the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

exact post selection inference with application to the lasso we develop a general approach to valid inference after model selection in a nutshell our approach produces post selection inferences with the same frequency guarantees as those given by data splitting but are more powerful at the core of our framework is a result that characterizes the distribution of a post selection estimator conditioned on the selection event we specialize the approach to model selection by the lasso to form valid condence intervals for the selected coecients and test whether all relevant variables have been included in the model

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

the pmc processes associated to the 1 2 1 2 bernoulli shift are also bernoulli it is proven that the prigogine misra courbage pmc processes associated to the 1 2 1 2 bernoulli shift are bernoulli shifts the bernoulli partitions are constructed explicitly by using the decomposition of the transition kernels of the pmc processes on the fibers of the stable manifold of the transformed point the generating property of these partitions is proved for any two symbol bernoulli shifts

physics like models of computation abstract reversible cellular automata are computer models that embody discrete analogues of the classical physics notions of space time locality and microscopic reversibility they are offered as a step towards models of computation that are closer to fundamental physics

resonance and web structure in discrete soliton systems the two dimensional toda lattice and its fully discrete and ultra discrete analogues we present a class of solutions of the two dimensional toda lattice equation its fully discrete analogue and its ultra discrete limit these solutions demonstrate the existence of soliton resonance and web like structure in discrete integrable systems such as differential difference equations difference equations and cellular automata ultra discrete equations

information criteria for variable selection under sparsity the optimization of an information criterion in a variable selection procedure leads to an additional bias which can be substantial for sparse high dimensional data one can compensate for the bias by applying shrinkage while estimating within the selected models this paper presents modified information criteria for use in variable selection and estimation without shrinkage the analysis motivating the modified criteria follows two routes the first which we explore for signal plus noise observations only proceeds by comparing estimators with and without shrinkage the second discussed for general regression models describes the optimization or selection bias as a double sided effect which we call a mirror effect among the numerous insignificant variables those with large noisy values appear more valuable than an arbitrary variable while in fact they carry more noise than an arbitrary variable the mirror effect is investigated for akaike s information criterion and for mallows cp with special attention paid to the latter criterion as a stopping rule in a least angle regression routine the result is a new stopping rule which focuses not on the quality of a lasso shrinkage selection but on the least squares estimator without shrinkage within the same selection 2014 biometrika trust

an energy conserved solitonic cellular automaton an energy conserved soliton cellular automaton is proposed it is a generalization of the park steiglitz and thurston model 1986 and is shown to contain richer solitonic phenomena a systematic comparison of their collision statistics is also given

soliton cellular automata abstract we study the evolution of an arbitrary initial configuration of a certain filter cellular automaton introduced by park steiglitz and thurston any given state can be thought of as a collection of particles we find that a the interaction properties of these particles are richer than the usual solitons in particular periodic particles may interact solitonically or they may recombine to form new periodic configurations even if two particles interact solitonically they may interact several times before they get separated with the faster particle moving to the left of the slower one b arbitrary initial data will decompose as t into a number of periodic particles and into a number of certain new periodic coherent structures which we call breathers the particles and the breathers are ordered according to their speed c we formulate the above cellular automaton as a difference equation this formulation implies that the coherent structures found here are a manifestation of the coupling between the linear part and the nonlinear part of the difference equation

the algebraic properties of finite cellular automata abstract the basic patterns by cellular automata have been phenomenologically classified into four types by wolfram i propose a new algebraic method to predict the types of patterns by the elementary cellular automata this method is one example of the application of brownian algebra which is very important in the area of cognitive science the classification carried out by this method is in good agreement with wolfram s classification a significant difference in the present classification is that class 3 by wolfram is divided into two types this difference is apparent in the property of the filter automata which are constructed by the same rule

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

degrees of freedom in lasso problems we derive the degrees of freedom of the lasso fit placing no assumptions on the predictor matrix x like the well known result of zou et al 2007 which gives the degrees of freedom of the lasso fit when x has full column rank we express our result in terms of the active set of a lasso solution we extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitrary predictor matrix x and an arbitrary penalty matrix d though our focus is degrees of freedom we establish some intermediate results on the lasso and generalized lasso that may be interesting on their own

asymptotic post selection inference for the akaike information criterion summaryignoring the model selection step in inference after selection is harmful in this paper we study the asymptotic distribution of estimators after model selection using the akaike information criterion first we consider the classical setting in which a true model exists and is included in the candidate set of models we exploit the overselection property of this criterion in constructing a selection region and we obtain the asymptotic distribution of estimators and linear combinations thereof conditional on the selected model the limiting distribution depends on the set of competitive models and on the smallest overparameterized model second we relax the assumption on the existence of a true model and obtain uniform asymptotic results we use simulation to study the resulting post selection distributions and to calculate confidence regions for the model parameters and we also apply the method to a diabetes dataset

