spatial realisations of kms states on the c algebras of higher rank graphs abstract several authors have recently been studying the equilibrium or kms states on the toeplitz algebras of finite higher rank graphs for graphs of rank one that is for ordinary directed graphs there is a natural dynamics obtained by lifting the gauge action of the circle to an action of the real line the algebras of higher rank graphs carry a gauge action of a higher dimensional torus and there are many potential dynamics arising from different embeddings of the real line in the torus previous results show that there is nonetheless a preferred dynamics for which the system exhibits a particularly satisfactory phase transition and that the unique kms state at the critical inverse temperature can then be implemented by integrating vector states against a measure on the infinite path space of the graph here we obtain a similar description of the kms state at the critical inverse temperature for other dynamics our spatial implementation is given by integrating against a measure on a space of paths which are infinite in some directions but finite in others our results are sharpest for the algebras of rank two graphs

kms states of quasi free dynamics on pimsner algebras abstract a continuous one parameter group of unitary isometries of a right hilbert c bimodule induces a quasi free dynamics on the cuntz pimsner c algebra of the bimodule and on its toeplitz extension the restriction of such a dynamics to the algebra of coefficients of the bimodule is trivial and the corresponding kms states of the toeplitz cuntz pimsner and cuntz pimsner c algebras are characterized in terms of traces on the algebra of coefficients this generalizes and sheds light onto various earlier results about kms states of the gauge actions on cuntz algebras cuntz krieger algebras and crossed products by endomorphisms we also obtain a more general characterization in terms of kms weights for the case in which the inducing isometries are not unitary and accordingly the restriction of the quasi free dynamics to the algebra of coefficients is nontrivial

partial actions and kms states on relative graph c algebras abstract the relative graph c algebras introduced by muhly and tomforde are generalizations of both graph algebras and their toeplitz extensions for an arbitrary graph e and a subset r of the set of regular vertices of e we show that the relative graph c algebra c e r is isomorphic to a partial crossed product for an action of the free group generated by the edge set on the relative boundary path space given a time evolution on c e r induced by a function on the edge set we characterize the kms states and ground states using an abstract result of exel and laca guided by their work on kms states for toeplitz cuntz krieger type algebras associated to infinite matrices we obtain complete descriptions of the convex sets of kms states of finite type and of kms states of infinite type whose associated measures are supported on recurrent infinite paths this allows us to give a complete concrete description of the convex set of all kms states for a big class of graphs which includes all graphs with finitely many vertices

the partial schur multiplier of a group abstract refining the technique worked out in previous papers we give a characterization up to equivalence of the factor sets of partial projective representation of a group g over an algebraically closed field k in terms of equalities satisfied by this allows one to conclude that any component of the partial schur multiplier p m g is an epimorphic image of a direct power of k moreover it is shown that any component of p m g is an epimorphic image of the component p m g g g of the equivalence classes of the totally defined partial factor sets examples with cyclic g are considered in particular the total component p m g g g is determined when g is an arbitrary finite cyclic group in this case p m g g g is a direct power of k

equilibrium states and entropy theory for nica pimsner algebras abstract we study the equilibrium simplex of nica pimsner algebras arising from product systems of finite rank on the free abelian semigroup first we show that every equilibrium state has a convex decomposition into parts parametrized by ideals on the unit hypercube secondly we associate every gauge invariant part to a sub simplex of tracial states of the diagonal algebra we show how this parametrization lifts to the full equilibrium simplices of non infinite type the finite rank entails an entropy theory for identifying the two critical inverse temperatures a the least upper bound for existence of non finite type equilibrium states and b the least positive inverse temperature below which there are no equilibrium states at all we show that the first one can be at most the strong entropy of the product system whereas the second is the infimum of the tracial entropies modulo negative values thus phase transitions can happen only in between these two critical points and possibly at zero temperature

fundamental group of simple c algebras with unique trace abstract we introduce the fundamental group f a of a unital simple c algebra a with a unique normalized trace we compute fundamental groups f a of several nuclear or non nuclear c algebras a k theoretical obstruction enables us to compute the fundamental group easily our study is essentially based on the computation of picard groups by kodaka

kms weights on graph c algebras abstract the paper contains a study of the gauge invariant kms weights for a generalized gauge action on a graph c algebra when the graph is irreducible and has the property that there are at most countably many roads to infinity in the graph a complete description is given of the structure of kms weights for the gauge action the structure is very rich and is identical with the structure of kms states for the restriction of the action to any corner defined by a projection in the fixed point algebra

improved algorithms for economic lot size problems many problems in inventory control production planning and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by a s manne 1958 and by h m wagner and t m whitin 1958 the manne wagner whitin model and its variants have been studied widely in the operations research and management science communities and a large number of algorithms have been proposed for solving various problems expressed in terms of this model most of which assume concave costs and rely on dynamic programming in this paper we show that for many of these concave cost economic lot size problems the dynamic programming formulation of the problem gives rise to a special kind of array called a monge array we then show how the structure of monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems we focus on uncapacitated problems i e problems without bounds on production inventory or backlogging capacitated problem

