coupled cell networks semigroups lie algebras and normal forms we introduce the concept of a semigroup coupled cell network and show that the collection of semigroup network vector fields forms a lie algebra this implies that near a dynamical equilibrium the local normal form of a semigroup network is a semigroup network itself networks without the semigroup property will support normal forms with a more general network architecture but these normal forms nevertheless possess the same symmetries and synchronous solutions as the original network we explain how to compute lie brackets and normal forms of coupled cell networks and we characterize the sn decomposition that determines the normal form symmetry this paper concludes with a generalization to nonhomogeneous networks with the structure of a semigroupoid

the boundary condition at an impedance wall in a non uniform duct with potential mean flow the boundary condition at an impedance wall in a duct with a steady mean flow requiring the specification of the normal component of acoustic particle velocity is examined it is found that when implemented in the weak formulation of the finite element method it can be considerably simplified the boundary condition would appear to require data which includes the tangential derivative of the tangential mean flow velocity the normal derivative of the normal component of mean flow velocity and the derivatives of the mean flow density and the boundary admittance along the boundary it is shown that with suitable rearrangement the normal and tangential velocity derivatives can be eliminated as can the derivatives of the mean flow density and admittance the boundary condition becomes only slightly more complicated than the corresponding boundary condition when mean flow is absent and is no more difficult to implement requiring only local values of tangential mean flow velocity density and admittance which are already required as data for the weak formulation of the field equation

lifting and separation procedures for the cut polytope the max cut problem and the associated cut polytope on complete graphs have been extensively studied over the last 25 years however in comparison only little research has been conducted for the cut polytope on arbitrary graphs in particular separation algorithms have received only little attention in this study we describe new separation and lifting procedures for the cut polytope on general graphs these procedures exploit algorithmic and structural results known for the cut polytope on complete graphs to generate valid and sometimes facet defining inequalities for the cut polytope on arbitrary graphs in a cutting plane framework we report computational results on a set of well established benchmark problems

improved conditioning of infinite elements for exterior acoustics an optimized version of the so called mapped wave envelope elements also known as astley leis elements is introduced these elements extend to infinity in one dimension and therefore provide an approach to the simulation of exterior acoustical problems in both frequency and time domains their formulation is improved significantly through the proper choice of polynomial bases in the direction of radiation in particular certain jacobi polynomials are identified which behave well with respect to conditioning of the system matrices as a consequence the size of the finite element discretization may reduce considerably without any loss of accuracy in addition the new polynomial bases lead to superior performance of the infinite elements in conjunction with iterative solvers

a comparison of approximate boundary conditions and infinite element methods for exterior helmholtz problems we compare the accuracy of a variety of approximate boundary conditions abcs and two versions of an infinite element method iem for approximating solutions of exterior helmholtz problems the infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not we find that the accuracy of the abcs decreases with increasing frequency and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the iems we show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field

on the cut polytope the cut polytopep c g of a graphg v e is the convex hull of the incidence vectors of all edge sets of cuts ofg we show some classes of facet defining inequalities ofp c g we describe three methods with which new facet defining inequalities ofp c g can be constructed from known ones in particular we show that inequalities associated with chordless cycles define facets of this polytope moreover for these inequalities a polynomial algorithm to solve the separation problem is presented we characterize the facet defining inequalities ofp c g ifg is not contractible tok 5 we give a simple characterization of adjacency inp c g and prove that for complete graphs this polytope has diameter one and thatp c g has the hirsch property a relationship betweenp c g and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied

an explicit equivalent positive semidefinite program for nonlinear 0 1 programs we consider the general nonlinear optimization problem in 0 1 variables and provide an explicit equivalent positive semidefinite program in 2n 1 variables the optimal values of both problems are identical from every optimal solution of the former one easily finds an optimal solution of the latter and conversely from every solution of the latter one may construct an optimal solution of the former for illustration the equivalent positive semidefinite program is explicated for quadratic 0 1 programs and max cut in mathbb r 3 for unconstrained 0 1 programs a special representation in terms of a weighted sum of squares is provided

classification of negatively pinched manifolds with amenable fundamental groups we give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups namely they are precisely the mobius band and the products of r with the total spaces of flat vector bundles over closed infranilmanifolds

a comparison of the sherali adams lov 341sz schrijver and lasserre relaxations for 0 1 programming sherali and adams sa90 lov asz and schrijver ls91 and recently lasserre las01b have proposed lift and project methods for constructing hierarchies of successive linear or semidefinite relaxations of a 0 1 polytope p subseteq or n converging to p in n steps lasserre s approach uses results about representations of positive polynomials as sums of squares and the dual theory of moments we present the three methods in a common elementary framework and show that the lasserre construction provides the tightest relaxations of p as an application this gives a direct simple proof for the convergence of the lasserre s hierarchy we describe applications to the stable set polytope and to the cut polytope

