an improved chattering free vsc scheme for uncertain dynamical systems a control strategy proposed by the authors in previous works to reduce the effect of chattering led to the solution of a differential inequality involving the first and second derivatives of the control signal and a parameter for a first order observer the analysis was carried out assuming this parameter to be constant in the present paper this assumption is removed thus allowing the solution of the differential inequality to be a function of a piecewise continuous first derivative of the control signal without need for assuming a priori knowledge of bounds to the plant trajectories

rbf methods in a stochastic volatility framework for greeks computation abstract in this paper we aim to apply a new proposed meshless approach for heston pde resolution in mathematical finance most classical models may be reformulated as partial differential equations pde which are commonly solved by finite difference and monte carlo methods alternatively bio inspired methods may be considered to select parameters and to solve said pdes in particular we focus on heston model pde and we solve it via radial basis functions rbf methods moreover some considerations on the computation of model parameters through learning approaches have been discussed we aim to price a vanilla call option focusing on the derivation of the formulae for its greeks profiles eventually we conclude rbfs are an accurate alternative method to price derivatives in a stochastic volatility framework especially since they allow for a fast and precise computation of greeks

brief paper simplex sliding mode methods for the chattering reduction control of multi input nonlinear uncertain systems the simplex sliding mode control method is further developed by considering uncertain control systems non affine in the control law in order to reduce chattering effects a set of integrators is added in the input channels the augmented system is then controlled by a switching logic based on the simplex control method as a result the original control vector turns out to be continuous a second order sliding mode observer is used when the sliding output is not available explicit conditions are identified about systems uncertainties and the simplex geometry in order to guarantee the convergence of the proposed methodology

linking population level models with growing networks a class of epidemic models we introduce a class of growing network models that are directly applicable to epidemiology we show how to construct a growing network model individual level model that generates the same epidemic level outcomes as a population level ordinary differential equation ode model for concreteness we analyze the susceptible infected si ode model of disease invasion first we give an illustrative example of a growing network whose population level variables are compatible with those of this ode model second we demonstrate that a growing network model can be found that is equivalent to the crump mode jagers cmj continuous time branching process of the si ode model of disease invasion we discuss the computational advantages that our growing network model has over the cmj branching process

variable structure systems nonlinear in the control law the most relevant results of utkin s work obtained for variable structure systems linear in the control law which slide on suitable manifolds in the state space are extended to some class of fully nonlinear plants the equivalence between the filippov solution concept is proved for this class further the approximability property convergence to the nonideal sliding motion to the ideal is shown to hold for an important subclass

developments in the theory of randomized shortest paths with a comparison of graph node distances there have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance the need for developing such distances has risen from the observation that the above mentioned common distances in many situations fail to take into account the global structure of the graph in this article we develop the theory of one family of graph node distances known as the randomized shortest path dissimilarity which has its foundation in statistical physics we show that the randomized shortest path dissimilarity can be easily computed in closed form for all pairs of nodes of a graph moreover we come up with a new definition of a distance measure that we call the free energy distance the free energy distance can be seen as an upgrade of the randomized shortest path dissimilarity as it defines a metric in addition to which it satisfies the graph geodetic property the derivation and computation of the free energy distance are also straightforward we then make a comparison between a set of generalized distances that interpolate between the shortest path distance and the commute time or resistance distance this comparison focuses on the applicability of the distances in graph node clustering and classification the comparison in general shows that the parametrized distances perform well in the tasks in particular we see that the results obtained with the free energy distance are among the best in all the experiments

behavior of variable structure control systems near the sliding manifold abstract a new definition of well posedness called generalized approximability is introduced for variable structure control systems described by ordinary differential equations this definition isolates the following basic property states fulfilling only approximately the sliding condition converge toward some well defined sliding state as the perturbations preventing exact sliding disappear approximability rules out ambiguous systems which defy successful implementation of sliding feedback controls the existence of the equivalent control is not required it is shown that approximability is in essence of a form of uniqueness of the filippov sliding state explicit criteria for approximability are obtained

multi input sliding mode control of a class of uncertain nonlinear systems an effective way to extend to the multi input case the variable structure control philosophy is based on a set of m 1 control vectors forming a simplex in r sup m and on the corresponding switching of the controlled system from one to another of m 1 different structures yet some problems arise when uncertainties are present in certain matrices characterizing the controlled systems in this paper conditions are identified under which even in the presence of uncertainty the convergence to the sliding manifold is ensured via the application of a multi input control strategy still based on a simplex of control vectors