kms states on c algebras associated to a family of commuting local homeomorphisms abstract we consider a family of commuting local homeomorphisms on a compact space and build a compactly aligned product system of hilbert bimodules the nica toeplitz algebra of this system carries a gauge action of a higher dimensional torus and there are many possible dynamics obtained by composing with different embeddings of the real line in this torus we study the kms states of these dynamics for large inverse temperatures including we describe the simplex of kms states on the nica toeplitz algebra we illustrate our main theorem by considering backward shifts on the infinite path spaces of a class of k graphs whose shift maps commute

on the c algebra of a locally injective surjection and its kms states it is shown that a locally injective surjection on a compact metric space is a factor of a local homeomorphism in such a way that the associated c algebras are isomorphic this is subsequently used to obtain upper and lower bounds for the possible values of kms states for generalized gauge actions on the c algebra

equilibrium and ground states from cayley graphs abstract we present a general framework for the study of kms states of generalized gauge actions on the c algebra of a cayley graph which is pointed by considering the neutral element of the group as a distinguished vertex we use this framework to give a concrete description of a particular kind of kms states on the c algebras that we call abelian kms states if the group is nilpotent all kms states are abelian and our analysis gives the full picture in this case we then describe the ground states that are limits of abelian kms states when the temperature goes to zero

incomplete generalized l statistics given data x 1 x n and a kernel h with m arguments serfling introduced the class of generalized l statistics gl statistics which is defined by taking linear combinations of the ordered h x i1 x im where i 1 i m ranges over all n n m distinct m tuples of 1 n in this paper we derive a class of incomplete generalized l statistics igl statistics by taking linear combinations of the ordered elements from a subset of h x i1 x im with size n n a special case is the class of incomplete u statistics introduced by blom under very general conditions the igl statistic is asymptotically equivalent to the gl statistic as soon as n n n as n which makes the igl much more computationally feasible we also discuss various ways of selecting the subset of h x i x im several examples are discussed in particular some new estimates of the scale parameter in nonparametric regression are introduced it is shown that these estimates are asymptotically equivalent to an igl statistic some extensions for example functionals other than l and multivariate kernels are also addressed

limit theorems for functionals of mixing processes with applications to u statistics and dimension estimation in this paper we develop a general approach for investigating the asymptotic distribution of functional xn f zn k k z of absolutely regular stochastic processes zn n z such functional occur naturally as orbits of chaotic dynamical systems and thus our results can be used to study probabilistic aspects of dynamical systems we first prove some moment inequalities that are analogous to those for mixing sequences with their help several limit theorems can be proved in a rather straightforward manner we illustrate this by re proving a central limit theorem of ibragimov and linnik then we apply our techniques to u statistics matrix equation with symmetric kernel h r r r we prove a law of large numbers extending results of aaronson burton dehling gilat hill and weiss for absolutely regular processes we also prove a central limit theorem under a different set of conditions than the known results of denker and keller as our main application we establish an invariance principle for u processes un h h indexed by some class of functions we finally apply these results to study the asymptotic distribution of estimators of the fractal dimension of the attractor of a dynamical system

labelled space c algebras as partial crossed products and a simplicity characterization abstract a partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space c algebras are isomorphic an improved characterization of simplicity for labelled space c algebras is given and applied to c algebras of subshifts

an efficient algorithm for the capacitated single item dynamic lot size problem abstract a dynamic programming based algorithm is developed for the single item lot size problem with concave costs and arbitrary capacities by making use of the extreme point properties of the problem first the set of all feasible cumulative production levels that may occur in an optimal solution is generated in the second stage a dynamic programming procedure is carried out over this set the worst case computational effort is equal to that of the standard dynamic programming approach but extensive computational tests with the algorithm indicate that for t period problems the computational effort does not exceed o t4 the performance of the algorithm is compared with the performance of the existing procedures in the literature for the general the constant capacity and the constant unit cost problems the computational results demonstrate that our algorithm is at least three times faster than the other procedures for all problem types considered

twisted cyclic theory equivariant kk theory and kms states given a c algebra a with a kms weight for a circle action we construct and compute a secondary invariant on the equivariant k theory of the mapping cone of a t a both in terms of equivariant kk theory and in terms of a seminite spectral ow this in particular puts the previously considered examples of cuntz algebras 9 and suq 2 13 in a general framework as a new example we consider the araki woods iii representations of the fermion algebra

dynamical entropy of c algebras and von neumann algebras the definition of the dynamical entropy is extended for automorphism groups ofc algebras as an example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density

