entanglement entropy from corner transfer matrix in forrester baxter non unitary rsos models using a corner transfer matrix approach we compute the bipartite entanglement renyi entropy in the off critical perturbations of non unitary conformal minimal models realised by lattice spin chains hamiltonians related to the forrester baxter rsos models bianchini et al 2015 j stat mech p03010 in regime iii this allows to show on a set of explicit examples that the renyi entropies for non unitary theories rescale near criticality as the logarithm of the correlation length with a coefficient proportional to the effective central charge this complements a similar result recently established for the size rescaling at the critical point bianchini et al 2015 j phys a math theor 48 04ft01 showing the expected agreement of the two behaviours we also compute the first subleading unusual correction to the scaling behaviour showing that it is expressible in terms of expansions of various fractional powers of the correlation length related to the differences between the conformal dimensions of fields in the theory and the minimal conformal dimension finally a few observations on the limit leading to the off critical logarithmic minimal models of pearce and seaton 2012 j stat mech p09014 are put forward

derivation of the matrix product ansatz for the heisenberg chain from the algebraic bethe ansatz we derive a matrix product representation of the bethe ansatz state for the xxx and xxz spin heisenberg chains using the algebraic bethe ansatz in this representation the components of the bethe eigenstates are expressed as traces of products of matrices which act on the tensor product of auxiliary spaces by changing the basis in we derive explicit finite dimensional representations for the matrices these matrices are the same as those appearing in the recently proposed matrix product ansatz by alcaraz and lazo 2006 j phys a math gen 39 11335 apart from normalization factors we also discuss the close relation between the matrix product representation of the bethe eigenstates and the six vertex model with domain wall boundary conditions korepin 1982 commun math phys 86 391 and show that the change of basis corresponds to a mapping from the six vertex model to the five vertex model

universal asymptotic eigenvalue distribution of density matrices and corner transfer matrices in the thermodynamic limit we study the asymptotic behavior of the eigenvalue distribution of the corner transfer matrix m ctm and the density matrix m dm in the density matrix renormalization group we utilize the relationship m dm m 4 ctm which holds for noncritical systems in the thermodynamic limit we derive the exact and universal asymptotic form of the m dm eigenvalue distribution for a class of integrable models in the massive regime for nonintegrable models the universal asymptotic form is also verified by numerical renormalization group calculations

nonlinear network description for many body quantum systems in continuous space we show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units using this wave function in variational monte carlo simulations of liquid 4 mathrm he in two and three dimensions we typically find a tenfold increase in accuracy over currently used wave functions furthermore subsequent stages of the iteration procedure define a set of increasingly good wave functions each with its own variational energy and variance of the local energy extrapolation to zero variance gives energies in close agreement with the exact values for two dimensional 4 mathrm he we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form a feature shared with the shadow wave function but now joined by much higher accuracy we also achieve significant progress for liquid 3 mathrm he in three dimensions improving previous variational and fixed node energies

strongly transitive geometric spaces associated to hypermodules abstract in this paper we use the strongly regular relation on hypermodules with canonical hypergroup over a given krasner hyperring in this way we consider the fundamental relation defined on a hypermodule and prove some results in this respect also we determine a family p m of subsets of a hypermodule m and we give sufficient conditions such that the geometric space m p m is strongly transitive and the relation is transitive

diagrammatics for su 2 invariant matrix product states we report on a systematic implementation of su 2 invariance for matrix product states mps with concrete computations cast in a diagrammatic language as an application we present a variational mps study of a spin 1 2 quantum chain for efficient computations we make systematic use of the su 2 symmetry at all steps of the calculations i the matrix space is set up as a direct sum of irreducible representations ii the local matrices with state valued entries are set up as superposition of su 2 singlet operators iii products of operators are evaluated algebraically by making use of identities for 3j and 6j symbols the remaining numerical computations like the diagonalization of the associated transfer matrix and the minimization of the energy expectation value are done in spaces free of symmetry degeneracies the energy expectation value is a strict upper bound of the true ground state energy and yields definite conclusions about the accuracy of density matrix renormalization group results reported in the literature furthermore we present explicit results with accuracy better than 10 4 for nearest and next nearest neighbour spin correlators and for general dimer dimer correlators in the thermodynamical limit of the spin heisenberg chain with frustration

