on the computational complexity of piecewise linear homotopy algorithms we show that piecewise linear homotopy algorithms may take a number of steps that grows exponentially with the dimension when solving a system of linear equations whose solution lies close to the starting point our examples are based on an example of murty exhibiting exponential growth for lemke s algorithm for the linear complementarity problem

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

approximate labelling for simplicial algorithms and two classes of special subsets of the sphere call a subset of rn complete if the origin is in its convex hull we are concerned with the construction of large finite sets of points on the unit sphere whose complete subsets are in some sense easy to describe our motivation comes from simplicial algorithms for approximating zeroes of functions we construct two classes of such subsets of the sphere both of which generalize a subset that corresponds to usual integer labelling

a constructive proof of ky fan s coincidence theorem we present a constructive proof for the well known ky fan s coincidence theorem through a simplicial algorithm in a finite number of steps the algorithm generates a simplex containing an approximate coincidence point in the limit when the mesh size converges to zero the sequence of approximations converges to a coincidence point

the asymmetric exclusion process and brownian excursions we consider the totally asymmetric exclusion process tasep in one dimension in its maximal current phase we show by an exact calculation that the non gaussian part of the fluctuations of density can be described in terms of the statistical properties of a brownian excursion numerical simulations indicate that the description in terms of a brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase

on the order of stable compensators abstract by means of two typical examples it is shown that in general the minimal order of a stabilizing stable compensator may not be bounded in terms of the plant order such bounds can only be given in the special case of plants with at most one right half plane zero implications for the simultaneous stabilization problem are elucidated

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

lattice gas models in contact with stochastic reservoirs local equilibrium and relaxation to the steady state extending the results of a previous work we consider a class of discrete lattice gas models in a finite interval whose bulk dynamics consists of stochastic exchanges which conserve the particle number and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials we establish here the local equilibrium structure of the stationary measures for these models further we prove as a law of large numbers that the time dependent empirical density field converges to a deterministic limit process which is the solution of the initial boundary value problem for a nonlinear diffusion equation

variable dimension algorithms basic theory interpretations and extensions of some existing methods in this paper we establish a basic theory for variable dimension algorithms which were originally developed for computing fixed points by van der laan and talman we introduce a new concept primal dual pair of subdivided manifolds and by utilizing it we propose a basic model which will serve as a foundation for constructing a wide class of variable dimension algorithms our basic model furnishes interpretations to several existing methods lemke s algorithm for the linear complementarity problem its extension to the nonlinear complementarity problem a variable dimension algorithm on conical subdivisions and merrill s algorithm we shall present a method for solving systems of equations as an application of the second method and an efficient implementation of the fourth method to which our interpretation leads us a method for constructing triangulations with an arbitrary refinement factor of mesh size is also proposed

coprime factorization controller reduction with bezout identity induced frequency weighting abstract this paper introduces a frequency weighted controller reduction scheme which offers good closed loop stability under use of the reduced order controller by combining the use of a stable fractional representation of the controller with a frequency weighting in the reduction procedure derived by consideration of the closed loop stability margin we formulate a frequency weighted controller reduction procedure with the weight simplified by the bezout identity some examples are used to illustrate the reduction procedure

a variable dimension fixed point algorithm and the orientation of simplices a variable dimension algorithm with integer labelling is proposed for solving systems ofn equations inn variables the algorithm is an integer labelling version of the 2 ray algorithm proposed by the author the orientation of lower dimensional simplices is studied and is shown to be preserved along a sequence of adjacent simplices

lower current large deviations for zero range processes on a ring we study lower large deviations for the current of totally asymmetric zero range processes on a ring with concave current density relation we use an approach by jensen and varadhan which has previously been applied to exclusion processes to realize current fluctuations by travelling wave density profiles corresponding to non entropic weak solutions of the hyperbolic scaling limit of the process we further establish a dynamic transition where large deviations of the current below a certain value are no longer typically attained by non entropic weak solutions but by condensed profiles where a non zero fraction of all the particles accumulates on a single fixed lattice site this leads to a general characterization of the rate function which is illustrated by providing detailed results for four generic examples of jump rates including constant rates decreasing rates unbounded sublinear rates and asymptotically linear rates our results on the dynamic transition are supported by numerical simulations using a cloning algorithm