a theoretical formulation of the dynamical response of a master structure coupled with elastic continuous fuzzy subsystems with discrete attachments we present the formulation of the dynamic response of a master structure coupled with a locally homogeneous and orthotropic structural fuzzy with discrete attachment composed of elastic continuous fuzzy subsystems as introduced by soize the master structure is the part of the coupled system which is accessible by classical modeling whereas the structural fuzzy represents systems connected to the master structure whose characteristics are imprecisely known a deterministic formulation of the boundary impedance of a general continuous structural fuzzy which models its action on the master structure is derived it is shown that the formulation is different from the solution proposed by soize in the context of the type i fuzzy law established from the deterministic model of a linear oscillator excited by its support finally the general boundary impedance is applied to the special situation of a structural fuzzy composed of elastic bars whose geometrical parameters are randomly defined and numerical results are presented

global stabilization for nonlinear uncertain systems with unmodeled actuator dynamics second order sliding mode control 2 smc algorithms are analyzed to assess their global convergence properties while standard first order sliding mode control 1 smc algorithms derive their effectiveness from the global solution of the well known reaching condition ss spl dot spl les k sup 2 s s 0 being the actual sliding manifold 2 smc is based on more complex differential inequalities for which a global solution could not exist the approach presented introduces a suitable commutation logic based on an online simple predictor that prevents an uncontrollable growth of the uncertainties due to this new commutation logic the global convergence of the state trajectory to the designed sliding manifold is ensured

asymptotically min max bias robust m estimates of scale for positive random variables abstract asymptotically min max bias robust m estimates of scale are obtained for positive random variables with e contaminated distributions using any one of a broad class of loss functions of positive and negative bias any such estimate is a scaled order statistic with the order statistic and scaling constant determined by e the nominal distribution and the loss function some calculations for specific cases show that for a large range of e the min max order statistic solution has a breakdown point near 5 and is well approximated by a scaled median some calculations and monte carlo results indicate that the asymptotic result has considerable finite sample size relevance by virtue of the squared bias being at least as large as the variance for rather modest sample sizes depending on e and by virtue of attractive mean squared error performance in the presence of even rather small fractions of contamination

sliding order and sliding accuracy in sliding mode control the synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered usually what is called sliding mode is employed in such synthesis this sliding mode is characterized in practice by a high frequency switching of the control it turns out that the deviation of the system from its prescribed constraints sliding accuracy is proportional to the switching time delay a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced these algorithms feature a bounded control continuously depending on time with discontinuities only in the control derivative it is also shown that the sliding accuracy is proportional to the square of the switching time delay

on the active periods of nonlinear shot noise abstract we study the temporal on and off structure of the recently introduced nonlinear shot noise model i eliazar j klafter pnas 102 2005 13779 i eliazar j klafter nonlinear shot noise levy noah joseph physica a 2006 to appear in which i shots of random magnitudes bombard a system stochastically in time ii the magnitudes of incoming shots decay to zero nonlinearly and iii the overall effect of the shots on the system is additive when the shot inflow and shot decay satisfy certain conditions the resulting shot noise alternates randomly between active periods in which the noise is on and silent periods in which noise is off the statistical properties of the active and silent periods are analyzed and the resulting on and off shot noise structure is explored explicit formulae for means variances laplace transforms and other statistics are derived in closed form based on this analysis shot noise systems are categorized into three classes transient null recurrent and recurrent and these classes are characterized both analytically and probabilistically within the null recurrent class systems whose active periods are governed by heavy tailed probability distributions are further characterized

smoothed lexis diagrams with applications to lung and breast cancer trends in taiwan cancer surveillance research often begins with a rate matrix also called a lexis diagram of cancer incidence derived from cancer registry and census data lexis diagrams with 3 or 5 year intervals for age group and for calendar year of diagnosis are often considered this simple smoothing approach suffers from a significant limitation important details useful in studying time trends may be lost in the averaging process involved in generating a summary rate this article constructs a smoothed lexis diagram and indicates its use in cancer surveillance research specifically we use a poisson model to describe the relationship between the number of new cases the number of people at risk and a smoothly varying incidence rate for the study of the incidence rate function based on the poisson model we use the standard lexis diagram to introduce priors through the coefficients of bernstein polynomials and propose a bayesian approach to construct a smoothed lexis diagram for the study of the effects of age

joint state and event observers for linear switching systems under irregular sampling joint estimation of states and events in linear regime switching systems is studied under irregular sampling schemes which stem from improved sampling and quantization methods for efficient utility of communication resources joint observability and sampling complexity are established extending shannon s sampling theorem and our recent results on sampling complexity to joint estimation problems observer design and convergence analysis are conducted for systems under noisy observations it is shown that our algorithms converge strongly with an error bound of the order o 1 n simulation examples are included to illustrate potential usages of the algorithms

