model categories of diagram spectra working in the category mathcal t of based spaces we give the basic theory of diagram spaces and diagram spectra these are functors mathcal d longrightarrow mathcal t for a suitable small topological category mathcal d when mathcal d is symmetric monoidal there is a smash product that gives the category of mathcal d spaces a symmetric monoidal structure examples include begin enumerate item prespectra as defined classically item symmetric spectra as defined by jeff smith item orthogonal spectra a coordinate free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category item gamma spaces as defined by graeme segal item mathcal w spaces an analogue of gamma spaces with finite sets replaced by finite cw complexes in the domain category end enumerate we construct and compare model structures on these categories with the caveat that gamma spaces are always connective these categories and their simplicial analogues are quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category monoids in these categories are strict ring spectra often the subcategories of ring spectra module spectra over a ring spectrum and commutative ring spectra are also model categories when this holds the respective categories of ring and module spectra are quillen equivalent and thus have equivalent homotopy categories this allows interchangeable use of these categories in applications 2000 mathematics subject classification primary 55p42 secondary 18a25 18e30 55u35

biset transformations of tambara functors abstract if we are given an h g biset u for finite groups g and h then any mackey functor on g can be transformed by u into a mackey functor on h in this article we show that the biset transformation is also applicable to tambara functors when u is right free and in fact forms a functor between the category of tambara functors on g and h this biset transformation functor is compatible with some algebraic operations on tambara functors such as ideal quotients or fractions in the latter part we also construct the left adjoint of the biset transformation

a pearson random walk with steps of uniform orientation and dirichlet distributed lengths a constrained diffusive random walk of n steps in d and a random flight in d which are equivalent were investigated independently in recent papers j stat phys 127 813 2007 j theor probab 20 769 2007 and j stat phys 131 1039 2008 the n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation conditioned on the sum of their lengths being equal to a given value l closed form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d 1 2 4 uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2d and of two steps in 4d

the spectrum of the burnside tambara functor on a finite cyclic p group abstract for a finite group g a tambara functor on g is regarded as a g bivariant analog of a commutative ring in this analogy previously we have defined an ideal of a tambara functor in this article we calculate the prime spectrum of the burnside tambara functor when g is a finite cyclic p group for a prime integer p

tambarization of a mackey functor and its application to the witt burnside construction abstract for an arbitrary group g a semi mackey functor is a pair of covariant and contravariant functors from the category of g sets and is regarded as a g bivariant analog of a commutative semi group in this view a g bivariant analog of a semi ring should be a semi tambara functor a tambara functor is firstly defined by tambara which he called a tnr functor when g is finite as shown by brun a tambara functor plays a natural role in the witt burnside construction it will be a natural question if there exist sufficiently many examples of tambara functors compared to the wide range of mackey functors in the first part of this article we give a general construction of a tambara functor from any mackey functor on an arbitrary group g in fact we construct a functor from the category of semi mackey functors to the category of tambara functors this functor gives a left adjoint to the forgetful functor and can be regarded as a g bivariant analog of the monoid ring functor in the latter part when g is finite we investigate relations with other mackey functorial constructions crossed burnside ring elliott s ring of g strings jacobson s f burnside ring all these lead to the study of the witt burnside construction

random evolutions are driven by the hyperparabolic operators we resolve the long standing problem of describing the multidimensional random evolutions by means of the telegraph equations this problem was posed by mark kac more than 50 years ago and has become the subject of intense discussion among researchers on whether the multidimensional random flights could be described by the telegraph equations similarly to the one dimensional case we give the exhaustive answer to this question and show that the multidimensional random evolutions are driven by the hyperparabolic operators composed of the telegraph operators and their integer powers the only exception is the 2d random flight whose transition density is the fundamental solution to the two dimensional telegraph equation the reason of the exceptionality of the 2d case is explained we also show that under the standard kac s condition the governing hyperparabolic operator turns into the generator of the brownian motion

a procedure for obtaining general nonlinear fokker planck equations abstract a procedure for deriving general nonlinear fokker planck equations fpes directly from the master equation is presented the nonlinear effects are introduced in the transition probabilities which present a dependence on the probabilities for finding the system in a given state it is shown that the fpes obtained from master equations describing transitions among discrete and continuous sets of states are identical within such a procedure we construct nonlinear fpes that appear to be very general our general fpes recover as particular cases nonlinear fpes investigated previously by many authors introduced on a purely phenomenological basis and they lead to the possibility of more complete and complex diffusive equations