hydrodynamics of stationary non equilibrium states for some stochastic lattice gas models we consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior which conserve the particle number and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials the unique stationary measures of these processes support a steady particle current from the reservoir of higher chemical potential into the lower and are non reversible we study the structure of the stationary measure in the hydrodynamic limit as the microscopic lattice size goes to infinity in particular we prove as a law of large numbers that the empirical density field converges to a deterministic limit which is the solution of the stationary transport equation and the empirical current converges to the deterministic limit given by fick s law

a modified integer labeling for complementarity algorithms nonlinear complementary problems can be solved by algorithms based on the principle of simplicial approximation we present such an algorithm that allows the choice of an arbitrary starting point without using an artificial labeling or an extra dimension furthermore the relation between the grid size of the triangulation and the accuracy of an approximate solution is investigated and it is shown that a combination of the algorithm with newton steps yields better accuracy finally the algorithm is adapted for solving systems of equations

a simplicial algorithm for stationary point problems on polytopes a simplicial variable dimension restart algorithm for the stationary point problem or variational inequality problem on a polytope is proposed given a polytope c in rn and a continuous function f c rn find a point x in c such that fx x fx x for any point x in c starting from an arbitrary point v in c the algorithm generates a piecewise linear path of points in c this path is followed by alternating linear programming pivot steps to follow a linear piece of the path and replacement steps in a simplicial subdivision of c within a finite number of function evaluations and linear programming pivot steps the algorithm finds an approximate stationary point the algorithm leaves the starting point v along a ray pointing to one of the vertices w of c the vertex w is obtained from the optimum solution of the linear programming problem maximize fv x subject to x c

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

exact large deviation functional of a stationary open driven diffusive system the asymmetric exclusion process we consider the asymmetric exclusion process asep in one dimension on sites i 1 n in contact at sites i 1 and i n with infinite particle reservoirs at densities a and b as a and b are varied the typical macroscopic steady state density profile x x a b obtained in the limit n l b a exhibits shocks and phase transitions here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile rho x text p n rho x sim exp l mathcal f a b rho x rho a rho b so that mathcal f is the large deviation functional a quantity similar to the free energy of equilibrium systems we find as in the symmetric purely diffusive case q 1 treated in an earlier work that mathcal f is in general a non local functional of x unlike the symmetric case however the asymmetric case exhibits ranges of the parameters for which mathcal f rho x is not convex and others for which mathcal f rho x has discontinuities in its second derivatives at x x in the latter ranges the fluctuations of order 1 sqrt n in the density profile near x are then non gaussian and cannot be calculated from the large deviation function

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

current fluctuations in stochastic systems with long range memory we propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history dependent rates long range temporal correlations are seen to alter the speed of the large deviation function in analogy with long range spatial correlations in equilibrium systems we give some illuminating examples and discuss the applicability of the gallavotti cohen fluctuation theorem

steady state and relaxation spectrum of the oslo rice pile model we show that the one dimensional oslo rice pile model is a special case of the abelian distributed processors model the exact steady state of the model is determined we show that the time evolution operator w for the system satisfies the equation w n 1 w n where n l l 1 2 for a pile with l sites this is used to prove that w has only one eigenvalue 1 corresponding to the steady state and all other eigenvalues are exactly zero also all connected time dependent correlation functions in the steady state of the pile are exactly zero for time difference greater that n generalization to other abelian critical height models where the critical thresholds are randomly reset after each toppling is briefly discussed

an exact formula for the statistics of the current in the tasep with open boundaries we study the totally asymmetric exclusion process on a finite one dimensional lattice with open boundaries i e in contact with two reservoirs at different potentials the total time integrated current through the system is a random variable that scales linearly with time in the long time limit we conjecture a parametric representation for the generating function of the cumulants of the current which is related to the large deviation function by laplace transform this formula is valid for all system sizes and for all values of the boundary coupling parameters

