4,004 research outputs found

    Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation

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    In this paper we provide rigorous proof for the convergence of an iterative voting-based image segmentation algorithm called Active Masks. Active Masks (AM) was proposed to solve the challenging task of delineating punctate patterns of cells from fluorescence microscope images. Each iteration of AM consists of a linear convolution composed with a nonlinear thresholding; what makes this process special in our case is the presence of additive terms whose role is to "skew" the voting when prior information is available. In real-world implementation, the AM algorithm always converges to a fixed point. We study the behavior of AM rigorously and present a proof of this convergence. The key idea is to formulate AM as a generalized (parallel) majority cellular automaton, adapting proof techniques from discrete dynamical systems

    The identification of cellular automata

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    Although cellular automata have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the CA rules given observations of the patterns. A solution using a polynomial realization to describe the CA rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the complexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of hybrid CA is introduced

    Generalised additive multiscale wavelet models constructed using particle swarm optimisation and mutual information for spatio-temporal evolutionary system representation

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    A new class of generalised additive multiscale wavelet models (GAMWMs) is introduced for high dimensional spatio-temporal evolutionary (STE) system identification. A novel two-stage hybrid learning scheme is developed for constructing such an additive wavelet model. In the first stage, a new orthogonal projection pursuit (OPP) method, implemented using a particle swarm optimisation(PSO) algorithm, is proposed for successively augmenting an initial coarse wavelet model, where relevant parameters of the associated wavelets are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be a redundant model. In the second stage, a forward orthogonal regression (FOR) algorithm, implemented using a mutual information method, is then applied to refine and improve the initially constructed wavelet model. The proposed two-stage hybrid method can generally produce a parsimonious wavelet model, where a ranked list of wavelet functions, according to the capability of each wavelet to represent the total variance in the desired system output signal is produced. The proposed new modelling framework is applied to real observed images, relative to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, and the associated identification results show that the new modelling framework is applicable and effective for handling high dimensional identification problems of spatio-temporal evolution sytems

    Complex network statistics to the design of fire breaks for the control of fire spreading

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    A computational approach for identifying efficient fuel breaks partitions for the containment of fire incidents in forests is proposed. The approach is based on the complex networks statistics, namely the centrality measures and cellular automata modeling. The efficiency of various centrality statistics, such as betweenness, closeness, Bonacich and eigenvalue centrality to select fuel breaks partitions vs. the random-based distribution is demonstrated. Two examples of increasing complexity are considered: (a) an artificial forest of randomly distributed density of vegetation, and (b) a patch from the area of Vesuvio, National Park of Campania, Italy. Both cases assume flat terrain and single type of vegetation. Simulation results over an ensemble of lattice realizations and runs show that the proposed approach appears very promising as it produces statistically significant better outcomes when compared to the random distribution approach

    Convergence Thresholds of Newton's Method for Monotone Polynomial Equations

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    Monotone systems of polynomial equations (MSPEs) are systems of fixed-point equations X1=f1(X1,...,Xn),X_1 = f_1(X_1, ..., X_n), ...,Xn=fn(X1,...,Xn)..., X_n = f_n(X_1, ..., X_n) where each fif_i is a polynomial with positive real coefficients. The question of computing the least non-negative solution of a given MSPE X⃗=f⃗(X⃗)\vec X = \vec f(\vec X) arises naturally in the analysis of stochastic models such as stochastic context-free grammars, probabilistic pushdown automata, and back-button processes. Etessami and Yannakakis have recently adapted Newton's iterative method to MSPEs. In a previous paper we have proved the existence of a threshold kf⃗k_{\vec f} for strongly connected MSPEs, such that after kf⃗k_{\vec f} iterations of Newton's method each new iteration computes at least 1 new bit of the solution. However, the proof was purely existential. In this paper we give an upper bound for kf⃗k_{\vec f} as a function of the minimal component of the least fixed-point μf⃗\mu\vec f of f⃗(X⃗)\vec f(\vec X). Using this result we show that kf⃗k_{\vec f} is at most single exponential resp. linear for strongly connected MSPEs derived from probabilistic pushdown automata resp. from back-button processes. Further, we prove the existence of a threshold for arbitrary MSPEs after which each new iteration computes at least 1/w2h1/w2^h new bits of the solution, where ww and hh are the width and height of the DAG of strongly connected components.Comment: version 2 deposited February 29, after the end of the STACS conference. Two minor mistakes correcte

    Deep Learning as a Parton Shower

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    We make the connection between certain deep learning architectures and the renormalisation group explicit in the context of QCD by using a deep learning network to construct a toy parton shower model. The model aims to describe proton-proton collisions at the Large Hadron Collider. A convolutional autoencoder learns a set of kernels that efficiently encode the behaviour of fully showered QCD collision events. The network is structured recursively so as to ensure self-similarity, and the number of trained network parameters is low. Randomness is introduced via a novel custom masking layer, which also preserves existing parton splittings by using layer-skipping connections. By applying a shower merging procedure, the network can be evaluated on unshowered events produced by a matrix element calculation. The trained network behaves as a parton shower that qualitatively reproduces jet-based observables.Comment: 26 pages, 13 figure

    Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow

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    Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA), as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these problems, we first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method
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