a new family of solvable pearson dirichlet random walks an n step pearson gamma random walk in d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations the gamma distribution of each step length has a shape parameter q 0 constrained random walks of n steps in d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value simple closed form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d d0 and any n 2 when q is either q frac d 2 1 d0 3 or q d 1 d0 2 le caer in j stat phys 140 728 751 2010 when the total walk length is chosen without loss of generality to be equal to 1 then the constrained step lengths have a dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a pearson dirichlet random walk the density of the endpoint position of a n step planar walk of this type n 2 with q d 2 was shown recently to be a weighted mixture of 1 floor n 2 endpoint densities of planar pearson dirichlet walks with q 1 beghin and orsingher in stochastics 82 201 229 2010 the previous result is generalized to any walk space dimension and any number of steps n 2 when the parameter of the pearson dirichlet random walk is q d 1 we rely on the connection between an unconstrained random walk and a constrained one which have both the same n and the same q d to obtain a closed form expression of the endpoint density the latter is a weighted mixture of 1 floor n 2 densities with simple forms equivalently expressed as a product of a power and a gauss hypergeometric function the weights are products of factors which depends both on d and n and bessel numbers independent of d

when a random walk of fixed length can lead uniformly anywhere inside a hypersphere a variation of the pearson rayleigh random walk in which the steps are i i d random vectors of exponential length and uniform orientation is considered conditioned on the total path length the probability density function of the position of the walker after n steps is determined analytically in one and two dimensions it is shown that in two dimensions n 3 marks a critical transition point in the behavior of the random walk by taking less than three steps and walking a total length l one is more likely to end the walk near the boundary of the disc of radius l while by taking more than three steps one is more likely to end near the origin somehow surprisingly by taking exactly three steps one can end uniformly anywhere inside the disc of radius l this means that conditioned on l the sum of three vectors of exponential length and uniform direction has a uniform probability density

isotropic random motion at finite speed with k erlang distributed direction alternations we study uniformly distributed direction of motion at finite speed where the direction alternations occur according to the renewal epochs of a k erlang pdf at first sight our generalizations of previous markovian results appears to be a small step however it must be seen as an important non markovian case where we have found closed form expressions for the pdf and the conditional characteristic function of this semi markov transport process we present detailed calculations of a three dimensional example for the 2 erlang case which is important not only from physical applications point of view but also to understand more general models for instance in principle the example of the 2 erlang case can be extended to a k erlang case k 3 4 but some of the mathematical expressions may be cumbersome

random flights connecting porous medium and euler poisson darboux equations in this paper we consider the porous medium equation and establish a relationship between its kompanets zel dovich barenblatt solution u xd t xd rd t 0 and random flights the time rescaled version of u xd t is the fundamental solution of the euler poisson darboux equation which governs the distribution of random flights performed by a particle whose displacements have a dirichlet probability distribution and choosing directions uniformly on a d dimensional sphere we consider the space fractional version of the euler poisson darboux equation and present the solution of the related cauchy problem in terms of the probability distributions of random flights governed by the classical euler poisson darboux equation furthermore this research is also aimed at studying the relationship between the solutions of a fractional porous medium equation and the fractional euler poisson darboux equation a considerable part of this paper is devoted to the analysis of the probabilistic tools of the solutions of the fractional equations the extension to the higher order euler poisson darboux equation is considered and the solutions are interpreted as compositions of laws of pseudoprocesses

adams filtration and generalized hurewicz maps for infinite loopspaces we study the hurewicz map begin aligned h pi x rightarrow r omega infty x end aligned where omega infty x is the 0th space of a spectrum x and r is the generalized homology theory associated to a connective commutative s algebra r we prove that the decreasing filtration of the domain associated to an r based adams resolution is compatible with a filtration of the range associated to the augmentation ideal filtration of the augmented commutative s algebra sigma infty omega infty x the proof of our main theorem makes much use of composition properties of this filtration and its interaction with topological andre quillen homology an application is a connectivity theorem localize away from p 1 and suppose x is c 1 connected with c 0 if alpha in pi x has adams filtration s and alpha cp s then h alpha 0 in r omega infty x when specialized to mod p homology this implies a finiteness theorem if h x mathbb z p is finitely presented as a module over the steenrod algebra then the image of the hurewicz map in h omega infty x mathbb z p is finite we illustrate these theorems with calculations of the mod 2 hurewicz image of bo its connected covers and omega infty tmf and the mod p hurewicz image of all the spaces in the bp and bp langle n rangle spectra en route we get new proofs of theorems of milnor and wilson in the special case when x is the suspension spectrum of a space z and r h mathbb z 2 we recover results announced by lannes and zarati in the 1980s relating the adams filtration of pi s z to dyer lashof length in h qz mathbb z 2 and generalize them to all primes p for any x we also get parallel results for the hurewicz map for morava e theory where pi x is now given the adams novikov filtration

ideals of tambara functors abstract for a finite group g a tambara functor on g is regarded as a g bivariant analog of a commutative ring in this article we consider a g bivariant analog of the ideal theory for tambara functors

random motions at finite speed in higher dimensions we present a general method of studying the transport process bold x t t 0 in the euclidean space m m 2 based on the analysis of the integral transforms of its distributions we show that the joint characteristic functions of bold x t are connected with each other by a convolution type recurrent relation this enables us to prove that the characteristic function fourier transform of bold x t in any dimension m 2 satisfies a convolution type volterra integral equation of second kind we give its solution and obtain the characteristic function of bold x t in terms of the multiple convolutions of the kernel of the equation with itself an explicit form of the laplace transform of the characteristic function in any dimension is given the complete solution of the problem of finding the initial conditions for the governing partial differential equations is given