economic lot sizing an o n log n algorithm that runs in linear time in the wagner whitin case we consider the n period economic lot sizing problem where the cost coefficients are not restricted in sign in their seminal paper h m wagner and t m whitin proposed an o n2 algorithm for the special case of this problem where the marginal production costs are equal in all periods and the unit holding costs are nonnegative it is well known that their approach can also be used to solve the general problem without affecting the complexity of the algorithm in this paper we present an algorithm to solve the economic lot sizing problem in o n log n time and we show how the wagner whitin case can even be solved in linear time our algorithm can easily be explained by a geometrical interpretation and the time bounds are obtained without the use of any complicated data structure furthermore we show how wagner and whitin s and our algorithm are related to algorithms that solve the dual of the simple plant location formulation of the economic lot sizing problem

semigroups of endomorphisms dirichlet series and phase transitions abstract we study phase transitions of c dynamical systems a in which a is the crossed product of a c algebra by a lattice semigroup of endomorphisms and is a one parameter subgroup of the dual action determined by a real valued scale on the semigroup we show that the kms equilibrium condition is equivalent to a markov type condition on the predual semigroup dynamical system and give criteria for the existence of equilibrium states and of phase transitions in terms of the semigroup action when the semigroup is an integer lattice the partition function of the real scale is a dirichlet series having an euler product expansion on their convergence region there is a phase transition whose geometry is fully determined by the ground states and is independent of the chosen scale generalizing a model recently constructed by bost and connes motivated by earlier work of julia as applications we simplify part of the proof the bost connes theorem on phase transition with spontaneous symmetry breaking and we discuss generalizations to other systems associated to subsets of primes and to number fields of class number 1

phase transition on exel crossed products associated to dilation matrices an integer matrix a md z induces a covering a of td and an endomorphism a f f a of c td for which there is a natural transfer operator l in this paper we compute the kms states on the exel crossed product c td a ln and its toeplitz extension we find that c td a ln has a unique kms state which has inverse temperature log deta its toeplitz extension on the other hand exhibits a phase transition at log deta and for larger the simplex of kms states is isomorphic to the simplex of probability measures on td

kms weights on groupoid and graph c algebras abstract the paper contains a description of the kms weights for the one parameter action on the reduced c algebra of a second countable locally compact hausdorff etale groupoid arising from a continuous real valued homomorphism satisfying two conditions the result is subsequently applied to identify the kms weights for the gauge action on a simple graph algebra the von neumann algebra generated by the gns representation of an extremal kms weight is a factor and tools are developed to determine its type the paper concludes with three examples to illustrate the results

c algebras of right lcm monoids and their equilibrium states we study the internal structure of c algebras of right lcm monoids by means of isolating the core semigroup c algebra as the coecient algebra of a fock type module on which the full semigroup c algebra admits a left action if the semigroup has a generalised scale we classify the kms states for the associated time evolution on the semigroup c algebra and provide sucient conditions for uniqueness of the kms state at inverse temperature in a critical interval

lyapunov spectra for kms states on cuntz krieger algebras we study relations between h kms states on cuntz krieger algebras and the dual of the perron frobenius operator mathcal l beta h ast generalising the well studied purely hyperbolic situation we obtain under mild conditions that for an expansive dynamical system there is a one one correspondence between h kms states and eigenmeasures of mathcal l beta h ast for the eigenvalue 1 we then apply these general results to study multifractal decompositions of limit sets of essentially free kleinian groups g which may have parabolic elements we show that for the cuntz krieger algebra arising from g there exists an analytic family of kms states induced by the lyapunov spectrum of the analogue of the bowen series map associated with g furthermore we obtain a formula for the hausdorff dimensions of the restrictions of these kms states to the set of continuous functions on the limit set of g if g has no parabolic elements then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with g

using stochastic approximation methods to compute optimal base stock levels in inventory control problems in this paper we consider numerous inventory control problems for which the base stock policies are known to be optimal and we propose stochastic approximation methods to compute the optimal base stock levels the existing stochastic approximation methods in the literature guarantee that their iterates converge but not necessarily to the optimal base stock levels in contrast we prove that the iterates of our methods converge to the optimal base stock levels moreover our methods continue to enjoy the well known advantages of the existing stochastic approximation methods in particular they only require the ability to obtain samples of the demand random variables rather than to compute expectations explicitly and they are applicable even when the demand information is censored by the amount of available inventory

amenability for fell bundles given a fell bundle b over a discrete group we construct its reduced cross sectional algebra c r b in analogy with the reduced crossed products defined for c dynamical systems when the reduced and full cross sectional algebras of b are isomorphic we say that the bundle is amenable we then formulate an approximation property which we prove to be a sufficient condition for amenability a theory of graded c algebras possessing a conditional expectation is developed with an eye on the fell bundle that one naturally associates to the grading we show for instance that all such algebras are isomorphic to c r b when the bundle is amenable we also study induced ideals in graded c algebras and obtain a generalization of results of str til and voiculescu on af algebras and of nica on quasi lattice ordered groups a brief comment is made on the relevance to our theory of a certain open problem in the theory of exact c algebras an application is given to the case of an fn grading of the cuntz krieger algebras oa recently discovered by quigg and raeburn specifically we show that the cuntz krieger bundle satisfies the approximation property and hence is amenable for all matrices a with entries in 0 1 even if a does not satisfy the well known property i studied by cuntz and krieger in their paper

