particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

quasi factors of zero entropy systems for minimal systems x t of zero topological entropy we demon strate the sharp difference between the behavior regarding entropy of the sys tems m x t and 2x t induced by t on the spaces m x of prob ability measures on x and 2x of closed subsets of x it is shown that the system m x t has itself zero topological entropy two proofs of this the orem are given the first uses ergodic theoretic ideas the second relies on the different behavior of the banach spaces ln and ln with respect to the existence of almost hilbertian central sections of the unit ball in contrast to this theorem we construct a minimal system x t of zero entropy with a minimal subsystem y t of 2 t whose entropy is positive school of mathematics tel aviv university ramat aviv israel e mail address glasner0math tau ac il institute of mathematics hebrew university jerusalem israel e mail address weissfmath huji ac il this content downloaded from 207 46 13 117 on sun 23 oct 2016 04 35 33 utc all use subject to http about jstor org terms

sparse antenna array optimization with the cross entropy method the interest in sparse antenna arrays is growing mainly due to cost concerns array size limitations etc formally it can be shown that their design can be expressed as a constrained multidimensional nonlinear optimization problem generally through lack of convex property such a multiextrema problem is very tricky to solve by usual deterministic optimization methods in this article a recent stochastic approach called cross entropy method is applied to the continuous constrained design problem the method is able to construct a random sequence of solutions which converges probabilistically to the optimal or the near optimal solution roughly speaking it performs adaptive changes to probability density functions according to the kullback leibler cross entropy the approach efficiency is illustrated in the design of a sparse antenna array with various requirements

structural properties of dendrite groups let g be the homeomorphism group of a dendrite we study the normal subgroups of g for instance there are uncountably many non isomorphic such groups g that are simple groups moreover these groups can be chosen so that any isometric g action on any metric space has a bounded orbit in particular they have the fixed point property fh

simplicity of some automorphism groups abstract let m be a countably infinite first order relational structure which is homogeneous in the sense of fraisse we show under the assumption that the class of finite substructures of m has the free amalgamation property along with the assumption that aut m is transitive on m but not equal to sym m that aut m is a simple group this generalises results of truss rubin and others the proof uses the polish group structure of the automorphism group and generalises to certain other homogeneous structures with prospects for further application

constrained least squares optimization in conformal array antenna synthesis the least mean square error of the constrained least squares optimization method is studied the phases of non zero goal values and the phases of non zero constraint values can be selected by a fast iteration for optimum fit to the goal function amplitude this kind of modified least squares optimization method opens up a fast and robust synthesis method for large conformal antenna arrays constraints can be written also for the element excitation amplitudes and a phase synthesis with predefined amplitudes can be done iterative weight correction technique is used for accurate sidelobe control synthesis examples of two dimensional elliptical and large three dimensional conformal antenna arrays are presented

on the predictability of discrete dynamical systems iii abstract given an integer n 2 a metrizable compact topological n manifold x with boundary and a finite positive borel measure on x we prove that most homeomorphisms f x x are non sensitive almost everywhere on x moreover we also prove that for most homeomorphisms f x x the non wandering set f has measure zero

generic stationary measures and actions let g be a countably infinite group and let be a generating probability measure on g we study the space of stationary borel probability measures on a topological g space and in particular on z g where z is any perfect polish space we also study the space of stationary measurable g actions on a standard nonatomic probability space equip the space of stationary measures with the weak topology when has finite entropy we show that a generic measure is an essentially free extension of the poisson boundary of g when z is compact this implies that the simplex of stationary measures on z g is a poulsen simplex we show that this is also the case for the simplex of stationary measures on 0 1 g we furthermore show that if the action of g on its poisson boundary is essentially free then a generic measure is isomorphic to the poisson boundary next we consider the space of stationary actions equipped with a standard topology known as the weak topology here we show that when g has property t the ergodic actions are meager we also construct a group g without property t such that the ergodic actions are not dense for some finally for a weaker topology on the set of actions which we call the very weak topology we show that a dynamical property e g ergodicity is topologically generic if and only if it is generic in the space of measures there we also show a glasner king type 0 1 law stating that every dynamical property is either meager or residual