phase transition for the maki thompson rumour model on a small world network we consider the maki thompson model for the stochastic propagation of a rumour within a population in this model the population is made up of spreaders ignorants and stiflers any spreader attempts to pass the rumour to the other individuals via pair wise interactions and in case the other individual is an ignorant it becomes a spreader while in the other two cases the initiating spreader turns into a stifler in a finite population the process will eventually reach an equilibrium situation where individuals are either stiflers or ignorants we extend the original hypothesis of homogenously mixed population by allowing for a small world network embedding the model in such a way that interactions occur only between nearest neighbours this structure is realized starting from a k regular ring and by inserting in the average c additional links in such a way that k and c are tuneable parameters for the population architecture we prove that this system exhibits a transition between regimes of localization where the final number of stiflers is at most logarithmic in the population size and propagation where the final number of stiflers grows algebraically with the population size at a finite value of the network parameter c a quantitative estimate for the critical value of c is obtained via extensive numerical simulations

dynamic rating curve assessment in unstable rivers using ornstein uhlenbeck processes 1 the procedure of fitting rating curves in channels where the stage discharge relationship is subject to changes driven by morphological processes remains one of the major unsolved problems in hydrometry this paper addresses this issue by formulating the stage discharge relationship as a steady flow one segmented power law model with parameters that are viewed as stochastic processes with characteristics associated with the temporal instabilities of the channel elements governing the stage discharge relationship a bayesian analysis with informative priors and time stage discharge measurements as forcing data is used to determine the most plausible model and its posterior parameter distributions using markov chain monte carlo simulation techniques and particle filtering the proposed framework is applied to data from gauging stations in two unstable rivers and one stable river in norway

discrete time generative reactive probabilistic processes with different advancing speeds we present a process algebra expressing probabilistic external internal choices multi way synchronizations and processes with different advancing speeds in the context of discrete time i e where time is not continuous but is represented by a sequence of discrete steps as in discrete time markov chains dtmcs to this end we introduce a variant of csp that employs a probabilistic asynchronous parallel operator whose synchronization mechanism is based on a mixture of the classical generative and reactive models of probability in particular differently from existing discrete time process algebras where parallel processes are executed in synchronous locksteps the parallel operator that we adopt allows processes with different probabilistic advancing speeds mean number of actions executed per time unit to be modeled moreover our generative reactive synchronization mechanism makes it possible to always derive dtmcs in the case of fully specified systems we then present a sound and complete axiomatization of probabilistic bisimulation over finite processes of our calculus that is a smooth extension of the axiom system for a standard process algebra thus solving the open problem of cleanly axiomatizing action restriction in the generative model as a further result we show that when evaluating steady state based performance measures which are expressible by attaching rewards to actions our approach provides an exact solution even if the advancing speeds are considered not to be probabilistic without incurring the state space explosion problem that arises with standard synchronous approaches we finally present a case study on multi path routing showing the expressiveness of our calculus and that it makes it particularly easy to produce scalable specifications

on the generation of random binary search trees we consider the computer generation of random binary search trees with n nodes for the standard random permutation model the algorithms discussed here output the number of external nodes at each level but not the shape of the tree this is important for example when one wishes to simulate the height of the binary search tree various paradigms are proposed including depth first search with pruning incremental methods in which the tree grows with random sized jumps and a tree growing procedure gleaned from birth and death processes the last method takes o log 4 n expected time

randomized shortest path problems two related models this letter addresses the problem of designing the transition probabilities of a finite markov chain the policy in order to minimize the expected cost for reaching a destination node from a source node while maintaining a fixed level of entropy spread throughout the network the exploration it is motivated by the following scenario suppose you have to route agents through a network in some optimal way for instance by minimizing the total travel cost nothing particular up to now you could use a standard shortest path algorithm suppose however that you want to avoid pure deterministic routing policies in order for instance to allow some continual exploration of the network avoid congestion or avoid complete predictability of your routing strategy in other words you want to introduce some randomness or unpredictability in the routing policy i e the routing policy is randomized this problem which will be called the randomized shortest path problem rsp is investigated in this work the global level of randomness of the routing policy is quantified by the expected shannon entropy spread throughout the network and is provided a priori by the designer then necessary conditions to compute the optimal randomized policy minimizing the expected routing cost are derived iterating these necessary conditions reminiscent of bellman s value iteration equations allows computing an optimal policy that is a set of transition probabilities in each node interestingly and surprisingly enough this first model while formulated in a totally different framework is equivalent to akamatsu s model 1996 appearing in transportation science for a special choice of the entropy constraint we therefore revisit akamatsu s model by recasting it into a sum over paths statistical physics formalism allowing easy derivation of all the quantities of interest in an elegant unified way for instance it is shown that the unique optimal policy can be obtained by solving a simple linear system of equations this second model is therefore more convincing because of its computational efficiency and soundness finally simulation results obtained on simple illustrative examples show that the models behave as expected