transfer matrix renormalization group method for general markov random fields abstract we seek the numerical calculation of partition functions of general markov random fields mrfs on an infinitely long twisted cylindrical lattice by using the transfer matrix renormalization group tmrg method the tmrg is a variant of the density matrix renormalization group dmrg which automatically truncates the hilbert space so that the properties of large systems can be precisely calculated while the dimension of the renormalized hilbert space remains constant we apply the tmrg to the decimation of the fundamental transfer matrix that we have proposed previously for general mrfs instead of the standard s e scheme for tmrg we propose a new e s e scheme and propose an alternative method for selecting the renormalized basis specifically the new e s e scheme keeps those singular value decomposition svd components of the fundamental transfer matrix that are relevant for the perron state and truncates the other irrelevant ones results for the ising model show that our method exhibits very impressive accuracy under a rather restricted computational resource simulations for another four general mrfs demonstrate that our tmrg method is superior to the classical monte carlo method in accuracy computational speed and in the possibility of treating a much larger system

thermodynamic model of social influence on two dimensional square lattice case for two features abstract we propose a thermodynamic multi state spin model in order to describe equilibrial behavior of a society our model is inspired by the axelrod model used in social network studies in the framework of the statistical mechanics language we analyze phase transitions of our model in which the spin interaction j is interpreted as a mutual communication among individuals forming a society the thermal fluctuations introduce a noise t into the communication which suppresses long range correlations below a certain phase transition point t t large scale clusters of the individuals who share a specific dominant property are formed the measure of the cluster sizes is an order parameter after spontaneous symmetry breaking by means of the corner transfer matrix renormalization group algorithm we treat our model in the thermodynamic limit and classify the phase transitions with respect to inherent degrees of freedom each individual is chosen to possess two independent features f 2 and each feature can assume one of q traits e g interests hence each individual is described by q 2 degrees of freedom a single first order phase transition is detected in our model if q 2 whereas two distinct continuous phase transitions are found if q 2 only evaluating the free energy order parameters specific heat and the entanglement von neumann entropy we classify the phase transitions t t q in detail the permanent existence of the ordered phase the large scale cluster formation with a non zero order parameter is conjectured below a non zero transition point t t q 0 5 in the asymptotic regime q

probabilistic low rank factorization accelerates tensor network simulations of critical quantum many body ground states we provide evidence that randomized low rank factorization is a powerful tool for the determination of the ground state properties of low dimensional lattice hamiltonians through tensor network techniques in particular we show that randomized matrix factorization outperforms truncated singular value decomposition based on state of the art deterministic routines in time evolving block decimation tebd and density matrix renormalization group dmrg style simulations even when the system under study gets close to a phase transition we report linear speedups in the bond or local dimension of up to 24 times in quasi two dimensional cylindrical systems

solving the master equation without kinetic monte carlo in multiscale modeling of heterogeneous catalytic processes one crucial point is the solution of a markovian master equation describing the stochastic reaction kinetics usually this is too high dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic monte carlo method in this study we break the curse of dimensionality for the direct solution of the markovian master equation by exploiting the tensor train format for this purpose the performance of the approach is demonstrated on a first principles based reduced model for the co oxidation on the ruo2 110 surface we investigate the complexity for increasing system size and for various reaction conditions the advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

spline approximation for cauchy principal value integrals abstract in this paper we prove the uniform convergence of some quadrature formulas based on spline approximation for cauchy principal value integrals of the type f b a w x f k x x y d x k 0 1 and we present some numerical applications in particular we apply our rules to the well known prandtl s integral equation

construction of coarse grained order parameters in nonequilibrium systems we develop a renormalization group rg procedure that includes important system specific features the key ingredient is to systematize the coarse graining procedure that generates the rg flow the coarse graining technology comes from the control and operator theoretic model reduction the resulting generalized rg is a consistent generalization of the wilsonian rg we apply the procedure to a deterministic nonlinear wave equation nlwe with probabilistic initial conditions we derive the form of the projection operator from the dynamics of the nlwe and then use it to generate the rg flow for the distribution of initial conditions the probability density of the initial conditions is chosen to be a boltzmann weight that is quartic in the field variables in our calculation we find that in contrast to conventional implementations of the rg naive power counting breaks down we also show that the resulting rg equations are different from those derived from the conventional rg

