calculation of acoustic radiation using equivalent sphere methods among the methods generally used to solve a problem in the domain of acoustic radiation the equivalent sources method offers an interesting alternative it consists in replacing the vibrating surface with a distribution of acoustic sources placed inside the structure the contribution of each source is determined in such a way that the acoustic field radiated by these sources verifies the same boundary conditions on the structure the number of unknowns in the problem is no longer directly linked to the number of mesh points on the structure as with boundary elements methods but to the number of equivalent sources employed in the model the equivalent source method is therefore of major interest if the acoustic radiation of the structure can be approximated with a sufficiently low number of sources this paper proposes its application when the equivalent source is a sphere in this case the number of unknowns is equal to the number of modes in contrast to the one point multipole the sphere has a surface surrounding a closed volume to express the boundary conditions although sphere multipole equivalence has been demonstrated the surface of the sphere allows normalization of the functions used leading to stabilization of the system to be resolved first the main acoustic radiation characteristics of a sphere and of the linear system verified by the modal coefficients of an equivalent sphere are presented the different parameters of the model are then studied position and radius of the equivalent sphere truncation of the series and influence of the spatial sampling mesh in the same vein a second approach is presented it consists of making each point of the structure correspond to a point of the sphere and the vibrating field at the surface of the sphere is deduced from that of the structure by simple geometric projection results can be obtained very quickly as no matrix inversion is required the accuracy of the results depends on the distance between the sphere and the structure finally an experimental validation that uses both methods is presented and shows interesting results when the structure is closed and when its shape is not too far removed from a sphere

nonnegative matrix factorization and i divergence alternating minimization abstract in this paper we consider the nonnegative matrix factorization nmf problem given an elementwise nonnegative matrix v r m n find for assigned k nonnegative matrices w r m k and h r k n such that v wh exact nontrivial nonnegative factorizations do not always exist hence it is interesting to pose the approximate nmf problem the criterion which is commonly employed is i divergence between nonnegative matrices the problem becomes that of finding for assigned k the factorization wh closest to v in i divergence an iterative algorithm em like for the construction of the best pair w h has been proposed in the literature in this paper we interpret the algorithm as an alternating minimization procedure a la csiszar tusnady and investigate some of its stability properties nmf is widespreading as a data analysis method in applications for which the positivity constraint is relevant there are other data analysis methods which impose some form of nonnegativity we discuss here the connections between nmf and archetypal analysis

finite size scaling of the three state potts model on a simple cubic lattice finite size scaling is studied for the three state potts model on a simple cubic lattice we show that the specific heat and the magnetic susceptibility scale accurately as the volume the correlation length exhibits behaviors expected for a genuine first order transition the one extracted from the unsubtracted correlation function shows a characteristic finite size behavior whereas the physical correlation length that characterizes the first excited state stays at a finite value and is discontinuous at the transition point

probability matrices non negative rank and parameterization of mixture models abstract in this paper we parameterize non negative matrices of sum one and rank at most two using the least possible number of parameters we also show how this parameterization relates to a class of statistical models known in probability and statistics as mixture models for contingency tables in particular we show how to use this parameterization to make some optimization problems computationally easier

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

finite size dependence of the helicity modulus within the mean spherical model the validity of the finite size scaling prediction about the existence of logarithmic corrections in the helicity modulus of three dimensional o n symmetric order parameter systems in confined geometries is studied for the three dimensional mean spherical model of geometryl 3 s d d 0 d 3 for a fully finite geometry the general case ofd p 0 periodic d a 0 antiperiodic d 0 0 free andd 1 0 fixed d p da d0 d1 d d 3 boundary conditions is considered whereas for film d 2 and cylinder d 1 geometries only the case of antiperiodic and or periodic boundary conditions is investigated the corresponding expressions for the finite size scaling function of the helicity modulus and its asymptotics in the vicinity below and above the bulk critical temperaturet c and the shifted critical temperaturet c l are derived the obtained results are not in agreement with the hypothesis of the existence of a log l correction term to the finite size behavior of the helicity modulus in the finite size critical region if d 3 in the case of film and cylinder geometries there are no logarithmic corrections in the case of a fully finite geometry a universal logarithmic correction term d 0 d 1 4 2da 1 2 lnl l is obtained only for t c t l lnl

amplitude exponent relation for the correlation length in the 2 1 dimensional ising model for the critical 2 1 d ising model defined on a square lattice with antiperiodic boundary conditions numerical studies suggest relations among the critical exponents and the finite size scaling amplitudes of correlation lengths similar to those obtained in 1 1 dimensions from conformal invariance

finite size effects and phase transition in the three dimensional three state potts model the three state potts model in three dimensions is studied by monte carlo and finite size scaling techniques using a histogram method recently proposed by ferrenberg and swendsen the finite size dependence for the maximum of the specific heat is found to scale with the volume of the system indicating that the phase transition is of first order the value of the latent heat per spin and the correlation length at the transition are estimated

acoustic scattering by a modified werner method a modified integral werner method is used to calculate pressure scattered by an axisymmetric body immersed in a perfect and compressible fluid subject to a harmonic acoustic field this integral representation is built as the sum of a potential of a simple layer and a potential of volume it is equivalent to the exterior helmholtz problem with neumann boundary condition for all real wave numbers of the incident acoustic field for elastic structure scattering problems the modified werner method is coupled with an elastodynamic integral formulation in order to account for the elastic contribution of the displacement field at the fluid structure interface the resulting system of integral equations is solved by the collocation method with a quadratic interpolation the introduction of a weighting factor in the modified werner method decreases the number of volume elements necessary for a good convergence of results this approach becomes very competitive when it is compared with other integral methods that are valid for all wave numbers a numerical comparison with an experiment on a tungsten carbide end capped cylinder allows a glimpse of the interesting possibilities for using the coupling of the modified werner method and the integral elastodynamic equation used in this research

a probabilistic view on finite size scaling in infinitely coordinated spherical models abstract it is shown that the finite size scaling functions of the infinitely coordinated spherical model are closely related to the limit probability distribution of a triangular array of properly normalized block spin variables the triangular array is defined with the aid of a two parameter family of gibbs distributions which approach the critical point together with the increase of the size of the system our consideration confirms the modification of finite size for infinitely coordinated systems suggested by botet jullien and pfeuty and extends it to the nonzero field case the explicit results rigorously derived here manifest the ensemble dependence of the relevant statistical distributionss which in turn produce different finite size scaling functions we demonstrate how the finite size scaling functions of the free energy can be determined from the relations between its first derivatives with respect to the temprature and magnetic field and expectation values of block spin variables whose asymptotic behavior is given by the smooth limit distribution a general conjecture pertaining to other models is stated too

finite size corrections for inclined interfaces in two dimensions exact results for ising and solid on solid models analysis of finite size corrections for the surface tension and surface stiffness coefficients in two dimensional models with inclined interfaces is presented we obtain a universal leading contribution proportional to lnl l for the 2d system of sizel by explicit calculations for restricted and unrestricted solid on solid models and the square lattice ising model we demonstrate the gaussian nature of rough interfaces with fixed ends and derive the leading 1 l type corrections for appropriate surface quantities

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

isomorphism of dimer configurations and spanning trees on finite square lattices one to one mappings of the close packed dimer configurations on a finite square lattice with free boundaries l onto the spanning trees of a related graph or two graph g are found the graph two graph g can be constructed from l by 1 deleting all the vertices of l with arbitrarily fixed parity of the row and column numbers 2 suppressing all the vertices of degree 2 except those of degree 2 in l 3 merging all the vertices of degree 1 into a single vertex g the matrix kirchhoff theorem reduces the enumeration problem for the spanning trees on g to the eigenvalue problem for the discrete laplacian on the square lattice l g g with mixed dirichlet neumann boundary conditions in at least one direction that fact explains some of the unusual finite size properties of the dimer model

on the convergence of multiplicative update algorithms for nonnegative matrix factorization nonnegative matrix factorization nmf is useful to find basis information of nonnegative data currently multiplicative updates are a simple and popular way to find the factorization however for the common nmf approach of minimizing the euclidean distance between approximate and true values no proof has shown that multiplicative updates converge to a stationary point of the nmf optimization problem stationarity is important as it is a necessary condition of a local minimum this paper discusses the difficulty of proving the convergence we propose slight modifications of existing updates and prove their convergence techniques invented in this paper may be applied to prove the convergence for other bound constrained optimization problems

logarithmic finite size corrections in the three dimensional mean spherical model the finite size scaling prediction about logarithmic corrections in the free energy arising from corners in the geometry of the system is tested on the three dimensional mean spherical model the general case of boundary conditions which are periodic ind 0 dimensions and free or fixed in the remaining 3 d dimensions is considered logarithmic and double logarithmic size corrections stemming from corners edges and surfaces are obtained

on reduced rank nonnegative matrix factorization for symmetric nonnegative matrices abstract let v r m n be a nonnegative matrix the nonnegative matrix factorization nnmf problem consists of finding nonnegative matrix factors w r m r and h r r n such that v wh lee and seung proposed two algorithms one of which finds nonnegative w and h such that v wh f is minimized after examining the case in which r 1 about which a complete characterization of the solution is possible we consider the case in which m n and v is symmetric we focus on questions concerning when the best approximate factorization results in the product wh being symmetric and on cases in which the best approximation cannot be a symmetric matrix finally we show that the class of positive semidefinite symmetric nonnegative matrices v generated via a soules basis admit for every 1 r rank v a nonnegative factorization wh which coincides with the best approximation in the frobenius norm to v in r n n of rank not exceeding r an example of applications in which nnmf factorizations for nonnegative symmetric matrices v arise is video and other media summarization technology where v is obtained from a distance matrix

correlation length of the three state potts model in three dimensions a monte carlo study is carried out for the three state potts model in three dimensions the correlation length is shown to remain finite and to be discontinuous at the transition point it is also shown that the transition exhibits genuine first order characteristics in all aspects

amplitude exponent relation for the correlation length in the spherical model for the critical spherical model in d r 1 dimensions finite size calculations of the spin spin and energy energy correlation lengths suggest relations among the critical exponents and the finite size scaling amplitudes of the correlation lengths similar to those obtained in 1 1 dimensions from conformal invariance for antiperiodic boundary conditions the results agree with numerical studies in the 2 1 dimensional ising model

structured nonnegative matrix factorization with applications to hidden markov realization and clustering abstract in this paper we study the structured nonnegative matrix factorization problem given a square nonnegative matrix p decompose it as p vav with v and a nonnegative matrices and with the dimension of a as small as possible we propose an iterative approach that minimizes the kullback leibler divergence between p and vav subject to the nonnegativity constraints on a and v with the dimension of a given the approximate structured decomposition p vav is closely related to the approximate symmetric decomposition p vv it is shown that the approach for finding an approximate structured decomposition can be adapted to solve the symmetric decomposition problem approximately finally we apply the nonnegative decomposition vav to the hidden markov realization problem and to the clustering of data vectors based on their distance matrix

learning non linear functions with factor graphs we show how to use a discrete variable factor graph for learning non linear continuous functions from examples the paper proposes a scheme for embedding soft quantization in a probabilistic bayesian graph the quantized input variables are grouped into a compound variable that is mapped through a stochastic matrix into the discrete output distribution specific output values are then obtained through a process of de quantization the information flow carried by message propagation is bi directional and an algorithm for learning the factor graph parameters is explicitly derived the model that can easily merge discrete and continuous variables is demonstrated with examples and simulations

test of finite size scaling predictions in three dimensions a constrained monomer dimer cmd model on decorated hypercubic lattices which is exactly solvable in any dimensionality d is studied the model is critical in the limit of maximal packing of the dimer configurations allowed by the constraint for d 2 it is equivalent to the rooted tree model on the square lattice considered by duplantier and david 1988 the validity of two finite size scaling predictions in higher dimensionalities is studied 1 the existence of logarithmic corrections in the free energy due to corners and ii the amplitude exponent relation for the pair correlation function the logarithmic finite size corrections are obtained for arbitrary d for boundary conditions which are periodic for d or 0 dimensions and free in the remaining d d dimensions dimer dimer correlation functions are studied at d 3 for a system finite in two dimensions and infinite in the third it is shown that the amplitude exponent relation for the cmd model holds for d 2 and breaks down for d 3

combined integral equation formulation and null field method for the exterior acoustic problem the numerical implementation of a combined integral equation and null field method used to solve the exterior neumann problem d s jones q j mech appl math xxvii 129 1974 is presented here the exterior helmholtz integral equation is solved on the radiating or scattering surface and the irregular frequencies are eliminated up to a given irregular frequency fm through the use of m additional null field equations an impedance matrix defined on the object surface is then obtained that can be used as an exact radiation condition in a finite element code the program and the numerical examples presented here are specialized to axisymmetrical problems a purely null field method is implemented and simple rules are defined that display its failure when applied to high aspect ratio objects and or in the high frequency range similar but less restricting rules are used to specify the numerical limitations of jones technique besides a few theoretical considerations clarify the role played by t

finite size logarithmic corrections in the free energy of the mean spherical model the validity of the finite size scaling prediction about the existence of logarithmic corrections in the free energy due to corners is studied by the example of the mean spherical model the general case of a hypercubic lattice of arbitrary dimensionality d 2 under boundary conditions which are periodic in d or 0 dimensions and free in the remaining d d dimensions is considered the critical regime as the size of the system l to infinity is specified by the asymptotic behaviour of the ratio l xi l where xi l is the correlation length fo the finite system new results are the double logarithmic corrections due to corners and logarithmic corrections due to one dimensional edges in the regime l xi l varies as ln l which takes place at the bulk critical point

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

resolving the order of phase transitions in monte carlo simulations the authors made a monte carlo simulation of the two dimensional potts model with q 3 4 and 5 to examine the question whether numerical methods can distinguish the order of a phase transition for the subtle cases that this model exemplifies they found that the finite size scaling test for susceptibilities has sufficient power for this purpose whereas the simple method of detecting metastability signals often fails

non negative matrix factorization with fixed row and column sums in this short note we focus on the use of the generalized kullback leibler kl divergence in the problem of non negative matrix factorization nm f we will show that when using the generalized kl divergence as cost function for nivif the row sums and the column sums of the original matrix are preserved in the approximation we will use this special characteristic in several approximation problems c 2007 elsevier inc all rights reserved

nonsymmetric first order transitions finite size scaling and tests for infinite range models finite size rounding of first order transitions is studied for the general case of nonsymmetric phases and nonperiodic boundary conditions the main features include the surface induced shift of the rounded transition on the scale 1 l while the order parameter discontinuity is rounded on the scale 1 ld this rounding is described by the universal scaling forms with scaling functions identical to those for the periodic symmetric case the proposed formalism applies to scalar order parameter single domain systems it is tested by exact calculations for a class of infinite range models