restricted ornstein uhlenbeck process and applications in neuronal models with periodic input signals restricted gauss markov processes are used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a lower reflecting boundary and periodic input signals the first passage time problem through a time dependent threshold is explicitly developed numerical simulation and asymptotic results for firing densities are provided

surmounting oscillating barriers path integral approach for weak noise we consider the thermally activated escape of an overdamped brownian particle over a potential barrier in the presence of periodic driving a time dependent path integral formalism is developed which allows us to derive asymptotically exact weak noise expressions for both the instantaneous and the time averaged escape rate our results comprise a conceptually different systematic treatment of the rate prefactor multiplying the exponentially leading arrhenius factor moreover an estimate for the deviations at finite noise strengths is provided and a supersymmetry type property of the time averaged escape rate is verified for piecewise parabolic potentials the rate expression can be evaluated in closed analytical form while in more general cases as exemplified by a cubic potential an action integral remains to be minimized numerically our comparison with very accurate numerical results demonstrates an excellent agreement with the theoretical predictions over a wide range of driving strengths and driving frequencies

first passage time statistics of brownian motion with purely time dependent drift and diffusion abstract systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a brownian motion bm driven by time dependent drift and diffusion coefficients modeling such systems requires solving the associated fokker planck equation subject to an absorbing barrier transitional probabilities are derived via the method of images whose applicability to time dependent problems is shown to be limited to state independent drift and diffusion coefficients that only depend on time and are proportional to each other first passage time statistics such as the survival probabilities and first passage time densities are obtained analytically the analysis includes the study of different functional forms of the time dependent drift and diffusion including power law time dependence and different periodic drivers as a case study of these theoretical results a stochastic model of water resources availability in snowmelt dominated regions is presented where both temperature effects and snow precipitation input are incorporated

qp structures of degree 3 and 4d topological field theory a bv algebra and a qp structure of the degree 3 is formulated a qp structure of degree 3 gives rise to lie algebroids up to homotopy and its algebraic and geometric structure is analyzed a new algebroid is constructed which derives a new topological field theory in 4 dimensions by the aksz construction

globalization for perturbative quantization of nonlinear split aksz sigma models on manifolds with boundary we describe a covariant framework to construct a globalized version for the perturbative quantization of nonlinear split aksz sigma models on manifolds with and without boundary and show that it captures the change of the quantum state as one changes the constant map around which one perturbs this is done by using concepts of formal geometry moreover we show that the globalized quantum state can be interpreted as a closed section with respect to an operator that squares to zero this condition is a generalization of the modified quantum master equation as in the bv bfv formalism which we call the modified differential quantum master equation

batalin vilkovisky formalism and integration theory on manifolds the correspondence between the bv formalism and integration theory on supermanifolds is established an explicit formula for the density on a lagrangian surface in a superspace provided with an odd symplectic structure and a volume form is proposed

statistics of entrance times abstract the statistical properties of the transitions of a discrete markov process are investigated in terms of entrance times a simple formula for their density is given and used to measure the synchronization of a process with a periodic driving force for the mcnamara wiesenfeld model of stochastic resonance we find parameter regions in which the transition frequency of the process is locked with the frequency of the external driving

escape rates in periodically driven markov processes we present an approximate analytical expression for the escape rate of time dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrateand fire model for neural spiking the novel approximation i s based on a discrete state markovian modeling of the full long time dynamics with time dependent rates it is valid in a wide parameter regime beyond the restraining limits of weak driving linear response and or weak noise the scheme is carefully tested and yields excellent agreement with three different numerical methods based on the langevin equation the fokker planck equation and an integral equation

non commutative batalin vilkovisky algebras homotopy lie algebras and the courant bracket we consider two different constructions of higher brackets first based on a grassmann odd nilpotent operator we define a non commutative generalization of the higher koszul brackets which are used in a generalized batalin vilkovisky algebra and we show that they form a homotopy lie algebra secondly we investigate higher so called derived brackets built from symmetrized nested lie brackets with a fixed nilpotent lie algebra element q we find the most general jacobi like identity that such a hierarchy satisfies the numerical coefficients in front of each term in these generalized jacobi identities are related to the bernoulli numbers we suggest that the definition of a homotopy lie algebra should be enlarged to accommodate this important case finally we consider the courant bracket as an example of a derived bracket we extend it to the big bracket of exterior forms and multi vectors and give closed formulas for the higher courant brackets