exponential convergence to quasi stationary distribution and q process for general almost surely absorbed markov processes we obtain necessary and sufficient conditions for exponential convergence to a unique quasi stationary distribution in the total variation norm these conditions also ensure the existence and exponential ergodicity of the q process the process conditioned to never be absorbed we apply these results to one dimensional birth and death processes with catastrophes multi dimensional birth and death processes infinite dimensional population models with brownian mutations and neutron transport dynamics absorbed at the boundary of a bounded domain

markov models of non gaussian exponentially correlated processes and their applications we consider three different methods of generating non gaussian markov processes with given probability density functions and exponential correlation functions all models are based on stochastic differential equations a number of analytically treatable examples are considered the results obtained can be used in different areas such as telecommunications and neurobiology

generation of compound non gaussian random processes with a given correlation function a compound representation of random processes is considered each independent component of such a process is considered as the solution of the proper stochastic differential equation sde this guarantees that the process obtained is stationary and ergodic the analytical expressions are developed for nonlinear coefficients of the generating sde theoretical results are compared with numerical simulation

statistical model with a standard γ distribution we study a statistical model consisting of n basic units which interact with each other by exchanging a physical entity according to a given microscopic random law depending on a parameter ensuremath lambda we focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard gamma distribution the model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity ensuremath lambda alternatively from the nature of the equilibrium distribution we show that the model can also be interpreted as a perfect gas at an effective temperature t ensuremath lambda where particles exchange energy in a space with an effective dimension d ensuremath lambda

exact probability distributions for noncorrelated random walk models a stochastic model for the idealized locomotion of cells is studied the cell is assumed to cover a polygonal line in n the times between turns are exponentially distributed and independent of the directions and the density of thenth directione does not depend on the n 1 th directione the resulting markov process x t d t for position and direction of the motion at timet is studied by using the integrodifferential equation for the transition function for example the joint distribution of x t d t is derived in closed form ifn 2 orn 3 and all chosen directions including the initial one are uniformly distributed for higher dimensions the combined fourier laplace transform ofx t is given the case of a fixed initial direction is also considered

residence time and collision statistics for exponential flights the rod problem revisited many random transport phenomena such as radiation propagation chemical biological species migration or electron motion can be described in terms of particles performing exponential flights for such processes we sketch a general approach based on the feynman kac formalism that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution we then illustrate the proposed method in the case of the so called rod problem a one dimensional system and discuss the relevance of the obtained results in the context of monte carlo estimators

improved estimation of defocus blur and spatial shifts in spatial domain a homotopy based approach this paper presents a homotopy based algorithm for the recovery of depth cues in the spatial domain the algorithm specifically deals with defocus blur and spatial shifts that is 2d motion stereo disparities and or zooming disparities these cues are estimated from two images of the same scene acquired by a camera evolving in time and or space we show that they can be simultaneously computed by resolving a system of equations using a homotopy method the proposed algorithm is tested using synthetic and real images the results confirm that the use of a homotopy method leads to a dense and accurate estimation of depth cues this approach has been integrated into an application for relief estimation from remotely sensed images

a family of random walks with generalized dirichlet steps we analyze a class of continuous time random walks in rd d 2 with uniformly distributed directions the steps performed by these processes are distributed according to a generalized dirichlet law given the number of changes of orientation we provide the analytic form of the probability density function of the position xd t t 0 reached at time t 0 by the random motion in particular we analyze the case of random walks with two steps in general it is a hard task to obtain the explicit probability distributions for the process xd t t 0 nevertheless for suitable values for the basic parameters of the generalized dirichlet probability distribution we are able to derive the explicit conditional density functions of xd t t 0 furthermore in some cases by exploiting the fractional poisson process the unconditional probability distributions of the random walk are obtained this paper extends in a more general setting the random walks with dirichlet displacements introduced in some prev

random walk models for search with particular reference to a bounded region abstract the position of a target moving randomly in an area is described the motion is a sequence of finite legs traversed at constant speed with exponentially distributed lengths and randomly oriented directions with respect to each other following kluyver 7 a new expression is derived for the distribution of the radius vector where the walk is of pearson type the relative directions of successive legs being u 0 2 this is followed by a study of such a walk within a circular area the purpose here is to investigate the effect of reflection policies at the boundary on the distribution of the position of the target within the area and on the coverage of the area by the walk

a set of new three parameter entropies in terms of a generalized incomplete gamma function abstract in this paper by considering the first three khinchin axioms k1 k3 and neglecting the fourth k4 a set of new three parameter entropies will be introduced which are expressed in terms of a generalized incomplete gamma function as s d c 1 c 2 p i d 1 1 c 1 ln p i 1 c 2 ln p i also its asymptotic behavior will be found and it will be shown that for some special values of parameters some known entropies like tsallis kaniadakis and abe entropies are recovered

