complex dynamics of cellular automata rule 119 abstract in this paper the dynamical behaviors of cellular automata rule 119 are studied from the viewpoint of symbolic dynamics in the bi infinite symbolic sequence space 2 it is shown that there exists one bernoulli measure global attractor of rule 119 which is also the nonwandering set of the rule moreover it is demonstrated that rule 119 is topologically mixing on the global attractor and possesses the positive topological entropy therefore rule 119 is chaotic in the sense of both li yorke and devaney on the global attractor it is interesting that rule 119 a member of wolfram s class ii which was said to be simple as periodic before actually possesses a chaotic global attractor in 2 finally it is noted that the method presented in this work is also applicable to studying the dynamics of other rules especially the 112 bernoulli shift rules therein

additive one dimensional cellular automata are chaotic according to devaney s definition of chaos abstract we study the chaotic behavior of a particular class of dynamical systems cellular automata we specialize the definition of chaos given by devaney for general dynamical systems to the case of cellular automata a dynamical system x f is chaotic according to devaney s definition of chaos if its transition map f is sensitive to the initial conditions topologically transitive and has dense periodic orbits on x our main result is the proof that all the additive one dimensional cellular automata defined on a finite alphabet of prime cardinality are chaotic in the sense of devaney

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

on topological dynamics of turing machines abstract we associate to a turing machine two dynamical systems which we call turing machine with moving tape tmt and turing machine with moving head tmh tmt are equivalent to generalized shifts of moore 1990 and they include two sided full shifts tmh are shift commuting maps of two sided sofic systems in both classes we characterize systems with the shadowing property show that a bijective expansive tmt is conjugate to a subshift of finite type and that topological entropy of every tmh is zero we conjecture that every tmt has a periodic point

a dynamical model of parallel computation on bi infinite time scale the aim of this article is to construct a dynamical model of parallel computation on bi infinite time scale our approach is similar to two sided symbolic dynamics however bi infinite sequences are transformed to bi infinite graphs for a suitable description of parallelism and concurrency

iterative tree automata abstract the iterative tree automaton is introduced as a binary tree connected network with sequential input and output at the root of the tree the real and linear time computational power of this type of systolic system as a language acceptor is studied it is shown that for real time computations the arity of the tree is essential while this is not the case for linear time computations our main result is that every t n time nondeterministic turing machine can be simulated by an ita in deterministic ct n time a number of properties of real and linear time ita are proved

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

abelian 2 class field towers over the cyclotomic mathbb z _2 extensions of imaginary quadratic fields for the cyclotomic mathbb z 2 extension k of an imaginary quadratic field k we consider whether the galois group g k of the maximal unramified pro 2 extension over k is abelian or not the group g k is abelian if and only if the nth layer of the mathbb z 2 extension has abelian 2 class field tower for all n 1 the purpose of this paper is to classify all such imaginary quadratic fields k in part by using iwasawa polynomials

modular elliptic curves and fermat s last theorem when andrew john wiles was 10 years old he read eric temple bell s the last problem and was so impressed by it that he decided that he would be the first person to prove fermat s last theorem this theorem states that there are no nonzero integers a b c n with n 2 such that an bn cn the object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular fermat s last theorem follows as a corollary by virtue of previous work by frey serre and ribet

role of initial conditions in the classification of the rule space of cellular automata dynamics in the qualitative classification of cellular automata ca rules by wolfram rev mod phys 55 601 1983 there exists a class of ca rules called class 4 which exhibit complex pattern formation and long lived dynamical activity long transients these properties of class 4 ca s has led to the conjecture that class 4 rules are universal turing machines i e they are bases for computational universality we describe the embedding of a small universal turing machine due to minski computation finite and infinite machines prentice hall englewood cliffs nj 1967 into a cellular automaton rule table this produces a collection of k 18 r 1 cellular automata all of which are computationally universal however we observe that these rules are distributed among the various wolfram classes more precisely we show that the identification of the wolfram class depends crucially on the set of initial conditions used to simulate the given ca this work among others indicates that a description of complex systems and information dynamics may need a new framework for nonequilibrium statistical mechanics