wheeled pro p file of batalin vilkovisky formalism using a technique of wheeled props we establish a correspondence between the homotopy theory of unimodular lie 1 bialgebras and the famous batalin vilkovisky formalism solutions of the so called quantum master equation satisfying certain boundary conditions are proven to be in 1 1 correspondence with representations of a wheeled dg prop which on the one hand is isomorphic to the cobar construction of the prop of unimodular lie 1 bialgebras and on the other hand is quasi isomorphic to the dg wheeled prop of unimodular poisson structures these results allow us to apply properadic methods for computing formulae for a homotopy transfer of a unimodular lie 1 bialgebra structure on an arbitrary complex to the associated quantum master function on its cohomology it is proven that in the category of quantum bv manifolds associated with the homotopy theory of unimodular lie 1 bialgebras quasi isomorphisms are equivalence relations it is shown that losev mnev s bf theory for unimodular lie algebras can be naturally extended to the case of unimodular lie 1 bialgebras and eventually to the case of unimodular poisson structures using a finite dimensional version of the batalin vilkovisky quantization formalism it is rigorously proven that the feynman integrals computing the effective action of this new bf theory describe precisely homotopy transfer formulae obtained within the wheeled properadic approach to the quantum master equation quantum corrections which are present in our bf model to all orders of the planck constant correspond precisely to what are often called higher massey products in the homological algebra

on the b twisted topological sigma model and calabi yau geometry we provide a rigorous perturbative quantization of the b twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps we prove that the first chern class of the target manifold is the obstruction to the quantization via batalin vilkovisky formalism when the first chern class vanishes i e on calabiyau manifolds the factorization algebra of observables gives rise to the expected topological correlation functions in the b model we explain a twisting procedure to generalize to the landau ginzburg case and show that the resulting topological correlations coincide with vafa s residue formula

geometry of batalin vilkovisky quantization the geometry ofp manifolds odd symplectic manifolds andsp manifolds p manifolds provided with a volume element is studied a complete classification of these manifolds is given this classification is used to prove some results about batalin vilkovisky procedure of quantization in particular to obtain a very general result about gauge independence of this procedure

a time domain approach to robust fault detection of linear time varying systems this paper gives the optimal solutions to several robust fault detection problems such as 2 and problems for linear time varying systems in a time domain which extends the previous results on linear time invariant systems in a frequency domain it is shown that all three problems have the same optimal detection filter and the filter is a simple observer obtained by solving a standard differential riccati equation finally an example is given to illustrate our results

noise induced anomalous diffusion over a periodically modulated saddle we study analytically and numerically the anomalous diffusion across periodically modulated parabolic potential within langevin and fokker planck descriptions we find that the probability of particles passing over the saddle is affected strikingly by the periodical modulation with average zero bias particularly the initial phase plays an important role in the modulation effect the effect of the correlation time of external ornstein uhlenbeck noise on dynamical process is also discussed a reduction in overpassing probability is observed due to finite correlation time

brief paper an lmi approach to h index and mixed h h fault detection observer design using the newly developed worst case fault sensitivity measure the index and the well known worst case robustness measure the norm this paper addresses the problem of index fault detection observer design and multiobjective fault detection observer design problems necessary and sufficient conditions for the existence of such a fault detection observer are given in terms of matrix inequalities both infinite frequency range case 0 and finite frequency range case 0 with overbar are considered iterative linear matrix inequality ilmi algorithms are given to obtain the solutions the effectiveness of the proposed approaches is shown by numerical examples