a relevant two qubit bell inequality inequivalent to the chsh inequality we computationally investigate the complete polytope of bell inequalities for two particles with small numbers of possible measurements and outcomes our approach is limited by pitowsky s connection of this problem to the computationally hard np problem despite this we find that there are very few relevant inequivalent inequalities for small numbers for example in the case with three possible 2 outcome measurements on each particle there is just one new inequality we describe mixed 2 qubit states which violate this inequality but not the chsh the new inequality also illustrates a sharing of bi partite non locality between three qubits something not seen using the chsh inequality it also inspires us to discover a class of bell inequalities with m possible n outcome measurements on each particle

the steady state lifting bifurcation problem associated with the valency on networks abstract in this paper we consider homogeneous coupled cell networks with asymmetric inputs networks where each cell receives exactly one input of each edge type the coupled cell systems associated with a network are the dynamical systems that respect the network structure there are subspaces determined solely by the network structure that are flow invariant under any such coupled cell system the synchrony subspaces for a homogeneous network with asymmetric inputs one of the eigenvalues of the jacobian matrix of any coupled cell system at an equilibrium in the full synchrony subspace corresponds to the valency of the network in this work we study the codimension one steady state bifurcations of coupled cell systems with a bifurcation condition associated with the valency we start by giving an adaptation of the perron frobenius theorem for the eigenspace associated with the valency showing that the dimension of that eigenspace equals the number of the network source components a network source component is a strongly connected component of the network whose cells receive inputs only from cells in the component each synchrony subspace determines a smaller network called quotient network the lifting bifurcation problem addresses the issue of understanding when the bifurcation branches of a network can be lifted from one of its quotient networks we consider the lifting bifurcation problem when the bifurcation condition is associated with the valency we give sufficient conditions on the number of source components for the answer to the lifting bifurcation problem to be positive and prove that those conditions are necessary and sufficient for a class of networks

a combinatorial approach to nonlocality and contextuality so far most of the literature on quantum contextuality and the kochen specker theorem seems either to concern particular examples of contextuality or be considered as quantum logic here we develop a general formalism for contextuality scenarios based on the combinatorics of hypergraphs which significantly refines a similar recent approach by cabello severini and winter csw in contrast to csw we explicitly include the normalization of probabilities which gives us a much finer control over the various sets of probabilistic models like classical quantum and generalized probabilistic in particular our framework specializes to quantum nonlocality in the case of bell scenarios which arise very naturally from a certain product of contextuality scenarios due to foulis and randall in the spirit of csw we find close relationships to several graph invariants the recently proposed local orthogonality principle turns out to be a special case of a general principle for contextuality scenarios related to the shannon capacity of graphs our results imply that it is strictly dominated by a low level of the navascues pironio acin hierarchy of semidefinite programs which we also apply to contextuality scenarios

lifting bell inequalities a bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers measurement settings or measurement outcomes in this article such liftings of bell inequalities are studied it is shown that if the original inequality defines a facet of the polytope of local joint outcome probabilities then the lifted one also defines a facet of the more complex polytope

correlation polytopes their geometry and complexity a family of polytopes correlation polytopes which arise naturally in the theory of probability and propositional logic is defined these polytopes are tightly connected to combinatorial problems in the foundations of quantum mechanics and to the ising spin model correlation polytopes exhibit a great deal of symmetry exponential size symmetry groups which leave the polytope invariant and act transitively on its vertices are defined using the symmetries a large family of facets is determined a conjecture concerning the full facet structure of correlation polytopes is formulated the conjecture however implies that np co np various complexity results are proved it is shown that deciding membership in a correlation polytope is an np complete problem and deciding facets is probably not even in np the relations between the polytope symmetries and its complexity are indicated

greechie diagrams nonexistence of measures in quantum logics and kochen specker type constructions we use greechie diagrams to construct finite orthomodular lattices realizable in the orthomodular lattice of subspaces in a three dimensional hilbert space such that the set of two valued states is not large i e full separating unital nonempty resp we discuss the number of elements of such orthomodular lattices of their sets of ortho generators and of their subsets that do not admit a large set of two valued states we show connections with other results of this type

new extremal problems for the riemannian recognition program via alexandrov geometry in its most general form the recognition problem in riemannian geometry asks for the identification of an unknown riemannian manifold via measurements of metric invariants on the manifold optimally one wants to recognize a manifold having made as few measurements as possible many results in riemannian geometry including pinching theorems can be viewed this way here we are only interested in measurements that assign real numbers to each complete riemannian manifold typical examples of such invariants are diameter volume curvature bounds etc when viewing one or several invariants i ii ii of this type as a map on a suitable class l of riemannian manifolds the following problems pose themselves

bounding the set of quantum correlations we introduce a hierarchy of conditions necessarily satisfied by any distribution p ensuremath alpha ensuremath beta representing the probabilities for two separate observers to obtain outcomes ensuremath alpha and ensuremath beta when making local measurements on a shared quantum state each condition in this hierarchy is formulated as a semidefinite program among other applications our approach can be used to obtain upper bounds on the quantum violation of an arbitrary bell inequality it yields for instance tight bounds for the violations of the collins et al inequalities