sur la structure galoisienne de certaines pro p extensions de corps de nombres soit k k la pro p extension maximale du corps de nombres k non ramifiee en dehors d un ensemble fini de places de k soit mathcal h un sous groupe ferme et distingue de g gal k k et soit rm g rm g sigma mathcal h le quotient dans des contextes arithmetiques dependant de et de la structure de g nous etudions ici la liberte du mathbb z p g module mathcal x mathcal h mathcal h mathcal h

the zassenhaus filtration massey products and representations of profinite groups abstract we consider the p zassenhaus filtration g n of a profinite group g suppose that g s n for a free profinite group s and a normal subgroup n of s contained in s n under a cohomological assumption on the n fold massey products which holds e g if g has p cohomological dimension 1 we prove that g n 1 is the intersection of all kernels of upper triangular unipotent n 1 dimensional representations of g over f p this extends earlier results by minac spira and the author on the structure of absolute galois groups of fields

topological transformations as a tool in the design of systolic networks abstract we introduce the notion of computational network cn which is a general model of an arbitrary finite or infinite system of parallel synchronized processors systolic network our basic and very useful tools are topological transformations of the space time diagrams unrollings of computations on cn we show that the topological transformations on unrollings can be used to design systolic networks to give simple proofs of their correctness and to demonstrate the equivalence of different networks for example we usedthe transformation technique to give a concise proof of a strengthened version of leiserson s and saxe s retiming lemma and systolic conversion theorem as a practical application we show the correctness of a simple algorithm for distributed sorting on a systolic ring many other examples are given

the kernel unipotent conjecture and the vanishing of massey products for odd rigid fields abstract a major difficult problem in galois theory is the characterization of profinite groups which are realizable as absolute galois groups of fields recently the kernel n unipotent conjecture and the vanishing n massey conjecture for n 3 were formulated these conjectures evolved in the last forty years as a byproduct of the application of topological methods to galois cohomology we show that both of these conjectures are true for odd rigid fields this is the first case of a significant family of fields where both of the conjectures are verified besides fields whose galois groups of p maximal extensions are free pro p groups we also prove the kernel unipotent conjecture for demushkin groups of rank 2 and establish various filtration results for free pro p groups provide examples of pro p groups which do not have the kernel n unipotent property compare various zassenhaus filtrations with the descending p central series and establish new type of automatic galois realization

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

graph theoretical characterization of invertible cellular automata abstract a cellular automaton is defined to be invertible if its induced global rule is surjective on the set of all finite configurations it is shown that all one dimensional invertible cellular automata are obtainable from invertible nearest pair ones i e cellular automata given by a rule matrix for these an algorithm is proposed which runs in a time which is a polynomial function of the number of letters of the alphabet the result is expressed in a graph theoretical way the cellular automaton is invertible if and only if two graphs constructed by the algorithm have no edges in common it follows that if the number of letters in the alphabet is a prime the only invertible cellular automata are those for which every row or column of the rule matrix is a permutation of the alphabet for composite alphabet cardinalities several methods analytical and computational ones to obtain more complicated invertible cellular automata are proposed and used to construct examples all four letter invertible automata are constructed

predicting nonlinear cellular automata quickly by decomposing them into linear ones we show that a wide variety of nonlinear cellular automata cas can be decomposed into a quasidirect product of linear ones these cas can be predicted by parallel circuits of depth o log2 t using gates with binary inputs or o log t depth if sum mod p gates with an unbounded number of inputs are allowed thus these cas can be predicted by idealized parallel computers much faster than by explicit simulation even though they are nonlinear this class includes any ca whose rule when written as an algebra is a solvable group we also show that cas based on nilpotent groups can be predicted in depth o log t or o 1 by circuits with binary or sum mod p gates respectively we use these techniques to give an efficient algorithm for a ca rule which like elementary ca rule 18 has diffusing defects that annihilate in pairs this can be used to predict the motion of defects in rule 18 in o log2 t parallel time