gauss markov processes in the presence of a reflecting boundary and applications in neuronal models abstract gauss markov processes restricted from below by special reflecting boundaries are considered and the transition probability density functions are determined furthermore the first passage time density through a time dependent threshold is studied by using analytical numerical and asymptotic methods the restricted gauss markov processes are then used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a reversal hyperpolarization potential and time varying input signals

asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime switching time distributions a detailed theoretical analysis of the dynamics of a sinusoidally driven noisy asymmetric bistable system is presented the results are valid for any two state system however the specific case of the duffing potential is considered in detail the dynamics are considered in the weak noise limit i e when the response of the system to the external periodic field is strongly nonlinear the system asymmetry is created by a nonzero dc component of the external force and manifests itself as an asymmetry between the mean switching times between the potential wells we obtain explicit analytic expressions for the whole hierarchy of switching time distributions including the residence time and return time distributions we also obtain expressions for the average residence times and describe how they depend on asymmetry together with an explicit expression for the difference between the residence times in the weak noise limit the results are presented in the context of using the switching dynamics to detect weak dc target signals

open closed homotopy algebra in mathematical physics in this paper we discuss various aspects of open closed homotopy algebras ochas presented in our previous paper inspired by zwiebach s open closed string field theory but that first paper concentrated on the mathematical aspects here we show how an ocha is obtained by extracting the tree part of zwiebach s quantum open closed string field theory we clarify the explicit relation of an ocha with kontsevich s deformation quantization and with the b models of homological mirror symmetry an explicit form of the minimal model for an ocha is given as well as its relation to the perturbative expansion of open closed string field theory we show that our open closed homotopy algebra gives us a general scheme for deformation of open string structures a algebras by closed strings l algebras

geometry of superspace with even and odd brackets the geometry of the superspace provided by two arbitrary poisson brackets of different gradings is studied it will be shown that the group of transformations that preserve these two brackets is finite dimensional

on the globalization of the poisson sigma model in the bv bfv formalism we construct a formal global quantization of the poisson sigma model in the bv bfv formalism using the perturbative quantization of aksz theories on manifolds with boundary and analyze the properties of the boundary bfv operator moreover we consider mixed boundary conditions and show that they lead to quantum anomalies i e to a failure of the modified differential quantum master equation we show that it can be restored by adding boundary terms to the action at the price of introducing corner terms in the boundary operator we also show that the quantum grothendieck bfv operator on the total space of states is a differential i e squares to zero which is necessary for a well defined bv cohomology

brief paper optimal fault detection for linear discrete time varying systems this paper deals with the problem of observer based fault detection for linear discrete time varying ldtv systems a problem formulation is first proposed to address the optimization of the fault detection filter fdf design which is expressed in terms of maximizing a finite horizon h h or h h performance index this formulation can be applied to fdf design of ldtv systems subject to l 2 norm bounded unknown inputs or stochastic noise sequences it is shown that a unified optimal solution to the fdf can be obtained by solving the discrete time riccati equation and the optimal fdf is not unique a numerical example is given to illustrate the proposed method

semidensities second class constraints and conversion in anti poisson geometry we consider khudaverdian s geometric version of a batalin vilkovisky bv operator e in the case of a degenerate anti poisson manifold the characteristic feature of such an operator aside from being a grassmann odd nilpotent second order differential operator is that it sends semidensities to semidensities we find a local formula for the e operator in arbitrary coordinates as an important application of this setup we consider the dirac antibracket on an antisymplectic manifold with antisymplectic second class constraints we show that the entire dirac construction including the corresponding dirac bv operator ed exactly follows from conversion of the antisymplectic second class constraints into first class constraints on an extended manifold

quantum l_ infty l algebras and the homological perturbation lemma quantum l infty algebras are a generalization of l infty algebras with a scalar product and with operations corresponding to higher genus graphs we construct a minimal model of a given quantum l infty algebra via the homological perturbation lemma and show that it s given by a feynman diagram expansion computing the effective action in the finite dimensional batalin vilkovisky formalism we also construct a homotopy between the original and this effective quantum l infty algebra