upper bound on the products of particle interactions in cellular automata abstract particle like objects are observed to propagate and interact in many spatially extended dynamical systems for one of the simplest classes of such systems one dimensional cellular automata we establish a rigorous upper bound on the number of distinct products that these interactions can generate the upper bound is controlled by the structural complexity of the interacting particles a quantity which is defined here and which measures the amount of spatio temporal information that a particle stores along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata thereby elucidating why that approach is of general utility the upper bound is tested against several relatively complex domain particle cellular automata and found to be tight

on measuring and correcting the effects of data mining and model selection abstract in the theory of linear models the concept of degrees of freedom plays an important role this concept is often used for measurement of model complexity for obtaining an unbiased estimate of the error variance and for comparison of different models i have developed a concept of generalized degrees of freedom gdf that is applicable to complex modeling procedures the definition is based on the sum of the sensitivity of each fitted value to perturbation in the corresponding observed value the concept is nonasymptotic in nature and does not require analytic knowledge of the modeling procedures the concept of gdf offers a unified framework under which complex and highly irregular modeling procedures can be analyzed in the same way as classical linear models by using this framework many difficult problems can be solved easily for example one can now measure the number of observations used in a variable selection process different modeling procedures such as a tree based regression and a

soliton turbulence in one dimensional cellular automata abstract statistical properties of cellular automata which support simple solitary waves are numerically studied under these rules spatio temporal patterns are sensitively dependent on the collision processes of solitons and other elementary excitations such as breathers kinks and nuclei patterns typically become randomized as collisions proceed turbulent states are realized after many collisions the resulting global patterns can be classified by the types of elementary excitations they contain in many turbulent states the spectra reveal a long range order with a k v anomaly for k 1 the irreversible process leading to turbulent equilibrium is characterized by the transient spectrum together with the allan variance the mean free motion of a soliton in the turbulent states is measured by the mutual information flow and the information loss is shown to obey an inverse power law the transient time to reach an attractor grows exponentially with system size which suggests that in the thermodynamic limit soliton turbulence is not an attractor but rather a transient state

exact post selection inference for sequential regression procedures abstractwe propose new inference tools for forward stepwise regression least angle regression and the lasso assuming a gaussian model for the observation vector y we first describe a general scheme to perform valid inference after any selection event that can be characterized as y falling into a polyhedral set this framework allows us to derive conditional post selection hypothesis tests at any step of forward stepwise or least angle regression or any step along the lasso regularization path because as it turns out selection events for these procedures can be expressed as polyhedral constraints on y the p values associated with these tests are exactly uniform under the null distribution in finite samples yielding exact type i error control the tests can also be inverted to produce confidence intervals for appropriate underlying regression parameters the r package selectiveinference freely available on the cran repository implements the new inference tools described in this article suppl

soliton like behavior in automata abstract we propose a new kind of automaton that uses newly computed site values as soon as they are available we call them filter automata fa they are analogous to infinite impulse response iir digital filters whereas the usual cellular automata ca correspond to finite impulse response fir digital filters it is shown that as a class the fa s are equivalent to ca s in the sense that the same array of space generation values can be produced they must be generated in a different order however a particular class of irreversible totalistic fa s are described that support a profusion of persistent structures that move at different speeds and these particle like patterns collide in nondestructive ways they often pass through one another with nothing more than a phase jump much like the solitons that arise in the solution of certain nonlinear differential equations histograms of speed displacement and period are given for neighborhood radii from 2 to 6 and particles with generators up to 16 bits wide we then present statistics for neighborhood radii 2 to 9 which show that collisions which preserve the identity of particles are very common

discussion on model confidence bounds for variable selection by yang li yuetian luo davide ferrari xiaonan hu and yichen qin

multi dimensional fast rule filter automata abstract group valued multi dimensional filter automata fulfilling a set of neighborhood axioms are considered and a corresponding extended fast rule theorem frt is derived these automata comprise the well known reversible and irreversible parity rule filter automata with solitonic behavior in one dimension the extended fast rule gives rise to a scanning algorithm with inherent parallel structure pipelining parallelism those automata which suffice the extended fast rule theorem are completely characterized in terms of local configuration functions in contrast to the one dimensional case in several dimensions the frt does not generally imply solitonic behavior therefore examples of solitonic and non solitonic collisions for particles in two dimensional automata are given

embedding computation in one dimensional automata by phase coding solitons it is shown that some kind of meaningful computation can be embedded in very simple microscopically homogeneous one dimensional automata and in particular filter automata with a parity next state rule a systematic procedure is given for generating moving periodic structures particles these particles exhibit soliton like properties that is they often pass through one another with phase shifts ways to encode information in the phase of these particles are discussed the search for useful logical operations is reduced to a search for paths in certain graphs as a demonstration of principle the details of implementing a carry ripple adder are given