on the influence of reflective boundary conditions on the statistics of poisson kac diffusion processes abstract we analyze the influence of reflective boundary conditions on the statistics of poisson kac diffusion processes and specifically how they modify the poissonian switching time statistics after addressing simple cases such as diffusion in a channel and the switching statistics in the presence of a polarization potential we thoroughly study poisson kac diffusion in fractal domains diffusion in fractal spaces highlights neatly how the modification in the switching time statistics associated with reflections against a complex and fractal boundary induces new emergent features of poisson kac diffusion leading to a transition from a regular behavior at shorter timescales to emerging anomalous diffusion properties controlled by walk dimensionality of the fractal set

universal first passage properties of discrete time random walks and levy flights on a line statistics of the global maximum and records abstract in these lecture notes i will discuss the universal first passage properties of a simple correlated discrete time sequence x 0 0 x 1 x 2 x n up to n steps where x i represents the position at step i of a random walker hopping on a continuous line by drawing independently at each time step a random jump length from an arbitrary symmetric and continuous distribution it includes e g the levy flights i will focus on the statistics of two extreme observables associated with the sequence i its global maximum and the time step at which the maximum occurs and ii the number of records in the sequence and their ages i will demonstrate how the universal statistics of these observables emerge as a consequence of pollaczek spitzer formula and the associated sparre andersen theorem

multiplicativity of the idempotent splittings of the burnside ring and the g sphere spectrum abstract we provide a complete characterization of the equivariant commutative ring structures of all the factors in the idempotent splitting of the g equivariant sphere spectrum including their hill hopkins ravenel norms where g is any finite group our results describe explicitly how these structures depend on the subgroup lattice and conjugation in g algebraically our analysis characterizes the multiplicative transfers on the localization of the burnside ring of g at any idempotent element which is of independent interest to group theorists as an application we obtain an explicit description of the incomplete sets of norm functors which are present in the idempotent splitting of the equivariant stable homotopy category

some applications of persistent random walks and the telegrapher s equation abstract a persistent random walk can be regarded as a multidimensional markov process the bias free telegraphers equation is 2 p t 2 1 t p t v 2 2 p it can be regarded as interpolating between the wave equation t and the diffusion equation t 0 previously it has found application in thermodynamics cf the review in rev mod phys 61 1989 41 62 1990 375 more recent applications are reviewed in the present article

exact solutions for isotropic random flights in odd dimensions we give a method to solve the isotropic random flight in arbitrary dimension and show that when the dimension is odd it leads to a piecewise polynomial expression for the probability density the method is based on the fact that the projection of an isotropic function has an inverse and on the fact that the convolution commutes with the projection and the inverse projection in order to develop this method the abel transform and its inverse are extended by comparing with the expression for the isotropic random flight obtained using the convolution theorem some integrals of bessel functions can be expressed as piecewise polynomials the expressions for the five dimensional case for 2 3 and 4 steps are found explicitly although the main result derived from this method concerns odd dimensions it also yields an analytical result in the four dimensional isotropic random flight which is derived here the results of this article can also be considered as results on the convolution with itself of an isotropic probability density whose support is the surface of a sphere

random motion with uniformly distributed directions and random velocity in this paper we deal with uniformly distributed direction of motion or isotropic motion at random speed or velocity where the direction alternations occur according to the renewal epochs of a general distribution we derive the renewal equation for the characteristic function of the transition density of the multidimensional motion then by using the renewal equation we study the behavior of the transition density near the sphere of its singularity for one two three and four dimensional cases to illustrate our solution methodology we present detailed calculations of many solvable examples

collision statistics for random flights with anisotropic scattering and absorption for a broad class of random walks with anisotropic scattering kernels and absorption we derive explicit formulas that allow expressing the moments of the collision number n v performed in a volume v as a function of the particle equilibrium distribution our results apply to arbitrary domains v and boundary conditions and allow assessing the hitting statistics for systems where the typical displacements are comparable to the domain size so that the diffusion limit is possibly not attained an example is discussed for one dimensional random flights with exponential displacements where analytical calculations can be carried out

homology and cohomology of e ring spectra every homology or cohomology theory on a category of e ring spectra is topological andre quillen homology or cohomology with appropriate coefficients analogous results hold more generally for categories of algebras over operads

nonlinear fokker planck equations whose stationary solutions make entropy like functionals stationary abstract the present study extends the correspondence principle of martinez et al that establishes a link between nonlinear fokker planck equations nlfpes and the variational principle approach of the theory of canonical ensembles by virtue of the extended correspondence principle we reobtain results of kaniadakis and quarati for bose and fermi systems and find relations similar to those derived by plastino and plastino and recently by borland concerning the entropy of nonextensive thermostatistics introduced in physics by tsallis moreover we propose nlfpes related to the renyi entropy and to the entropy proposed by sharma and mittal the latter comprises tsallis entropy and the renyi entropy

