on the landscape’s topography. We discuss possible reasons for the discrepancy between our results and the reports of faster adaptation of sexual population
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