radial basis function partition of unity methods for pricing vanilla basket options meshfree methods based on radial basis function rbf approximation are becoming widely used for solving pde problems they are flexible with respect to the problem geometry and highly accurate a disadvantage of these methods is that the linear system to be solved becomes dense for globally supported rbfs a remedy is to introduce localisation techniques such as partition of unity rbf partition of unity methods rbf pum allow for a significant sparsification of the linear system and lower the computational effort in this work we apply a global rbf method as well as rbf pum to problems in option pricing we consider one and two dimensional vanilla options in order to price american options we employ a penalty approach a penalty term suitable for american multi asset call options has been designed rbf pum is shown to be competitive compared with a finite difference method and a global rbf method it is as accurate as the global rbf method but significantly faster the results for rbf pum look promising for extension to higher dimensional problems

on the sliding mode control of multivariable nonlinear systems sliding mode control of multivariable nonlinear systems is addressed from the perspective of linear differential algebra for a special but large class of linearizable systems known as differentially flat systems essential orders and differential flatness are shown to be a relevant concept and a sensible requirement respectively associated with the possibilities of designing static or dynamical sliding mode multivariable feedback regulators for nonlinear systems

the vss approach to the model reference control of nonminimum phase linear plants a nontrivial application of the discontinuous control system theory based on filippov s solution concept is presented the problem addressed is the model reference output feedback control of linear plants with non hurwitzian numerator in the transfer function a solution in the case of known systems is presented first an error state equation whose state is accessible is then derived for the case in which the plant parameters are unknown in the case in which some bounds on the plant characteristics are supposed known a pair of discontinuous signals acting on both the plant and the model is chosen causing the error state to vanish asymptotically

a proof of convergence for ant algorithms a proof of convergence for ant algorithms is developed ant algorithms were modeled as branching random processes the branching random walk and branching wiener process to derive rates of birth and death of ant paths substitution is then carried out in birth death processes which proves that a stable distribution is surely reached this indicates that ant algorithms converge with probability one this analogy models ant algorithms complexity parameters such as the number of cycles the degrees of freedom of problem and the number of ants

edge detection in noisy data using finite mixture distribution analysis abstract an algorithm which identifies discontinuities in noisy data is presented the signal is modelled as step edges with additive normally distributed noise present using finite mixture analysis and information criteria a variable number of mixtures are identified together with the location of the respective edges separating them the problem is solved using a dynamic programming approach which ensures globally optimal edge positions according to the signal model of a finite mixture of normal distributions the computational complexity is of order mn 2 where m is the number of discontinuities in the mixture and n is the number of data points in the signal the algorithm is tested on a range of real and synthetic signals and yields as accurate edge positions as a corresponding minimum square error method among applications for this algorithm is edge detection in medical images and examples from ultrasound imaging are included

population dynamics in presence of state dependent fluctuations we discuss a model of a system of interacting populations for the case when i the growth rates and the coefficients of interaction among the populations depend on the populations densities and ii the environment influences the growth rates and this influence can be modelled by a gaussian white noise the system of model equations for this case is a system of stochastic differential equations with i deterministic part in the form of polynomial nonlinearities and ii state dependent stochastic part in the form of multiplicative gaussian white noise we discuss both the cases when the formal integration of the stochastic differential equations leads i to integrals of ito kind or ii to integrals of stratonovich kind the systems of stochastic differential equations are reduced to the corresponding fokker planck equations for the ito case and for the case of 1 population analytic results are obtained for the stationary p d f of the population density for the case of more than one population and for both the ito case and stratonovich case the detailed balance conditions are not satisfied as a result the exact analytic solutions of the corresponding fokker planck equations for the stationary p d f s for the population densities are not known we obtain approximate solutions for this case by the method of adiabatic elimination

multi input sliding mode control of nonlinear uncertain non affine systems with mono directional actuation in this paper the multi input sliding mode control of nonlinear uncertain non affine systems with mono directional actuators is considered the geometric properties of the regular simplices of vectors are exploited by the mono directional actuation system the proposed full state feedback control method introduces integrators in the input channel and suitably modifies the sliding output to be steered to zero the resulting high frequency gain matrix hfgm which is the matrix multiplying the control vector turns out to be affected by time and state dependent uncertainties an effective use of the integral sliding mode method in connection with a non conventional simplex based switching logic is introduced the proposed simplex control procedure is adequately designed to avoid any possible unbounded increment of the control actions despite the presence of integrators in the input channel and the exploitation of mono directional devices