a structure theorem for actions of semisimple lie groups we consider a connected semisimple lie group g with finite center an admissible probability measure on g and an ergodic g u space x v we first note lemma 0 1 that x v has a unique maximal projective factor of the form g q vo where q is a parabolic subgroup of g and then prove 1 theorem 1 if every noncompact simple factor of g has real rank at least two then the maximal projective factor is nontrivial unless v is a g

homeomorphic measures on stationary bratteli diagrams we study the set s of ergodic probability borel measures on stationary non simple bratteli diagrams which are invariant with respect to the tail equivalence relation r equivalently the set s is formed by ergodic probability measures invariant with respect to aperiodic substitution dynamical systems the paper is devoted to the classification of measures from s with respect to a homeomorphism the properties of the clopen values set s are studied it is shown that for every measure s there exists a subgroup g r such that s g 0 1 a criterion of goodness is proved for such measures based on this result the measures from s are classified up to a homeomorphism we prove that for every good measure s there exist countably many measures i i n s such that the measures and i are homeomorphic but the tail equivalence relations on the corresponding bratteli diagrams are not orbit equivalent

mobius orthogonality for generalized morse kakutani flows the prouhet thue morse sequence and its generalizations have occured in many settings morse kakutani flow refers to kakutani s 1967 generalization of the morse minimal flow 1922 these flows are bbb z 2 skew products of almost one to one extensions of the adding machine x rightarrow x 1 on the 2 adic completion of bbb z generalized morse kakutani flow is a k skew product of similar construct with base flow a factor of x rightarrow x 1 on the profinite completion of bbb z and k any compact group abelian or not of countable density the principal result is that sarnak s m o bius orthogonality conjecture holds for a restricted class of generalized morse kakutani flows

cross entropy method for electromagnetic optimization with constraints and mixed variables an elegant and simple approach is presented for electromagnetic em optimizations especially when mixed variables and or constraints are involved in mixed variable optimization some variables are continuous can take any value within a range and others are discrete can take only values from a database an example constraint is when the total length of a device under optimization is specified our approach can handle such optimization problems and is based on an abstract probabilistic evolutionary optimization algorithm called the cross entropy ce method we believe that this is the first application of ce with full wave em simulations a quick performance benchmarking on two test functions was performed to compare convergence of ce and two other established optimization algorithms then the advantages of the ce method when simultaneously optimizing a mix of discrete and continuous variables and imposing geometric constraints are illustrated finally six resonant cavity antennas rcas were optimized and one was prototyped and tested to verify predicted results this one layer superstrate rca prototype has a measured peak directivity of 17 6 dbi with a 3 db directivity bandwidth of 51 and lower sidelobes outperforming all such prototypes in the literature

pointwise theorems for amenable groups in this paper we prove the pointwise ergodic theorem for general locally compact amenable groups along folner sequences that obey some restrictions these restrictions are mild enough so that such sequences exist for all amenable groups we also prove a generalization of the shannon mcmillan breiman theorem to all discrete amenable groups

turbulence amalgamation and generic automorphisms of homogeneous structures we study topological properties of conjugacy classes in polish groups with emphasis on automorphism groups of homogeneous countable structures we first consider the existence of dense conjugacy classes the topological rokhlin property we then characterize when an automorphism group admits a comeager conjugacy class answering a question of truss and apply this to show that the homeomorphism group of the cantor space has a comeager conjugacy class answering a question of akin hurley and kennedy finally we study polish groups that admit comeager conjugacy classes in any dimension in which case the groups are said to admit ample generics we show that polish groups with ample generics have the small index property generalizing results of hodges hodkinson lascar and shelah and arbitrary homomorphisms from such groups into separable groups are automatically continuous moreover in the case of oligomorphic permutation groups they have uncountable cofinality and the bergman property these results in particular apply to automorphism groups of many stable 0 categorical structures and of the random graph in this connection we also show that the infinite symmetric group s has a unique non trivial separable group topology for several interesting groups we also establish serre s properties fh and fa