tame kernels of cubic cyclic fields there are many results describing the structure of the tame kernels of algebraic number fields and relating them to the class numbers of appropriate fields in the present paper we give some explicit results on tame kernels of cubic cyclic fields table 1 collects the results of computations of the structure of the tame kernel for all cubic fields with only one ramified prime p 7 p 5 000 in particular we investigate the structure of the 7 primary and 13 primary parts of the tame kernels the theoretical tools we develop based on reflection theorems and singular primary units enable the determination of the structure even of 7 primary and 13 primary parts of the tame kernels for all fields as above the results are given in tables 2 and 3

some undecidability results for asynchronous transducers and the brin thompson group 2v using a result of kari and ollinger we prove that the torsion problem for elements of the brin thompson group 2v is undecidable as a result we show that there does not exist an algorithm to determine whether an element of the rational group r of grigorchuk nekrashevich and sushchanskii has finite order a modification of the construction gives other undecidability results about the dynamics of the action of elements of 2v on cantor space arzhantseva lafont and minasyanin prove in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem to our knowledge 2v furnishes the first concrete example of such a group and gives an example of a direct undecidability result in the extended family of r thompson type groups

growth rates _ homology and volumes of hyperbolic 3 manifolds it is shown that if m is a closed orientable irreducible 3 manifold and n is a nonnegative integer and if h 1 m z p has rank n 2 for some prime p then every n generator subgroup of 1 m has infinite index in 1 m and is in fact contained in infinitely many finite index subgroups of 1 m this result is used to estimate the growth rates of the fundamental group of a 3 manifold in terms of the rank of the z p homology

a hierarchical classification of cellular automata abstract a central issue in the theory of cellular automata is classification a classification is a structure imposed on the space of automata which groups together cellular automata with related properties in this paper a classification based on the action of cellular automata on n step markov measures is presented this classification is hierarchical and parametric an algorithm is described which efficiently constructs all rules in a given class at a given level of the hierarchy the utility of the classification is explored in the study of the invariant statistical properties of next nearest neighbor cellular automata on two states per cell

the iwasawa conjecture for totally real fields let f be a totally real number field let p be a prime number and for any integer n let fun denote the group of nth roots of unity let 41 be a p adic valued artin character for f and let f be the extension of f attached to 4 i e so that 4 is the character of a faithful representation of gal f f we will assume that f is also totally real for a number field k let k denote the cyclotomic zp extension of k following greenberg we say that 4 is of type s if f n fc f and of type w if 4 is one dimensional with f p c fcc deligne and ribet in dr following kubota and leopoldt for the case f q have proved the existence of a p adic l function associated to a one dimensional artin character 4 with f totally real this function lp s 4 is continuous for s e zp 1 and even at s 1 if 4 is not trivial and satisfies the following interpolation property

regular unimodal systems and factors of finite automata abstract dynamical systems at the edge of chaos which have been considered as models of self organization phenomena are marked by their ability to perform nontrivial computations to distinguish them from systems with limited computing power we formulate two simplicity criteria for general dynamical systems and apply them to unimodal systems on real interval we say that a dynamical system is regular if it yields a regular language when observed through arbitrary almost disjoint cover finite automata are regarded as dynamical systems on zero dimensional spaces and their factors yield another class of simple dynamical systems these two criteria coincide on subshifts since a subshift is regular iff it is a factor of a finite automation sofic systems a unimodal system on real interval is regular if it has only a finite number of periodic points and nonrecursive otherwise on the other hand each s unimodal system with finite periodic or preperiodic kneading sequence is a factor of a finite automaton thus preperiodic s unimodal systems are factors of finite automata which are not regular

