freezing and collapse of flexible polymers on regular lattices in three dimensions we analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face centered cubic lattices by means of sophisticated chain growth methods in contrast to the bond fluctuation polymer model in certain parameter ranges where these two conformational transitions were found to merge in the thermodynamic limit we conclude from our results that the two transitions remain well separated in the limit of infinite chain lengths the reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here

finite size corrections and scaling dimensions of solvable lattice models an analytic method a general analytic method for calculating finite size corrections central charges and scaling dimensions of solvable lattice models is presented the approach is to solve the special functional equations or inversion identities satisfied by the commuting row transfer matrices of these lattice models at criticality for purposes of illustration the method is applied to calculate the central charge c 4 5 and leading magnetic scaling dimension x 2 15 of hard hexagons these numbers are rational due to special values of rogers dilogarithms

generalized levinson durbin and burg algorithms abstract a basic recursive property of orthogonal projections is presented which leads easily to a variety of different prediction algorithms examples are the classical levinson durbin and burg algorithms and a subset whittle algorithm of penm and terrell in addition some new algorithms are derived including easily applied algorithms for the recursive calculation of best h step predictors and a burg algorithm for the best subset predictor the relation to lattice algorithms is discussed

singular higher order divergence conforming bases of additive kind and moments method applications to 3d sharp wedge structures we present new subsectional singular divergence conforming vector bases that incorporate the edge conditions for conducting wedges the bases are of additive kind because obtained by incrementing the regular polynomial vector bases with other subsectional basis sets that model the singular behavior of the unknown vector field in the wedge neighborhood singular bases of this kind complete to arbitrarily high order are described in a unified and consistent manner for curved quadrilateral and triangular elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements our singular bases guarantee normal continuity along the edges of the elements allowing for the discontinuity of tangential components adequate modelling of the divergence and removal of spurious solutions these singular high order bases provide more accurate and efficient numerical solutions of surface integral problems several test case problems are considered in the paper thereby obtaining highly accurate numerical results for the current and charge density induced on 3d sharp wedge structures the results are compared with other solutions when available and confirm the faster convergence of these bases on wedge problems

gradient singular hierarchical finite elements for vector electromagnetics new tetrahedral finite elements are described for the analysis of vector electromagnetic fields they are singular elements that are more accurate than conventional polynomial based elements near sharp edges and corners they are hierarchical meaning that elements of different orders accuracies are available and may be placed together in the same mesh without violating continuity of the field the elements are formed from a series of scalar singular elements by taking the gradient and are therefore called gradient singular results using the new elements in p adaptive analysis orders 1 to 3 demonstrate that when they are used in place of conventional elements the scattering parameters are as much as 10 times more accurate for the same number of unknowns

multifractal model of asset returns with leverage effect abstract multifractal processes are a relatively new tool of stock market analysis their power lies in the ability to take multiple orders of autocorrelations into account explicitly in the first part of the paper we discuss the framework of the lux model and refine the underlying phenomenological picture we also give a procedure of fitting all parameters to empirical data we present a new approach to account for the effective length of power law memory in volatility the second part of the paper deals with the consequences of asymmetry in returns we incorporate two related stylized facts skewness and leverage autocorrelations into the model then from monte carlo measurements we show that this asymmetry significantly increases the mean squared error of volatility forecasts based on a filtering method we give evidence on similar behavior in empirical data

critical and multicritical o n models soluble o n models on the square lattice are found via the yang baxter equations in a parameter space of three coupling constants a number of distinct soluble cases are found for each value of n some of these constitute critical or multicritical points in the phase diagram for all solutions the free energy per spin can be determined using the bethe ansatz by studying the finite size corrections at the critical points the critical exponents and the central charge can be found in some cases analytically and failing that numerically by extrapolation of exact results for finite size systems

discretely holomorphic parafermions and integrable loop models we define parafermionic observables in various lattice loop models including examples where no kramers wannier duality holds for a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these variables are discretely holomorphic they satisfy a lattice version of the cauchy riemann equations as long as the boltzmann weights satisfy certain linear constraints in the cases considered the weights then also satisfy the critical yang baxter equations with the spectral parameter being related linearly to the angle of the elementary rhombus

