edgeworth expansions of stochastic trading time abstract under most local and stochastic volatility models the underlying forward is assumed to be a positive function of a time changed brownian motion it relates nicely the implied volatility smile to the so called activity rate in the market following young and dewitt morette 1986 8 we propose to apply the duru kleinert process cum time transformation in path integral to formulate the transition density of the forward the method leads to asymptotic expansions of the transition density around a gaussian kernel corresponding to the average activity in the market conditional on the forward value the approximation is numerically illustrated for pricing vanilla options under the cev model and the popular normal sabr model the asymptotics can also be used for monte carlo simulations or backward integration schemes

bergman kernel from path integral we rederive the expansion of the bergman kernel on kahler manifolds developed by tian yau zelditch lu and catlin using path integral and perturbation theory and generalize it to supersymmetric quantum mechanics one physics interpretation of this result is as an expansion of the projector of wave functions on the lowest landau level in the special case that the magnetic field is proportional to the kahler form this is relevant for the quantum hall effect in curved space and for its higher dimensional generalizations other applications include the theory of coherent states the study of balanced metrics noncommutative field theory and a conjecture on metrics in black hole backgrounds discussed in 24 we give a short overview of these various topics from a conceptual point of view this expansion is noteworthy as it is a geometric expansion somewhat similar to the dewitt seeley gilkey et al short time expansion for the heat kernel but in this case describing the long time limit without depending on supersymmetry

boundary integral equations for the scattering of electromagnetic waves by a homogeneous chiral obstacle the time harmonic scattering of electromagnetic waves by a homogeneous chiral media are considered herein the scattering problem is reduced using bohren s decomposition to an equivalent boundary integral equation which is shown to be uniquely solvable except for a discrete set of values of electromagnetic parameters of the scatterer it should be noted that the boundary integral operators appearing in this equation are the same as for a dielectric scatterer and hence their mapping properties are well known

low frequency behavior of solutions to electromagnetic scattering problems in chiral media this paper deals with the low frequency scattering problem by a conducting object in a chiral medium using boundary integral equation methods we obtain the limit of the scattered field solution of the drude born fedorov equations as frequency tends to zero making use of a hodge decomposition of the tangent fields shows that the asymptotics strongly depend on the topological properties of the domains under consideration the asymptotic expansion s dependence on the chirality parameter is shown completely

statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

functional determinants in quantum field theory functional determinants of differential operators play a prominent role in theoretical and mathematical physics and in particular in quantum field theory they are however difficult to compute in non trivial cases for one dimensional problems a classical result of gel fand and yaglom dramatically simplifies the problem so that the functional determinant can be computed without computing the spectrum of eigenvalues here i report recent progress in extending this approach to higher dimensions i e functional determinants of partial differential operators with applications in quantum field theory

special attention network in this note a social network model for opinion formation is proposed in which a person connected to q partners pays an attention 1 q to each partner the mutual attention between two connected persons i and j is taken equal to the geometric mean 1 qiqj opinion is represented as usual by an ising spin s 1 and mutual attention is given through a two spin coupling jij jq qiqj q being the average connectivity in the network connectivity diminishes attention and only persons with low connectivity can pay special attention to each other leading to a durable common or opposing opinion the model is solved in mean field approximation and a critical temperature tc proportional to jq is found which is independent of the number of persons n for large n

one loop integrals at finite temperature a method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature the regularization of the integrals yields expressions which have a non polynomial nature in the inverse temperature a comparison with previously published results is presented and the advantages of the present technique are discussed

time domain green dyadics for temporally dispersive bi isotropic media time domain green dyadics for linear homogeneous temporally dispersive bi isotropic media are presented a complex time dependent electromagnetic field is introduced approximation to the complex field from an electric point dipole in an unbounded bi isotropic medium with respect to the slowly varying components second forerunner approximation is obtained numerical examples are presented surface integral equations for the tangential components of the electromagnetic fields are derived for two standard scattering problems

on single integral equations for the transmission problem of acoustics the transmission problem namely scattering of time harmonic waves in a compressible fluid by a fluid inclusion with different material properties is usually formulated as a pair of coupled boundary integral equations over the interface s between the inclusion and the exterior fluid in this paper however we consider methods for solving the transmission problem using a single integral equation over s for a single unknown function in fact we derive four different integral equations using a hybrid of the direct green s theorem and indirect layer ansatz methods and give conditions for the unique solvability of each and for the subsequent construction of the solution to the transmission problem some of our single integral equations are fredholm integral equations of the second kind with weakly singular kernels thus these equations all of which appear to be new are attractive computationally

collocation method for fractional quantum mechanics we show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional laplacian using a collocation approach based on little sinc functions which discretizes the schrodinger equation on a uniform grid the different boundary conditions are naturally implemented using sets of functions with the appropriate behavior good convergence properties are observed a comparison with results based on a wentzel kramers brillouin analysis is performed