geometrically exact intrinsic theory for dynamics of curved and twisted anisotropic beams a formulation is presented for the nonlinear dynamics of initially curved and twisted anisotropic beams when the applied loads at the ends of and distributed along the beam are independent of the deformation neither displacement nor rotation variables appear an intrinsic formulation like well known special cases of these equations governing nonlinear dynamics of rigid bodies and nonlinear statics of beams the complete set of intrinsic equations has a maximum degree of nonlinearity equal to two advantages of such a formulation are demonstrated with a simple example when the initial curvature and twist are constant along the beam two space time conservation laws are shown to exist one being a work energy relation and the other a generalized impulse momentum relation these laws can be used for example as benchmarks to check the accuracy of any proposed solution including time marching and finite element schemes the structure of the intrinsic equations suggests parallel approaches to spatial and temporal discretization a particularly simple spatial discretization scheme is presented for the special case of the nonlinear static behavior of end loaded beams that by virtue of the kirchhoff analogy leads to a time marching scheme for the dynamics of a pivoted rigid body in a gravity field this time marching scheme conserves both the angular momentum about a vertical line passing through the pivot and total mechanical energy whereas the analogous spatial discretization scheme for the nonlinear static behavior of end loaded beams satisfies analogous integrals of deformation along the beam span remarkably a straightforward generalization of these discretization schemes is shown to satisfy both space time conservation laws for the nonlinear dynamics of beams when the applied loads are constant within a space time element

an introduction to stochastic modeling stochastic modeling probability review the major discrete distributions rtant continuous distributions some elementary exercises useful functions integrals and sums conditional probability and conditional expectation the discrete case the dice game craps random sums conditioning on a continuous random variable markov chains introduction definitions transition probability matrices of a markov chain some markov chain models first step analysis some special markov chains functionals of random walks and success runs another look at first step analysis the long run behavior of markov chains regular transition probability matrices examples the classification of states the basic limit theorem of markov chains reducible markov chains sequential decisions and markov chains poisson processes the poisson distribution and the poisson processes the law of rare events distributions associated with the poisson process the uniform distribution and poisson processes spatial poisson processes compound and marked poisson processes continuous time markov chains pure birth processes ptire death processes birth and death processes the limiting behavior of birth and death processes birth and death processes with absorbing states finite state continuous time markov chains set valued processes renewal phenomena definition of a renewal process and related concepts some examples of renewal processes the poisson process viewed as a renewal process the asymptotic 3ehavior as renewal process

numerical determination of hitting time distributions from their laplace transforms one dimensional diffusions abstract in a previous paper we studied a method to determine the probability density of barrier crossing times by a brownian motion from the knowledge of its laplace transform this knowledge combined with the method of maximum entropy yields quite good reconstructions the aim of this work is to extend the previous analysis in two directions on one hand we consider diffusions with non constant coefficients this forces us to determine the laplace transform numerically or by means of simulations on the other hand and this is the gist of this note as numerical problems involve errors we consider as well two possible extensions of the maximum entropy procedure which allow us to incorporate those errors into the probability reconstruction process

reduced order observer in the sliding mode control of nonlinear nonaffine systems the note considers the variable structure control of nonlinear known nonaffine systems when the state vector is not completely available and the use of observers is required the strategy of introducing integrators in the input channel is exploited to enlarge the class of tractable control systems a new reduced order observer is proposed and conditions are found under which it is proven the convergence to the unique ideal solution of both system and observer the control problem is solved by forcing a sliding regime for the observer while satisfying an exponential stability criterion for the observation error state equation

sharp asymptotics for the quasi stationary distribution of birth and death processes we study a general class of birth and death processes with state space mathbb n that describes the size of a population going to extinction with probability one this class contains the logistic case the scale of the population is measured in terms of a carrying capacity k when k is large the process is expected to stay close to its deterministic equilibrium during a long time but ultimately goes extinct our aim is to quantify the behavior of the process and the mean time to extinction in the quasi stationary distribution as a function of k for large k we also give a quantitative description of this quasi stationary distribution it turns out to be close to a gaussian distribution centered about the deterministic long time equilibrium when k is large our analysis relies on precise estimates of the maximal eigenvalue of the corresponding eigenvector and of the spectral gap of a self adjoint operator associated with the semigroup of the process