group presentation p adic analytic groups and lattices in mathrm sl _2 mathbf c groups by using their pro p completions this method is based on the observation that if x r is a presentation of the finitely generated f g group f then x r considered as a presentation for a pro p group is actually a presentation for t the pro p completion of f first we prove a generalization of a theorem of golod and shafarevich cf h theorem let g be a p adic analytic pro p group different from zp the p adic integers if x r is a minimal presentation of g then 1x 2 iri 2

investigating topological chaos by elementary cellular automata dynamics we apply the two different definitions of chaos given by devaney and by knudsen for general discrete time dynamical systems dtds to the case of elementary cellular automata i e 1 dimensional binary cellular automata with radius 1 a dtds is chaotic according to the devaney s definition of chaos iff it is topologically transitive has dense periodic orbits and it is sensitive to initial conditions a dtds is chaotic according to the knudsen s definition of chaos iff it has a dense orbit and it is sensitive to initial conditions we enucleate an easy to check property left or rightmost permutivity of the local rule associated with a cellular automaton which is a sufficient condition for d chaotic behavior it turns out that this property is also necessary for the class of elementary cellular automata finally we prove that the above mentioned property does not remain a necessary condition for chaoticity in the case of non elementary cellular automata

a note on the rule classification for square homogeneous cellular automata abstract we give the dynamical sense for the qualitative ideas of wolfram s and stauffer s classifications for the elementary two dimensional cellular automata with four nearest neighbours the new sense arises from the attracting role of the so called subshifts

on the limit sets of cellular automata the limit sets of cellular automata defined by wolfram play an important role in applications of cellular automata to complex systems a number of results on limit sets are proved considering both finite and infinite configurations of cellular automata the main concern of this paper is with testing membership and essential emptiness of limit sets for linear and two dimensional cellular automata

uber pro p fundamentalgruppen markierter arithmetischer kurven let k be a global field p an odd prime number dierent from char k and s t disjoint finite sets of primes of k let g t k p g k t p k be the galois group of the maximal p extension of k which is unramified outside s and completely split at t we prove the existence of a finite set of primes s0 which can be chosen disjoint from any given setm of dirichlet density zero such that the cohomology of g t s0 k p coincides with the etale cohomology of the associated marked arithmetic curve in particular cd g t s0 k p 2 furthermore we can choose s0 in such a way that k t s s0 p realizes the maximal p extension kp p of the local field kp for all p2 s s0 the cup product h 1 g t s0 k p fp h 1 g t s0 k p fp h 2 g t s0 k p fp is surjective and the decomposition groups of the primes in s establish a free product inside g t s0 k p this generalizes previous work of the author where similar results were shown in the case t under the restrictive assumption p cl k and p 2 k

quasi periodic configurations and undecidable dynamics for tilings infinite words and turing machines we describe turing machines tilings and infinite words as dynamical systems and analyze some of their dynamical properties it is known that some of these systems do not always have periodic configurations we prove that they always have quasi periodic configurations and we quantify quasi periodicity we then study the decidability of dynamical properties for these systems in analogy to rice s theorem for computable functions we derive a theorem that characterizes dynamical system properties that are undecidable as an illustration of this result we prove that topological entropy is undecidable for turing machines and for tilings

mild pro p groups and galois groups of p extensions of ℚ in this paper we introduce a new class of finitely presented pro pgroups g of cohomological dimension 2 called mild groups if d g r g are respectively the minimal number of generators and relations of g we give an infinite family of mild groups g with r g d g and d g 2 arbitrary these groups can be constructed with g g g finite answering a question of kuzmin if g gs p is the galois group of the maximal p extension of q unramified outside a finite set of primes s and p 6 2 we show that g is mild for a co final class of sets s even in the case p s

the notion of dimension in geometry and algebra this talk reviews some mathematical and physical ideas related to the notion of dimension after a brief historical introduction various modern constructions from fractal geometry noncommutative geometry and theoretical physics are invoked and compared glenn gould disapproved of his own recording of goldberg variations there is a lot of piano playing going on there and i mean that as the most disparaging comment possible nyrb oct 7 2004 p 10