multigraph approach to quantum non locality non contextuality nc and bell inequalities can be expressed as bounds for positive linear combinations s of probabilities of events exclusive events in s can be represented as adjacent vertices of a graph called the exclusivity graph of s in the case that events correspond to the outcomes of quantum projective measurements quantum probabilities are intimately related to the grotschel lovasz schrijver theta body of the exclusivity graph then one can easily compute an upper bound to the maximum quantum violation of any nc or bell inequality by optimizing s over the theta body and calculating the lovasz number of the corresponding exclusivity graph in some cases this upper bound is tight and gives the exact maximum quantum violation however in general this is not the case the reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in bell inequality and similar scenarios an interesting question is whether there is a graph theoretical concept which accounts for this problem here we show that for any given n partite bell inequality an edge coloured multigraph composed of n single colour graphs can be used to encode the relationships of exclusivity between each party s parts of the events then the maximum quantum violation of the bell inequality is exactly given by a refinement of the lovasz number that applies to these edge coloured multigraphs we show how to calculate upper bounds for this number using a hierarchy of semi definite programs and calculate upper bounds for i3 i3322 and the three bipartite bell inequalities whose exclusivity graph is a pentagon the multigraph theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

solving max cut to optimality by intersecting semidefinite and polyhedral relaxations we present a method for finding exact solutions of max cut the problem of finding a cut of maximum weight in a weighted graph we use a branch and bound setting that applies a dynamic version of the bundle method as bounding procedure this approach uses lagrangian duality to obtain a nearly optimal solution of the basic semidefinite max cut relaxation strengthened by triangle inequalities the expensive part of our bounding procedure is solving the basic semidefinite relaxation of the max cut problem which has to be done several times during the bounding process we review other solution approaches and compare the numerical results with our method we also extend our experiments to instances of unconstrained quadratic 0 1 optimization and to instances of the graph equipartition problem the experiments show that our method nearly always outperforms all other approaches in particular for dense graphs where linear programming based methods fail our method performs very well exact solutions are obtained in a reasonable time for any instance of size up to n 100 independent of the density for some problems of special structure we can solve even larger problem classes we could prove optimality for several problems of the literature where to the best of our knowledge no other method is able to do so

efficient semidefinite branch and cut for map mrf inference we propose a branch and cut b c method for solving general map mrf inference problems the core of our method is a very efficient bounding procedure which combines scalable semidefinite programming sdp and a cutting plane method for seeking violated constraints in order to further speed up the computation several strategies have been exploited including model reduction warm start and removal of inactive constraints we analyze the performance of the proposed method under different settings and demonstrate that our method either outperforms or performs on par with state of the art approaches especially when the connectivities are dense or when the relative magnitudes of the unary costs are low we achieve the best reported results experiments show that the proposed algorithm achieves better approximation than the state of the art methods within a variety of time budgets on challenging non submodular map mrf inference problems

error estimation and adaptivity for the finite element method in acoustics 2d and 3d applications this paper is dedicated to the control of accuracy and to the adaptivity of the finite element simulation of sound propagation assuming time harmonic behaviour the mathematical models are given as boundary value problems for the helmholtz equation two singularities inherent to the operator are demonstrated the k singularity related to the phase shift between the exact and the numerical waves and the singularity corresponding to the singularity at the eigenfrequencies two a posteriori error estimators are developed and the numerical tests show that due to these specific singularities error control cannot in general be accomplished by just transplanting methods that work well in static computations furthermore for low wave numbers it is necessary also to control the influence of the geometric or physical singularities an h adaptive version with refinement is applied to 2d and 3d real life problems

connes embedding problem and tsirelson s problem we show that tsirelson s problem concerning the set of quantum correlations and connes embedding problem on finite approximations in von neumann algebras known to be equivalent to kirchberg s qwep conjecture are essentially equivalent specifically tsirelson s problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting c algebras connes embedding problem asks whether any separable ii1 factor is a subfactor of the ultrapower of the hyperfinite ii1 factor we show that an affirmative answer to connes question implies a positive answer to tsirelson s conversely a positive answer to a matrix valued version of tsirelson s problem implies a positive one to connes problem

on the filling radius of positively curved alexandrov spaces it was shown by f wilhelm that gromov s filling radius of any positively curved closed riemannian manifolds are less than that of the round sphere unless they are isometric to each other in this short paper we adapt his proof to see that the same is true for any positively curved closed alexandrov spaces as well

structural dynamics of viscoelastic sandwich plates by the partition of unity finite element method the scope of this research concerns the passive damping of structural vibrations by the use of viscoelastic layers it is motivated by the need for efficient numerical tools to deal with the medium frequency behaviour of industrial viscoelastic sandwich products the sandwich modelling technique is based on the use of an interface element the two deformable plates are modelled by special plate elements while the intermediate dissipative layer is modelled with interface elements this interface element is based on the first order shear deformation theory and assume constant peel and shear stresses in the polymer thickness this element couples the lower and upper layers without additional degrees of freedom the partition of unity finite element method pufem is applied to the development of enriched mindlin plate elements the element shape functions are obtained as the product of partition of unity functions with arbitrary chosen enrichment functions polynomial enrichment leads to the generation of high order polynomial shape functions and is therefore similar to a p fem technique numerical examples illustrate the use of both pufem mindlin plate elements and interface elements for the simulation of viscoelastic sandwich structures