controller reduction concepts and approaches the problem of passing from a linear time invariant high order controller designed for a linear time invariant plant of presumably high order to a low order approximation of the controller is discussed the approximation problem is often best posed as a frequency weighted l sub infinity approximation problem many different controller representations are possible giving different performances of the various reduction algorithms

performance bounds for coprime factor controller reductions this paper investigates the performance of coprime factor based controller reduction methods we show that under some mild conditions closed loop performance bounds can be derived for observer based controllers the results in this paper lay a mathematical foundation for using coprime factor controller reduction methods in certain classes of controller reduction problems

sampling rare fluctuations of height in the oslo ricepile model we describe a new monte carlo algorithm for studying large deviations of the height of the pile from its mean value in the oslo ricepile model we have used it to generate events which have probabilities of order 10 1000 these simulations check our qualitative argument pradhan p and dhar d 2006 phys rev e 73 021303 that in the steady state of the oslo ricepile model the probability of large negative height fluctuations h l about the mean varies as exp 4l3 as l with held fixed and 0

density large deviations for multidimensional stochastic hyperbolic conservation laws we investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law when the conductivity and dif fusivity matrices are proportional i e an einstein like relation is satisfied the problem has been solved in 4 when this proportionality does not hold we compute explicitly the large deviation function for a step like density profile and we show that the associated optimal current has a non trivial structure we also derive a lower bound for the large deviation function valid for a general weak solution and leave the general large deviation function upper bound as a conjecture

universal large deviation function of the kardar parisi zhang equation in one dimension using the bethe ansatz we calculate the whole large deviation function of the displacement of particles in the asymmetric simple exclusion process asep on a ring when the size of the ring is large the central part of this large deviation function takes a scaling form independent of the density of particles we suggest that this scaling function found for the asep is universal and should be characteristic of all the systems described by the kardar parisi zhang equation in 1 1 dimension simulations done on two simple growth models are in reasonable agreement with this conjecture

the octahedral algorithm a new simplicial fixed point algorithm a new variable dimension simplicial algorithm for the computation of solutions of systems of nonlinear equations or the computation of fixed points is presented it uses the restrart technique of merrill to improve the accuracy of the solution the algorithm is shown to converge quadratically under certain conditions the algorithm should be efficient and relatively easy to implement

a class of indefinite dogleg path methods for unconstrained minimization in this paper we propose a convenient curvilinear search method to solve trust region problems arising from unconstrained optimization problems the curvilinear paths we set forth are dogleg paths generated mainly by employing bunch parlett factorization for general symmetric matrices that may be indefinite this method is easy to implement and globally convergent it is proved that the method satisfies the first and second order stationary point convergence properties and that the convergence rate is quadratic under commonly used conditions on functions numerical experiments are conducted to compare this method with some existing methods

linear system approximation via covariance equivalent realizations abstract a truncation technique for model reduction to simultaneously match a specified number of output covariance derivatives is described these covariance equivalent realizations which match q 1 covariance derivatives are called q covers in general q covers are not unique the additional freedom is used herein so that the q cover obtained also matches q markov parameters the truncation technique uses a form of the observability matrices of the full order system to determine a priori the order required of the reduced order model to match a specified number of output covariance derivatives and markov parameters the resulting realization is shown to be independent of the basis of the complete model to within a unitary transformation stability conditions for the reduced order model are also described and the relationships are established between stochastically equivalent realizations and the q covers

on the computation of fixed points in the product space of unit simplices and an application to noncooperative n person games in this paper an algorithm based on the principle of simplicial approximation is introduced to compute fixed points of upper semicontinuous point to set mappings from the product space s of unit simplices into itself the algorithm is a modification of an algorithm introduced in an earlier paper the main feature is that it starts with an arbitrary chosen point in s and that the triangulation of s depends on the starting point moreover the algorithm can terminate with a non full dimensional subsimplex yielding a good approximation an application is given for non cooperative n person games where s is the strategy space some computational experiences are given

current reservoirs in the simple exclusion process we consider the symmetric simple exclusion process in the interval n n with additional birth and death processes respectively on n k n k 0 and n n k the exclusion is speeded up by a factor n2 births and deaths by a factor n assuming propagation of chaos a property proved in a companion paper de masi et al http arxiv org abs 1104 3447 we prove convergence in the limit n to the linear heat equation with dirichlet condition on the boundaries the boundary conditions however are not known a priori they are obtained by solving a non linear equation the model simulates mass transport with current reservoirs at the boundaries and the fourier law is proved to hold

a unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm we present a unified description of a class of restart fixed point algorithms including merrill s method and several variable dimension algorithms for their implementation on computers based on this description we show that some pivot saving techniques originally developed for the homotopy methods can be applied to the class we also propose a new variable dimension algorithm having 3 n 1 rays along which we can move toward a solution some numerical comparisons of the simplicial restart algorithms merrill s method the 2n method the octahedral method and the new one support that the latter two methods are more efficient than the others

the computation of a continuum of constrained equilibria the equilibria of a model of an exchange economy with price rigidities are called constrained equilibria a simplicial algorithm on the unit cube is proposed to compute an approximation of a continuum of zero points of the excess demand correspondence of such an economy this continuum of zero points corresponds to a continuum of constrained equilibria of the economy linking the two so called trivial equilibria moreover the convergence properties of the algorithm and the accuracy of the approximate constrained equilibria obtained by the algorithm are discussed finally an example is given as an illustration

computation of current cumulants for small nonequilibrium systems we analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems recently discussed in the framework of full counting statistics for mesoscopic systems this method is based on identifying the current cumulants from a rayleigh schrodinger perturbation expansion for the generating function here it is derived from a simple path distribution identity and extended to the joint statistics of multiple currents for a possible thermodynamical interpretation we compare this approach to a generalized onsager machlup formalism we present calculations for a boundary driven kawasaki dynamics on a one dimensional chain both for attractive and repulsive particle interactions

probability distribution of residence times of grains in models of rice piles we study the probability distribution of residence time of a grain at a site and its total residence time inside a pile in different rice pile models the tails of these distributions are dominated by the grains that get deeply buried in the pile we show that for a pile of size l the probabilities that the residence time at a site or the total residence time is greater than t both decay as 1 t ln t x for l omega or 1 and values of x and omega in the two cases are different in the oslo rice pile model we find that the probability of the residence time t i at a site i being greater than or equal to t is a nonmonotonic function of l for a fixed t and does not obey simple scaling for model in d dimensions we show that the probability of minimum slope configuration in the steady state for large l varies as exp kappal d 2 where kappa is a constant and hence gamma d 2

oslo rice pile model is a quenched edwards wilkinson equation the oslo rice pile model is a sandpile like paradigmatic model of self organized criticality soc in this paper it is shown that the oslo model is in fact exactly a discrete realization of the much studied quenched edwards wilkinson equation qew nattermann et al j phys ii france 2 1483 1992 this is possible by choosing the correct dynamical variable and identifying its equation of motion it establishes for the first time an exact link between soc models and the field of interface growth with quenched disorder this connection is obviously very encouraging as it suggests that established theoretical techniques can be brought to bear with full strength on some of the hitherto elusive problems of soc

model reduction via balanced realizations an extension and frequency weighting techniques two model reduction methods for discrete systems related to balanced realizations are described the first is a technique which utilizes the least controllable and observable subsystem in deriving a balanced discrete reduced order model for this technique as l sup infinity norm bound on the reduction error is given the second method is a frequency weighting technique for discrete and continuous time systems where the input normal or output normal realizations are modified to include a simple frequency weighting for this technique l sup infinity norm bounds on the weighted reduction errors are obtained

large deviation functional of the weakly asymmetric exclusion process we obtain the large deviation functional of a density profile for the asymmetric exclusion process of l sites with open boundary conditions when the asymmetry scales like l 1 we recover as limiting cases the expressions derived recently for the symmetric ssep and the asymmetric asep cases in the asep limit the nonlinear differential equation one needs to solve can be analysed by a method which resembles the wkb method

robust controller design based on reduced order plants two dual controller design methods are proposed for linear time invariant multi input multi output systems where designs based on a reduced order plant robustly stabilizer higher order plants with additional poles or zeros in the stable region the additional poles or zeros are considered as multiplicative perturbations of the reduced plant the methods are tailored towards closed loop stability and performance and they yield estimates for the stability robustness and performance of the final design they can be considered as formalizations of two classical heuristic model reduction techniques one method neglects a plant pole sufficiently far to the left of dominant poles and the other cancels a sufficiently small stable plant zero with a pole at the origin