quantized arnold cat maps can be entropic k systems automorphisms on the irrational rotation algebra with respect to their ergodic properties are studied especially it is shown that for a dense set of the rotation parameter cat maps are entropic k systems

local entropy theory for a countable discrete amenable group action in the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action for such an action we introduce entropy tuples in both topological and measure theoretic settings and build the variational relation be tween these two kinds of entropy tuples by establishing a local variational principle for a given finite open cover moreover based the idea of topological entropy pairs we introduce and study two special classes of such an action uniformly positive entropy and completely positive entropy note that in the building of the local variational principle following romagnoli s ideas two kinds of measure theoretic entropy are introduced for finite borel covers these two kinds of entropy turn out to be the same where danilenko s orbital approach becomes an inevitable tool

the rohlin property for shifts on uhf algebras and automorphisms of cuntz algebras abstract we show that the shift on the uhf algebra m n has the rohlin property for any odd n hence by brotteli et al the crossed product of a uhf algebra by a shift ergodic theory dynam systems 13 1993 615 626 for any n 2 3 and that any automorphism of the cuntz algebra o n n m is outer for any m 0

on homeomorphic bernoulli measures on the cantor space let be the bernoulli measure on the cantor space given as the infinite product of two point measures with weights and it is a long standing open problem to characterize those and such that and are topologically equivalent i e there is a homeomorphism from the cantor space to itself sending to the possibly weaker property of and being continuously reducible to each other is equivalent to a property of and called binomial equivalence in this paper we define an algebraic property called refinability and show that if and are refinable and binomially equivalent then and are topologically equivalent next we show that refinability is equivalent to a fairly simple algebraic property finally we give a class of examples of binomially equivalent and refinable numbers in particular the positive numbers and such that and are refinable so the corresponding measures are topologically equivalent

independence in topological and c dynamics we develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods one of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties we also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to c dynamics

entropy chaos and weak horseshoe for infinite dimensional random dynamical systems in this paper we study the complicated dynamics of infinite dimensional random dynamical systems that include deterministic dynamical systems as their special cases in a polish space without assuming any hyperbolicity we prove if a continuous random map has a positive topological entropy then it contains a topological horseshoe we also show that the positive topological entropy implies the chaos in the sense of li yorke the complicated behavior exhibited here is induced by the positive entropy but not the randomness of the system 2017 wiley periodicals inc

systematic measures of biological networks ii degeneracy complexity and robustness this paper is part ii of a two part series devoted to the study of systematic measures in a complex bionetwork modeled by a system of ordinary differential equations in this part we quantify several systematic measures of a biological network including degeneracy complexity and robustness we will apply the theory of stochastic differential equations to define degeneracy and complexity for a bionetwork robustness of the network will be defined according to the strength of attractions to the global attractor based on the study of stationary probability measures and entropy made in part i of this series we will investigate some fundamental properties of these systematic measures in particular the connections between degeneracy complexity and robustness 2016 wiley periodicals inc

a global local synthesis approach for large non regular arrays a method is proposed for the synthesis of large planar non regular arrays assuming constant magnitude for the excitation of the elements the approach which combines global and local optimization is based on distinguishing aperture type and non coherent parts of the array factor the following constraints are considered minimal separation of the antennas maximum size of the array and fixed mainbeam width the level of the sidelobes is reduced via the minimization of a new type of flexible averaging cost function based on an lp norm possible applications of this model lie in the field of radio astronomy satellite communications and radar systems the proposed optimization strategy consists of three successive steps designed to be independent of each other starting with an equivalent continuous aperture the first two steps act as global transformations of the radial and azimuthal positions of the elements in the initial array while the third step performs a local optimization of individual elements of the array this last step heavily relies on computations of the gradient of the cost function which can be done quickly using an fft based procedure the method is illustrated for several large scale examples by considering as inputs four different types of non regular arrays