the partition of unity finite element method for short wave acoustic propagation on non uniform potential flows a novel numerical method is proposed for modelling time harmonic acoustic propagation of short wavelength disturbances on non uniform potential flows the method is based on the partition of unity finite element method in which a local basis of discrete plane waves is used to enrich the conventional finite element approximation space the basis functions are local solutions of the governing equations they are able to represent accurately the highly oscillatory behaviour of the solution within each element while taking into account the convective effect of the flow and the spatial variation in local sound speed when the flow is non uniform many wavelengths can be included within a single element leading to ultra sparse meshes results presented in this article will demonstrate that accurate solutions can be obtained in this way for a greatly reduced number of degrees of freedom when compared to conventional element or grid based schemes numerical results for lined uniform two dimensional ducts and for non uniform axisymmetric ducts are presented to indicate the accuracy and performance which can be achieved numerical studies indicate that the pollution effect associated with cumulative dispersion error in conventional finite element schemes is largely eliminated

special short wave elements for flow acoustics a numerical formulation based on the partition of unity method pum is proposed for modelling the propagation of short acoustic waves on irrotational mean flows the method seeks to reduce the pollution error which exists in conventional fe schemes at high frequencies by using a local basis which is enriched by plane wave solutions of the convected helmholtz equation initially the method is demonstrated with reference to a one dimensional model consisting of a variable area converging diverging duct with mean flow next a simple two dimensional model of a straight duct with uniform flow is considered in both cases the accuracy and the conditioning of the numerical solution is investigated for ranges of frequency and mach number characteristic of aero engine bypass ducts

the strong perfect graph theorem a graph g is perfect if for every induced subgraph h the chromatic number of h equals the size of the largest complete subgraph of h and g is berge if no induced subgraph of g is an odd cycle of length at least five or the complement of one the strong perfect graph conjecture berge 1961 asserts that a graph is perfect if and only if it is berge a stronger conjecture was made recently by conforti cornu ejols and vuiskovi c that every berge graph either falls into one of a few basic classes or admits one of a few kinds of separation designed so that a minimum counterexample to berge s conjecture cannot have either of these properties in this paper we prove both of these conjectures

with respect to whom are you critical abstract for any compact riemannian surface s and any point y in s q y 1 denotes the set of all points in s for which y is a critical point and q y 1 its cardinality we proved 2 together with imre barany that q y 1 1 and that equality for all y s characterizes the surfaces homeomorphic to the sphere here we show for any orientable surface s and any point y s the following two main results there exists an open and dense set of riemannian metrics g on s for which y is critical with respect to an odd number of points in s and this is sharp if s is the torus then q y 1 5 and if s has genus g 2 then q y 1 8 g 5 properties involving points at globally maximal distance on s are eventually presented

a radius sphere theorem the purpose of this paper is to present an optimal sphere theorem for metric spaces analogous to the celebrated rauch berger klingenberg sphere theorem and the diameter sphere theorem in riemannian geometry there has lately been considerable interest in studying spaces which are more singular than riemannian manifolds a natural reason for doing this is because gromov hausdorff limits of riemannian manifolds are almost never riemannian manifolds but usually only inner metric spaces with various nice properties the kind of spaces we wish to study here are the so called alexandrov spaces alexandrov spaces are finite dimensional inner metric spaces with a lower curvature bound in the distance comparison sense this definition might seem a little ambiguous since there are many ways in which one can define finite dimensionality and lower curvature bounds the foundational work by plaut in pi however shows that these different possibilities for definitions are equivalent the structure of alexandrov spaces was studied in bgp pi and p in particular if x is an alexandrov space and p e x then the space of directions ep at p is an alexandrov space of one less dimension and with curvature 1 furthermore a neighborhood of p in x is homeomorphic to the linear cone over one of the important implications of this is that the local structure of n dimensional alexandrov spaces is determined by the structure of n l dimensional alexandrov spaces with curvature 1 sphere theorems in this context seem to be particularly interesting for if one can give geometric characterizations of

convergent relaxations of polynomial optimization problems with noncommuting variables we consider optimization problems with polynomial inequality constraints in noncommuting variables these noncommuting variables are viewed as bounded operators on a hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints such problems arise naturally in quantum theory and quantum information science to solve them we introduce a hierarchy of semidefinite programming relaxations which generates a monotone sequence of lower bounds that converges to the optimal solution we also introduce a criterion to detect whether the global optimum is reached at a given relaxation step and show how to extract a global optimizer from the solution of the corresponding semidefinite programming problem

graph fibrations and symmetries of network dynamics abstract dynamical systems with a network structure can display remarkable phenomena such as synchronisation and anomalous synchrony breaking a methodology for classifying patterns of synchrony in networks was developed by golubitsky and stewart they showed that the robustly synchronous dynamics of a network is determined by its quotient networks this result was recently reformulated by deville and lerman who pointed out that the reduction from a network to a quotient is an example of a graph fibration the current paper exploits this observation and demonstrates the importance of self fibrations of network graphs self fibrations give rise to symmetries in the dynamics of a network we show that every network admits a lift with a semigroup or semigroupoid of self fibrations the resulting symmetries impact the global dynamics of the network and can therefore be used to explain and predict generic scenarios for synchrony breaking also when the network has a trivial symmetry groupoid then every robust synchrony in the lift is determined by symmetry we finish this paper with a discussion of networks with interior symmetries and nonhomogeneous networks