on the andre quillen homology of tambara functors abstract we lift to equivariant algebra three closely related classical algebraic concepts abelian group objects in augmented commutative algebras derivations and kahler differentials we define mackey functor objects in the category of tambara functors augmented to a fixed tambara functor r and we show that the usual square zero extension gives an equivalence of categories between these mackey functor objects and ordinary modules over r we then describe the natural generalization to tambara functors of a derivation building on the intuition that a tambara functor has products twisted by arbitrary finite g sets and we connect this to square zero extensions in the expected way finally we show that there is an appropriate form of kahler differentials which satisfy the classical relation that derivations out of r are the same as maps out of the kahler differentials

the crossed burnside rings iii the dress construction for a tambara functor abstract we discuss the dress construction for a tambara functor associated to a finite commutative monoid with action of a finite group

families of fokker planck equations and the associated entropic form for a distinct steady state probability distribution with a known external force field a method of finding entropic form for a given stationary probability distribution and specified potential field is discussed using the steady state fokker planck equation as examples starting with the boltzmann and tsallis distribution and knowing the force field we obtain the boltzmann gibbs and tsallis entropies also the associated entropy for the gamma probability distribution is found which seems to be in the form of the gamma function moreover the related fokker planck equations are given for the boltzmann tsallis and gamma probability distributions

n dimensional nonlinear fokker planck equation with time dependent coefficients an n dimensional nonlinear fokker planck equation is investigated here by considering the time dependence of the coefficients where drift controlled and source terms are present we exhibit the exact solution based on the generalized gaussian function related to the tsallis statistics furthermore we show that a rich class of diffusive processes including normal and anomalous ones can be obtained by changing the time dependence of the coefficients

twice scattered particles in a plane are uniformly distributed it was recently shown physica a 216 299 315 1995 that in two dimensions the sum of three vectors each of whose lengths is exponentially distributed whose direction is uniformly distributed and such that the sum of their lengths is l is uniformly distributed on a disk of radius l we state here this random walk result in terms of scattering of particles as follows in two dimensions twice isotropically scattered particles by random i e poisson distributed scatterers are uniformly distributed we show that there is no other dimension d and no other number of scatterings s for which the corresponding result i e uniform distribution on a d dimensional sphere after s scatterings holds

a homotopy method for eigenvalue assignment using decentralized state feedback this paper addresses the following problem given an interconnected system m composed of n subsystems of the form a i b i k i i 1 n a i b i a controllable pair and where the off diagonal blocks of m lie in the image of the appropriate b i then is it possible to arbitrarily assign the characteristic polynomial of m by a suitable selection of the characteristic polynomials of a i b i k i moreover is it possible to compute the appropriate characteristic polynomials of the a i b i k i or equivalently construct the k i needed to do so the first question is answered by constructing a mapping f r n rightarrow r n which maps a prescribed set of n of the feedback gains elements of k i i 1 n to the n coefficients of the characteristic polynomial of m the question then becomes given a p in r n does f x p have a solution the answer is found by constructing a homotopy h r n x o 1 rightarrow r n where h x 1 f x and h x 0 is some trivial function degree theory is then applied to guarantee that there exists an x t such that h x t t p for all t in 0 1 the parameterized sard s theorem is then utilized to prove that with probability 1 x t is a smooth curve and hence can be followed numerically from x 0 to x 1 by the solution of a differential equation davidenko s method

counting statistics a feynman kac perspective by building upon a feynman kac formalism we assess the distribution of the number of collisions in a given region for a broad class of discrete time random walks in absorbing and nonabsorbing media we derive the evolution equation for the generating function of the number of collisions and we complete our analysis by examining the moments of the distribution and their relation to the walker equilibrium density some significant applications are discussed in detail in particular we revisit the gambler s ruin problem and generalize to random walks with absorption the arcsine law for the number of collisions on the half line

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

asymptotic relation for the transition density of the three dimensional markov random flight on small time intervals we consider the markov random flight varvec x t t 0 in the three dimensional euclidean space mathbb r 3 with constant finite speed c 0 and the uniform choice of the initial and each new direction at random time instants that form a homogeneous poisson flow of rate lambda 0 series representations for the conditional characteristic functions of varvec x t corresponding to two and three changes of direction are obtained based on these results an asymptotic formula as t rightarrow 0 for the unconditional characteristic function of varvec x t is derived by inverting it we obtain an asymptotic relation for the transition density of the process we show that the error in this formula has the order o t 3 and therefore it gives a good approximation on small time intervals whose lengths depend on lambda an asymptotic formula as t rightarrow 0 for the probability of being in a three dimensional ball of radius r ct is also derived estimate of the accuracy of the approximation is analysed