partial dynamical systems and the kms condition given a countably infinite 0 1 matrix a without identically zero rows let a be the cuntz krieger algebra recently introduced by the authors and a be the toeplitz extension of a once the latter is seen as a cuntz pimsner algebra as recently shown by szymanski we study the kms equilibrium states of c dynamical systems based on a and a with dynamics satisfying for the canonical generating partial isometries s x and arbitrary real numbers n x 1 the kms states on both a and a are completely characterized for certain values of the inverse temperature according to the position of relative to three critical values defined to be the abscissa of convergence of certain dirichlet series associated to a and the n x our results for a are derived from those for a by virtue of the former being a covariant quotient of the latter when the matrix a is finite these results give theorems of olesen and pedersen for n and of enomoto fujii and watatani for a as particular cases

hecke algebras of semidirect products and the finite part of the connes marcolli c algebra abstract we study a c dynamical system arising from the ring inclusion of the 2 2 integer matrices in the rational ones the orientation preserving affine groups of these rings form a hecke pair that is closely related to a recent construction of connes and marcolli our dynamical system consists of the associated reduced hecke c algebra endowed with a canonical dynamics defined in terms of the determinant function we show that the schlichting completion also consists of affine groups of matrices over the finite adeles and we obtain results about the structure and induced representations of the hecke c algebra in a somewhat unexpected parallel with the one dimensional case studied by bost and connes there is a group of symmetries given by an action of the finite integral ideles and the corresponding fixed point algebra decomposes as a tensor product over the primes this decomposition allows us to obtain a complete description of a natural class of equilibrium states which conjecturally includes all kms states for 0 1

functional limit theorems for u processes un processus u est une collection de statistiques u indicees par une famille de noyaux symetriques on utilise la theorie limite classique pour demontrer pour le processus u des analogues du theoreme central limite pour les processus empiriques

finding optimal s s policies is about as simple as evaluating a single policy in this paper a new algorithm for computing optimal s s policies is derived based upon a number of new properties of the infinite horizon cost function c s s as well as a new upper bound for optimal order up to levels s and a new lower bound for optimal reorder levels s the algorithm is simple and easy to understand its computational complexity is only 2 4 times that required to evaluate a specific single s s policy the algorithm applies to both periodic review and continuous review inventory systems

dynamical approximation entropies and topological entropy in operator algebras dynamical entropy invariants based on a general approximation approach are introduced for c and w algebra automorphisms this includes a noncommutative extension of topological entropy

the value of multistage stochastic programming in capacity planning under uncertainty this paper addresses a general class of capacity planning problems under uncertainty which arises for example in semiconductor tool purchase planning using a scenario tree to model the evolution of the uncertainties we develop a multistage stochastic integer programming formulation for the problem in contrast to earlier two stage approaches the multistage model allows for revision of the capacity expansion plan as more information regarding the uncertainties is revealed we provide analytical bounds for the value of multistage stochastic programming vms afforded over the two stage approach by exploiting a special substructure inherent in the problem we develop an efficient approximation scheme for the difficult multistage stochastic integer program and prove that the proposed scheme is asymptotically optimal computational experiments with realistic scale problem instances suggest that the vms for this class of problems is quite high moreover the quality and performance of the approximation scheme is very satisfactory fortunately this is more so for instances for which the vms is high

kms states on nica toeplitz hbox c c algebras given a quasi lattice ordered group g p and a compactly aligned product system x of essential hbox c correspondences over the monoid p we show that there is a bijection between the gauge invariant hbox kms beta states on the nica toeplitz algebra mathcal nt x of x with respect to a gauge type dynamics on one side and the tracial states on the coefficient algebra a satisfying a system in general infinite of inequalities on the other this strengthens and generalizes a number of results in the literature in several directions we do not make any extra assumptions on p and x and our result can in principle be used to study kms states at any finite inverse temperature beta under fairly general additional assumptions we show that there is a critical inverse temperature beta c such that for beta beta c all hbox kms beta states are of gibbs type hence gauge invariant in which case we have a complete classification of hbox kms beta states in terms of tracial states on a while at beta beta c we have a phase transition manifesting itself in the appearance of hbox kms beta states that are not of gibbs type in the case of right angled artin monoids we show also that our system of inequalities for traces on a can be reduced to a much smaller system a finite one when the monoid is finitely generated most of our results generalize to arbitrary quasi free dynamics on mathcal nt x