bfv complex and higher homotopy structures we present a connection between the bfv complex abbreviation for batalin fradkin vilkovisky complex and the strong homotopy lie algebroid associated to a coisotropic submanifold of a poisson manifold we prove that the latter structure can be derived from the bfv complex by means of homotopy transfer along contractions consequently the bfv complex and the strong homotopy lie algebroid structure are l quasi isomorphic and control the same formal deformation problem

technical communique finite horizon h fault estimation for linear discrete time varying systems with delayed measurements in this paper the finite horizon h fault estimation problem is addressed for a class of linear discrete time varying systems with both instantaneous and delayed measurements by using the reorganized innovation approach the considered measurements are reorganized into a tractable form based on which we introduce an associated stochastic system in a krein space then by applying the innovation analysis and projection theory in the krein space a necessary and sufficient condition for the existence of the finite horizon h fault estimator is obtained subsequently a fault estimator is designed to achieve the specified h performance criterion in terms of the solution to a set of riccati difference equations finally a simulation example is employed to show the effectiveness of the proposed fault estimation approach

minimal models of quantum homotopy lie algebras via the bv formalism using the batalin vilkovisky formalism of mathematical physics an explicit construction for the minimal model of a quantum l algebra is given as a formal super integral the approach taken herein to these formal integrals is axiomatic and they can be approached using perturbation theory to obtain combinatorial formulae as shown in the appendix additionally there exists a canonical differential graded lie algebra morphism mapping formal functions on homology to formal functions on the whole space an inverse l algebra morphism to this differential graded lie algebra morphism is constructed as a formal super integral using the batalin vilkovisky formalism of mathematical physics an explicit construction for the minimal model of a quantum l algebra is given as a formal super integral the approach taken herein to these formal integrals is axiomatic and they can be approached using perturbation theory to obtain combinatorial formulae as shown in the appendix additionally there exists a canonical differential graded lie algebra morphism mapping formal functions on homology to formal functions on the whole space an inverse l algebra morphism to this differential graded lie algebra morphism is constructed as a formal super integral

numerical method for solving stochastic differential equations with dichotomous noise we propose a numerical method for solving stochastic differential equations with dichotomous markov noise the numerical scheme is formulated such that i the stochastic formula used follows the stratonovichtaylor form over the entire range of noise correlation times including the gaussian white noise limit and ii the method is readily applicable to dynamical systems driven by arbitrary types of noise provided there exists a way to describe the random increment of the stochastic process expressed in the stratonovich taylor form we further propose a simplified taylor scheme that significantly reduces the computation time while still satisfying the moment properties up to the required order the accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions

a path integral approach to the kontsevich quantization formula we give a quantum field theory interpretation of kontsevich s deformation quantization formula for poisson manifolds we show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory its batalin vilkovisky quantization yields a superconformal field theory the associativity of the star product and more generally the formality conjecture can then be understood by field theory methods as an application we compute the center of the deformed algebra in terms of the center of the poisson algebra

event based h filtering for sampled data systems this paper is concerned with event based h filtering for sampled data systems first an event based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated as a result communication resources can be saved significantly while preserving the desired h performance second the resulting filtering error system is modeled as a system with an interval time varying delay by employing the lyapunov krasovskii functional approach a new bounded real lemma brl is established such that the filtering error system is asymptotically stable with the prescribed h performance third by performing an invertible linear transformation on the filtering error system a linear matrix inequality lmi based sufficient condition which is equivalent to the condition in the brl is obtained on the feasibility of the event based h filtering problem consequently suitable h filters and the event parameters in the event condition can be co designed provided that a set of lmis are satisfied finally a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method

an h_ i h_ infty optimization approach to event triggered fault detection for linear discrete time systems in this article a new event triggered h i h infty optimization fault detection fd scheme is proposed for linear discrete time systems a linear discrete time system with varying sampling periods is first presented to describe the dynamics of an event triggered system based on this an observer based fault detection filter fdf is constructed as an event triggered residual generator so that the generated residual signal is completely decoupled from the event triggered transmission error the design of event triggered fdf is formulated as a multiobjective optimization problem denoted by h i h infty and an optimal solution can be obtained by recursive calculation of riccati equations in addition an event triggered residual evaluation strategy is also presented comparing with the existing event triggered fd schemes the major contribution of this article is to decouple the residual signals from the event triggered transmission errors completely and consequently the fd performance can be improved significantly moreover an optimal tradeoff between the robustness of residual to unknown input and the sensitivity of residual to fault is achieved in the sense of h i h infty optimization while the design of fdf and event generator can be carried out independently to demonstrate the effectiveness of the proposed method a vehicle lateral dynamic system is used as a simulation example