catch estimation in the presence of declining catch rate due to gear saturation summary one strategy for estimating total catch is to employ two separate surveys that independently estimate total fishing effort and catch rate with the estimator for total catch formed by their product survey designs for estimating catch rate often involve interviewing the fishermen during their fishing episodes such roving designs result in incomplete episode data and characteristically have employed a model in which the catch rate is assumed to be constant over time this article extends the problem to that of estimating total catch in the presence of a declining catch rate due e g to gear saturation using a gill net fishery as an example a mean of ratios type of estimator for the catch rate together with its variance estimator are developed their performance is examined using simulations with special attention given to effects of restrictions on the roving survey window finally data from a fraser river gill net fishery are used to illustrate the use of the proposed estimator and to compare results with those from an estimator based on a constant catch rate

preferential attachment in sexual networks many social networks are characterized by a highly uneven distribution of links the observed skewed distributions have in several cases been attributed to preferential attachment pa a tendency among nodes in a growing network to form new links preferentially to nodes with high numbers of links we test the pa conjecture in sexual contact networks a maximum likelihood estimation based expectation maximization fitting technique is used to model new partners over a 1 year period based on the number of partners in foregoing periods of 2 years 4 years and lifetime the pa model is modified to account for individual heterogeneity in the inclination to find new partners and fitted to norwegian survey data on heterosexual men and women results show evidence of nonrandom sublinear pa when comparing the growth in 3 to 5 year periods the potential implications of these findings are discussed

towards a stability theory of general hybrid dynamical systems in recent work we proposed a general model for hybrid dynamical systems whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time for such systems we introduced the usual concepts of lyapunov and lagrange stability we showed that it is always possible to transform this class of hybrid dynamical systems into another class of dynamical systems with equivalent qualitative properties but defined on real time r 0 the motions of this class of systems are in general discontinuous this class of systems may be finite or infinite dimensional for the above discontinuous dynamical systems and hence for the above hybrid dynamical systems we established the principal lyapunov stability theorems as well as lagrange stability theorems for some of these we also established converse theorems we demonstrated the applicability of these results by means of specific classes of hybrid dynamical systems in the present paper we continue the work described above in doing so we first develop a general comparison theory for the class of hybrid dynamical systems resp discontinuous dynamical systems considered herein making use of stability preserving mappings we then show how these results can be applied to establish some of the principal lyaponov stability theorems for the latter we also state and prove a converse theorem not considered previously finally to demonstrate the applicability of our results we consider specific examples throughout the paper

control of nonlinear variable structure systems etude des systemes de commande decrits par des equations d etat extension de la theorie des systemes de commande discontinue a structure variable a quelques cas non lineaires

regime switching volatility calibration by the baum welch method regime switching volatility models provide a tractable method of modelling stochastic volatility currently the most popular method of regime switching calibration is the hamilton filter we propose using the baum welch algorithm an established technique from engineering to calibrate regime switching models instead we demonstrate the baum welch algorithm and discuss the significant advantages that it provides compared to the hamilton filter we provide computational results of calibrating and comparing the performance of the baum welch and the hamilton filter to s p 500 and nikkei 225 data examining their performance in and out of sample

approximability properties for second order sliding mode control systems new definitions of approximability are presented for nonlinear second order sliding mode control systems such robustness properties are compared with those already known for first order methods sufficient conditions are obtained for second order regularization a sliding error estimate is derived and some relevant examples are discussed

tensor product markov chains abstract we analyze families of markov chains that arise from decomposing tensor products of irreducible representations this illuminates the burnside brauer theorem for building irreducible representations the mckay correspondence and pitman s 2 m x theorem the chains are explicitly diagonalizable and we use the eigenvalues eigenvectors to give sharp rates of convergence for the associated random walks for modular representations the chains are not reversible and the analytical details are surprisingly intricate in the quantum group case the chains fail to be diagonalizable but a novel analysis using generalized eigenvectors proves successful

non linear unstable response of hanging chains abstract a chain hanging under its own weight is the canonical system to study the transition from taut to low tension chain behaviour the three dimensional non linear dynamics of a hanging chain driven harmonically from the top demonstrate rich dynamic behaviour as a function of frequency and forcing level the response may also result in catastrophic collapse at the lower end the driving mechanism is the loss of tension near the lower end when the response is dominated by large impulse like tension peaks the subsequent behaviour is that of an impulsively loaded cable characteristic of low tension lines

analytic treatment of consensus achievement in the single type zealotry voter model abstract we introduce zealots of one opinion in the voter model on a complete graph and examine how they affect consensus achievement using first step analysis for markov chains to obtain an exact solution we find that the mean consensus time scales with the population size n increasing the number of zealots z will decrease the consensus time in a power law fashion for large z the mean magnetization was also analytically obtained and was found to contain an exponential dependence on z the dynamics for the complete graph are qualitatively similar to those obtained in another study for the barabasi albert network in general the existence of zealots serves to hasten consensus except in the case where only a few zealots oppose the vast majority