a path integral approach to asset liability management functional integrals constitute a powerful tool in the investigation of financial models in the recent econophysics literature this technique was successfully used for the pricing of a number of derivative securities in the present contribution we introduce this approach to the field of asset liability management we work with a representation of cash flows by means of a two dimensional delta function perturbation in the case of a brownian model and a geometric brownian model we derive closed form solutions for a finite horizon alm policy the results are numerically and graphically illustrated

valuation of stochastic interest rate securities with time dependent variance abstract we consider the problem of how to prize general securities whose payoff at maturity only depends on the interest rate r t at the time of exercise where r t is supposed to be a stochastic feller process we show how to generalize the results of cox et al econometrica 53 2 1985 385 regarding bond valuation to a situation where the stochastic evolution of r t under the martingale probability involves time dependent coefficients and the payoff is arbitrary the solution to this problem is given in terms of the propagator for the heat operator with a potential this propagator is constructed in terms of a classical harmonic oscillator with time dependent frequency

on a complex differential riccati equation we consider a nonlinear partial differential equation for complex valued functions which is related to the two dimensional stationary schrodinger equation and enjoys many properties similar to those of the ordinary differential riccati equation such as the famous euler theorems the picard theorem and others besides these generalizations of the classical one dimensional results we discuss new features of the considered equation including an analogue of the cauchy integral theorem

self similar variational perturbation theory for critical exponents we extend field theoretic variational perturbation theory by self similar approximation theory which greatly accelerates convergence this is illustrated by recalculating the critical exponents of o n symmetric ensuremath phi 4 theory from only three loop perturbation expansions in 4 ensuremath dimensions we obtain analytic results for the exponents which are close to those derived recently from ordinary field theoretic variational perturbational theory to seventh order in particular the specific heat exponent is found to be in good agreement with best measured exponent ensuremath alpha ensuremath approx ensuremath 0 0127 of the specific heat peak in superfluid helium found in a satellite experiment in addition our analytic expressions reproduce also the exactly known large n behavior of the exponents

on the reduction of the multidimensional stationary schrodinger equation to a first order equation and its relation to the pseudoanalytic function theory given a particular solution of a one dimensional stationary schrodinger equation this equation of second order can be reduced to a first order linear ordinary differential equation this is done with the aid of an auxiliary riccati differential equation in the present work we show that the same fact is true in a multidimensional situation also for simplicity we consider the case of two or three independent variables one particular solution of the stationary schrodinger equation allows us to reduce this second order equation to a linear first order quaternionic differential equation as in the one dimensional case this is done with the aid of an auxiliary quaternionic riccati equation the resulting first order quaternionic equation is equivalent to the static maxwell system and is closely related to the dirac equation in the case of two independent variables it is the well known vekua equation from theory of pseudoanalytic or generalized analytic functions nevertheless we show that even in this case it is very useful to consider not only complex valued functions solutions of the vekua equation but complete quaternionic functions in this way the first order quaternionic equation represents two separate vekua equations one of which gives us solutions of the schrodinger equation and the other one can be considered as an auxiliary equation of a simpler structure moreover for the auxiliary equation we always have the corresponding bers generating pair f g the base of the bers theory of pseudoanalytic functions and what is very important the bers derivatives of solutions of the auxiliary equation give us solutions of the main vekua equation and as a consequence of the schrodinger equation based on this fact we obtain an analogue of the cauchy integral theorem for solutions of the stationary schrodinger equation other results from theory of pseudoanalytic functions can be written for solutions of the schrodinger equation moreover for an ample class of potentials in the schrodinger equation which includes for instance all radial potentials this new approach gives us a simple procedure allowing us to obtain an infinite sequence of solutions of the schrodinger equation from one known particular solution

localization transition of stiff directed lines in random media dimensions which is strongly supported by identical free energy distributions this shows that pair interactionsin the replicated hamiltonian determine the nature of directed line localization transitions with consequences forthe critical behavior of the kardar parisi zhang kpz equation furthermore we quantify how the persistencelength of the stiff directed line is reduced by disorder doi 10 1103 physreve 86 060102 pacs number s 05

path integral approach to the pricing of timer options with the duru kleinert time transformation in this paper a time substitution as used by duru and kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models we present general pricing formulas for both the perpetual timer call options and the finite time horizon timer call options these general results allow us to find closed form pricing formulas for both the perpetual and the finite time horizon timer options under the 3 2 stochastic volatility model as well as under the heston stochastic volatility model for the treatment of timer options under the 3 2 model we will rely on the path integral for the morse potential with the heston model we will rely on the kratzer potential

a priori estimates for a singular limit approximation of the constitutive laws for chiral media in the time domain abstract the equations for the evolution of electromagnetic fields in chiral media in the time domain are nonlocal in time in this work we study the validity of a singular limit local in time approximation for these nonlocal in time equations by estimating the size of the difference of the fields as predicted by both models in particular we establish an a priori estimate for this difference depending on the time horizon properties of the domain spatial properties of the initial data and the source terms and the chirality measure of the approximating model