polynomial time algorithms for stochastic uncapacitated lot sizing problems in 1958 wagner and whitin published a seminal paper on the deterministic uncapacitated lot sizing problem a fundamental model that is embedded in many practical production planning problems in this paper we consider a basic version of this model in which problem parameters are stochastic the stochastic uncapacitated lot sizing problem we define the production path property of an optimal solution for our model and use this property to develop a backward dynamic programming recursion this approach allows us to show that the value function is piecewise linear and right continuous we then use these results to show that a full characterization of the optimal value function can be obtained by a dynamic programming algorithm in polynomial time for the case that each nonleaf node contains at least two children moreover we show that our approach leads to a polynomial time algorithm to obtain an optimal solution to any instance of the stochastic uncapacitated lot sizing problem regardless of the structur

stochastic lot sizing problem with inventory bounds and constant order capacities abstract in this paper we study the stochastic version of lot sizing problems with inventory bounds and order capacities customer demands inventory bounds and costs are subject to uncertainty and dependent with each other throughout the finite planning horizon two models in stochastic programming are developed the first one has inventory bound constraints and the second one has both inventory bound and order capacity constraints we explore structural properties of the two models and develop o n 2 and o n 2 t log n dynamic programming algorithms for them respectively our model also generalizes the deterministic lot sizing problem with inventory bounds for some cases when applied to the deterministic versions our algorithms outperform existing deterministic algorithms

storage space capacitated inventory system with r q policies we deal with an inventory system with limited storage space for a single item or multiple items for the single item system customers demand is stochastic the inventory is controlled by a continuous review r q policy goods are replenished to the inventory system with a constant lead time an optimization problem with a storage space constraint is formulated for computing a single item r q policy that minimizes the long run average system cost based on some existing results in the single item r q policy without a storage space constraint in the literature useful structural properties of the optimization problem are attained an efficient algorithm with polynomial time computational complexity is then proposed for obtaining the optimal solutions for the multi item system each item possesses its particular customers demand that is stochastic its own r q policy that controls the inventory and its individual lead time that is constant an important issue in such inventory systems is the allocation of the storage space to the items and the values of r and q for each item we formulate an optimization problem with a storage space constraint for multi item r q policies based on the results in the single item r q policy with a storage space constraint we find useful structural properties of the optimization problem an efficient algorithm with polynomial time computational complexity is then proposed for obtaining undominated solutions

kms states entropy and the variational principle in full c dynamical systems to any periodic and full c dynamical system an invertible operator s acting on the banach space of trace functionals of the fixed point algebra is canonically associated kms states correspond to positive eigenvectors of s a perron frobenius type theorem asserts the existence of kms states at inverse temperatures equals the logarithms of the inner and outer spectral radii of s extremal kms states examples arising from subshifts in symbolic dynamics self similar sets in fractal geometry and noncommutative metric spaces are discussed

type iii1 equilibrium states of the toeplitz algebra of the affine semigroup over the natural numbers abstract we complete the analysis of kms states of the toeplitz algebra t n n of the affine semigroup over the natural numbers recently studied by raeburn and the first author by showing that for every inverse temperature in the critical interval 1 2 the unique kms state is of type iii1 we prove this by reducing the type classification from t n n to that of the symmetric part of the bost connes system with a shift in inverse temperature to carry out this reduction we first obtain a parametrization of the nica spectrum of n n in terms of an adelic space combining a characterization of traces on crossed products due to the second author with an analysis of the action of n n on the nica spectrum we can also recover all the kms states of t n n originally computed by raeburn and the first author our computation sheds light on why there is a free transitive circle action on the extremal kms states for 2 that does not ostensibly come from an action of t on the c algebra

technical note solving linear cost dynamic lot sizing problems in o n log n time in this paper we study capacitated dynamic lot sizing problems with or without backorders under the assumption that production costs are linear that is there are no setup costs these two dynamic lot sizing problems with or without backorders are minimum cost flow problems on an underlying network that possess a special structure we show how the well known successive shortest path algorithm for the minimum cost flow problem can be used to solve these problems in o n2 time where n is the number of periods in the dynamic lot sizing problems and how with the use of dynamic trees we can solve these problems in o n log n time our algorithm also extends to the dynamic lot sizing problem with integer variables and convex production costs with running time o n log n log u where u is the largest demand value

lot sizing with production and delivery time windows we study two different lot sizing problems with time windows that have been proposed recently for the case of production time windows in which each client specific order must be produced within a given time interval we derive tight extended formulations for both the constant capacity and uncapacitated problems with wagner whitin non speculative costs for the variant with nonspecific orders known to be equivalent to the problem in which the time windows can be ordered by time we also show equivalence to the basic lot sizing problem with upper bounds on the stocks here we derive polynomial time dynamic programming algorithms and tight extended formulations for the uncapacitated and constant capacity problems with general costs for the problem with delivery time windows we use a similar approach to derive tight extended formulations for both the constant capacity and uncapacitated problems with wagner whitin non speculative costs

a new approach to recent constructions of c algebras from modular index theory abstract we present a new approach to c algebras recently constructed in the context of modular index theory by carey phillips putnam and rennie it turns out that their constructions can be identified with full corners of ideals in semigroup c algebras this new point of view leads to a systematic analysis of these algebras and their canonical maximal abelian subalgebras