efficiency and implementation of simplicial zero point algorithms in this paper we compare the efficiency of several simplicial variable dimension algorithms to do so we first treat the issues of degeneracy and accelerating we present a device for solving degeneracy furthermore we compare several accelerating techniques the technique of iterated quasi newton steps after each major cycle of the simplicial algorithm is implemented in a computer code which is used to compare the efficiency of the n 1 ray 2n ray 2n ray and 3n 1 ray algorithms except for the n 1 ray algorithm the number of function evaluations does not differ very much between the various algorithms it appeared however that the 2n algorithm needs considerably less computation time

fluctuations in the weakly asymmetric exclusion process with open boundary conditions we investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state we show that these fluctuations are given in the macroscopic limit by a centered gaussian field and we compute explicitly its covariance function we use two approaches the first method is dynamical and based on fluctuations around the hydrodynamic limit we prove that the density fluctuations evolve macroscopically according to an autonomous stochastic equation and we search for the stationary distribution of this evolution the second approach which is based on a representation of the steady state as a sum over paths allows one to write the density fluctuations in the steady state as a sum over two independent processes one of which is the derivative of a brownian motion the other one being related to a random path in a potential

simplicial approximation of solutions to the nonlinear complementarity problem with lower and upper bounds ideas of a simplicial variable dimension restart algorithm to approximate zero points onrn developed by the authors and of a linear complementarity problem pivoting algorithm are combined to an algorithm for solving the nonlinear complementarity problem with lower and upper bounds the algorithm can be considered as a modification of the2n ray zero point finding algorithm onrn it appears that for the new algorithm the number of linear programming pivot steps is typically less than for the2n ray algorithm applied to an equivalent zero point problem this is caused by the fact that the algorithm utilizes the complementarity conditions on the variables

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

a new variable dimension algorithm for the fixed point problem we propose a new variable dimension algorithm for solving a system ofn equations inn variables the algorithm solves a sequence of subproblems consisting of the first several equations the dimension of subproblems does not however increase monotonically a convergence condition is also presented

antishocks in the asep with open boundaries conditioned on low current we study the time evolution of the asep on a finite lattice with l sites and open boundaries conditioned on an atypically low current up to a finite time t by an exact computation we show that for a one parameter family of boundary densities and a special value of the conditioned current an initial product measure with an antishock at site k evolves into a convex combination of such antishocks at sites k the weights p k t k 0 are shown to be the transition probabilities of simple biased random walk with reflecting boundaries we compute explicitly these transition rates our result implies that the antishock remains microscopically stable under the locally conditioned dynamics

exact probability function for bulk density and current in the asymmetric exclusion process we examine the asymmetric simple exclusion process with open boundaries a paradigm of driven diffusive systems having a nonequilibrium steady state transition we provide a full derivation and expanded discussion and digression on results previously reported briefly in m depken and r stinchcombe phys rev lett 93 040602 2004 in particular we derive an exact form for the joint probability function for the bulk density and current both for finite systems and also in the thermodynamic limit the resulting distribution is non gaussian and while the fluctuations in the current are continuous at the continuous phase transitions the density fluctuations are discontinuous the derivations are done by using the standard operator algebraic techniques and by introducing a modified version of the original operator algebra as a by product of these considerations we also arrive at a very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra like the partition function in equilibrium systems this normalization constant is shown to completely characterize the fluctuations albeit in a very different manner

open asep in the weakly asymmetric regime we consider asep on a bounded interval and on a half line with sources and sinks on the full line bertini and giacomin in 1997 proved convergence under weakly asymmetric scaling of the height function to the solution of the kpz equation we prove here that under similar weakly asymmetric scaling of the sources and sinks as well the bounded interval asep height function converges to the kpz equation on the unit interval with neumann boundary conditions on both sides different parameter for each side and likewise for the half line asep to kpz on a half line this result can be interpreted as showing that the kpz equation arises at the triple critical point maximal current high density low density of the open asep 2018 wiley periodicals inc