higher massey products in the cohomology of mild pro p groups abstract translating results due to j labute into group cohomological language a schmidt proved that a finitely presented pro p group g is mild and hence of cohomological dimension cd g 2 if h 1 g f p u v as f p vector space and the cup product h 1 g f p h 1 g f p h 2 g f p maps u v surjectively onto h 2 g f p and is identically zero on v v this has led to important results in the study of p extensions of number fields with restricted ramification in particular in the case of tame ramification in this paper we extend labute s theory of mild pro p groups with respect to weighted zassenhaus filtrations and prove a generalization of the above result for higher massey products which allows to construct mild pro p groups with defining relations of arbitrary degree we apply these results to one relator pro p groups and obtain some new evidence of an open question due to serre

profinite braid groups galois representations and complex multiplications in this paper we consider two closely correlated subjects one is a pro i analogue of the braid group and the other is a construction of the universal 1 adic power series for complex multiplications of fermat type or equivalently for jacobi sums both arise from and constitute a first step in the study of the canonical representation of the absolute galois group gq gal q q in the outer automorphism group of the profinite fundamental group of pq o 1 oo

on galois representations arising from towers of coverings of p1 0 1 we propose a new way to describe universally thel adic galois representations associated to each almost pro l tower of etale coverings ofp1 0 1 this generalizes our universal power series for jacobi sums cf i which arises from the tower of fermat curves of degreeln n and contains the case of the tower of modular curves of level 2mln m fixed n as another important special case as a fundamental tool we shall establish and use an almost pro l version of the theorems of blanchfield and of lyndon in fox free differential calculus

on tame pro p galois groups over basic mathbb z _p extensions for a prime number p and a finite set s of prime numbers congruent to 1 modulo p we consider the galois group of the maximal pro p extension unramified outside s over the mathbb z p extension of the rational number field in this paper we give a family of s for which the galois group is a metacyclic pro p group with an application to greenberg s conjecture

computation of supersonic turbulent shear layer mixing with mild compressibility effects turbulent supersonic shear layer mixing has been computed using the usa series multizone reynolds averaged navier stokes solver which is based on an implicit finite volume total variation diminishing tvd formulation for the convection terms three shear layer cases were run using three turbulence models each 1 algebraic 2 one equation k l and 3 two equation k e

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

on the dynamics and recursive properties of multidimensional symbolic systems we study the sub dynamics of multidimensional shifts of finite type and sofic shifts and the action of cellular automata on their limit sets such a subaction is always an effective dynamical system i e it is isomorphic to a subshift over the cantor set the complement of which can be written as the union of a recursive sequence of basic sets our main result is that to varying degrees this recursive theoretic condition is also sufficient we show that the class of expansive subactions of multidimensional sofic shifts is the same as the class of expansive effective systems and that a general effective system can be realized modulo a small extension as the subaction of a shift of finite type or as the action of a cellular automaton on its limit set after removing a dynamically trivial set as applications we characterize in terms of their computational properties the numbers which can occur as the entropy of cellular automata and construct sfts and cas with various interesting properties

circular sets of prime numbers and p extensions of the rationals zusammenfassung sei p eine ungerade primzahl und s eine endliche menge von primzahlen kongruent 1 modulo p wir zeigen da die gruppe gs q p von kohomologischer dimension 2 ist wenn das verschlingungsdiagramm zu s und p einer gewissen technischen bedingung genaugt und wir zeigen da gs q p in diesen faallen eine dualitaatsgruppe ist au erdem untersuchen wir das zerlegungsverhalten von primstellen in der erweiterung qs p q und wir setzen die kohomologie von gs q p zur etalkohomolgie des schemas spec z is in beziehung schlie lich berechnen wir den dualisierenden modul abstract let p be an odd prime number and let s be a nite set of prime numbers congruent to 1 modulo p we prove that the group gs q p has cohomological dimension 2 if the linking diagram attached to s and p satis es a certain technical condition and we show that gs q p is a duality group in these cases furthermore we investigate the decomposition behaviour of primes in the extension qs p q and we relate the cohomology of gs q p to the etale cohomology of the scheme spec z i s finally we calculate the dualizing module