approximate and real trajectories for generic dynamical systems abstract in this paper we show that generic dynamical systems have a weak shadowing property namely that for a generic dynamical system in the space of discrete continuous dynamical systems on a compact manifold m with the usual c 0 topology given 0 there exists a 0 such that trajectories are close to real trajectories there are no dimensional restrictions on this result we also give some results on the inverse problem of tracing real trajectories by trajectories these problems are motivated by questions regarding the validity of numerical solutions of differential equations

turbulence representations and trace preserving actions we establish criteria for turbulence in certain spaces of c algebra repre sentations and apply this to the problem of nonclassiability by countable structures for group actions on a standard atomless probability space x and on the hypernite ii1 factor r we also prove that the conjugacy action on the space of free actions of a countably innite amenable group on r is turbulent and that the conjugacy action on the space of ergodic measure preserving ows on x is generically turbulent

on li yorke pairs the li yorke definition of chaos proved its value for interval maps in this paper it is considered in the setting of general topological dynamics we adopt two opposite points of view on the one hand sufficient conditions for li yorke chaos in a topological dynamical system are given we solve a long standing open question by proving that positive entropy implies li yorke chaos on the other hand properties of dynamical systems without li yorke pairs are investigated in addition to having entropy 0 they are minimal when transitive and the property is stable under factor maps arbitrary products and inverse limits finally it is proved that minimal systems without li yorke pairs are disjoint from scattering systems

limit sets of typical continuous functions abstract given a metrizable compact topological n manifold x with boundary and a finite positive borel measure on x we prove that for the typical continuous function f x x it is true that for every point x in a full measure subset of x the limit set f x is a cantor set of hausdorff dimension zero f maps f x homeomorphically onto itself each point of f x has a dense orbit in f x and f is non sensitive at each point of f x moreover the function x f x is continuous almost everywhere

crossed products and entropy of automorphisms abstract let a be an exact c algebra let g be a locally compact group and let a g be a c dynamical system each automorphism g induces a spatial automorphism ad g on the reduced crossed product a g in this paper we examine the question first raised by e stormer of when the topological entropies of g and ad g coincide this had been answered by n brown for the particular case of discrete abelian groups using different methods we extend his result to preservation of entropy for g when the subgroup of aut g generated by the corresponding inner automorphism ad g has compact closure this property is satisfied by all elements of a wide class of groups called locally fia this class includes all abelian groups both discrete and continuous as well as all compact groups

dynamical entropy in banach spaces we introduce a version of voiculescu brown approximation entropy for isometric automorphisms of banach spaces and develop within this framework the connection between dynamics and the local theory of banach spaces as discovered by glasner and weiss our fundamental result concerning this contractive approximation entropy or ca entropy characterizes the occurrence of positive values both geometrically and topologically this leads to various applications for example we obtain a geometric description of the topological pinsker factor and show that a c algebra is type i if and only if every multiplier inner automorphism has zero ca entropy we also examine the behaviour of ca entropy under various product constructions and determine its value in many examples including isometric automorphisms of l p for 1 p and noncommutative tensor product shifts

compact group automorphisms addition formulas and fuglede kadison determinants for a countable amenable group and an element f in the integral group ring z being invertible in the group von neumann algebra of we show that the entropy of the shift action of on the pontryagin dual of the quotient of z by its left ideal generated by f is the logarithm of the fuglede kadison determinant of f for the proof we establish an p version of rufus bowen s denition of topological entropy addition formulas for group extensions of countable amenable group actions and an approximation formula for the fuglede kadison determinant of f in terms of the determinants of perturbations of the compressions of f