fluctuation statistics in networks a stochastic path integral approach we investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors the nodes carry generalized charge that may be randomly transferred from one node to another our goal is to find the time evolution of the probability distribution of charges in the network the building blocks of our theoretical approach are 1 known probability distributions for the connector currents 2 physical constraints such as local charge conservation and 3 a time scale separation between the slow charge dynamics of the nodes and the fast current fluctuations of the connectors we integrate out fast current fluctuations and derive a stochastic path integral representation of the evolution operator for the slow charges the statistics of charge fluctuations may be found from the saddle point approximation of the action once the probability distributions on the discrete network have been studied the continuum limit is taken to obtain a statistical field theory we find a correspondence between the diffusive field theory and a langevin equation with gaussian noise sources leading nevertheless to nontrivial fluctuation statistics to complete our theory we demonstrate that the cascade diagrammatics recently introduced by nagaev naturally follows from the stochastic path integral by generalizing the principle of minimal correlations we extend the diagrammatics to calculate current correlation functions for an arbitrary network one primary application of this formalism is that of full counting statistics fcs the motivation for why it was developed in the first place we stress however that the formalism is suitable for general classical stochastic problems as an alternative approach to the traditional master equation or doi peliti technique the formalism is illustrated with several examples both instantaneous and time averaged charge fluctuation statistics in a mesoscopic chaotic cavity as well as the fcs and new results for a generalized diffusive wire

thermodynamic formula for the cumulant generating function of time averaged current the cumulant generating function of time averaged current is studied from an operational viewpoint specifically for interacting brownian particles under nonequilibrium conditions we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added where the modified system is characterized by a variational principle the formula reminds us of einstein s fluctuation theory in equilibrium statistical mechanics furthermore since the formula leads to the fluctuation dissipation relation when the linear response regime is focused on it is regarded as an extension of the linear response theory to that valid beyond the linear response regime the formula is also related to previously known theories such as the donsker varadhan theory the additivity principle and the least dissipation principle but it is not derived from them examples of its application are presented for a driven brownian particle on a ring subject to a periodic potential

the kpz limit of asep with boundary it was recently proved in corwin and shen cpam cs16 that under weakly asymmetric scaling the height functions for asep with sources and sinks converges to the hopf cole solution of the kpz equation with inhomogeneous neumann boundary conditions in their assumptions cs16 chose positive values for the neumann boundary condition and they assumed initial data which is close to stationarity by developing more extensive heat kernel estimates we clarify and extend their results to negative values of the neumann boundary parameters and we also show how to generalize their results to empty initial data which is very far from stationarity combining our result with barraquand et al duke math j bbcw17 we obtain the laplace transform of the one point distribution for half line kpz and use this to confirm t1 3 scale goe tracy widom long time fluctuations at the origin

the d1 triangulation of rn for simplicial algorithms for computing solutions of nonlinear equations we present a new triangulation of n which is called the d1 triangulation for computing zero points or fixed points of nonlinear mappings the d1 triangulation subdivides the unit cube and is based on very elementary pivot rules we compare the d1 triangulation to several well known triangulations of n which triangulate the unit cube according to several measures of efficiency the new triangulation is superior such as the number of simplices in the unit cube the diameter of a triangulation the average directional density and the surface density

a homotopy for solving large sparse and structured fixed point problems we consider here the problem of solving a system of n nonlinear equations in n variables when n is large but the underlying mapping has a sparse jacobian and is also structured we present a homotopy having a variable dimension feature whose implementation in a pl algorithm effectively exploits the sparsity of the jacobian and separability of the mapping the implementation given here uses the cholesky factorization and is thus stable an application to a large system is also discussed