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

analysis of path integrals at low temperature box formula occupation time and ergodic approximation we study the low temperature behavior of path integrals for a simple one dimensional model starting from the feynman kac formula we derive a new functional representation of the density matrix at finite temperature in terms of the occupation times for brownian motions constrained to stay within boxes with finite sizes from that representation we infer a kind of ergodic approximation which only involves double ordinary integrals as shown by its applications to different potentials the ergodic approximation turns out to be quite efficient especially in the low temperature regime where other usual approximations fail

on the representation of inhomogeneous linear force free fields it is shown that there is a false assumption hidden in the description of a relaxed state with inhomogeneous boundary conditions as the vector sum of a potential field satisfying the boundary conditions and a sum of eigenfunctions of the associated eigenvalue problem expanded by certain coefficients in particular although the jensen and chu formula 1984 can provide the correct expansion coefficients it contains an implicit paradox in its derivation according to a general vector theorem the same paradox led chu et al 1999 to be concerned about a contradiction obtained by taking the curl of their magnetic field expansion which if permitted becomes inconsistent with a current normal to the surface the assumption that the curl can be commuted across an infinite sum of terms is the mechanism leading to these apparently paradoxical conclusions two mechanisms for resolving this apparent paradox are possible one of which will be described in some detail below and the other discussed further in a forthcoming more theoretical paper laurence et al 2000 the decomposition of the magnetic field above is valid with convergence in the mean squared sense but a decomposition of the current needs to be reinterpreted in terms of negative sobolev spaces to avoid this and remain in a more easily managable and familiar setting we derive the expansion coefficients in a way that involves the commuting of the inverse curl as opposed to the curl and the series the resulting series converges in a mean square sense when this is done the calculation can conform to the general vector theorem and a new gauge invariant expression for the coefficients is obtained however the consequence of the non commutability is nullified in the jensen and chu formula in both simply and multiply connected domains by the important extra requirement of a boundary condition on the vector potential eigenfunctions this excludes magnetic field eigenfunctions that carry flux but there remains a complete set for the expansion and all flux is carried by the potential field the two formulas are then identical on a different issue it is shown that if the general expansion is taken over a half space by combining positive and negative eigenvalue terms then the coefficients are anisotropic that is they are tensors except when evaluated at the first eigenvalue a specific example is presented to illustrate the situation and to validate the new method of deriving the coefficients

dynamics of two externally driven coupled quantum oscillators interacting with separate baths based on path integrals abstract the paper deals with the problem of dynamics of externally driven open quantum systems using the path integral methods we found an analytical expression for time dependent density matrix of two externally driven coupled quantum oscillators interacting with different baths of oscillators it is shown that at the zeroing of external forces the density matrix becomes identical to the previously obtained one for freely developing coupled oscillators mean values of observables and all elements of the covariance matrix composed by coordinates and momenta of two driven coupled oscillators are calculated the time dependent mean values dispersions and covariances of coordinates of coupled oscillators at given external forces are numerically studied it is shown that the larger the coupling constant the larger is the disturbances of the second oscillator due to external action on the first oscillator coupled dynamics of forced oscillators at relatively large coupling constant is demonstrated at different thermodynamic conditions

regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions the boundary integral equations bies in their original forms which govern the electromagnetic em wave scattering in three dimensional space contain at least a hypersingularity 1 r sup 3 or a cauchy singularity 1 r sup 2 usually both thus obtaining reliable numerical solutions using such equations requires considerable care especially when developing systematic numerical integration procedures for realistic problems regularized bies for the numerical computation of time harmonic em scattering fields due to arbitrarily shaped scatterers are introduced two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration both approaches differ from all existing approaches to em scattering problems both work for integral equations initially containing either hypersingularities or cauchy singularities without the need to introduce surface divergences or other derivatives of the em fields on the boundary also neither approach is limited to flat surfaces nor flat element models of curved surfaces the muller linear combination of the electric and magnetic field integral equations efie and mfie is used to avoid the resonance difficulty that is usually associated with integral equation based formulations some preliminary numerical results for em scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions

green function of the double fractional fokker planck equation path integral and stochastic differential equations the statistics of rare events the so called black swan events is governed by non gaussian distributions with heavy power like tails we calculate the green functions of the associated fokker planck equations and solve the related stochastic differential equations we also discuss the subject in the framework of path integration

