412 research outputs found
On some properties of the semigroup of a machine which are preserved under state minimization
Some results on special types of semigroups of transformations of a set (including permutation groups) are developed and combined with the fundamental results of Paull and Unger on state minimization of incompletely specified sequential machines to obtain some properties of the transformation semigroup of such a machine which are preserved in all minimum state machines (strong preservation), or in at least one (weak preservation) minimum state machine. The principal results are that for permutation machines (those whose states are permuted by every input) there is strong preservation and for simple machines (those whose semigroups have no proper ideals) there is weak preservation. A number of further properties of permutation machines in the satisfaction and minimum state relations are developed
Effective Theories for Circuits and Automata
Abstracting an effective theory from a complicated process is central to the
study of complexity. Even when the underlying mechanisms are understood, or at
least measurable, the presence of dissipation and irreversibility in
biological, computational and social systems makes the problem harder. Here we
demonstrate the construction of effective theories in the presence of both
irreversibility and noise, in a dynamical model with underlying feedback. We
use the Krohn-Rhodes theorem to show how the composition of underlying
mechanisms can lead to innovations in the emergent effective theory. We show
how dissipation and irreversibility fundamentally limit the lifetimes of these
emergent structures, even though, on short timescales, the group properties may
be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure
Preliminary Concepts for Economic Systems Analysis
In preparing theoretical tools to analyze economic systems we need several fundamental concepts that are often applied in various scientific investigations outside economic studies. Amongst others, the concept of autopoiesis, which was introduced by Niklas Luhmann into his sociological systems theory, is the most important in constructing a theoretical model to explain the working of economic systems. An autopoietic system may be regarded as the functional core by which other elementary concepts such as homeostasis, machinery, corporate system and social entropy can be logically connected. In conclusion, all economic systems are contained in distinct social systems of autopoietic character and incorporated with them as a subsystem or partially independent system.system, autopoiesis
Total variation denoising in anisotropy
We aim at constructing solutions to the minimizing problem for the variant of
Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the
gradient flow of its underlying anisotropic total variation functional. We
consider a naturally defined class of functions piecewise constant on
rectangles (PCR). This class forms a strictly dense subset of the space of
functions of bounded variation with an anisotropic norm. The main result shows
that if the given noisy image is a PCR function, then solutions to both
considered problems also have this property. For PCR data the problem of
finding the solution is reduced to a finite algorithm. We discuss some
implications of this result, for instance we use it to prove that continuity is
preserved by both considered problems.Comment: 34 pages, 9 figure
Local Causal States and Discrete Coherent Structures
Coherent structures form spontaneously in nonlinear spatiotemporal systems
and are found at all spatial scales in natural phenomena from laboratory
hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary
climate dynamics. Phenomenologically, they appear as key components that
organize the macroscopic behaviors in such systems. Despite a century of
effort, they have eluded rigorous analysis and empirical prediction, with
progress being made only recently. As a step in this, we present a formal
theory of coherent structures in fully-discrete dynamical field theories. It
builds on the notion of structure introduced by computational mechanics,
generalizing it to a local spatiotemporal setting. The analysis' main tool
employs the \localstates, which are used to uncover a system's hidden
spatiotemporal symmetries and which identify coherent structures as
spatially-localized deviations from those symmetries. The approach is
behavior-driven in the sense that it does not rely on directly analyzing
spatiotemporal equations of motion, rather it considers only the spatiotemporal
fields a system generates. As such, it offers an unsupervised approach to
discover and describe coherent structures. We illustrate the approach by
analyzing coherent structures generated by elementary cellular automata,
comparing the results with an earlier, dynamic-invariant-set approach that
decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht
Controlled Sequential Monte Carlo
Sequential Monte Carlo methods, also known as particle methods, are a popular
set of techniques for approximating high-dimensional probability distributions
and their normalizing constants. These methods have found numerous applications
in statistics and related fields; e.g. for inference in non-linear non-Gaussian
state space models, and in complex static models. Like many Monte Carlo
sampling schemes, they rely on proposal distributions which crucially impact
their performance. We introduce here a class of controlled sequential Monte
Carlo algorithms, where the proposal distributions are determined by
approximating the solution to an associated optimal control problem using an
iterative scheme. This method builds upon a number of existing algorithms in
econometrics, physics, and statistics for inference in state space models, and
generalizes these methods so as to accommodate complex static models. We
provide a theoretical analysis concerning the fluctuation and stability of this
methodology that also provides insight into the properties of related
algorithms. We demonstrate significant gains over state-of-the-art methods at a
fixed computational complexity on a variety of applications
Hierarchical coordinate systems for understanding complexity and its evolution with applications to genetic regulatory networks
Original article can be found at : http://www.mitpressjournals.org/ Copyright MIT PressBeyond complexity measures, sometimes it is worth in addition investigating how complexity changes structurally, especially in artificial systems where we have complete knowledge about the evolutionary process. Hierarchical decomposition is a useful way of assessing structural complexity changes of organisms modeled as automata, and we show how recently developed computational tools can be used for this purpose, by computing holonomy decompositions and holonomy complexity. To gain insight into the evolution of complexity, we investigate the smoothness of the landscape structure of complexity under minimal transitions. As a proof of concept, we illustrate how the hierarchical complexity analysis reveals symmetries and irreversible structure in biological networks by applying the methods to the lac operon mechanism in the genetic regulatory network of Escherichia coli.Peer reviewe
Higher-order Projected Power Iterations for Scalable Multi-Matching
The matching of multiple objects (e.g. shapes or images) is a fundamental
problem in vision and graphics. In order to robustly handle ambiguities, noise
and repetitive patterns in challenging real-world settings, it is essential to
take geometric consistency between points into account. Computationally, the
multi-matching problem is difficult. It can be phrased as simultaneously
solving multiple (NP-hard) quadratic assignment problems (QAPs) that are
coupled via cycle-consistency constraints. The main limitations of existing
multi-matching methods are that they either ignore geometric consistency and
thus have limited robustness, or they are restricted to small-scale problems
due to their (relatively) high computational cost. We address these
shortcomings by introducing a Higher-order Projected Power Iteration method,
which is (i) efficient and scales to tens of thousands of points, (ii)
straightforward to implement, (iii) able to incorporate geometric consistency,
(iv) guarantees cycle-consistent multi-matchings, and (iv) comes with
theoretical convergence guarantees. Experimentally we show that our approach is
superior to existing methods
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