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

permutation congruent transformations of the freudenthal triangulation with minimum surface density linear transformations of the freudenthal triangulation with permutation congruent simplexes are characterized and within this class those transformations yielding minimum normalized surface density are identified

current large deviations for asymmetric exclusion processes with open boundaries we study the large deviation functional of the current for the weakly asymmetric simple exclusion process in contact with two reservoirs we compare this functional in the large drift limit to the one of the totally asymmetric simple exclusion process in particular to the jensen varadhan functional conjectures for generalizing the jensen varadhan functional to open systems are also stated

exact joint density current probability function for the asymmetric exclusion process we study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system we further consider the thermodynamic limit showing that the resulting distribution is non gaussian and that the density fluctuations have a discontinuity at the continuous phase transition while the current fluctuations are continuous the derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra

piecewise linear homotopy algorithms for sparse systems of nonlinear equations when piecewise linear homotopy algorithms are applied to the problem of approximating a zero of a sparse function f r n to r n a large piece of linearity can be traversed in one step by using a suitable linear system the linear system has n rows and n 1 columns but is subject to a number of inequalities depending on the sparsity pattern of f we show how an algorithm can be implemented using these large pieces in particular we demonstrate how to update the linear system corresponding to one large piece to obtain the appropriate system for an adjacent large piece one measure of the complexity of such an implementation is the number of inequalities that may be required for any one piece we prove that there can be no more than o n 3 2 such inequalities and that this bound is essentially tight the argument is purely combinatorial finally we provide guidelines on when such a large piece implementation should be used instead of much simpler small piece implementations for piecew

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

static large deviations for a reaction diffusion model we consider the superposition of a symmetric simple exclusion dynamics speeded up in time with a spin flip dynamics in a one dimensional interval with periodic boundary conditions we prove the large deviations principle for the empirical measure under the stationary state we deduce from this result that the stationary state is concentrated on the stationary solutions of the hydrodynamic equation which are stable

a better triangulation for wright s 2n ray algorithm abstract we give a triangulation for wright s 2n ray algorithm to compute solutions of nonlinear equations according to measures of efficiency of triangulations it is better than any other available triangulation for the 2n ray algorithm

brief simultaneously stabilizing controller design for a class of mimo systems it is shown that a class of linear time invariant multi input multi output plants can be simultaneously stabilized this class of plants all have the same number of zeros at infinity at zero or both but no other zeros in the unstable region if they have zeros at zero or infinity then their gain matrices at zero and infinity also satisfy a positive definiteness condition there is no restriction on the poles of the plants considered in this class an explicit design procedure is proposed to achieve simultaneously stabilizing controllers all simultaneously stabilizing controllers for this class of plants are also characterized in terms of a parameter matrix that satisfies a unimodularity condition

current fluctuations in the one dimensional symmetric exclusion process with open boundaries we calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of n sites with open boundary conditions for large system size n the generating function of the integrated current depends on the densities a and b of the two reservoirs and on the fugacity z the parameter conjugated to the integrated current through a single parameter based on our expressions for these first four cumulants we make a conjecture which leads to a prediction for all the higher cumulants in the case a 1 and b 0 our conjecture gives the same universal distribution as the one obtained by lee levitov and yakovets for one dimensional quantum conductors in the metallic regime

a class of simplicial restart fixed point algorithms without an extra dimension in an earlier paper we introduced an algorithm for approximating a fixed point of a mapping on the product space of unit simplices ideas of that paper are used to construct a class of triangulations ofrn more precisely for somek 1 k n and positive integersm1 mk with sumn a triangulation ofrn is obtained by triangulating the cells which are formed by taking the product of given triangulations ofrmj j 1 k the triangulation of each cell will be defined in relation to an arbitrarily chosen pointv inrn being the starting point of the algorithm fork n we obtain thek triangulation originally due to todd each element of the class can be used to find a simplex which approximates a fixed point of a mapping onrn by generating a unique path of adjacent simplices of variable dimension starting with the pointv

calculation of the transition matrix and of the occupation probabilities for the states of the oslo sandpile model the oslo sandpile model or if one wants to be precise ricepile model is a cellular automaton designed to model experiments on granular piles displaying self organized criticality we present an analytic treatment that allows the calculation of the transition probabilities between the different configurations of the system from here using the theory of markov chains we can obtain the stationary occupation distribution which tells us that the phase space is occupied with probabilities that vary in many orders of magnitude from one state to another our results show how the complexity of this simple model is built as the number of elements increases and allow for small system sizes the exact calculation of the avalanche size distribution and other properties related to the profile of the pile