local structure theory for cellular automata abstract the mean field theory for cellular automata wolfram and schulman and seiden is generalized to the local structure theory the local structure theory is a sequence of finitely parameterized models of the statistical features of a cellular automaton s evolution the n th model in the sequence takes into account correlations in terms of the probability of blocks of n states a class of measures the n block measures is introduced the local structure operator of order n maps n block measures to n block measures in a manner which reflects the cellular automaton map on blocks of states the fixed points of the map on measures approximate the invariant measures of the cellular automaton the ability of the local structure theory to model evolution from uncorrelated initial distributions is studied the theory gives exact results in simple cases in more complex cases monte carlo numerical experiments suggest that an accurate statistical portrait of cellular automaton evolution is obtained the invariant measures of a cellular automaton and the stability of these measures may be obtained from the local structure theory the local structure theory appears to be a powerful method for characterization and classification of cellular automata nearest neighbor cellular automata with two states per cell are studied using this method

implementation of a one equation turbulence model within a stabilized finite element formulation of a symmetric advective diffusive system the success of stabilized finite element methods for symmetric advective diffusive formulations of the laminar navier stokes equations has motivated extension of these concepts to turbulent flows a one equation model which preserves the symmetry of the system s advective and diffusive matrices has been developed this model is based on the work of norris and reynolds and utilizes a transport equation for the turbulent velocity scale q and an algebraic relation for the turbulent length scale l from these two quantities an eddy viscosity can be calculated this model has been implemented by way of a galerkin least squares finite element method solutions are presented which verify the good behavior of the formulation

computation theoretic aspects of cellular automata abstract cellular automata may be viewed as computational models of complex systems they also can be seen as continuous functions on a particular family of compact metric spaces this paper surveys results largely motivated by an attempt to answer questions posed by the latter approach by means of techniques from the former

computational mechanics of cellular automata an example abstract we illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space time behavior of elementary one dimensional cellular automaton rule 54 the dominant regular domain of the cellular automation is identified and a domain filter is constructed to locate and classify defects in the domain the primary particles are identified and a range of interparticle interactions is studied the deterministic equation of motion of the filtered space time behavior is derived filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higher level defects particle interactions and secondary domains we define the emergence time at which the space time behavior condenses into configurations consisting only of domains particles and particle interactions taken together these techniques serve as the basis for the investigation of pattern evolution and self organization in this representative system

from dynamics on surfaces to rational points on curves has no integer solutions with x y z 1 inspiring generations of work in number theory its proof was finally achieved by wiles a qualitative result finite fermat was obtained earlier by faltings it says the fermat equation has only a finite number of solutions for each given n up to rescaling this paper is an appreciation of some of the topological intuitions behind number theory it aims to trace a logical path from the classification of surface diffeomorphisms to the proof of finite fermat the route we take is the following

additive cellular automata and global injectivity abstract we employ algebraic methods to investigate the global injectivity of additive cellular automata when the state alphabet is a finite commutative ring the set of local rules of such additive cellular automata in d 1 dimensions itself forms a ring the invertible elements in this ring correspond to the globally injective additive cellular automata we indicate how one determines the invertible elements and thus the globally injectibe cellular automata in particular we show that in contrast to the general situation the global injectivity of additive cellular automata in d 1 dimensions is decidable construction of local rules for the inverse cellular automata is illustrated through examples a strict upper bound on the radius of the inverse cellular automata is obtained in the special case of linear cellular automata with state alphabet the ring of integers modulo m we count the globally injective cellular automata of up to a given radius we show that in one dimension a non globally injective additive cellular automaton is either not injective on spatially periodic configurations of any period n n or the set of n 0 such that the cellular automation is injective on spatially periodic configurations of period n has positive density in n