path integral solutions for klein gordon particle in vector plus scalar generalized hulthen and woods saxon potentials the green s function for a klein gordon particle under the action of vector plus scalar deformed hulthen and woods saxon potentials is evaluated by exact path integration explicit path integration leads to the green s function for different shapes of the potentials from the singularities of the latter green s function the bound states are extracted for q 1 and 1 ln q r the analytic expression of the energy spectrum and the normalized wave functions for the l states are obtained within the framework of an approximation to the centrifugal term when the deformation parameter q is 0 q 1 or q 0 it is found that the quantization conditions are transcendental equations involving the hypergeometric function that require a numerical solution for the s state energy levels particular cases of these potentials are also discussed briefly

diagonalization of bounded linear operators on separable quaternionic hilbert space by using the representation of its complex conjugate pairs we have investigated the diagonalization of a bounded linear operator on separable infinite dimensional right quaternionic hilbert space the sufficient condition for diagonalizability of quaternionic operators is derived the result is applied to anti hermitian operators which is essential for solving schrodinger equation in quaternionic quantum mechanics

systematically accelerated convergence of path integrals we present a new analytical method that systematically improves the convergence of path integrals of a generic n fold discretized theory using it we calculate the effective actions s p for p or 9 which lead to the same continuum amplitudes as the starting action but that converge to that continuum limit as 1 n p we checked this derived speedup in convergence by performing monte carlo simulations on several different models

application of sinc collocation method for solving an inverse problem in this article the identification of an unknown time dependent source term in an inverse problem of parabolic type with nonlocal boundary conditions is considered the main approach is to change the inverse problem to a system of volterra integral equations the resulting integral equations are convolution type which by using sinc collocation method are replaced by a system of linear algebraic equations the convergence analysis is included and it is shown that the error in the approximate solution is bounded in the infinity norm by the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system to show the efficiency of the present method an example is presented the method is easy to implement and yields very accurate results

constructing green s function for the time dependent maxwell system in anisotropic dielectrics a method of constructing explicit formulae for green s matrix function of the time dependent maxwell system for a homogeneous non dispersive dielectric with a general form of the anisotropy is described this method consists of two parts in the first part a matrix function depending on the time variable and three fourier parameters is determined this matrix function being the fourier image of green s matrix function with respect to three space variables is constructed in an explicit form the second part of the method is the inverse fourier transform of the determined matrix function the robustness and advantages of this method are confirmed by numerical experiments examples of simulations of electromagnetic fields in anisotropic crystals are presented

electromagnetic scattering by a homogeneous chiral obstacle boundary integral equations and low chirality approximations time harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle the corresponding transmission problem is reduced to a pair of coupled integral equations over s where s is the interface between the obstacle and the surrounding medium this is done using a generalization of the stratton chu representation that is valid for chiral media the integral equations obtained are a generalization of those obtained by muller for a homogeneous dielectric obstacle finally we develop approximations for low chirality obstacles these approximations can be computed using simple modifications to existing codes for solving muller s equations

on the emergence of scaling in weighted networks abstract general conditions for the appearance of the power law distribution of total weights concentrated in vertices of complex network systems are established by use of the rate equation approach for networks evolving by connectivity governed attachment of every new node to p 1 exiting nodes and by ascription to every new link a weight taken from algebraic distributions independent of network topologies it is shown that the distribution of the total weight w asymptotically follows the power law p w w with the exponent 0 2 the power law dependence of the weight distribution is also proved to hold for asymptotically large w in the case of networks in which a link between nodes i and j carries a load w ij determined by node degrees k i and k j at the final stage of the network growth according to the relation w ij k i k j with 1 0 for this class of networks the scaling exponent describing the weight distribution is found to satisfy the relationship 1 where is the scaling index characterizing the distribution of node degrees n k k

collocation on uniform grids in this paper we derive four sets of sinc like functions defined on a finite interval and obeying different boundary conditions the functions in each set are orthogonal and their nodes are uniformly distributed on the interval we have applied each set to solve a large class of eigenvalue equations with different boundary conditions both on finite intervals and on the real line showing that precise numerical results can be obtained efficiently and rapidly a comparison with results available in the literature is also performed

scale free properties of weighted networks with connectivity driven topology abstract the rate equations are used to study the scale free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices an analysis of these equations shows that the degree distribution and thereby the weight distribution remain unchanged when the probability rate of attaching new nodes is replaced with an unnormalized rate determined by the ratio of the degree of a randomly selected old node to the maximal node degree at the current stage of the network evolution such a modification of the attachment rule is argued to accelerate considerable numerical simulations of both unweighted and weighted networks belonging to the class of investigated evolving systems it is also proved that the studied rate equations have a solution corresponding to the total weight concentrated at individual vertices distribution displaying the power law behavior for asymptotically large weights