stable sets and mean li yorke chaos in positive entropy systems abstract it is shown that in a topological dynamical system with positive entropy there is a measure theoretically rather big set such that a multivariant version of mean li yorke chaos happens on the closure of the stable or unstable set of any point from the set it is also proved that the intersections of the sets of asymptotic tuples and mean li yorke tuples with the set of topological entropy tuples are dense in the set of topological entropy tuples respectively

graph theoretic structure of maps of the cantor space abstract in this paper we develop unifying graph theoretic techniques to study the dynamics and the structure of spaces h 0 1 n and c 0 1 n the space of homeomorphisms and the space of self maps of the cantor space respectively using our methods we give characterizations which determine when two homeomorphisms of the cantor space are conjugate to each other we also give a new characterization of the comeager conjugacy class of the space h 0 1 n the existence of this class was established by kechris and rosendal and a specific element of this class was described concretely by akin glasner and weiss our characterization readily implies many old and new dynamical properties of elements of this class for example we show that no element of this class has a li yorke pair implying the well known glasner weiss result that there is a comeager subset of h 0 1 n each element of which has topological entropy zero our analogous investigation in c 0 1 n yields a surprising result there is a comeager subset of c 0 1 n such that any two elements of this set are conjugate to each other by an element of h 0 1 n our description of this class also yields many old and new results concerning dynamics of a comeager subset of c 0 1 n

weakly almost periodic functions model theoretic stability and minimality of topological groups we investigate the automorphism groups of aleph 0 categorical structures and prove that they are exactly the roelcke precompact polish groups we show that the theory of a structure is stable if and only if every roelcke uniformly continuous function on the automorphism group is weakly almost periodic analysing the semigroup structure on the weakly almost periodic compactification we show that continuous surjective homomorphisms from automorphism groups of stable aleph 0 categorical structures to hausdorff topological groups are open we also produce some new wap trivial groups and calculate the wap compactification in a number of examples

quantitative concentration of stationary measures abstract we consider an ito stochastic differential equation and study the asymptotic behaviors of stationary measures of the corresponding fokker planck equation in the vicinity of a deterministic attractor or a repeller by establishing global measure estimates in domains of interest we show gaussian like behaviors of these measures in the basins of the attractor and the repeller not only do our results quantify the concentration results of stationary measures obtained in huang et al 2018 but also they are valid near a usual attractor resp repeller instead of a strong attractor resp repeller assumed in huang et al 2018 our approach in conducting the measure estimates is based on a new idea of constructing a sequence of lyapunov functions anti lyapunov functions in the basin of attraction resp expansion of the attractor resp repeller as applications of these measure estimates we also derive upper bounds for the differential entropy and establish certain entropy dimension inequalities

good measures on cantor space while there is up to homeomorphism only one cantor space i e one zero dimensional perfect compact nonempty metric space there are many measures on cantor space which are not topologically equivalent the clopen values set for a full nonatomic measure is the countable dense subset u u is clopen of the unit interval it is a topological invariant for the measure for the class of good measures it is a complete invariant a full nonatomic measure is good if whenever u v are clopen sets with u v there exists w a clopen subset of v such that w u these measures have interesting dynamical properties they a re exactly the measures which arise from uniquely ergodic minimal systems on cantor space for some of them there is a unique generic measure preserving homeomorphism that is within the polish group of such homeomorphisms there is a dense g conjugacy class

generically there is but one self homeomorphism of the cantor set we describe a self homeomorphism r of the cantor set x and then show that its conjugacy class in the polish group h x of all homeomorphisms of x forms a dense g subset of h x we also provide an example of a locally compact second countable topological group which has a dense conjugacy class

homogeneous probability measures on the cantor set abstract we show that every homeomorphism between closed measure zero subsets extends to a measure preserving auto homeomorphism whenever the cantor set is endowed with a suitable probability measure this is valid both for the standard product measure as well as for the universal homogeneous rational measure

amenable actions of groups the equivalence between different characterizations of amenable actions of a locally compact group is proved in particular this answers a question raised by r j zimmer in 1977