a langevin approach for the microscopic dynamics of nonlinear fokker planck equations abstract for stochastic processes defined by nonlinear fokker planck equations a microscopic dynamics is proposed in terms of generalized langevin equations these langevin equations can for example be used to model stochastic processes with mean field interactions and random walks related to the generalized thermostatistics suggested by tsallis

witt vectors and tambara functors abstract we give a combinatorial description of the ring of g witt vectors on a polynomial algebra over the integers for every finite group g using this description we show that the functor which takes a commutative ring with trivial action of g to its ring of witt vectors coincides with the left adjoint of the algebraic functor from the category of g tambara functors to the category of commutative rings with an action of g

probability law for the euclidean distance between two planar random flights we consider two independent symmetric markov random flights z1 t and z2 t performed by the particles that simultaneously start from the origin of the euclidean plane mathbb r 2 in random directions distributed uniformly on the unit circumference s1 and move with constant finite velocities c1 0 c2 0 respectively the new random directions are taking uniformly on s1 at random time instants that form independent homogeneous poisson flows of rates 1 0 2 0

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

two step dirichlet random walks abstract random walks of n steps taken into independent uniformly random directions in a d dimensional euclidean space d 2 which are characterized by a sum of step lengths which is fixed and taken to be 1 without loss of generality are named dirichlet when this constraint is realized via a dirichlet law of step lengths the latter continuous multivariate distribution which depends on n positive parameters generalizes the beta distribution n 2 it is simply obtained from n independent gamma random variables with identical scale factors previous literature studies of these random walks dealt with symmetric dirichlet distributions whose parameters are all equal to a value q which takes half integer or integer values in the present work the probability density function of the distance from the endpoint to the origin is first made explicit for a symmetric dirichlet random walk of two steps it is valid for any positive value of q and for all d 2 the latter pdf is used in turn to express the related density of a random walk of two steps whose step length is distributed according to an asymmetric beta distribution which depends on two parameters namely q and q s where s is a positive integer

the diffusion limit of transport equations derived from velocity jump processes in this paper we study the diffusion approximation to a transport equation that describes the motion of individuals whose velocity changes are governed by a poisson process we show that under an appropriate scaling of space and time the asymptotic behavior of solutions of such equations can be approximated by the solution of a diffusion equation obtained via a regular perturbation expansion in general the resulting diffusion tensor is anisotropic and we give necessary and sufficient conditions under which it is isotropic we also give a method to construct approximations of arbitrary high order for large times in a second paper part ii we use this approach to systematically derive the limiting equation under a variety of external biases imposed on the motion depending on the strength of the bias it may lead to an anisotropic diffusion equation to a drift term in the flux or to both our analysis generalizes and simplifies previous derivations that lead to the classical patlak keller segel alt

first passage times for random walks in bounded domains we present a novel computational method of first passage times between a starting site and a target site of regular bounded lattices we derive accurate expressions for all the moments of this first passage time validated by numerical simulations their range of validity is discussed we also consider the case of a starting site and two targets in addition we present the extension to continuous brownian motion these results are of great relevance to any system involving diffusion in confined media

collision densities and mean residence times for d dimensional exponential flights in this paper we analyze some aspects of exponential flights a stochastic process that governs the evolution of many random transport phenomena such as neutron propagation chemical or biological species migration and electron motion we introduce a general framework for d dimensional setups and emphasize that exponential flights represent a deceivingly simple system where in most cases closed form formulas can hardly be obtained we derive a number of exact where possible or asymptotic results among which are the stationary probability density for two dimensional systems a long standing issue in physics and the mean residence time in a given volume bounded or unbounded domains as well as scattering or absorbing domains are examined and monte carlo simulations are performed so as to support our findings

random flights through spaces of different dimensions we shall study random flights that start in a space of one given dimension and after performing a definite number of steps continue to develop in a space of higher dimension we show that if the difference of the dimension of spaces is even then the probability density describing the composite flight can be expressed as marginalizations of the probability density associated to a random flight in the space of less dimensions this dimensional reduction is a consequence of gegenbauer addition theorem

statistical aspects of random fragmentations three random fragmentation of an interval processes are investigated for each of them there is a splitting probability and a probability not to split at each step of the fragmentation process whose overall effect is to stabilize the global number of splitting events some of their statistical features are studied in each case among which fragments size distribution partition function structure of the underlying random fragmentation tree occurrence of a phase transition in the first homogeneous model splitting probability does not depend on fragments size at each step in the next two fragmentation models splitting probability is fragments length dependent in the first such models fragments further split with probability one if their sizes exceed some cutoff value only in a second model considered splitting probability of finite size objects is assumed to increase algebraically with fragments size at each step the impact of these dependencies on statistical properties of the resulting random partitions are studied several examples are supplied

some two and three dimensional persistent random walks abstract we formulate non markovian versions of the persistent random walk in two and three dimensions and in continuous time these models can be regarded as being generalizations of the original pearson random walk and of the freely jointed chain which has been of some importance in polymer physics solutions for the probability density of the displacement of the random walker can be furnished for a restricted essentially markovian set of these models it is shown that in two dimensions the solution to one of these models is equivalent to the solution to an inhomogeneous telegrapher s equation it does not appear to be possible starting from a similar model in three dumensions to find any form of the telegrapher s equation that follows from our solution of the equations in the fourier laplace transform domains