probability of stochastic processes and spacetime geometry abstract we made a first attempt to associate a probabilistic description of stochastic processes like birth death processes with spacetime geometry in the schwarzschild metrics on distance scales from the macro to the micro domains we idealize an ergodic system in which system states communicate through a curved path composed of transition arrows where each arrow corresponds to a positive analogous birth or death rate

spectral theory of metastability and extinction in a branching annihilation reaction we apply the spectral method recently developed by the authors to calculate the statistics of a reaction limited multistep birth death process or chemical reaction that includes as elementary steps branching a 2a and annihilation 2a 0 the spectral method employs the generating function technique in conjunction with the sturm liouville theory of linear differential operators we focus on the limit when the branching rate is much higher than the annihilation rate and obtain accurate analytical results for the complete probability distribution including large deviations of the metastable long lived state and for the extinction time statistics the analytical results are in very good agreement with numerical calculations furthermore we use this example to settle the issue of the lacking boundary condition in the spectral formulation

filling of a poisson trap by a population of random intermittent searchers we extend the continuum theory of random intermittent search processes to the case of n independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi infinite track each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state we assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process the hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target the particle is removed from the system after delivering its cargo as a further generalization of previous models we assume that up to n successive particles can find the target and deliver its cargo assuming that the rate of target detection scales as 1 n we show that there exists a well defined mean field limit n rightarrow infty in which the stochastic model reduces to a deterministic system of linear reaction hyperbolic equations for the concentrations of particles in each of the internal states these equations decouple from the stochastic process associated with filling the target with cargo the latter can be modeled as a poisson process in which the time dependent rate of filling lambda t depends on the concentration of stationary particles within the target domain hence we refer to the target as a poisson trap we analyze the efficiency of filling the poisson trap with n particles in terms of the waiting time density f n t the latter is determined by the integrated poisson rate mu t int 0 t lambda s ds which in turn depends on the solution to the reaction hyperbolic equations we obtain an approximate solution for the particle concentrations by reducing the system of reaction hyperbolic equations to a scalar advection diffusion equation using a quasi steady state analysis we compare our analytical results for the mean field model with monte carlo simulations for finite n we thus determine how the mean first passage time mfpt for filling the target depends on n and n

non linear shot noise levy noah joseph abstract we introduce and study a generic non linear shot noise system model shots of random magnitudes arrive to the system stochastically following an arbitrary time homogeneous poisson point process after hitting the system the magnitude of an arriving shot decays to zero the decay is governed by an arbitrary differential equation dynamics shots are independent and their overall effect on the system is additive the system s noise level at time t equals the sum of the magnitudes at time t of all the shots arriving to the system prior to time t the resulting shot noise is i a levy process when the decay dynamics are degenerate ii a levy driven ornstein uhlenbeck process when the decay dynamics are linear and iii a stationary non markov process when the decay dynamics are non linear the resulting shot noise admits an underlying levy structure which we explicitly compute and can yield both the noah effect and the joseph effect closed form analytic formulae for various statistics are derived including the log laplace transform and cumulants of the stationary noise level the process auto covariance function and the process range of dependence

the time rescaling theorem and its application to neural spike train data analysis measuring agreement between a statistical model and a spike train data series that is evaluating goodness of fit is crucial for establishing the model s validity prior to using it to make inferences about a particular neural system assessing goodness of fit is a challenging problem for point process neural spike train models especially for histogram based models such as perstimulus time histograms psth and rate functions estimated by spike train smoothing the time rescaling theorem is a well known result in probability theory which states that any point process with an integrable conditional intensity function may be transformed into a poisson process with unit rate we describe how the theorem may be used to develop goodness of fit tests for both parametric and histogram based point process models of neural spike trains we apply these tests in two examples a comparison of psth inhomogeneous poisson and inhomogeneous markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers inhomogeneous poisson inhomogeneous gamma and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity to help make the logic behind the time rescaling theorem more accessible to researchers in neuroscience we present a proof using only elementary probability theory arguments we also show how the theorem may be used to simulate a general point process model of a spike train our paradigm makes it possible to compare parametric and histogram based neural spike train models directly these results suggest that the time rescaling theorem can be a valuable tool for neural spike train data analysis

application of the generalized α method to the time integration of the cable dynamics equations abstract the box method is a popular finite difference scheme for solving the cable dynamics equations in ocean engineering applications in this paper we analyze the shortcomings of the temporal integration defined by the box method and propose a new procedure that retains the box method s spatial discretization but employs the generalized method for temporal discretization the stability and accuracy of the generalized method as applied to the cable dynamics equations are developed this analysis procedure demonstrates the formulation of the semi discrete governing equations using spatial finite differences and the applicability of amplification matrix stability analysis to finite difference problems an example is presented that demonstrates the robustness of the new approach