ordered structures and large conjugacy classes abstract this article is a contribution to the following problem does there exist a polish non archimedean group equivalently automorphism group of a fraisse limit that is extremely amenable and has ample generics as fraisse limits whose automorphism groups are extremely amenable must be ordered i e equipped with a linear ordering we focus on ordered fraisse limits we prove that automorphism groups of the universal ordered boron tree and the universal ordered poset have a comeager conjugacy class but no comeager 2 dimensional diagonal conjugacy class we formulate general conditions implying that there is no comeager conjugacy class comeager 2 dimensional diagonal conjugacy class or non meager 2 dimensional topological similarity class in the automorphism group of an ordered fraisse limit we also provide a number of applications of these results

weak shadowing for discrete dynamical systems on nonsmooth manifolds abstract in j math anal appl 189 1995 409 423 corless and pilyugin proved that weak shadowing is a c 0 generic property in the space of discrete dynamical systems on a compact smooth manifold m in our paper we give another proof of this theorem which does not assume that m has a differential structure moreover our method also works for systems on some compact metric spaces that are not manifolds such as a hilbert cube or generally a countably infinite cartesian product of manifolds with boundary and a cantor set

shifts of finite type as fundamental objects in the theory of shadowing shifts of finite type and the notion of shadowing or pseudo orbit tracing are powerful tools in the study of dynamical systems in this paper we prove that there is a deep and fundamental relationship between these two concepts let x be a compact totally disconnected space and f x rightarrow x a continuous map we demonstrate that f has shadowing if and only if the system f x is conjugate to the inverse limit of a directed system satisfying the mittag leffler condition and consisting of shifts of finite type in particular this implies that in the case that x is the cantor set f has shadowing if and only if f x is the inverse limit of a sequence satisfying the mittag leffler condition and consisting of shifts of finite type moreover in the general compact metric case where x is not necessarily totally disconnected we prove that f has shadowing if f x is a factor of the inverse limit of a sequence satisfying the mittag leffler condition and consisting of shifts of finite type by a quotient that almost lifts pseudo orbits

a note on the lyapunov equation some results on the sensitivity of the solution of the stable lyapunov equation are shown to follow easily from well known theorems of functional analysis

random walks on random coset spaces with applications to furstenberg entropy we determine the range of furstenberg entropy for stationary ergodic actions of nonabelian free groups by an explicit construction involving random walks on random coset spaces

a characterization of homeomorphic bernoulli trial measures we give conditions which given two bernoulli trial measures determine whether there exists a homeomorphism of cantor space which sends one measure to the other answering a question of oxtoby we then provide examples relating these results to the notions of good and refinable measures on cantor space

on characters of inductive limits of symmetric groups abstract in the paper we completely describe characters central positive definite functions of simple locally finite groups that can be represented as inductive limits of products of symmetric groups under block diagonal embeddings each such group g defines an infinite graded graph that encodes the embedding scheme the group g acts on the space x of infinite paths of the associated graph by changing initial edges of paths assuming the finiteness of the set of ergodic measures for the system x g we establish that each non regular indecomposable character g c is uniquely determined by the formula g 1 fix g 1 k fix g k where 1 k are g ergodic measures fix g x x g x x and 1 k 0 1 we illustrate our results on the group of rational permutations of the unit interval

δ weakly mixing subset in positive entropy actions of a nilpotent group abstract the notion of weakly mixing subsets is introduced for countable torsion free discrete group actions it is shown that for a finitely generated torsion free discrete nilpotent group action positive topological entropy implies the existence of weakly mixing subsets and while there exists a finitely generated torsion free discrete solvable group action which has positive topological entropy but without any weakly mixing subsets