dispersion analysis and error estimation of galerkin finite element methods for the helmholtz equation when applying numerical methods for the computation of stationary waves from the helmholtz equation one obtains numerical waves that are dispersive also in non dispersive media the numerical wave displays a phase velocity that depends on the parameter k of the helmholtz equation in dispersion analysis the phase difference between the exact and the numerical solutions is investigated in this paper the authors recent result on the phase difference for one dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic it is then shown that previous error estimates in h1 norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only on the other hand recently proven error estimates for constant resolution contain a pollution term with certain assumptions on the exact solution this term is of the order of the phase difference thus a link is established between the results of dispersion analysis and the results of numerical analysis throughout the paper the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems special attention is given to the performance of the galerkin method with a higher order of polynomial approximation p h p version

simple unified form for the major no hidden variables theorems two examples are given that substantially simplify the no hidden variables theorem of kochen and specker greatly reducing the number of observables considered and requiring no intricate geometric argument while one of the examples also obeys a more powerful version of bell s theorem the other does not the examples provide a new perspective on both of these fundamental theorems and on the relation between them

modelling of short wave diffraction problems using approximating systems of plane waves this paper describes a finite element model for the solution of helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element the approach is based on partition of unity isoparametric elements at each finite element node the potential is expanded in a discrete series of planar waves each propagating at a specified angle these angles can be uniformly distributed or may be carefully chosen they can also be the same for all nodes of the studied mesh or may vary from one node to another the implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres the wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced issues related to the integration and the conditioning are also discussed

every point is critical abstract we show that for any compact alexandrov surface s without boundary and any point y in s there exists a point x in s for which y is a critical point moreover we prove that uniqueness characterizes the surfaces homeomorphic to the sphere among smooth orientable surfaces

a comparison of two trefftz type methods the ultraweak variational formulation and the least squares method for solving shortwave 2 d helmholtz problems trefftz methods for the numerical solution of partial differential equations pdes on a given domain involve trial functions which are defined in subdomains are generally discontinuous and are solutions of the governing pde or its adjoint within each subdomain the boundary conditions and matching conditions between subdomains must be enforced separately an interesting novel result presented in this paper is that the least squares method lsm and the ultraweak variational formulation two methods already established for solving the helmholtz equation can be derived in the framework of the trefftz type methods in the first case the boundary conditions and interelement continuity are enforced by means of a least squares procedure in the second a galerkin type weighted residual method is used another goal of the work is to assess the relative efficiency of each method for solving shortwave problems in acoustics and to study the stability of each method the numerical performance of each scheme is assessed with reference to two 2 d test problems acoustic propagation in an uniform soft walled duct and propagation in an l shaped domain the latter involving singular behaviour at a sharp corner

on the relationship between convex bodies related to correlation experiments with dichotomic observables in this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization especially cut polyhedra such a relationship was established in avis et al 2005 j phys a math gen 38 10971 87 with respect to bell inequalities we show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by tsirelson 1993 hadronic j suppl 8 329 45 to represent hidden deterministic behaviours quantum behaviours and no signalling behaviours among other things our results allow a unique representation of these bodies give a necessary condition for vertices of the no signalling polytope and give a method for bounding the quantum violation of bell inequalities by means of a body that contains the set of quantum behaviours optimization over this latter body may be performed efficiently by semidefinite programming in the second part of the paper we apply these results to the study of classical correlation functions we provide a complete list of tight inequalities for the two party case with m n dichotomic observables when m 4 n 4 and when min m n 3 and give a new general family of correlation inequalities

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

quantum correlations are tightly bound by the exclusivity principle it is a fundamental problem in physics of what principle limits the correlations as predicted by our current description of nature based on quantum mechanics one possible explanation is the global exclusivity principle recently discussed in phys rev lett 110 060402 2013 in this work we show that this principle actually has a much stronger restriction on the probability distribution we provide a tight constraint inequality imposed by this principle and prove that this principle singles out quantum correlations in scenarios represented by any graph our result implies that the exclusivity principle might be one of the fundamental principles of nature

forced vibrations in the medium frequency range solved by a partition of unity method with local information a new approach for the computation of the forced vibrations up to the medium frequency range is formulated for thin plates it is based on the partition of unity method pum first proposed by babuska and used here to solve the elastodynamic problem the paper focuses on the introduction of local information in the basis of the pum coming from previous approximations in order to enhance the accuracy of the solution the method may be iterative and generates a pum approximation leading to smaller models compared with the finite element ones required for a same accuracy level it shows very promising results in terms of frequency range accuracy and computational time copyright 2004 john wiley sons ltd

application of an efficient wave based prediction technique for the analysis of vibro acoustic radiation problems recently a new numerical prediction technique has been developed for the analysis of vibro acoustic problems in bounded domains this wave based prediction technique adopts an indirect trefftz approach unlike the conventional element based methods the novel technique uses wave functions that exactly satisfy the governing dynamic equations to describe the dynamic variables fine domain discretizations are no longer required and the resulting model sizes are much smaller than with the element based methods this results in a more time efficient prediction technique which also allows handling of mid frequency applications this paper discusses how the wave based prediction technique can be used for vibro acoustic radiation problems in unbounded domains its beneficial characteristics compared to the element based methods are demonstrated through a validation example

a mapped finite and infinite partition of unity method for convected acoustic radiation in axisymmetric domains a mapped infinite partition of unity method is developed to solve frequency domain acoustic applications for convected radiation in axisymmetric domains the paper presents the formulation and the discretization technique the partition of unity method is coupled with infinite elements based on the astley leis conjugated formulation the performances of the method are analysed on two applications convected propagation in an uniform duct and dipole radiation the aim of such a method compared to the classical finite element method is to solve shortwave applications with a respectable level of accuracy

nonlinear dynamics of networks the groupoid formalism a formal theory of symmetries of networks of coupled dynamical systems stated in terms of the group of permutations of the nodes that preserve the network topology has existed for some time global network symmetries impose strong constraints on the corresponding dynamical systems which affect equilibria periodic states heteroclinic cycles and even chaotic states in particular the symmetries of the network can lead to synchrony phase relations resonances and synchronous or cycling chaos symmetry is a rather restrictive assumption and a general theory of networks should be more flexible a recent generalization of the group theoretic notion of symmetry replaces global symmetries by bijections between certain subsets of the directed edges of the network the input sets now the symmetry group becomes a groupoid which is an algebraic structure that resembles a group except that the product of two elements may not be defined the groupoid formalism makes it possible to extend group theoretic methods to more general networks and in particular it leads to a complete classification of robust patterns of synchrony in terms of the combinatorial structure of the network many phenomena that would be nongeneric in an arbitrary dynamical system can become generic when constrained by a particular network topology a network of dynamical systems is not just a dynamical system with a high dimensional phase space it is also equipped with a canonical set of observables the states of the individual nodes of the network moreover the form of the underlying ode is constrained by the network topology which variables occur in which component equations and how those equations relate to each other the result is a rich and new range of phenomena only a few of which are yet properly understood

necessary conditions for extended noncontextuality in general sets of random variables in this paper we explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by kujala et al phys rev lett 115 150401 2015 using graph theoretical terms this extended definition avoids the assumption of the pre sheaf or non disturbance condition which states that if two contexts overlap then the marginal distribution obtained for the intersection must be the same a restriction that will never be perfectly satisfied in real experiments with this we are able to derive necessary conditions for extended noncontextuality for any set of random variables based on the geometrical aspects of the graph approach which can be tested directly with experimental data in any contextuality experiment and which reduce to traditional necessary conditions for noncontextuality if the non disturbance condition is satisfied

the symmetric traveling salesman polytope revisited in this paper we present a tour of the symmetric traveling salesman polytope focusing on inequalities that can be defined on sets of nodes most widely known inequalities are of this type many papers have appeared that give increasingly complex valid inequalities for this polytope but little intuition on why these inequalities are valid has been given to help in understanding these inequalities we develop an intuition into their validity by giving a unifying way of defining them through a sequential lifting procedure this procedure is based on lifting the slack variables associated with subtour elimination inequalities defined on sets of nodes called teeth we apply this procedure to some known classes of valid inequalities for the traveling salesman polytope tsp respectively comb brush star path and bipartition inequalities where the lifting coefficients are sequence independent for comb star and bipartition inequalities we provide new and noninductive proofs of validity directly inspired by this lifting procedure we also give an example where a facet defining inequality is derived from the lifting procedure but where the lifting coefficients are sequence dependent we finally study the ladder inequalities and show that they can be generated by an extension of the general procedure where the lifted variables are different from the slack variables of subtour elimination inequalities

three dimensional perfectly matched layer for the absorption of electromagnetic waves the perfectly matched layer is a technique of free space simulation developed for solving unbounded electromagnetic problems with the finite difference time domain method referred to as pml this technique has been described in a previous paper for two dimensional problems the present paper is devoted to the three dimensional case the theory of the perfectly matched layer is generalized to three dimensions and some numerical experiments are shown to illustrate the efficiency of this new method of free space simulation

generating facets for the cut polytope of a graph by triangular elimination the cut polytope of a graph arises in many fields although much is known about facets of the cut polytope of the complete graph very little is known for general graphs the study of bell inequalities in quantum information science requires knowledge of the facets of the cut polytope of the complete bipartite graph or more generally the complete k partite graph lifting is a central tool to prove certain inequalities are facet inducing for the cut polytope in this paper we introduce a lifting operation named triangular elimination applicable to the cut polytope of a wide range of graphs triangular elimination is a specific combination of zero lifting and fourier motzkin elimination using the triangle inequality we prove sufficient conditions for the triangular elimination of facet inducing inequalities to be facet inducing the proof is based on a variation of the lifting lemma adapted to general graphs the result can be used to derive facet inducing inequalities of the cut polytope of various graphs from those of the complete graph we also investigate the symmetry of facet inducing inequalities of the cut polytope of the complete bipartite graph derived by triangular elimination

bifurcations from regular quotient networks a first insight abstract we consider regular identical edge identical node networks whose cells can be grouped into classes by an equivalence relation the identification of cells in the same class determines a new network the quotient network in terms of the dynamics this corresponds to restricting the coupled cell systems associated with a network to flow invariant subspaces given by equality of certain cell coordinates assuming a bifurcation occurs for a coupled cell system restricted to the quotient network we ask how that bifurcation lifts to the overall space surprisingly for certain networks new branches of solutions occur besides the ones that occur in the quotient network to investigate this phenomenon we develop a systematic method that enumerates all networks with a given quotient we also prove necessary conditions for the existence of solution branches not predicted by the quotient we then apply our method to two particular quotient networks namely two and three cell bidirectional rings we show there are no additional bifurcating solution branches when the quotient network is a two cell bidirectional ring however two of the 12 five cell networks that have the three cell bidirectional ring as a quotient network exhibit bifurcating solutions that do not occur in the quotient itself thus network architecture sometimes forces the existence of bifurcating branches in addition to the ones determined by the quotient

an application of combinatorial optimization to statistical physics and circuit layout design we study the problem of finding ground states of spin glasses with exterior magnetic field and the problem of minimizing the number of vias holes on a printed circuit board or contacts on a chip subject to pin preassignments and layer preferences the former problem comes up in solid state physics and the latter in very large scale integrated vlsi circuit design and in printed circuit board design both problems can be reduced to the max cut problem in graphs based on a partial characterization of the cut polytope we design a cutting plane algorithm and report on computational experience with it our method has been used to solve max cut problems on graphs with up to 1 600 nodes

manifolds with minimal radial curvature bounded from below and big volume we prove that a convergence in the gromov hausdorff distance of manifolds with minimal radial curvature bounded from below by 1 to the standard sphere is equivalent to a volume convergence

state independent proof of kochen specker theorem with 13 rays quantum contextuality as proved by kochen and specker and also by bell should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified however for the simplest system capable of exhibiting contextuality a qutrit the quantum contextuality is verified only state dependently in experiment because too many at least 31 observables are involved in all the known state independent tests here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states thus our inequality facilitates a state independent test of the quantum contextuality for an indivisible quantum system we also provide a record breaking state independent proof of the kochen specker theorem with 13 directions determined by 26 points on the surface of a magic cube

on cuts and matchings in planar graphs we study the max cut problem in graphs not contractible tok5 and optimum perfect matchings in planar graphs we prove that both problems can be formulated as polynomial size linear programs

kochen specker vectors some reference citations in the text of this paper are incorrect and should be amended as listed below the reference list is correct as published page 1579 line 5 23 34 38 39 should read 23 34 35 36 page 1579 line 9 40 should read 37 page 1580 line 8 31 33 35 should read 31 33 38 page 1580 line 14 36 should read 39 page 1580 line 36 36 should read 39 page 1580 line 38 37 should read 40 page 1580 line 42 38 should read 35 page 1581 line 3 of caption 33 35 should read 33 38 page 1583 line 12 41 should read 42 page 1587 line 9 39 should read 36 page 1587 line 11 39 should read 36 page 1587 line 18 38 39 should read 35 36 page 1587 line 37 39 should read 36 page 1589 line 18 39 46 47 should read 36 46 47 page 1590 line 2 39 should read 36 age 1590 line 3 39 should read 36

entropic inequalities and marginal problems a marginal problem asks whether a given family of marginal distributions for some set of random variables arises from some joint distribution of these variables here we point out that the existence of such a joint distribution imposes nontrivial conditions already on the level of shannon entropies of the given marginals these entropic inequalities are necessary but not sufficient criteria for the existence of a joint distribution for every marginal problem a list of such shannon type entropic inequalities can be calculated by fourier motzkin elimination and we offer a software interface to a fourier motzkin solver for doing so for the case that the hypergraph of given marginals is a cycle graph we provide a complete analytic solution to the problem of classifying all relevant entropic inequalities and use this result to bound the decay of correlations in stochastic processes furthermore we show that shannon type inequalities for differential entropies are not relevant for continuous variable marginal problems non shannon type inequalities are both in the discrete and in the continuous case in contrast to other approaches our general framework easily adapts to situations where one has additional conditional independence requirements on the joint distribution as in the case of graphical models we end with a list of open problems a complementary article discusses applications to quantum nonlocality and contextuality

two party bell inequalities derived from combinatorics via triangular elimination we establish a relation between the two party bell inequalities for two valued measurements and a high dimensional convex polytope called the cut polytope in polyhedral combinatorics using this relation we propose a method triangular elimination to derive tight bell inequalities from facets of the cut polytope this method gives two hundred million inequivalent tight bell inequalities from currently known results on the cut polytope in addition this method gives general formulae which represent families of infinitely many bell inequalities these results can be used to examine general properties of bell inequalities

diffraction of short waves modelled using new mapped wave envelope finite and infinite elements we consider a two dimensional wave diffraction problem from a closed body such that the complex progressive wave potential satisfies the sommerfield condition and the helmholtz equation we are interested in the case where the wavelength is much smaller than any other length dimensions of the problem we introduce new mapped wave envelope infinite elements to model the potential in the far field and test them for some simple dirichlet boundary condition problems they are used in conjuction with wave envelope finite elements developed earlier 1 to model the potential in the near field an iterative procedure is used in which an initial estimate of the phase is iteratively improved the iteration scheme by which the wave envelope and phase are recovered is described in detail copyright 1999 john wiley sons ltd

graph approach to quantum systems using a graph approach to quantum systems we show that descriptions of 3 dim kochen specker ks setups as well as descriptions of 3 dim spin systems by means of greechie diagrams a kind of lattice that we find in the literature are wrong correct lattices generated by mckay megill pavicic mmp hypergraphs and hilbert subspace equations are given to enable future exhaustive generation of 3 dim ks setups by means of our recently found stripping technique bipartite graph generation is used to provide us with lattices with equal numbers of elements and blocks orthogonal triples of elements up to 41 of them we obtain several new results on such lattices and hypergraphs in particular on properties such as superposition and orthoraguesian equations

a kochen specker theorem for integer matrices and noncommutative spectrum functors abstract we investigate the possibility of constructing kochen specker uncolorable sets of idempotent matrices whose entries lie in various rings including the rational numbers the integers and finite fields most notably we show that there is no kochen specker coloring of the n n idempotent integer matrices for n 3 thereby illustrating that kochen specker contextuality is an inherent feature of pure matrix algebra we apply this to generalize recent no go results on noncommutative spectrum functors showing that any contravariant functor from rings to sets respectively topological spaces or locales that restricts to the zariski prime spectrum functor for commutative rings must assign the empty set respectively empty space or locale to the matrix ring m n r for any integer n 3 and any ring r an appendix by alexandru chirvasitu shows that kochen specker colorings of idempotents in partial subalgebras of m 3 f for a perfect field f can be extended to partial algebra morphisms into the algebraic closure of f

cut polytopes boolean quadratic polytopes and nonnegative quadratic pseudo boolean functions in this paper we present a class of valid inequalities as well as a class of facets for the cut polytope of the complete graph it is shown that many of the known classes of valid inequalities e g triangle hypermetric and cycle inequalities belong to this class by specializing some of the parameters large classes of facets can be defined it is shown that each of these classes contains at least n 3n 3 facets where n 10 denotes the number of vertices and that the corresponding separation problems are polynomially solvable these results are based on a one to one correspondence established between the set of valid inequalities facets for the cut polytope of kn 1 and the set of nonnegative extremal quadratic pseudo boolean functions in n variables

testing the odd bicycle wheel inequalities for the bipartite subgraph polytope in their paper on facets of the bipartite subgraph polytope barahona grotschel and mahjoub pose the question is there a polynomial time algorithm testing the odd bicycle wheel inequalities this note describes such an algorithm

one third integrality in the max cut problem given a graphg v e the metric polytopes g is defined by the inequalitiesx f x c f f 1 for f subseteq c f odd c cycle ofg and 0 xe 1 fore e optimization overs g provides an approximation for the max cut problem the graphg is called 1 d integral if all the vertices ofs g have their coordinates in i d 0 i d we prove that the class of 1 d integral graphs is closed under minors and we present several minimal forbidden minors for 1 3 integrality in particular we characterize the 1 3 integral graphs on seven nodes we study several operations preserving 1 d integrality in particular thek sum operation for 0 k 3 we prove that series parallel graphs are characterized by the following stronger property all vertices of the polytopes g x l x u are 1 3 integral for every choice of 1 3 integral boundsl u on the edges ofg

the shannon capacity of a graph and the independence numbers of its powers the independence numbers of powers of graphs have been long studied under several definitions of graph products and in particular under the strong graph product we show that the series of independence numbers in strong powers of a fixed graph can exhibit a complex structure implying that the shannon capacity of a graph cannot be approximated up to a subpolynomial factor of the number of vertices by any arbitrarily large yet fixed prefix of the series this is true even if this prefix shows a significant increase of the independence number at a given power after which it stabilizes for a while

on the spread of positively curved alexandrov spaces it was proved by f wilhelm that gromov s filling radius of closed positively curved manifolds with a uniform lower bound on sectional curvature attains the maximum with the round sphere recently the author proved that this is also the case for closed finite dimensional alexandrov spaces with a positive lower curvature bound these were proved as a corollary of a comparison theorem for the invariant called spread of those spaces in this paper we extend the latter result to infinite dimensional alexandrov spaces

hidden variables joint probability and the bell inequalities it is shown that the following statements about a quantum correlation experiment are mutually equivalent 1 there is a deterministic hidden variables model for the experiment 2 there is a factorizable stochastic model 3 there is one joint distribution for all observables of the experiment returning the experimental probabilities 4 there are well defined compatible joint distributions for all pairs and triples of commuting and noncommuting observables 5 the bell inequalities hold