time dependent potential scattering in chiral media electromagnetic waves propagating in a homogeneous three dimensional unbounded chiral medium are considered we define a chiral operator and study potential scattering relative to this operator a spectral analysis of associated operators is obtained based on the plancherel theory of the fourier transform using the generalised eigenfunction expansion theory we give an integral representation of the solution a discussion of asymptotic equality of solutions is provided and the associated wave operator introduced

statistics of weighted treelike networks we study the statistics of growing networks with a tree topology in which each link carries a weight k i k j theta where k i and k j are the node degrees at the end points of link ij network growth is governed by preferential attachment in which a newly added node attaches to a node of degree k with rate a k k lambda for general values of theta and lambda we compute the total weight of a network as a function of the number of nodes n and the distribution of link weights generically the total weight grows as n for lambda theta 1 and superlinearly otherwise the link weight distribution is predicted to have a power law form that is modified by a logarithmic correction for the case lambda 0 we also determine the node strength defined as the sum of the weights of the links that attach to the node as function of k using known results for degree correlations we deduce the scaling of the node strength on k and n

on a quaternionic maxwell equation for the time dependent electromagnetic field in a chiral medium maxwell s equations for the time dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation its fundamental solution satisfying the causality principle is obtained which allows us to solve the time dependent chiral maxwell system with sources

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

transport in weighted networks partition into superhighways and roads transport in weighted networks is dominated by the minimum spanning tree mst the tree connecting all nodes with the minimum total weight we find that the mst can be partitioned into two distinct components having significantly different transport properties characterized by centrality the number of times a node or link is used by transport paths one component superhighways is the infinite incipient percolation cluster for which we find that nodes or links with high centrality dominate for the other component roads which includes the remaining nodes low centrality nodes dominate we find also that the distribution of the centrality for the infinite incipient percolation cluster satisfies a power law with an exponent smaller than that for the entire mst the significance of this finding is that one can improve significantly the global transport by improving a tiny fraction of the network the superhighways

end to end distribution for a wormlike chain in arbitrary dimensions we construct an efficient methodology for calculating wormlike chain statistics in arbitrary d dimensions over all chain rigidities from fully rigid to completely flexible the structure of our exact analytical solution for the end to end distribution function for a wormlike chain in arbitrary d dimensions in fourier laplace space i e fourier transformed end position and laplace transformed chain length adopts the form of an infinite continued fraction which is advantageous for its compact structure and stability for numerical implementation we then proceed to present a step by step methodology for performing the fourier laplace inversion in order to make full use of our results in general applications asymptotic methods for evaluating the laplace inversion power law expansion and rayleigh schrodinger perturbation theory are employed in order to improve the accuracy of the numerical inversions of the end to end distribution function in real space we adapt our results to the evaluation of the single chain structure factor rendering simple closed form expressions that facilitate comparison with scattering experiments using our techniques the accuracy of the end to end distribution function is enhanced up to the limit of the machine precision we demonstrate the utility of our methodology with realizations of the chain statistics giving a general methodology that can be applied to a wide range of biophysical problems

social inertia in collaboration networks this work is a study of the properties of collaboration networks employing the formalism of weighted graphs to represent their one mode projection the weight of the edges is directly the number of times that a partnership has been repeated this representation allows us to define the concept of social inertia that measures the tendency of authors to keep on collaborating with previous partners we use a collection of empirical datasets to analyze several aspects of the social inertia 1 its probability distribution 2 its correlation with other properties and 3 the correlations of the inertia between neighbors in the network we also contrast these empirical results with the predictions of a recently proposed theoretical model for the growth of collaboration networks

quaternionic factorization of the schrodinger operator and its applications to some first order systems of mathematical physics we show that an ample class of physically meaningful partial differential systems of first order such as the dirac equation with different one component potentials static maxwell s system and the system describing the force free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a schrodinger equation with quaternionic potential and in some situations this last can be diagonalized the rich variety of methods developed for different problems corresponding to the schrodinger equation can be applied to the systems considered in the present work

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

cluster expansions in the 2 1 d ising model the cluster expansion methods of nickel are applied to calculate high temperature series for the vacuum energy and specific heat the susceptibility and the mass gap in the 2 1 d ising model critical points and critical exponents are estimated for the square and triangular lattices the results demonstrate universality with the 3d ising model within errors exact linked cluster expansions are formulated for the quantities above and their convergence and scaling properties are investigated

variational collocation on finite intervals in this paper we study a set of functions defined on an interval of finite width which are orthogonal and which reduce to the sinc functions when the appropriate limit is taken we show that these functions can be used within a variational approach to obtain accurate results for a variety of problems we have applied them to the interpolation of functions on finite domains and to the solution of the schrodinger equation and we have compared the performance of the present approach with others