on proximality with banach density one abstract let x t be a topological dynamical system a pair of points x y x 2 is called banach proximal if for any e 0 the set n z d t n x t n y e has banach density one we study the structure of the banach proximal relation a useful tool is the notion of the support of a topological dynamical system we show that a dynamical system is strongly proximal if and only if every pair in x 2 is banach proximal a subset s of x is banach scrambled if every two distinct points in s form a banach proximal pair but not asymptotic we construct a dynamical system with the whole space being a banach scrambled set even though the banach proximal relation of the full shift is of first category it has a dense mycielski invariant banach scrambled set we also show that for an interval map it is li yorke chaotic if and only if it has a cantor banach scrambled set

asymptotic abelianness weak mixing and property t let g be a second countable locally compact group and h a closed subgroup we characterize the lack of kazhdan s property t for the pair g h by the genericity of g actions on the hyperfinite ii1 factor with a certain asymptotic abelianness property relative to h as well as by the genericity of measure preserving g actions on a nonatomic standard probability space that are weakly mixing for h the latter furnishes a definitive generalization of a classical theorem of halmos for single automorphisms and strengthens a recent result of glasner thouvenot and weiss on generic ergodicity we also establish a weak mixing version of glasner and weiss s characterization of property t for discrete g in terms of the invariant state space of a bernoulli shift and show that on the car algebra a type of norm asymptotic abelianness is generic for g actions when g is discrete and admits a nontorsion abelian quotient

operational independence and tensor products of c algebras complete c independence of operator algebras is introduced equivalent characterization is given for c subalgebras to be completely independent in terms of maximal tensor product besides the independence of banach algebras is considered and we showed that hahn banach independence is a generalization of c independence and discussed hahn banach independence in mn a where a is a c algebra among others we characterize independence of operator algebras by projective and injective c tensor product in terms of simultaneous extensions of completely positive maps

on the benefits of laplace samples in solving a rare event problem using cross entropy method the convergence quality of the cross entropy ce optimizer relies critically on the mechanism meant for randomly generating data samples in agreement with the inference drawn in the earlier works the fast simulated annealing fsa and fast evolutionary programming fep since tracing a near global optimum embedded on a nonconvex search space can be viewed as a rare event problem a ce algorithm constructed using a long tailed distribution is intuitively attractive for effectively exploring the optimization landscape based on this supposition a set of ce algorithms employing the cauchy logistic and laplace distributions are experimentally validated in a wide range of optimization functions which are shifted rotated expanded and or composed characterized by convex unimodal discontinuous noisy and multimodal fitness landscapes the laplace distribution has been demonstrated to be more suitable for the ce optimization since the samples drawn have jump lengths long enough to elude local optima and short enough to preserve sufficient candidates in the global optimum neighborhood besides a theoretical analysis has been carried out to understand the following i benefits offered by the long tailed distributions towards evasion of local optima ii link between the variation in scale parameter estimate and the probability of producing candidate solutions arbitrarily close to the global optimum

the topological rohlin property and topological entropy for a compact metric space x let g h x denote the group of self homeomorphisms with the topology of uniform convergence the group g acts on itself by conjugation and we say that x satisfies the topological rohlin property if this action has dense orbits we show that the hilbert cube the cantor set and with a slight modification also even dimensional spheres satisfy this property we also show that zero entropy is generic for homeomorphisms of the cantor set whereas it is infinite entropy which is generic for homeomorphisms of cubes of dimension d 2 and the hilbert cube

generic automorphisms of homogeneous structures let g be a permutation group on the set usually we take n o we seek a notion of genericity for members of g the idea is that a member of g should be generic if it is in some sense typical we argue that the following is the correct definition suppose that g is endowed with a metric so that it becomes a complete metric space it follows that the baire category theorem holds and we may use the notions of meagre and comeagre sets

chaos among self maps of the cantor space glasner and weiss have shown that a generic homeomorphism of the cantor space has zero topological entropy hochman has shown that a generic transitive homeomorphism of the cantor space has the property that it is topologically conjugate to the universal odometer and hence far from being chaotic in any sense we show that a generic self map of the cantor space has zero topological entropy moreover we show that a generic self map of the cantor space has no periodic points and hence is not devaney chaotic nor devaney chaotic on any subsystem however we exhibit a dense subset of the space of all self maps of the cantor space each element of which has infinite topological entropy and is devaney chaotic on some subsystem