directed random walk with random restarts the sisyphus random walk in this paper we consider a particular version of the random walk with restarts random reset events which suddenly bring the system to the starting value we analyze its relevant statistical properties like the transition probability and show how an equilibrium state appears formulas for the first passage time high water marks and other extreme statistics are also derived we consider counting problems naturally associated with the system finally we indicate feasible generalizations useful for interpreting different physical effects

nonlinear system stabilization via hierarchical switching control a nonlinear control system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed specifically using equilibria dependent lyapunov functions a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems the switching nonlinear controller architecture is designed based on a generalized lower semicontinuous lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria the proposed framework provides a rigorous alternative to designing gain scheduled feedback controllers and guarantees local and global closed loop system stability for general nonlinear systems

on the dynamical sliding mode control of nonlinear systems the consequences of the differential algebraic approach in the sliding mode control of nonlinear single input single output systems are reviewed in tutorial fashion input dependent sliding surfaces possibly including time derivatives of the input signal are shown to arise naturally from elementary differential algebraic results pertaining to the fliess s generalized controller canonical forms of nonlinear systems this class of switching surfaces generally leads to chattering free dynamically synthesized sliding regimes in which the highest time derivative of the input signal undergoes all the bang bang type discontinuities examples illustrating the obtained results are also included

real states of stable sliding mode control systems states of nonlinear sliding mode control systems are considered which approximately verify the sliding condition on the unbounded time horizon if the equivalent control achieves uniform exponential stability it is shown that such real states are ultimately bounded with arbitrarily small bound provided the sliding error is sufficiently small the proof requires a new converse lyapunov theorem for constrained motions

dynamic output feedback for observed variable stucture control systems abstract a global exponential observer is built explicitly for some classes of nonlinear variable structure observed control systems by using piecewise continuous output feedback control laws or the continuous equivalent control for the observer the unavailable state vector is asymptotically kept on the sliding manifold with exponential decaying error some explicit examples are presented

convergence of percolation probability functions to cumulative distribution functions on square lattices with 1 0 neighborhood abstract we consider a percolation model on square lattices with sites weighted by beta distributed random variables s beta a b with a positive real parameters a 0 and b 0 using the monte carlo method we estimate the percolation probability p as a relative frequency p averaged over the target subset of sites on a square lattice as a result of the comparative analysis we formulate two empirical hypotheses the first on the correspondence of percolation thresholds p c to p 0 quantiles where level p 0 0 592746 coincides with the percolation threshold for the site percolation model on a square lattice of random variables s i weighing sites of the square lattice and the second on the convergence of statistical estimates of percolation probability functions p p to cumulative distribution functions f s i p of these variables s i for the supercritical values of the occupation probability p p c

asymptotic linearization on uncertain systems by variable structure control abstract a nonlinear control system with uncertain dynamics described by a single ordinary differential equation with scalar control and available state is given based on knowledge of upper and lower estimates of the unknown dynamics we show that the system can be transformed to an asymptotically equivalent linear model arbitrarily fixed described by a single linear ordinary differential equation of the same order by using an explicitly described discontinuous feedback control law of variable structure type the linear behaviour is obtained up to an arbitrarily fast exponentially decaying error term

estimation of current reliability in a duane based reliability growth model in this article i investigate the statistical inference concerning the current field stage reliability of a reliability growth model the model assuming a step intensity structure evolves from the physical consideration of the duane learning curve property and incorporates the effect of a testanalyze and fix program that is typically undertaken in a developmental testing program both exact and large sample distributional results are derived for the maximum likelihood and the least squares estimators of the current intensity under the assumption that the step intensity model represents the reality i provide an assessment of the extent of misspecification when the widely used power law process model is fit to the failure data of a system experiencing recurrent failures extensive simulation results are carried out to supplement the theoretical findings an illustration with a dataset is provided as a demonstration of the application of the inference results

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

simplex methods for nonlinear uncertain sliding mode control we develop a new analysis of the behavior of simplex control methods applied to multiple input multiple output nonlinear control systems under uncertainties according to such sliding mode control methods the control vector is constrained to belong to a finite set of fixed or varying vectors with an appropriate switching logic to guarantee the specified sliding condition bounded uncertainties acting on the nominal system are allowed the proposed sliding control methodology relies on the knowledge of the nominal system only we prove rigorously the convergence of these methods to the sliding manifold in a finite time under explicit quantitative conditions on the system parameters and the available bounds of the uncertainty application to a robotic problem is discussed and a nonlinear example is presented