two dimensional o n model in a staggered field nienhuis truncated o n model gives rise to a model of self avoiding loops on the hexagonal lattice each loop having a fugacity of n we study such loops subjected to a particular kind of staggered field w which for n has the geometrical effect of breaking the three phase coexistence linked to the three colourability of the lattice faces we show that at t 0 for w 1 the model flows to the ferromagnetic potts model with q n2 states with an associated fragmentation of the target space of the coulomb gas for t 0 there is a competition between t and w which gives rise to multicritical versions of the dense and dilute loop universality classes via an exact mapping and numerical results we establish that the latter two critical branches coincide with those found earlier in the o n model on the triangular lattice using transfer matrix studies we have found the renormalization group flows in the full phase diagram in the t w plane with fixed n superposing three copies of such hexagonal lattice loop models with staggered fields produces a variety of one or three species fully packed loop models on the triangular lattice with certain geometrical constraints possessing integer central charges 0 c 6 in particular we show that benjamini and schramm s rgb loops have fractal dimension df 3 2

field singularities at metal dielectric wedges the wedges discussed are the dielectric wedge the metallic 90 deg corner on a dielectric plane and the adjacent 90 deg metallic and dielectric corners the field components perpendicular to the edge may become infinite according to a law 1 r n numerical data are given for n and plots of lines of force of bar e or bar h are shown

model selection and the principle of minimum description length this article reviews the principle of minimum description length mdl for problems of model selection by viewing statistical modeling as a means of generating descriptions of observed data the mdl framework discriminates between competing models based on the complexity of each description this approach began with kolmogorov s theory of algorithmic complexity matured in the literature on information theory and has recently received renewed attention within the statistics community here we review both the practical and the theoretical aspects of mdl as a tool for model selection emphasizing the rich connections between information theory and statistics at the boundary between these two disciplines we find many interesting interpretations of popular frequentist and bayesian procedures as we show mdl provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared we illustrate the mdl principle by considering problems in regression nonpar

semi flexible interacting self avoiding trails on the square lattice abstract self avoiding walks self interacting via nearest neighbours isaw and self avoiding trails interacting via multiply visited sites isat are two models of the polymer collapse transition of a polymer in a dilute solution on the square lattice it has been established numerically that the collapse transition of each model lies in a different universality class it has been shown that by adding stiffness to the isaw model a second low temperature phase eventuates and a more complicated phase diagram ensues with three types of transition that meet at a multi critical point for large enough stiffness the collapse transition becomes first order interestingly a phase diagram of a similar structure has been seen to occur in an extended isat model on the triangular lattice without stiffness it is therefore of interest to see the effect of adding stiffness to the isat model we have studied by computer simulation a generalised model of self interacting self avoiding trails on the square lattice with a stiffness parameter added intriguingly we find that stiffness does not change the order of the collapse transition for isat on the square lattice for a very wide range of stiffness weights while at the lengths considered there are clear bimodal distributions for very large stiffness our numerical evidence strongly suggests that these are simply finite size effects associated with a crossover to a first order phase transition at infinite stiffness

manhattan lattice theta point exponents from kinetic growth walks and exact results from the nienhuis o n model kinetic growth walks kgw on the manhattan lattice have previously been shown to be equivalent to the static problem of interacting self avoiding walks on that lattice at the theta temperature here we illustrate how a complete set of exponents for the static problem including the crossover exponent phi and surface exponents at the ordinary and special transition points may be obtained from simulations of kinetic walks in the process we find that phi m 0 430 or 0 006 which encompasses the conjectured value 3 7 approximately 0 42857 for the theta point on an isotropic lattice our numerics confirm a predicted set of exponents for both the bulk and surface transitions in addition to results such as the exact internal energy at the bulk transition furthermore we point out that a recently examined variant of the nienhuis o n model can be mapped onto theta point walks on the manhattan lattice which allows identification of the scaling dimensions for that problem and thereby provides a method for proving all the numerical conjectures

curl conforming hierarchical vector bases for triangles and tetrahedra a new family of hierarchical vector bases is proposed for triangles and tetrahedra these functions span the curl conforming reduced gradient spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 preliminary results confirm that the new bases produce reasonably well conditioned matrices

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

a new exactly solvable case of an o n model on a hexagonal lattice a new solvable case of o n model on a hexagonal lattice is presented it is shown that the model has a phase transition at n 2 this phase transition can be interpreted as phase transition between percolating and non percolating phases

critical exponents of manhattan hamiltonian walks in two dimensions from potts and o n models we consider a set of hamiltonian circuits filling a manhattan lattice i e a square lattice with alternating traffic regulation we show that the generating function with fugacityz of this set is identical to the critical partition function of aq state potts model on an unoriented square lattice withq1 2 z the set of critical exponents governing correlations of hamiltonian circuits is derived using a coulomb gas technique these exponents are also found to be those of an o n vector model in the low temperature phase withn q1 2 z the critical exponents in the limitz 0 are then those of spanning trees q 0 and of dense polymers n 0 t tc corresponding to a conformal theory with central chargec 2 this shows that the manhattan orientation and the hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of hamiltonian walks

parameter estimation and forecasting for multiplicative log normal cascades we study the well known multiplicative log normal cascade process in which the multiplication of gaussian and log normally distributed random variables yields time series with intermittent bursts of activity due to the nonstationarity of this process and the combinatorial nature of such a formalism its parameters have been estimated mostly by fitting the numerical approximation of the associated non gaussian probability density function to empirical data cf castaing et al physica d 46 177 1990 more recently alternative estimators based upon various moments have been proposed by beck physica d 193 195 2004 and kiyono et al phys rev e 76 041113 2007 in this paper we pursue this moment based approach further and develop a more rigorous generalized method of moments gmm estimation procedure to cope with the documented difficulties of previous methodologies we show that even under uncertainty about the actual number of cascade steps our methodology yields very reliable results for the estimated intermittency parameter employing the levinson durbin algorithm for best linear forecasts we also show that estimated parameters can be used for forecasting the evolution of the turbulent flow we compare forecasting results from the gmm and kiyono et al s procedure via monte carlo simulations we finally test the applicability of our approach by estimating the intermittency parameter and forecasting of volatility for a sample of financial data from stock and foreign exchange markets

order parameters of the dilute a models the free energy and local height probabilities of the dilute a models with borken 2 symmetry are calculated analytically using inversion and corner transfer matrix methods these models possess four critical branches the first two branches provide new realizations of the unitary minimal series and the other two branches give a direct product of this series with an ising model we identify the integrable perturbations which move the dilute a models away from the critical limit generalized order parameters are defined and their critical exponents extracted the associated conformal weights are found to occur on the diagonal of the relevant kac table in an appropriate regime the dilute a3 model lies in the universality class of the ising model in a magnetic field in this case we obtain the magnetic exponent 15 directly without the use of scaling relations

critical properties of the izergin korepin and solvable o n models and their related quantum spin chains the central charge of the izergin korepin model the corresponding quantum spin chain and the o n model is calculated analytically via the bethe ansatz the calculation extends a technique recently developed for the zamolodchikov fateev model in addition critical exponents and the central charge for these models are obtained from numerical solutions of bethe ansatz equations for finite systems as a physical application the authors find the exponents v 12 23 and gamma 53 46 for the theta transition of polymers in two dimensions

boundary critical behavior of d 2 self avoiding walks on correlated and uncorrelated vacancies in this paper we present exact results for the critical exponents of interacting self avoiding walks with ends at a linear boundary effective interactions are mediated by vacancies correlated and uncorrelated on the dual lattice by choosing different boundary conditions several ordinary and special regimes can be described in terms of clusters geometry and of critical and lowtemperature properties of the mathcal o n 1 model in particular the problem of boundary exponents at the point is fully solved and implications for point universality are discussed the surface crossover exponent at the special transition of noninteracting self avoiding walks is also interpreted in terms of percolation dimensions

a scaling theory of the collapse transition in geometric cluster models of polymers and vesicles much effort has been expended in the past decade to calculate numerically the exponents at the collapse transition point in walk polygon and animal models the crossover exponent phi has been of special interest and sometimes is assumed to obey the relation 2 alpha 1 phi with the alpha the canonical thermodynamic exponent that characterizes the divergence of the specific heat the reasons for the validity of this relation are not widely known the authors present a scaling theory of collapse transitions in such models the free energy and canonical partition functions have finite length scaling forms whilst the grand partition function has a tricritical scaling form the link between the grand and canonical ensembles leads to the above scaling relation they then comment on the validity of current estimates of the crossover exponent for interacting self avoiding walks in two dimensions and propose a test involving the scaling relation which may be used to check these values

the o n model on the triangular lattice to find critical points of o n models on the triangular lattice we apply two methods first we investigate the yang baxter equations on the triangular lattice we find only solvable points directly related to those for the square lattice second we construct intersections with the potts model this yields eight branches of critical points parametrized by n we establish the equivalence of these branches with the known critical points of the o n model on the square lattice transfer matrix calculations are performed to obtain the conformal anomaly and the thermal exponent of these branches these results include a numerical analysis of a q 3 potts tricritical point we find analytic relations between potts and o n models as well as among o n models with different values of n and among potts models with different values of q

higher order hybrid fem mom technique for analysis of antennas and scatterers a novel higher order large domain hybrid computational electromagnetic technique based on the finite element method fem and method of moments mom is proposed for three dimensional analysis of antennas and scatterers in the frequency domain the geometry of the structure is modeled using generalized curved parametric hexahedral and quadrilateral elements of arbitrary geometrical orders the fields and currents on elements are modeled using curl and divergence conforming hierarchical polynomial vector basis functions of arbitrary approximation orders and the galerkin method is used for testing the elements can be as large as about two wavelengths in each dimension as multiple mom objects are possible in a global exterior region the mom part provides much greater modeling versatility and potential for applications especially in antenna problems than just as a boundary integral closure to the fem part the examples demonstrate excellent accuracy convergence efficiency and versatility of the new fem mom technique and very effective large domain meshes that consist of a very small number of large flat and curved fem and mom elements with p refined field and current distributions of high approximation orders the reduction in the number of unknowns is by two orders of magnitude when compared to available data for low order fem mom modeling

identification of a polymer growth process with an equilibrium multicritical collapse phase transition the meeting point of swollen collapsed and crystalline polymers we have investigated a polymer growth process on the triangular lattice where the configurations produced are self avoiding trails we show that the scaling behavior of this process is similar to the analogous process on the square lattice however while the square lattice process maps to the collapse transition of the canonical interacting self avoiding trail isat model on that lattice the process on the triangular lattice model does not map to the canonical equilibrium model on the other hand we show that the collapse transition of the canonical isat model on the triangular lattice behaves in a way reminiscent of the point of the interacting self avoiding walk isaw model which is the standard model of polymer collapse this implies an unusual lattice dependency of the isat collapse transition in two dimensions by studying an extended isat model we demonstrate that the growth process maps to a multicritical point in a larger parameter space in this extended parameter space the collapse phase transition may be either point like second order or first order and these two are separated by a multicritical point it is this multicritical point to which the growth process maps furthermore we provide evidence that in addition to the high temperature gaslike swollen polymer phase coil and the low temperature liquid drop like collapse phase globule there is also a maximally dense crystal like phase crystal at low temperatures dependent on the parameter values the multicritical point is the meeting point of these three phases our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the isaw and isat models in two dimensions as well as the behavior of the trail growth process

critical behaviour and conformal anomaly of the o n model on the square lattice finite size scaling and transfer matrix techniques are used to determine the conformal anomaly and critical exponents of o n models on the square lattice these calculations were performed on five branches of critical points parametrised by n the results for two of the branches agree with the known universal properties of the o n model as derived for the honeycomb lattice finite size convergence is poor for most of the third branch so that in this case the classification in terms of known models is uncertain the authors data show that the fourth branch can be interpreted in terms of a combination of a low temperature o n and a critical ising model finally the numerical results for the o n model on the remaining branch agree accurately with the known results for the low temperature o n 1 model they prove this equivalence by means of an exact mapping

collapse transition of self avoiding trails on the square lattice abstract the collapse transition of an isolated polymer has been modelled by many different approaches including lattice models based on self avoiding walks and self avoiding trails in two dimensions previous simulations of kinetic growth trails which map to a particular temperature of interacting self avoiding trails showed markedly different behaviour for what was argued to be the collapse transition than that which has been verified for models based of self avoiding walks on the other hand it has been argued that kinetic growth trails represent a special simulation that does not give the correct picture of the standard equilibrium model in this work we simulate the standard equilibrium interacting self avoiding trail model on the square lattice up to lengths over 2 000 000 steps and show that the results of the kinetic growth simulations are in fact entirely in accord with standard simulations of the temperature dependent model in this way we verify that the collapse transition of interacting self avoiding walks and trails are indeed in different universality classes in two dimensions

an analytic treatment of finite size corrections in the spin 1 antiferromagnetic xxz chain it is known that the standard method for calculating finite size corrections in bethe ansatz solvable systems is not applicable to the takhtajan babujian model and its anisotropic xxz generalisation the authors develop a new analytic method explicitly avoiding root densities and associated problems nonlinear integral equations are derived whose solutions yield the correct central charges c 1 and c 3 2 for the spin 1 2 and spin 1 xxz chains respectively in the spin 1 case the authors obtain as a by product the finite size deviation of the bethe ansatz roots from the 2 string formation

non conformal domain decomposition method with mixed true second order transmission condition for solving large finite antenna arrays a non overlapping and non conformal domain decomposition method ddm is presented for modeling large finite antenna arrays two major benefits of the proposed ddm a a mixed true second order transmission condition sotc with corner edge penalty terms is developed to facilitate fast convergence in the ddm iterations numerical experiments indicate that the convergence of ddm with the aforementioned sotc is insensitive to the sizes of arrays and b the non conformal property of the proposed ddm permits the use of completely independent discretization for each of the sub domains we demonstrate the performance of the proposed approach through several large scale problems

multilevel characteristic basis finite element method ml cbfem an efficient version of a domain decomposition algorithm for large scale electromagnetic problems we introduce a memory efficient version of the characteristic basis finite element method cbfem which combines the domain decomposition with the use of characteristic basis functions cbfs that are tailored for each individual subdomain although the conventional cbfem is inherently an efficient approach the final number of unknowns is primarily determined by the size or the number of the subdomains the larger the size of the subdomains or fewer the number the less is the final number of unknowns however if we employ large subdomains it is more difficult to generate cbfs for each subdomain due to the memory bottleneck in utilizing direct solution techniques employed to generate the cbfs in the proposed multilevel approach referred to herein as the multilevel cbfem ml cbfem we first decompose the computational domain into several smaller subdomains and generate the cbfs for each subdomain in a conventional manner then these bases are combined in a multilevel fashion to derive the cbfs for larger subdomains in each level the cbfs are created by using the bases in the lower level this approach also called nested cbfem leads to a considerable reduction in the matrix size and memory and thus makes use of direct solvers efficiently

a fem domain decomposition method for photonic and electromagnetic band gap structures this paper introduces an efficient domain decomposition algorithm for the solution of time harmonic electromagnetic fields arising in three dimensional finite size photonic band gap and electromagnetic band gap structures the method is based on the finite element approximation and a nonoverlapping domain decomposition method a set of cement unknowns on the inter domain interfaces has been explicitly introduced to enforce the appropriate field continuities the introduction of these extra unknowns allows for nonconforming nonmatching triangulations across domain eliminating the need for periodic mesh to ensure and improve the convergence of the outer iteration loop robin transmission condition is used to communicate information across interfaces the resulting system of equations is solved with a fast algorithm that loosely resembles the well known finite element tearing and interconnecting algorithm in this algorithm the method solves in the preprocessing step for the robin primal subdomain problems multiple times by exciting one dual unknown at a time this step generates an iteration matrix that is then used to update the dual unknowns in the outer loop iteration the present method becomes extremely efficient for problems with geometric repetitions such as photonic and electromagnetic band gap structures

small sample effects in time series analysis a new asymptotic theory and a new estimate on introduit un modele mathematique qui couvre les effets des petits echantillons dans l approximation de whittle 1953 on montre que l estimation du maximum de vraisemblance exacte est toujours optimale dans ce modele

polynomial tapered two stage least squares method in nonlinear regression nonlinear models play an important role in various scientific disciplines and engineering the parameter estimation of these models should be efficient to make better decisions ordinary least squares ols method is used for estimating the parameters of nonlinear regression models when all regression assumptions are satisfied if there is a problem with these assumptions ols fails to give efficient results this paper examines the efficiency of parameter estimation under the problem of autocorrelated errors some methods have been proposed in order to overcome the problem and obtain efficient parameter estimates especially for autoregressive ar processes one of the most commonly used method is two stage least squares 2sls this method is based on generalized least squares in this paper a novel approach is proposed for 2sls method by evaluating a polynomial tapering procedure on autocorrelated errors this new method is called tapered two stage least squares t2sls the finite sample properties and improvements of t2sls are explored by means of some real life examples and a monte carlo simulation study both numerical and experimental results reveal that t2sls can give more efficient parameter estimates especially in small samples under the autocorrelation problem when compared to ols and 2sls

singular higher order complete vector bases for finite methods this paper presents new singular curl and divergence conforming vector bases that incorporate the edge conditions singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements the curl divergence conforming singular bases guarantee tangential normal continuity along the edges of the elements allowing for the discontinuity of normal tangential components adequate modeling of the curl divergence and removal of spurious modes solutions these singular high order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems sample numerical results confirm the faster convergence of these bases on wedge problems

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

finite element analysis of complex antennas and arrays various technical issues are addressed in the frequency and time domain finite element analysis of complex antennas and arrays that may consist of fine structures and composite materials the paper starts with the finite element formulation of a generic antenna problem formulation for the modeling of general electrically and magnetically dispersive lossy and anisotropic materials in the time domain finite element analysis is presented for the first time this is followed by discussion of three typical techniques for truncation of the finite element computational domain via the use of absorbing boundary conditions perfectly matched layers and boundary integral equations it then describes the modeling of antenna feeds using a current probe including an improved model a voltage gap and a waveguide port boundary condition after that numerical approaches to modeling infinite phased arrays large finite arrays and antenna platform interaction are presented including two novel domain decomposition algorithms in both the frequency and time domains numerical examples are given to demonstrate the capability and application of the finite element analysis of a variety of complex antennas and arrays