on the presence of periodic configurations in turing machines and in counter machines a configuration of a turing machine is given by a tape content together with a particular state of the machine petr k rka has conjectured that every turing machine when seen as a dynamical system on the space of its configurations has at least one periodic orbit in this paper we provide an explicit counterexample to this conjecture we also consider counter machines and prove that in this case the problem of determining if a given machine has a periodic orbit in configuration space is undecidable

separated flow predictions using a hybrid k l backflow model a new hybrid one equation k l backflow model has been used to compute several turbulent flow problems involving detached flow regions the model incorporates algebraic near wall treatments for the kinetic energy of turbulence fc the length scale l and the eddy viscosity the near wall formulation depends on whether the flow is attached or detached this approach obviates the need to use wall functions agreement between predictions and experimental data is generally very good throughout the mach number range

arithmetic representations of cellular automata abstract one and two dimensional cellular automata ca are described in terms of a rithmetic relations interpreted as finite state machines ca are shown to be equivalent to an updating unit that reads processes and writes data on the array of cells for 2d von neumann ca dynamics is described as a linear lattice of locally coupled 1d ca the coupling is between nearest neighbors through a set of subrules equivalent to the usual rules for von neumann neighborhoods finally a measure theoretic entropy for one dimensional ca is introduced to characterize spatial complexity and some numerical results are presented

parameter characterization of two dimensional cellular automata rule space cellular automata ca are discrete dynamical systems formed by a great number of identical and simple components with local connectivity it has been proved that the problem of forecasting the dynamical behavior of ca is undecidable based upon parameterizations of ca rule space several approximations have been investigated the majority of these studies are focused on the one dimensional ca the present work generalizes for the two dimensional space the definition of three parameters previously published in the one dimensional context sensitivity neighborhood dominance and activity propagation as an example of the application of such generalized parameters some simulations about the computational task known as the density classification task are reported

on galois groups of unramified pro p extensions let p be an odd prime satisfying vandiver s conjecture we consider two objects the galois group x of the maximal unramified abelian pro p extension of the compositum of all z p extensions of q p and the galois group mathfrak g of the maximal unramified pro p extension of q mu p infty we give a lower bound for the height of the annihilator of x as an iwasawa module under some mild assumptions on bernoulli numbers we provide a necessary and sufficient condition for mathfrak g to be abelian the bound and the condition in the two results are given in terms of special values of a cup product pairing on cyclotomic p units we obtain in particular that for p 1 000 greenberg s conjecture that x is pseudo null holds and mathfrak g is in fact abelian

mild pro 2 groups and 2 extensions of q with restricted ramification abstract using the mixed lie algebras of lazard we extend the results of the first author on mild groups to the case p 2 in particular we show that for any finite set s 0 of odd rational primes we can find a finite set s of odd rational primes containing s 0 such that the galois group of the maximal 2 extension of q unramified outside s is mild we thus produce a projective system of such galois groups which converge to the maximal pro 2 quotient of the absolute galois group of q unramified at 2 and our results also allow results of alexander schmidt on pro p fundamental groups of marked arithmetic curves to be extended to the case p 2 over a global field which is either a function field of characteristic 2 or a totally imaginary number field

formal languages and global cellular automaton behavior abstract a connection is made between the description of one dimensional cellular automata as dynamical systems acting on a compact metric space and as computational systems acting on strings operators are defined which determine a bijective correspondence between subshifts of infinite configurations and languages of finite strings under this correspondence families of languages give rise to families of subshifts regular languages correspond to sofic subshifts families of subshifts corresponding to context free context sensitive and recursively enumerable languages are introduced and their closure properties under forward and backward cellular automaton images studied