a topological field theory for milnor s triple linking number the subject of this work is a topological field theory with a non semisimple gauge group and local observables that are both metric independent and gauge invariant the observables consist of the holonomies of connections around three arbitrary loops and contain not only three dimensional vector fields but also a set of one dimensional scalar fields the gauge invariance is achieved by requiring non trivial gauge transformations in the scalar field sector the importance of theories of this kind in the statistical physics of linked polymer rings is discussed the presence of fields of different dimensions is the novel feature of the proposed model which retains many properties of the non abelian chern simons field theories and has the advantage to be exactly solvable its only one relevant amplitude has been computed here in closed form from its expression it is possible to isolate the milnor s triple linking number a link invariant which has physical applications in the dynamics of fluids and solar magnetohydrodynamics

stochastic calculus for assets with non gaussian price fluctuations abstract from the path integral formalism for price fluctuations with non gaussian distributions we derive the appropriate stochastic calculus replacing ito s calculus for stochastic fluctuations

solving the helmholtz equation for membranes of arbitrary shape numerical results i calculate the modes of vibration of membranes of arbitrary shape using a collocation approach based on little sinc functions the matrix representation of the pde obtained using this method is explicit and does not require the calculation of integrals to illustrate the virtues of this approach i have considered a large number of examples part of them are taken from the literature and part of them new when possible i have tested the accuracy of these results by comparing them with the exact results when available or with results from the literature in particular in the case of the l shaped membrane the first example discussed in the paper i show that it is possible to extrapolate the results obtained with different grid sizes to obtain highly precise results finally i also show that the present collocation technique can be easily combined with conformal mapping to provide numerical approximations to the energies which quite rapidly converge to the exact results

information transmission using non poisson regular firing in many cortical areas neural spike trains do not follow a poisson process in this study we investigate a possible benefit of non poisson spiking for information transmission by studying the minimal rate fluctuation that can be detected by a bayesian estimator the idea is that an inhomogeneous poisson process may make it difficult for downstream decoders to resolve subtle changes in rate fluctuation but by using a more regular non poisson process the nervous system can make rate fluctuations easier to detect we evaluate the degree to which regular firing reduces the rate fluctuation detection threshold we find that the threshold for detection is reduced in proportion to the coefficient of variation of interspike intervals

a new method for studying the vibration of non homogeneous membranes abstract we present a method to solve the helmholtz equation for a non homogeneous membrane with dirichlet boundary conditions at the border of arbitrary two dimensional domains the method uses a collocation approach based on a set of localized functions called little sinc functions which are used to discretize two dimensional regions we have performed extensive numerical tests and we have compared the results obtained with the present method with the ones available from the literature our results show that the present method is very accurate and that its implementation for general problems is straightforward

weight driven growing networks we study growing networks in which each link carries a certain weight randomly assigned at birth and fixed thereafter the weight of a node is defined as the sum of the weights of the links attached to the node and the network grows via the simplest weight driven rule a newly added node is connected to an already existing node with the probability which is proportional to the weight of that node we show that the node weight distribution n w has a universal tail that is it is independent of the link weight distribution n w approximately w 3 as w infinity results are particularly neat for the exponential link weight distribution when n w is algebraic over the entire weight range

self adapting network topologies in congested scenarios most studies in complex networks assume that once a link is created between two nodes it is never deleted however there is a recent interest towards systems where links can be rapidly rewired an important issue in that type of networks is to discover the topology that given a search algorithm optimizes the search process in this paper we present a system model that depending on the current network congestion makes nodes to establish link connections so that the resulting topologies tend to a starlike when congestion is small and to randomlike topologies when congestion becomes relevant those topologies have been shown to be optimal in the above mentioned conditions such a model can be easily implemented in practice and therefore may be relevant in areas as the topology management of peer to peer networks

fokker planck equation and path integral representation of the fractional ornstein uhlenbeck process with two indices this paper considers the fokker planck equation and path integral formulation of the fractional ornstein uhlenbeck process parametrized by two indices the effective fokker planck equation of this process is derived from the associated fractional langevin equation the path integral representation of the process is constructed and the basic quantities are evaluated

ising model on networks with an arbitrary distribution of connections we find the exact critical temperature t c of the nearest neighbor ferromagnetic ising model on an equilibrium random graph with an arbitrary degree distribution p k we observe an anomalous behavior of the magnetization magnetic susceptibility and specific heat when p k is fat tailed or loosely speaking when the fourth moment of the distribution diverges in infinite networks when the second moment becomes divergent t c approaches infinity the phase transition is of infinite order and size effect is anomalously strong