the dynamics of weakly reversible population processes near facets this paper concerns the dynamical behavior of weakly reversible deterministically modeled population processes near the facets codimension one faces of their invariant manifolds and proves that the facets of such systems are repelling it has been conjectured that any population process whose network graph is weakly reversible has strongly connected components is persistent we prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets or siphons an important application of this work pertains to chemical reaction systems that are complex balancing for these systems it is known that within the interior of each invariant manifold there is a unique equilibrium the global attractor conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies our results pertaining to weakly reversible systems imply that thi

generalized specification property and distributionally scrambled sets abstract suppose the dynamical system x f has generalized specification property in this paper we research the existence of the invariant mycielski distributionally scrambled sets for dynamical system x f moreover some properties about measure center are discussed and a dichotomy theorem is proved

kesten s theorem for invariant random subgroups an invariant random subgroup of the countable group is a ran dom subgroup of whose distribution is invariant under conjuga tion by all elements of we prove that for a nonamenable invariant random subgroup h the spectral radius of every finitely supported random walk on i s strictly less than the spectral radius of the corresponding random walk on h this generalizes a result of kesten who proved this for normal subgroups as a byproduct we show that for a cayley graph g of a linear group with no amenable normal subgroups any sequence of finite quotients of g that spectrally approximates g converges to g in benjamini schramm convergence in particular this implies that infinite sequences of finite d regular ramanujan schreier graphs have essentially large girth

on the k property of quantized arnold cat maps we prove that some quantized arnold cat maps are entropic k systems this result was formulated by h narnhofer j math phys 33 1502 1510 1992 but the fact that the optimal decomposition for the multi channel entropy constructed there is not strictly local was not appropriately taken care of we propose a strictly local decomposition based on a construction of voiculescu

stationary measures and equidistribution for orbits of nonabelian semigroups on the torus let be a semigroup of d d nonsingular integer matrices and consider the action of on the torus t we assume throughout that the action is strongly irreducible there is no subtorus invariant under a finite index subsemigroup of the strong irreducibility assumption in particular implies that acts ergodically on t equipped with the lebesgue measure m therefore the orbit of lebesgue almost every x t is dense and in an appropriate sense even becomes equidistributed however when is cyclic there is a set of full hausdorff dimension of exceptional points x for which x fails to be dense when is bigger the distribution of individual orbits can be expected to be much more restrictive an important result in this direction is due to furstenberg who showed for d 1 in which case 1 an abelian semigroup never satisfies condition 1 indeed the group generated by a semigroup satisfying 1 is nonamenable assumption 2 is a technical condition which is in particular satisfied when is a zariski dense semigroup of sld z 16

strong asymptotic abelianness for entropic k systems we prove that in entropick systems of type ii1 the automorphism is strongly asymptotically abelian

evolutionary programming in electromagnetic optimization a review in this paper we review recent advances in evolutionary programming ep and its implementation in various antenna microwave frequency selective surfaces and rf circuit optimization problems ep unlike the other two paradigms of evolutionary computational techniques namely genetic algorithms ga and evolution strategies es uses a mutation only variation operator where adaptive and or self adaptive techniques exist or can easily be designed for adapting the parameters of mutation operator during the evolution process we present the so called meta ep and design of its mutation operator using gaussian cauchy and poisson mutations as well as a hybrid of these mutations for continuous discrete and mixed parameter electromagnetic optimization problems in addition an efficient hybrid use of ep gradient search methods and cluster analysis as well as a novel hybrid ep ga algorithm are discussed examples presented include optimizations of corrugated horn antennas multilayered stacked microstrip antennas yagi uda arrays partially reflective surfaces dielectric filters meander line polarizer and rf duplexers