the use of modified quasi interpolatory splines for the solution of the prandtl equation abstract modified quasi interpolatory splines are used for the numerical solution of the generalized prandtl equation a nystrom type method is applied based on inserting in the integral equation a modified quasi interpolatory spline instead of the unknown function the integral equation can then be solved by collocation and evaluation of suitable cauchy principal value integrals necessary conditions have been established for demonstrating that the approximate solution of the equation converges to the true solution

a finite tame wild trichotomy theorem for tensor diagrams abstract in this paper we consider the problem of determining when two tensor networks are equivalent under a heterogeneous change of basis in particular to a tensor or string diagram in a certain monoidal category which we call tensor diagrams we formulate an associated abelian category of representations each representation corresponds to a tensor network on that diagram we then classify which tensor diagrams give rise to categories that are finite tame or wild in the traditional sense of representation theory for those tensor diagrams of finite and tame type we classify the indecomposable representations our main result is that a tensor diagram is wild if and only if it contains a vertex of degree at least three otherwise it is of tame or finite type

a non perturbative real space renormalization group scheme based on the original idea of the density matrix renormalization group dmrg i e to include the missing boundary conditions between adjacent blocks of the blocked quantum system we present a rigorous and non perturbative mathematical formulation for the real space renormalization group idea conceived by kadanoff and further developed by wilson this is achieved by using additional hilbert spaces called auxiliary spaces in the construction of each single isolated block which is then termed a superblock in accordance with the original nomenclature on this superblock we define two maps called embedding and truncation for successively integrating out the small scale structure our method overcomes the known difficulties of the numerical dmrg i e the limitation to zero temperature and one space dimension

generalization of the tensor renormalization group approach to 3 d or higher dimensions abstract in this paper a way of generalizing the tensor renormalization group trg is proposed mathematically the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is discovered a theoretical contraction framework is therefore proposed furthermore the canonical polyadic decomposition is introduced to tensor network theory a numerical verification of this method on the 3 d ising model is carried out

piecewise cubic interpolatory polynomials and approximate solution of singular integral equations abstract a method based on piecewise cubic interpolatory polynomials for the numerical solution of singular integral equations of cauchy type is considered the class of interpolatory functions under consideration is the class of x splines of particular interest is the size of the matrix of linear algebraic equations it is shown that one can get matrices of order n n where n is the number of node points on the interval of integration the analysis becomes considerably simpler for the case when the node points are equally spaced numerical results from the x spline method are compared with those obtained using other methods

density matrix renormalization group study of the correlation function of the bilinear biquadratic spin 1 chain using the recently developed density matrix renormalization group approach we study the correlation function of the spin 1 chain with quadratic and biquadratic interactions this allows us to define and calculate the periodicity of the ground state which differs markedly from that in the classical analogue combining our results with other studies we predict three phases in the region where the quadratic and biquadratic terms are both positive

on the choice of the density matrix in the stochastic tmrg in applications of the density matrix renormalization group to nonhermitean problems the choice of the density matrix is not uniquely prescribed by the algorithm we demonstrate that for the recently introduced stochastic transfer matrix dmrg stochastic tmrg the necessity to use open boundary conditions makes asymmetrical reduced density matrices as used for renormalization in quantum tmrg an inappropriate choice an explicit construction of the largest left and right eigenvectors of the full transfer matrix allows us to show why symmetrical density matrices are the correct physical choice

entanglement entropy and conformal field theory we review the conformal field theory approach to entanglement entropy in 1 1 dimensions we show how to apply these methods to the calculation of the entanglement entropy of a single interval and the generalization to different situations such as finite size systems with boundaries and the case of several disjoint intervals we discuss the behaviour away from the critical point and the spectrum of the reduced density matrix quantum quenches as paradigms of non equilibrium situations are also considered

extrapolation cam theory for critical exponents we propose and test a new method for generating canonical sequences for analysis by the coherent anomaly method cam from non mean field approximations by intentionally underestimating the rate of convergence of exact diagonalization values for the mass or energy gaps of finite systems we form families of sequences of gap estimates the gap estimates cross zero with generically nonzero linear terms in their taylor expansions so that for each member of these sequences of estimates thus the cam can be used to determine our freedom in deciding exactly how to underestimate the convergence allows us to choose the sequence that displays the clearest coherent anomaly we demonstrate this approach on the two dimensional ferromagnetic ising model for which we also use it on the three dimensional ferromagnetic ising model finding in good agreement with other estimates finally we apply it to an antiferromagnetic spin 1 heisenberg chain finding at the phase transition between the haldane phase and the dimerized phase in agreement with the field theoretic prediction although the specific systems used to test the extrapolation cam procedure involve finite system sizes the method could be applied to other finite approximations such as systematic variational approximations