exact solutions of the dirac equation with harmonic pseudoscalar scalar or electric potential a new class of exact solutions is obtained in explicit form for the dirac equation with a pseudoscalar or scalar or electric static potential the potential may be an arbitrary harmonic function the gradient squared of which is a constant it is shown that the set of such potentials is sufficiently ample the simplest example is the linear function another example is the function where is an arbitrary analytic function depending on the complex variable the solutions are obtained using the technique of biquaternionic projection operators which itself is interesting since its possible applications are not limited to the situation considered in this paper

on the existence of force free magnetic fields with small nonconstant α in exterior domains the existence of force free magnetic fields in the exterior domain of some compact simply connected surface s is proved via an iteration scheme the iteration starts with an arbitrary exterior vacuum field which contains flux tubes originating and ending on s at one cross section of such a flux tube with s an arbitrary function is prescribed for small values of in the holder norm 1 0 1 the iteration is shown to converge to a force free field with the prescribed values of in a flux tube which is close to the vacuum flux tube and 0 outside the force free field is close in the holder norm 1 to the starting vacuum field in particular it has the same field line topology the same boundary values on s and satisfies the same decay conditions in spatial infinity it is in general three dimensional and requires no continuous symmetries

scaling in weighted networks and complex systems abstract network systems evolving by preferential attachment of new vertices and by link loading are considered the probability of node attaching is assumed to depend linearly on degrees of existing nodes to which new ones are connected the rule of the network loading allows both deterministic and random processes of distributing weights among links specifically the rule is determined by assigning to each link a weight dependent on randomly modified intervals between times at which linked vertices are connected to the system this enables the investigation of the influence of local and global loading processes on statistical properties of weighted networks it is demonstrated that for different values of parameters controlling these processes the distribution of weights concentrated at vertices of such networks displays a large variety of scale free and truncated scale free behaviors it is also shown that statistical properties of the studied weighted networks and statistical properties of some complex evolving spatial systems exhibit a close relationship

option pricing from path integral for non gaussian fluctuations natural martingale and application to truncated levy distributions within a path integral formalism for non gaussian price fluctuations we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options stocks and bonds the resulting formula is evaluated for truncated levy distributions

linear stochastic degenerate sobolev equations and applications in this paper a general class of linear stochastic degenerate sobolev equations with additive noise is considered this class of systems is the infinite dimensional analogue of linear descriptor systems in finite dimensions under appropriate assumptions the mild and strong well posedness for the initial value problem are studied using elements of the semigroup theory and properties of the stochastic convolution the final value problem is also examined and it is proved that this is uniquely strongly solvable and the solution is continuously dependent on the final data based on the results of the forward and backward problem the conditions for the exact controllability are investigated for a special but important class of these equations the abstract results are illustrated by applications in complex media electromagnetics in the one dimensional stochastic dirac equation in the non relativistic limit and in a potential application in input output analysis in economics

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

superpositions of probability distributions probability distributions which can be obtained from superpositions of gaussian distributions of different variances v ensuremath sigma 2 play a favored role in quantum theory and financial markets such superpositions need not necessarily obey the chapman kolmogorov semigroup relation for markovian processes because they may introduce memory effects we derive the general form of the smearing distributions in v which do not destroy the semigroup property the smearing technique has two immediate applications it permits simplifying the system of kramers moyal equations for smeared and unsmeared conditional probabilities and can be conveniently implemented in the path integral calculus in many cases the superposition of path integrals can be evaluated much easier than the initial path integral three simple examples are presented and it is shown how the technique is extended to quantum mechanics

concentrated ring loadings in a full space or half space solutions for transverse isotropy and isotropy in this analysis solutions for concentrated ring loading in a transversely isotropic full space or half space are found the elastic field is derived by integrating the known fundamental point force solutions along a circular ring three cases of ring loading are considered taking the z axis along the material axis the z 0 plane is the isotropic plane the first case studied is when the ring load is in the z direction referred to as normal loading the other two cases are shear ring loads directed in the plane of isotropy in the first instance the ring load is unidirectional and independently applied in either the x or y direction the second case considers the axisymmetric radial and axisymmetric torsional ring loads the solution for ring loading applied to the surface of a half space is first obtained subsequently the solutions for ring loading in a full space and buried ring loads in a half space are found in all cases the elastic displacement and stress fields are evaluated in terms of closed form expressions containing complete elliptic integrals of the first second and third kinds an interesting feature of the full space solution is that the potential function and its radial derivatives exhibit a cylindrical discontinuity for negative z values however it is shown that these discontinuous functions do provide continuous displacement and stress fields a limiting form of the solutions for transverse isotropy also provides the corresponding results for isotropic materials

on beltrami fields with nonconstant proportionality factor the equation rot x x x 0 is considered where is a nonvanishing complex valued function its quaternionic reformulation is obtained which is used for constructing integral representations for solutions in the case when is a function of one variable we show that in this case the solution of the considered equation reduces to the solution of three different schrodinger equations with potentials depending on one variable