semidensities on odd symplectic supermanifolds we consider semidensities on a supermanifold e with an odd symplectic structure we define a new operator action on semidensities as the proper framework for the batalin vilkovisky bv formalism we establish relations between semidensities on e and differential forms on lagrangian surfaces we apply these results to batalin vilkovisky geometry another application is to 1 1 codimensional surfaces in e we construct a kind of pull back of semidensities to such surfaces this operation and the operator are used for obtaining integral invariants for 1 1 codimensional surfaces

a note on semidensities in antisymplectic geometry we revisit khudaverdian s geometric construction of an odd nilpotent operator e that sends semidensities to semidensities on an antisymplectic manifold we find a local formula for the e operator in arbitrary coordinates and we discuss its connection to batalin vilkovisky quantization

a cellular topological field theory we present a construction of cellular bf theory in both abelian and non abelian variants on cobordisms equipped with cellular decompositions partition functions of this theory are invariant under subdivisions satisfy a version of the quantum master equation and satisfy atiyah segal type gluing formula with respect to composition of cobordisms

semiclassical approximation in batalin vilkovisky formalism the geometry of supermanifolds provided with aq structure i e with an odd vector fieldq satisfying q q 0 ap structure odd symplectic structure and ans structure volume element or with various combinations of these structures is studied the results are applied to the analysis of the batalin vilkovisky approach to the quantization of gauge theories in particular the semiclassical approximation in this approach is expressed in terms of reidemeister torsion

non commutative periods and mirror symmetry in higher dimensions we study an analog for higher dimensional calabi yau manifolds of the standard predictions of mirror symmetry we introduce periods associated with non commutative deformations of calabi yau manifolds these periods define a map on the moduli space of such deformations which is a local isomorphism using these non commutative periods we introduce invariants of variations of semi infinite generalized hodge structures living over the moduli space it is shown that the generating function of such invariants satisfies the system of wdvv equations exactly as in the case of gromov witten invariants we prove that the total collection of rational gromov witten invariants of complete intersection calabi yau manifold can be identified with the collection of invariants of variations of generalized semi infinite hodge structures attached to the mirror variety the basic technical tool utilized is the deformation theory

brief an lmi approach to design robust fault detection filter for uncertain lti systems in this paper the robust fault detection filter design problem for uncertain linear time invariant lti systems with both unknown inputs and modelling errors is studied the basic idea of our study is to use an optimal residual generator assuming no modelling errors as the reference residual model of the robust fault detection filter design for uncertain lti systems with modelling errors and based on it to formulate the robust fault detection filter design as an h model matching problem by using some recent results of h optimization a solution of the optimization problem is then presented via a linear matrix inequality lmi formulation the main results include the development of an optimal reference residual model the formulation of robust fault detection filter design problem the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the lmi solution parameters the determination of adaptive threshold for fault detection an illustrative design example is employed to demonstrate the effectiveness of the proposed approach

first passage and first exit times of a bessel like stochastic process we study a stochastic process x t which is a particular case of the rayleigh process and whose square is the bessel process with various applications in physics chemistry biology economics finance and other fields the stochastic differential equation is dx t nd x t dt 2d dw t where w t is the wiener process the drift term can arise from a logarithmic potential or from taking x t as the norm of a multidimensional random walk due to the singularity of the drift term for x t 0 different natures of boundary at the origin arise depending on the real parameter n entrance exit and regular for each of them we calculate analytically and numerically the probability density functions of first passage times or first exit times nontrivial behavior is observed in the case of a regular boundary