fully simple semihypergroups transitive digraphs and sequence a000712 abstract fully simple semihypergroups have been introduced in 9 motivated by the study of the transitivity of the fundamental relation in semihypergroups here we determine a transversal of isomorphism classes of fully simple semihypergroups with a right absorbing element the structure of that transversal can be described by means of certain transitive acyclic digraphs moreover we prove that if n is an integer 2 then the number of isomorphism classes of fully simple semihypergroups of size n 1 with a right absorbing element is the n 1 th term of sequence a000712 in 20 namely k 0 n p k p n k where p k denotes the number of nonincreasing partitions of integer k

applications of the α relation to krasner hyperrings abstract this paper deals with a special type of hyperrings called krasner hyperring the main tool is the studding of the relation the relation was introduced by davvaz and vougiouklis indeed we use the relation in a given krasner hyperring in this way the relation is the smallest equivalence relation on a krasner hyperring r such that r is a commutative ring results are obtained on krasner hyperrings derived hyperrings and parts

elucidating reaction mechanisms on quantum computers with rapid recent advances in quantum technology we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers here we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems using the open problem of biological nitrogen fixation in nitrogenase as an example we discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms to significantly increase their accuracy and enable hitherto intractable simulations our resource estimates show that even when taking into account the substantial overhead of quantum error correction and the need to compile into discrete gate sets the necessary computations can be performed in reasonable time on small quantum computers our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources

nilpotent groups derived from hypergroups in this paper we introduce the smallest equivalence relation on a hypergroup h such that the quotient h the set of all equivalence classes is a nilpotent group the characterization of nilpotent groups via strongly regular relations is investigated and several results on the topic are presented

series expansions from the corner transfer matrix renormalization group method ii asymmetry and high density hard squares the corner transfer matrix renormalization group method is a method claimed to be subexponential for numerically calculating physical quantities of statistical mechanical models in a previous paper we extended this method to generate series expansions here we show how to extend both the original and series methods to deal with asymmetry in any model we discuss the cases of rotational translational and reflection asymmetry and give some improvements to the method this is demonstrated by an application of the method to generate series for the hard square model in the high density regime producing 51 terms of the partition function and 48 terms of the order parameter these series are analysed producing estimates of the critical point and exponents and showing the likely presence of a confluent singularity with exponent 17 8 in the order parameter

series expansions from the corner transfer matrix renormalization group method the hard squares model the corner transfer matrix renormalization group method is an efficient method for evaluating physical quantities in statistical mechanical models it originates from baxter s corner transfer matrix equations and method and was developed by nishino and okunishi in 1996 in this paper we review and adapt this method previously used for numerical calculations to derive series expansions we use this to calculate 92 terms of the partition function of the hard squares model we use the resulting series to provide evidence supporting the claim that the method is subexponential in the number of generated terms and briefly analyse the singularities of the function

calculation of reduced density matrices from correlation functions it is shown that for solvable fermionic and bosonic lattice systems the reduced density matrices can be determined from the properties of the correlation functions this provides the simplest way to these quantities which are used in the density matrix renormalization group method

hyperrings and α relations a general approach abstract the study of the equivalence relations of particular multialgebras for which the factor multialgebras are universal algebras satisfying certain identities is a very important and intensively studied topic in multialgebra theory and not only our paper provides a general multialgebraic approach for the construction of all these relations and also some important and interesting properties concerning the construction of the corresponding factor universal algebra one of the purposes of our approach is to improve some results concerning relations of hyperrings and krasner hyperrings and we will do this in the last sections of this paper

transposition hypergroups noncommutative join spaces the study of various kinds of algebraic hypergroups is unified in the theory of transposition hypergroups the hyperoperation in any hypergroup has two inverses given bya b x a xb andb a x a bx a transposition hypergroup is a hypergroup where transposition b a c d impliesad bc holds the algebra of transposition hypergroups is developed closed subhypergroupsnthat are reflexive a n n a have distinguished structural significance the quotient space of a transposition hypergroup modulo a reflexive closed subhypergroup forms a transposition hypergroup that is a polygroup then generalizations of the isomorphism theorems and the jordan holder theorem of group theory are obtained