consequences of the h theorem from nonlinear fokker planck equations a general type of nonlinear fokker planck equation is derived directly from a master equation by introducing generalized transition rates the h theorem is demonstrated for systems that follow those classes of nonlinear fokker planck equations in the presence of an external potential for that a relation involving terms of fokker planck equations and general entropic forms is proposed it is shown that at equilibrium this relation is equivalent to the maximum entropy principle families of fokker planck equations may be related to a single type of entropy and so the correspondence between well known entropic forms and their associated fokker planck equations is explored it is shown that the boltzmann gibbs entropy apart from its connection with the standard linear fokker planck equation may be also related to a family of nonlinear fokker planck equations

branching exponential flights travelled lengths and collision statistics the evolution of several physical and biological systems ranging from neutron transport in multiplying media to epidemics or population dynamics can be described in terms of branching exponential flights a stochastic process which couples a galton watson birth death mechanism with random spatial displacements within this context one is often called to assess the length lv that the process travels in a given region v of the phase space or the number of visits nv to this same region in this paper we address this issue by resorting to the feynman kac formalism which allows characterizing the full distribution of lv and nv and in particular deriving explicit moment formulas some other significant physical observables associated to lv and nv such as the survival probability are discussed as well and results are illustrated by revisiting the classical example of the rod model in nuclear reactor physics

a homotopy based approach for computing defocus blur and affine transform simultaneously this paper presents a homotopy based algorithm for a simultaneous recovery of defocus blur and the affine parameters of apparent shifts between planar patches of two pictures these parameters are recovered from two images of the same scene acquired by a camera evolving in time and or space and for which the intrinsic parameters are known using limited taylor s expansion one of the images and its partial derivatives is expressed as a function of the partial derivatives of the two images the blur difference the affine parameters and a continuous parameter derived from homotopy methods all of these unknowns can thus be directly computed by resolving a system of equations at a single scale the proposed algorithm is tested using synthetic and real images the results confirm that dense and accurate estimation of the previously mentioned parameters can be obtained

fractional klein gordon equations and related stochastic processes this paper presents finite velocity random motions driven by fractional klein gordon equations of order alpha in 0 1 a key tool in the analysis is played by the mcbride s theory which converts fractional hyper bessel operators into erdelyi kober integral operators special attention is payed to the fractional telegraph process whose space dependent distribution solves a non homogeneous fractional klein gordon equation the distribution of the fractional telegraph process for alpha 1 coincides with that of the classical telegraph process and its driving equation converts into the homogeneous klein gordon equation fractional planar random motions at finite velocity are also investigated the corresponding distributions obtained as well as the explicit form of the governing equations fractionality is reflected into the underlying random motion because in each time interval a binomial number of deviations b n alpha with uniformly distributed orientation are considered the parameter n of b n alpha is itself a random variable with fractional poisson distribution so that fractionality acts as a subsampling of the changes of direction finally the behaviour of each coordinate of the planar motion is examined and the corresponding densities obtained extensions to n dimensional fractional random flights are envisaged as well as the fractional counterpart of the euler poisson darboux equation to which our theory applies

one dimensional hyperbolic transport positivity and admissible boundary conditions derived from the wave formulation abstract we consider the one dimensional cattaneo equation for transport of scalar fields such as solute concentration and temperature in mass and heat transport problems respectively although the cattaneo equation admits a stochastic interpretation at least in the one dimensional case negative concentration values can occur in boundary value problems on a finite interval this phenomenon stems from the probabilistic nature of this model the stochastic interpretation provides constraints on the admissible boundary conditions as can be deduced from the wave formulation here presented moreover as here shown energetic inequalities and the dissipative nature of the equation provide an alternative way to derive the same constraints on the boundary conditions derived by enforcing positivity the analysis reported is also extended to transport problems in the presence of a biasing velocity field several general conclusions are drawn from this analysis that could be extended to the higher dimensional case

derivation of nonlinear fokker planck equations by means of approximations to the master equation nonlinear fokker planck equations fpes are derived as approximations to the master equation in cases of transitions among both discrete and continuous sets of states the nonlinear effects introduced through the transition probabilities are argued to be relevant for many real phenomena within the class of anomalous diffusion problems the nonlinear fpes obtained appear to be more general than some previously proposed on a purely phenomenological basis ones in spite of this the same kind of solution applies i e it is shown that the time dependent tsallis s probability distribution is a solution of both equations obtained either from discrete or continuous sets of states and that the corresponding stationary solution is in the infinite time limit a stable solution

short hyperuniform random walks random walks of two steps with fixed sums of lengths of 1 taken into uniformly random directions in d dimensional euclidean spaces d ge 2 are investigated to construct continuous step length distributions which make them hyperuniform the endpoint positions of hyperuniform walks are spread out in the unit ball as the projections in the walk space of points uniformly distributed on the surface of the unit hypersphere of some k dimensional euclidean space k d unique symmetric continuous step length distributions exist for given d and k provided that d k 2d the walk becomes uniform on the unit ball when k d 2 the symmetric densities reduce to simple polynomials for uniform random walks and are mixtures of two pairs of asymmetric beta distributions