kms states on c algebras associated to higher rank graphs consider a higher rank graph of rank k both the cuntz krieger algebra and the toeplitz cuntz krieger algebra of the graph carry natural gauge actions of the torus tk and restricting these gauge actions to one parameter subgroups of tk gives dynamical systems involving actions of the real line we study the kms states of these dynamical systems we find that for large inverse temperatures the simplex of kms states on the toeplitz cuntz krieger algebra has dimension d one less than the number of vertices in the graph we also show that there is a preferred dynamics for which there is a critical inverse temperature c for larger than c there is a d dimensional simplex of kms states when c and the one parameter subgroup is dense there is a unique kms state and this state factors through the cuntz krieger algebra as in previous studies for k 1 our main tool is the perron frobenius theory for irreducible non negative matrices though here we need a version of the theory for commuting families of matrices

tensor algebras of product systems and their c envelopes abstract let g p be an abelian lattice ordered group and let x be a compactly aligned product system over p with coefficients in a we show that the c envelope of the nica tensor algebra n t x coincides with both sehnem s covariance algebra a x p and the co universal c algebra n o x r for injective gauge compatible nica covariant representations of carlsen larsen sims and vittadello we give several applications of this result on both the selfadjoint and non selfadjoint operator algebra theory first we guarantee the existence of n o x r thus settling a problem of carlsen larsen sims and vittadello which was open even for abelian lattice ordered groups as a second application we resolve a problem posed by skalski and zacharias on dilating isometric representations of product systems to unitary representations as a third application we characterize the c envelope of the tensor algebra of a finitely aligned higher rank graph which also holds for topological higher rank graphs as a final application we prove reduced hao ng isomorphisms for generalized gauge actions of discrete groups on c algebras of product systems this generalizes recent results that were obtained by various authors in the case where g p z n

a review of goodness of fit tests for pareto distributions abstract pareto distributions are the most popular models in economics and finance hence it is essential to have a wide spectrum of tools for checking their goodness of fit to a given data set this paper provides the first review of known goodness of fit tests for pareto distributions over twenty tests are reviewed their powers are compared by simulation

a robust analysis of crossover designs using multisample generalized l statistics abstract in a crossover study some or all subjects receive more than one treatment sequentially using a clinical example as motivation we develop multisample generalized l statistics gl statistics to estimate and test for treatment effects in crossovers when the distribution of the response data deviates from normality the basic idea is to adapt simple l statistics such as the trimmed mean and median to data with dependencies gl statistics may be applied to crossovers with more than two periods and or sequences these designs are useful for experiments with two treatments in which carryover and treatment effects might be aliased in the commonly used two period two sequence design as well as for experiments with more than two treatments for data analysis with large samples the asymptotic properties of the gl statistics suggest that the generalized trimmed mean and generalized median often should be strongly consistent and normal a simulation study of a four sequence two period crossover desi

a simple forward algorithm to solve general dynamic lot sizing models with n periods in 0n log n or 0n time this paper is concerned with the general dynamic lot size model or generalized wagner whitin model let n denote the number of periods into which the planning horizon is divided we describe a simple forward algorithm which solves the general model in 0n log n time and 0n space as opposed to the well known shortest path algorithm advocated over the last 30 years with 0n2 time a linear i e 0n time and space algorithm is obtained for two important special cases a models without speculative motives for carrying stock i e where in each interval of time the per unit order cost increases by less than the cost of carrying a unit in stock b models with nondecreasing setup costs we also derive conditions for the existence of monotone optimal policies and relate these to known planning horizon and other results from the literature

k theory for partial crossed products by discrete groups the notion of a partial crossed product of a c algebra by the group of integers introduced by r exel is generalized to a partial crossed product by any discrete group a reduced partial crossed product is defined and some of the standard facts relating amenability and k amenability to ordinary crossed products are extended to this case the exact sequence of pimsner and voiculescu for reduced crossed products by the free group on n generators is generalized to this setting this result is used to calculate the k groups of an amalgamated product of two finite dimensional c algebras over a common maximal commutative subalgebra

a fully polynomial time approximation scheme for single item stochastic inventory control with discrete demand the single item stochastic inventory control problem is to find an inventory replenishment policy in the presence of independent discrete stochastic demands under periodic review and finite time horizon in this paper we prove that this problem is intractable and design for it a fully polynomial time approximation scheme

kms states on the c algebra of a higher rank graph and periodicity in the path space we study the kms states of the c algebra of a strongly connected finite k graph we find that there is only one 1 parameter subgroup of the gauge action that can admit a kms state the extreme kms states for this preferred dynamics are parameterised by the characters of an abelian group that captures the periodicity in the infinite path space of the graph we deduce that there is a unique kms state if and only if the k graph c algebra is simple giving a complete answer to a question of yang when the k graph c algebra is not simple our results reveal a phase change of an unexpected nature in its toeplitz extension