parallelization strategies for density matrix renormalization group algorithms on shared memory systems shared memory smp parallelization strategies for density matrix renormalization group dmrg algorithms enable the treatment of complex systems in solid state physics we present two different approaches by which parallelization of the standard dmrg algorithm can be accomplished in an efficient way the methods are illustrated with dmrg calculations of the two dimensional hubbard model and the one dimensional holstein hubbard model on contemporary smp architectures the parallelized code shows good scalability up to at least eight processors and allows us to solve problems which exceed the capability of sequential dmrg calculations

symmetry respecting real space renormalization for the quantum ashkin teller model we use a simple real space renormalization group approach to investigate the critical behavior of the quantum ashkin teller model a one dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously this approach which is based on exploiting the on site symmetry of the model has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse field ising model our investigation explores this approach in more generality in a model in which the critical behavior has a richer structure but which reduces to the simpler ising case at a special point we demonstrate that the correlation length critical exponent as predicted from this real space renormalization group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality near the ising special point the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods although the accuracy decreases away from the decoupled ising model point

a generalization of the injectivity condition for projected entangled pair states we introduce a family of tensor network states that we term semi injective projected entangled pair states pepss they extend the class of injective pepss and include other states like the ground states of the aklt and the czx models in square lattices we construct parent hamiltonians for which semi injective pepss are unique ground states we also determine the necessary and sufficient conditions for two tensors to generate the same family of such states in two spatial dimensions using this result we show that the third cohomology labeling of symmetry protected topological phases extends to semi injective pepss

ordered regular equivalence relations on ordered semihypergroups abstract in this paper we introduce the concept of ordered regular strongly ordered regular equivalence relation on an ordered semihypergroup moreover we use hyperfilters to construct a strongly ordered regular equivalence relation on an ordered semihypergroup for which the corresponding quotient structure is a semilattice finally we construct an ordered regular equivalence relation on an ordered semihypergroup by hyperideals such that the corresponding quotient structure is also an ordered semihypergroup under a related order relation which is an answer to the open problem given by b davvaz p corsini and t changphas in european journal of combinatorics

fully simple semihypergroups abstract in this paper we consider the class of semihypergroups h such that all subsemihypergroups k h are simple and when k 3 the fundamental relation k is not transitive for these semihypergroups we prove that hyperproducts of elements in h have size 2 and the quotient semigroup h is trivial this last result allows us to completely characterize these semihypergroups in terms of a small set of simple semihypergroups of size 3 finally we solve a problem on strongly simple semihypergroups introduced in 11

low rank tensor recovery via iterative hard thresholding abstract we study extensions of compressive sensing and low rank matrix recovery matrix completion to the recovery of low rank tensors of higher order from a small number of linear measurements while the theoretical understanding of low rank matrix recovery is already well developed only few contributions on the low rank tensor recovery problem are available so far in this paper we introduce versions of the iterative hard thresholding algorithm for several tensor decompositions namely the higher order singular value decomposition hosvd the tensor train format tt and the general hierarchical tucker decomposition ht we provide a partial convergence result for these algorithms which is based on a variant of the restricted isometry property of the measurement operator adapted to the tensor decomposition at hand that induces a corresponding notion of tensor rank we show that subgaussian measurement ensembles satisfy the tensor restricted isometry property with high probability under a certain almost optimal bound on the number of measurements which depends on the corresponding tensor format these bounds are extended to partial fourier maps combined with random sign flips of the tensor entries finally we illustrate the performance of iterative hard thresholding methods for tensor recovery via numerical experiments where we consider recovery from gaussian random measurements tensor completion recovery of missing entries and fourier measurements for third order tensors

relaxation times in the asep model using a dmrg method we compute the largest relaxation times for the totally asymmetric exclusion process tasep with open boundary conditions with a dmrg method this allows us to reach much larger system sizes than in previous numerical studies we are then able to show that the phenomenological theory of the domain wall indeed predicts correctly the largest relaxation time for large systems besides we can obtain results even when the domain wall approach breaks down and show that the kpz dynamical exponent z 3 2 is recovered in the whole maximal current phase

frustration free gapless hamiltonians for matrix product states for every matrix product state mps one can always construct a so called parent hamiltonian this is a local frustration free hamiltonian which has the mps as ground state and is gapped whenever that parent hamiltonian has a degenerate ground state space the so called non injective case we construct another uncle hamiltonian which is also local and frustration free has the same ground state space but is gapless and its spectrum is mathbb r the construction is obtained by linearly perturbing the matrices building up the state in a random direction and then taking the limit where the perturbation goes to zero for mps where the parent hamiltonian has a unique ground state the so called injective case we also build such uncle hamiltonian with the same properties in the thermodynamic limit

cubic splines and approximate solution of singular integral equations of concern here is the numerical solution of singular integral equations of cauchy type i e equations involving principal value integrals the unknown function is expressed as the product of an appropriate weight function and a cubic spline the problem is reduced to a system of linear algebraic equations which is solved for the approximate values of the function at the knots an estimate is provided for the maximum error of the approximate solution numerical results from the spline method are compared with those obtained using other methods

on manifolds of tensors of fixed tt rank recently the format of tt tensors hackbusch and kuhn in j fourier anal appl 15 706 722 2009 oseledets in siam j sci comput 2009 submitted oseledets and tyrtyshnikov in siam j sci comput 31 5 2009 oseledets and tyrtyshnikov in linear algebra appl 2009 submitted has turned out to be a promising new format for the approximation of solutions of high dimensional problems in this paper we prove some new results for the tt representation of a tensor u in mathbb r n 1 times cdots times n d and for the manifold of tensors of tt rank underline r as a first result we prove that the tt or compression ranks r i of a tensor u are unique and equal to the respective separation ranks of u if the components of the tt decomposition are required to fulfil a certain maximal rank condition we then show that the set mathbb t of tt tensors of fixed rank underline r locally forms an embedded manifold in mathbb r n 1 times cdots times n d therefore preserving the essential theoretical properties of the tucker format but often showing an improved scaling behaviour extending a similar approach for matrices conte and lubich in m2an 44 759 2010 we introduce certain gauge conditions to obtain a unique representation of the tangent space mathcal t u mathbb t of mathbb t and deduce a local parametrization of the tt manifold the parametrisation of mathcal t u mathbb t is often crucial for an algorithmic treatment of high dimensional time dependent pdes and minimisation problems lubich in from quantum to classical molecular dynamics reduced methods and numerical analysis 2008 we conclude with remarks on those applications and present some numerical examples

a renormalization group theory of cultural evolution abstract we present a theory of cultural evolution based upon a renormalization group scheme we consider rational but cognitively limited agents who optimize their decision making process by iteratively updating and refining the mental representation of their natural and social environment these representations are built around the most important degrees of freedom of their world cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequate order parameter as the importance of social interactions increases or agents become more intelligent we observe and quantify a series of dynamic phase transitions by which cultural coherence advances in the society a similar phase transition may explain the so called cultural explosion in human evolution some 50 000 years ago

polygroups derived from cogroups abstract a polygroup is a completely regular reversible in itself multigroup in the sense of dresher and ore 4 these systems occur naturally in the study of algebraic logic 1 2 some algebraic and combinatorial properties were developed in 3 the question of whether or not q 2 group the class of double quotients of groups is the same as the class of all chromatic polygroups is important for many reasons in this paper double quotients of groups are constructed in a natural way from cogroups cogroups were introduced by eaton 5 in an attempt to axiomatize d hypergroups i e systems obtainable from groups by right coset decompositions with respect to not necessarily normal subgroups eaton s axioms apply only to finite systems utumi 7 formulated a general notion and gave an example of a cogroup not isomorphic to a d hypergroup utumi s scalar partition hypergroups appear in section 2 the main results in section 3 show that polygroups derivable from cogroups are chromatic and they include all double quotients of groups

set relations and set systems induced by some families of integral domains abstract in this paper given an integral domain u we investigate the main properties of a relation m o d which is based on the interrelation between subdomains of u and finitely generated unitary submodules of u we shall characterize it in terms of a second relation between n tuples u 1 u n of elements of u and subdomains d of u defined by the vanishing in u 1 u n of some polynomial p z 1 z n belonging to a specific subset of the polynomial ring in several variables d z 1 z n such an equivalence shall be used in order to introduce three specific collections of subdomains x u b u and p u whose algebraic properties present a close connection with geometrical and combinatorial properties induced by m o d on the other hand the characterization of the subdomains of x u leads to the more general problem of finding a map associating with a subdomain d of u a collection d of subdomains of k u such that the intersection of some or of any member of d gives d in this perspective in the present paper we shall study two further collections of subdomains of u denoted respectively by e u and l u whose main properties are related to those of the families p u and b u finally our investigation of all the aforementioned subdomain families shall be also related to the study of pairs e where e u 0 and is an idempotent ring endomorphism of u whose kernel agrees with the ideal of u generated by e we shall exhibit several results concerning the membership of u and of u e to the above subdomain families

quasioptimality of maximum volume cross interpolation of tensors we consider a cross interpolation of high dimensional arrays in the tensor train format we prove that the maximum volume choice of the interpolation sets provides the quasioptimal interpolation accuracy that differs from the best possible accuracy by the factor which does not grow exponentially with dimension for nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms we justify the theoretical results and measure speed and accuracy of the proposed algorithm with numerical experiments

minimal order semihypergroups of type u on the right ii abstract we prove a new characterization of the heart w h and of the derived d h of a finite semihypergroup h of type u on the right in terms of its hyperproducts consequently we characterize the minimal size of the proper semihypergroups h of type u on the right such that w h d h h w h d h h or w h d h h moreover we obtain new results on the fundamental relations and on finite semihypergroups of type u on the right in particular we prove that is transitive is transitive if h 8 and that there exist semihypergroups of type u on the right of size 9 where is not transitive hence the minimal size for a semihypergroup of type u on the right to have a nontransitive is 9

density matrices for a chain of oscillators we consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density matrix renormalization group calculations both for one site and for half of the chain these are found to be exponentials of bosonic operators their spectra which are correspondingly exponential are determined and discussed the results for large systems are obtained from the relation to a two dimensional gaussian model

the use of piecewise quadratic polynomials for the solution of singular integral equations of cauchy type abstract a method for the numerical solution of singular integral equations of cauchy type is developed the unknown function is expressed as a product of a weight function and a continuous function t the continuous function t is approximated by piecewise quadratic polynomials and the singular integral equation is reduced to a linear algebraic system numerical examples are given and comparisons are made with the widely used gauss type methods

on local convergence of alternating schemes for optimization of convex problems in the tensor train format alternating linear schemes als with the alternating least squares algorithm a notable special case provide one of the simplest and most popular choices for the treatment of optimization tasks by tensor methods an according adaptation of als for the recent tt tensor train format i v oseledets siam j sci comput 33 2011 pp 2295 2317 known in quantum computations as matrix product states has recently been investigated in s holtz t rohwedder and r schneider siam j sci comput 34 2012 pp a683 a713 with the present work the positive practical experience with tt als is backed up with an according local linear convergence theory for the optimization of convex functionals j the main assumption entering the proof is that the redundancy introduced by the tt parametrization tau matches the null space of the hessian of the induced functional j j circ tau and we give conditions under which this assumption can be expected to hold in particular this is the case if

accurate lower bounds on 2 d constraint capacities from corner transfer matrices we analyse the capacity of several 2 d constraint families the exclusion coloring parity and charge model families using baxter s corner transfer matrix formalism combined with the corner transfer matrix renormalization group method of nishino and okunishi we calculate very tight lower bounds and estimates on the growth rates of these models our results strongly improve previous known lower bounds and lead to the surprising conjecture that the capacity of the even and charge 3 constraints are identical

isomorphism classes of the hypergroups of type u on the right of size five by means of a blend of theoretical arguments and computer algebra techniques we prove that the number of isomorphism classes of hypergroups of type u on the right of order five having a scalar bilateral identity is 14751 in this way we complete the classification of hypergroups of type u on the right of order five started in our preceding papers m de salvo d freni g lo faro a new family of hypergroups and hypergroups of type u on the right of size five far east j math sci 26 2 2007 393 418 m de salvo d freni g lo faro a new family of hypergroups and hypergroups of type u on the right of size five part two mathematicki vesnik 60 2008 23 45 m de salvo d freni g lo faro on the hypergroups of type u on the right of size five with scalar identity submitted for publication in particular we obtain that the number of isomorphism classes of such hypergroups is 14865

characterizations of strongly ordered regular relations on ordered semihypergroups abstract in this paper we give the fundamental normal homomorphism theorem of ordered semihypergroups moreover we characterize the strongly ordered regular relations on an ordered semihypergroup by means of the chain and obtain that the set of all strongly ordered regular relations on an ordered semihypergroup consists a complete lattice finally the subset of an ordered semihypergroup can serve as some ordered regular ordered semilattice relation class is determined