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

on random flights with non uniformly distributed directions this paper deals with a new class of random flights in d d 2 characterized by non uniform probability distributions on the multidimensional sphere these random motions differ from similar models appeared in literature where the directions are taken according to the uniform law the family of angular probability distributions introduced in this paper depends on a parameter 0 which gives the anisotropy of the motion furthermore we assume that the number of changes of direction performed by the random flight is fixed the time lengths between two consecutive changes of orientation have joint probability distribution given by a dirichlet density function

a homotopy approach to improving pem identification of armax models homotopy methods are applied to the non convex optimization problem that arises in prediction error estimation using armax model structures a concrete algorithm is proposed and its performance is studied by monte carlo simulation

a generalization of the dress construction for a tambara functor and its relation to polynomial tambara functors abstract for a finite group g semi mackey functors and semi tambara functors are regarded as g bivariant analogs of semi groups and semi rings respectively in fact if g is trivial they agree with the ordinary semi groups and semi rings and many naive algebraic properties concerning rings and groups have been extended to these g bivariant analogous notions in this article we investigate a g bivariant analog of the semi group rings with coefficients just as a coefficient ring r and a monoid q yield the semi group ring r q our construction enables us to make a tambara functor t m out of a semi mackey functor m and a coefficient tambara functor t this construction is a composant of the tambarization and the dress construction as expected this construction is the one uniquely determined by the righteous adjoint property besides in analogy with the trivial group case if m is a mackey functor then t m is equipped with a natural hopf structure moreover as an application of the above construction we also obtain some g bivariant analogs of the polynomial rings

the exact probability distribution of a two dimensional random walk a calculation is made of the exact probability distribution of the two dimensional displacement of a particle at timet that starts at the origin moves in straight line paths at constant speed and changes its direction after exponentially distributed time intervals where the lengths of the straight line paths and the turn angles are independent the angles being uniformly distributed this random walk is the simplest model for the locomotion of microorganisms on surfaces its weak convergence to a wiener process is also shown

globally optimal rational approximation using homotopy continuation methods homotopy continuation methods are applied to the nonlinear problem of approximating a higher order system by a lower order rational model such that the mean square modeling error is minimized a homotopy function is constructed which creates distinct paths from each of the known solutions of a simple problem to each of the solutions of the desired nonlinear problem this homotopy function guarantees that the globally optimum rational approximation solution may be determined by finding all the solutions a simple numerical continuation algorithm is described for following the paths to the optimum solution a numerical example is included which demonstrates that the globally optimum model will be obtained by applying this homotopy continuation method

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

the tambara structure of the trace ideal for cyclic extensions abstract this paper explores the tambara functor structure of the trace ideal of a galois extension in the case of a pro cyclic extension we are able to explicitly determine the generators of the ideal furthermore we show that the absolute trace ideal of a cyclic group is strongly principal when viewed as an ideal of the burnside tambara functor applying our results we calculate the trace ideal for extensions of finite fields the appendix determines a formula for the norm of a quadratic form over an arbitrary finite extension of a finite field

on the fractions of semi mackey and tambara functors for a finite group g a semi mackey resp tambara functor is regarded as a g bivariant analog of a commutative monoid resp ring as such some naive algebraic constructions are generalized to this g bivariant setting in this article as a g bivariant analog of the fraction of a ring we consider fraction of a tambara and a semi mackey functor by a multiplicative semi mackey subfunctor

cauchy s formulas for random walks in bounded domains cauchy s formula was originally established for random straight paths crossing a body b rn and basically relates the average chord length through b to the ratio between the volume and the surface of the body itself the original statement was later extended in the context of transport theory so as to cover the stochastic paths of pearson random walks with exponentially distributed flight lengths traversing a bounded domain some heuristic arguments suggest that cauchy s formula may also hold true for pearson random walks with arbitrarily distributed flight lengths for such a broad class of stochastic processes we rigorously derive a generalized cauchy s formula for the average length travelled by the walkers in the body and show that this quantity depends indeed only on the ratio between the volume and the surface provided that some constraints are imposed on the entrance step of the walker in b similar results are also obtained for the average number of collisions performed by the walker in b

defect theory for maximal ideals and simple functors keywords green functor source green correspondence maximal ideal finite group fixed point algebra defect theory for g algebras defect group restriction transfer conjugation defect pair functorial ideal simple g functors reference ctg article 1991 002doi 10 1016 0021 8693 91 90168 8 record created on 2008 12 16 modified on 2017 05 12