applications of entropy of product systems higher rank graphs abstract we consider c algebras of finite higher rank graphs along with their rotational action we show how the entropy theory of product systems with finite frames applies to identify the phase transitions of the dynamics we compute the positive inverse temperatures where symmetry breaks and in particular we identify the subharmonic parts of the gauge invariant equilibrium states our analysis applies to positively weighted rotational actions through a recalibration of the entropies

longcrisp a test for bump hunting in longitudinal data we propose an extension of the harezlak and heckman j comput graph statist 2001 10 4 713 729 test for detecting local extrema to the longitudinal data setting we use penalized spline regression techniques statist sci 1996 11 89 102 to provide a computationally efficient method of testing for relatively large data sets we estimate the p values of our test longcrisp with a smoothed bootstrap our simulation studies indicate that the test is generally conservative and has power exceeding 70 per cent at the alpha 0 1 nominal level in most considered settings finally we apply our testing procedure to the longitudinal measurements of body mass index of former prisoners of war in vietnam and conclude that the mean population curve exhibits non monotone behaviour

crossed products by finite index endomorphisms and kms states abstract given a unital c algebra a an injective endomorphism a a preserving the unit and a conditional expectation e from a to the range of we consider the crossed product of a by relative to the transfer operator l 1e when e is of index finite type we show that there exists a conditional expectation g from the crossed product to a which is unique under certain hypothesis we define a gauge action on the crossed product algebra in terms of a central positive element h and study its kms states the main result is if h 1 and e ab e ba for all a b a e g when a is commutative then the kms states are precisely those of the form g where is a trace on a satisfying the identity a l h ind e a where ind e is the jones kosaki watatani index of e

estimating densities of functions of observations abstract density estimates such as histograms and more sophisticated versions are important in applied and theoretical statistics in applied statistics a density estimate gives the data analyst a graphical overview of the shape of the distribution this overview allows the data analyst to arrive immediately at a qualitative impression of the location scale and various aspects of the extremes of the distribution in theoretical statistics the shape of the density allows the researcher to link the data to families of curves perhaps indexed parametrically by estimating a density nonparametrically certain aspects of the data can be viewed without the restriction of a priori imposing limitations of a class of parametric curves in this article we introduce density estimation for functions of observations to motivate the study one type of function used is the interpoint distance between observations arising in spatial statistics from the fields of biometry and regional science a second type of func

circle actions on c algebras partial automorphisms and a generalized pimsner voiculescu exact sequence abstract we introduce a method to study c algebras possessing an action of the circle group from the point of view of their internal structure and their k theory under relatively mild conditions our structure theorem shows that any c algebra where an action of the circle is given arises as the result of a construction that generalizes crossed products by the group of integers such a generalized crossed product construction is carried out for any partial automorphism of a c algebra where by a partial automorphism we mean an isomorphism between two ideals of the given algebra our second main result is an extension to crossed products by partial automorphisms of the celebrated pimsner voiculescu exact sequence for k groups the representation theory of the algebra arising from our construction is shown to parallel the representation theory for c dynamical systems in particular we generalize several of the main results relating to regular and covariant representations of crossed products

hecke algebras for protonormal subgroups we introduce the term protonormal to refer to a subgroup h of a group g such that for every x in g the subgroups x 1hx and h commute as sets if moreover g h is a hecke pair we show that the hecke algebra h g h is generated by the range of a canonical partial representation of g vanishing on h as a consequence we show that there exists a maximum c norm on h g h generalizing previous results by brenken hall laca larsen kaliszewski landstad and quigg when there exists a normal subgroup n of g containing h as a normal subgroup we prove a new formula for the product of the generators and give a very clean description of h g h in terms of generators and relations we also give a description of h g h as a crossed product relative to a twisted partial action of the group g n on the group algebra of n h based on our presentation of h g h in terms of generators and relations we propose a generalized construction for hecke algebras in case g h does not satisfy the hecke condition

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

the flow of weights and the cuntz pimsner algebras we describe the flows of weights for von neumann algebras arising from kms states for the gauge actions of the cuntz pimsner algebras in terms of poisson tail boundaries

on the existence of conformal measures a general notion of conformal measure is introduced and some basic properties are studied sufficient conditions for the existence of these measures are obtained using a general construction principle the geometric properties of conformal measures relate equilibrium states and hausdorff measures this is shown for invariant subsets of s under expanding maps

finite digraphs and kms states abstract the paper contains a description of the kms states of a generalized gauge action on the c algebra of a finite graph

kms states on pimsner algebras associated with c dynamical systems abstract we examine the theory of the kms states on pimsner algebras arising from multivariable unital c dynamical systems as an application we show that pimsner algebras of piecewise conjugate classical systems attain the same kms states even though it is still an open problem whether or not they are isomorphic

limit theorems for functionals of moving averages let x n i 1 a i e n 1 where the e i are i i d with mean 0 and finite second moment and the a i are either summable or regularly varying with index 1 1 2 the sequence x n has short memory in the former case and long memory in the latter for a large class of functions k a new approach is proposed to develop both central n rate and noncentral non n rate limit theorems for s n n 1 n k x n ek x n specifically we show that in the short memory case the central limit theorem holds for s n and in the long memory case s n can be decomposed into two asymptotically uncorrelated parts that follow a central limit and a non central limit theorem respectively further we write the noncentral part as an expansion of uncorrelated components that follow noncentral limit theorems connections with the usual hermite expansion in the gaussian setting are also explored

equilibrium states on the cuntz pimsner algebras of self similar actions we consider a family of cuntz pimsner algebras associated to self similar group actions and their toeplitz analogues both families carry natural dynamics implemented by automorphic actions of the real line and we investigate the equilibrium states the kms states for these dynamical systems we find that for all inverse temperatures above a critical value the kms states on the toeplitz algebra are given in a very concrete way by traces on the full group algebra of the group at the critical inverse temperature the kms states factor through states of the cuntz pimsner algebra if the self similar group is contracting then the cuntz pimsner algebra has only one kms state we apply these results to a number of examples including the self similar group actions associated to integer dilation matrices and the canonical self similar actions of the basilica group and the grigorchuk group

phase transition on the toeplitz algebra of the affine semigroup over the natural numbers abstract we show that the group q q of orientation preserving affine transformations of the rational numbers is quasi lattice ordered by its subsemigroup n n the associated toeplitz c algebra t n n is universal for isometric representations which are covariant in the sense of nica we give a presentation of t n n in terms of generators and relations and use this to show that the c algebra q n recently introduced by cuntz is the boundary quotient of q q n n in the sense of crisp and laca the toeplitz algebra t n n carries a natural dynamics which induces the one considered by cuntz on the quotient q n and our main result is the computation of the kms equilibrium states of the dynamical system t n n r for all values of the inverse temperature for 1 2 there is a unique kms state and the kms 1 state factors through the quotient map onto q n giving the unique kms state discovered by cuntz at 2 there is a phase transition and for 2 the kms states are indexed by probability measures on the circle there is a further phase transition at where the kms states are indexed by the probability measures on the circle but the ground states are indexed by the states on the classical toeplitz algebra t n

equilibrium states on operator algebras associated to self similar actions of groupoids on graphs abstract we consider self similar actions of groupoids on the path spaces of finite directed graphs and construct examples of such self similar actions using a suitable notion of graph automaton self similar groupoid actions have a cuntz pimsner algebra and a toeplitz algebra both of which carry natural dynamics lifted from the gauge actions we study the equilibrium states the kms states on the resulting dynamical systems above a critical inverse temperature the kms states on the toeplitz algebra are parametrised by the traces on the full c algebra of the groupoid and we describe a program for finding such traces the critical inverse temperature is the logarithm of the spectral radius of the incidence matrix of the graph and at the critical temperature the kms states on the toeplitz algebra factor through states of the cuntz pimsner algebra under a verifiable hypothesis on the self similar action there is a unique kms state on the cuntz pimsner algebra we discuss an explicit method of computing the values of this kms state and illustrate with examples

kms states on the c algebras of finite graphs abstract we consider a finite directed graph e and the gauge action on its toeplitz cuntz krieger algebra viewed as an action of r for inverse temperatures larger than a critical value c we give an explicit construction of all the kms states if the graph is strongly connected then there is a unique kms c state and this state factors through the quotient map onto c e our approach is direct and relatively elementary

a branch and cut algorithm for the stochastic uncapacitated lot sizing problem this paper addresses a multi stage stochastic integer programming formulation of the uncapacitated lot sizing problem under uncertainty we show that the classical l s inequalities for the deterministic lot sizing polytope are also valid for the stochastic lot sizing polytope we then extend the l s inequalities to a general class of valid inequalities called the inequalities and we establish necessary and sufficient conditions which guarantee that the inequalities are facet defining a separation heuristic for inequalities is developed and incorporated into a branch and cut algorithm a computational study verifies the usefulness of the inequalities as cuts

x y band and modified s s policy this paper considers the stochastic single item periodic review inventory problem most importantly we assume a finite production capacity per period and a production cost function containing a fixed as well as a variable component with stationary data a convex expected holding and shortage cost function we show that generally the modified s s policy is not optimal to the finite horizon problems the optimal policy does however show a systematic pattern which we call the x y band structure this x y band policy is interpreted as follows whenever the inventory level drops below x order up to capacity when the inventory level is above y do nothing if the inventory level is between x and y however the ordering pattern is different from problem to problem although the x and y bounds may change from period to period we prove the existence of a pair of finite x and y values that can apply for all the periods i e bounds on individual bounds one calculation for such x and y bounds that are tight in some cases is also provided by exploring the x y band structure we can drastically reduce the computation effort for finding the optimal policies