green functions and propagation of waves in strongly inhomogeneous media we show that green functions of second order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well known properties of the green functions of operators with bounded coefficients we discuss some consequences of such an anomalous short or long distance behaviour for a diffusion and wave propagation in an inhomogeneous medium

boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle time harmonic electromagnetic waves are scattered by a homogeneous dielectric obstacle the corresponding electromagnetic transmission problem is reduced to a single integral equation over s for a single unknown tangential vector field where s is the interface between the obstacle and the surrounding medium in fact several different integral equations are derived and analysed including two previously known equations due to e marx and j r mautz and two new singular integral equations mautz s equation is shown to be uniquely solvable at all frequencies a new uniquely solvable singular integral equation is also found the paper also includes a review of methods using pairs of coupled integral equations over s it is these methods that are usually used in practice although single integral equations seem to offer some computational advantages

criticality on networks with topology dependent interactions weighted scale free networks with topology dependent interactions are studied it is shown that the possible universality classes of critical behavior which are known to depend on topology can also be explored by tuning the form of the interactions at fixed topology for a model of opinion formation simple mean field and scaling arguments show that a mapping gamma gamma mu 1 mu describes how a shift of the standard exponent gamma of the degree distribution can absorb the effect of degree dependent pair interactions j ij proportional to k i k j mu where k i stands for the degree of vertex i this prediction is verified by extensive numerical investigations using the cavity method and monte carlo simulations the critical temperature of the model is obtained through the bethe peierls approximation and with the replica technique the mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network

a variational sinc collocation method for strong coupling problems we have devised a variational sinc collocation method vscm which can be used to obtain accurate numerical solutions to many strong coupling problems sinc functions with an optimal grid spacing are used to solve the linear and nonlinear schrodinger equations and a lattice 4 model in 1 1 our results indicate that errors decrease exponentially with the number of grid points and that a limited numerical effort is needed to reach high precision

strong coupling expansion analysis of the false vacuum decay rate of the lattice phi4 model in 1 1 dimensions strong coupling expansion is performed for the lattice 4 model in 1 1 dimensions because the strong coupling limit itself is not solvable we employed numerical calculations so as to set up unperturbed eigensystems restricting the number of hilbert space bases we performed linked cluster expansion up to 11th order we carried out an alternative simulation by means of the density matrix renormalization group thereby we confirmed that our series expansion data with a convergence acceleration trick are in good agreement with the simulation result through the analytic continuation to the domain of negative biquadratic interaction we obtain the false vacuum decay rate contrary to common belief that the tunnelling phenomenon lies out of perturbative treatments our series expansion reproduces the instanton theory behaviour for a high potential barrier for a shallow barrier in contrast our result tells us that the relaxation is no longer described by an instanton but the decay rate acquires notable enhancement

fluctuation driven dynamics of the internet topology we study the dynamics of the internet topology based on empirical data on the level of the autonomous systems it is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the internet dynamics the network s overall growth can be described approximately by a single characteristic degree growth rate g eff approximately 0 016 and the fluctuation strength sigma eff approximately 0 14 together with the vertex growth rate alpha approximately 0 029 a stochastic model which incorporates these values and an adaptation rule newly introduced reproduces several features of the real internet topology such as the correlations between the degrees of different vertices

first and second order phase transitions in scale free networks we study first and second order phase transitions of ferromagnetic lattice models on scale free networks with a degree exponent gamma using the example of the q state potts model we derive a general self consistency relation within the frame of the weiss molecular field approximation which presumably leads to exact critical singularities depending on the value of gamma we have found three different regimes of the phase diagram as a general trend first order transitions soften with decreasing gamma and the critical singularities at the second order transitions are gamma dependent

anharmonic oscillator and the optimized basis expansion we introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one dimensional anharmonic oscillators we present several methods of analytically fixing the nonlinear variational parameter specified by the domain of the trigonometric basis functions we show that the optimized parameter enables us to determine the energy spectrum to an arbitrary accuracy also using the harmonic oscillator basis functions we indicate that the resulting optimal frequency agrees with the one obtained by the principle of the minimal sensitivity

phase space path integral calculation of the wigner function the wigner function w q p is formulated as a phase space path integral whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths the approach has similarities to the path centroid method in the configuration space path integral paths can be classified by the midpoint of their ends short paths where the midpoint is close to q p and which lie in regions of low energy low p function of the hamiltonian will dominate and the enclosed area will determine the sign of the wigner function as a demonstration the method is applied to a sequence of density matrices interpolating between a poissonian number distribution and a number state each member of which can be represented exactly by a discretized path integral with a finite number of vertices saddle point evaluation of these integrals recovers up to a constant factor the wkb approximation to the wigner function of a number state

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved