the geometric structure of unit dual quaternion with application in kinematic control abstract in this paper the geometric structure especially the lie group related properties of unit dual quaternion is investigated the exponential form of unit dual quaternion and its approximate logarithmic mapping are derived correspondingly lie group and lie algebra on unit dual quaternions and the approximate logarithms are explored respectively afterwards error and metric based on unit dual quaternion are given which naturally result in a new kinematic control model with unit dual quaternion descriptors finally as a case study a generalized proportional control law using unit dual quaternion is developed

dynkin s isomorphism theorem and the ray knight theorems in the case of diffusions we show that the isomorphism theorem of dynkin and the ray knight theorems can be derived from each other our proof uses additivity properties of squared bessel processes and an absolute continuity relation between squared bessel processes of dimensions one and three

convergence of vertex reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model in this paper we define an extension of the supersymmetric hyperbolic nonlinear sigma model introduced by zirnbauer we show that it arises as a weak joint limit of a time changed version introduced by sabot and tarres of the vertex reinforced jump process it describes the asymptotics of rescaled crossing numbers rescaled fluctuations of local times asymptotic local times on a logarithmic scale endpoints of paths and last exit trees

a generalization of permanents and determinants a method is developed for expanding arbitrary powers of the characteristic polynomial of a matrix the coefficients are expressed in terms of matrix functions generalizing those of the permanent and determinant the expansions have applications in probability theory

locating multiple optima using particle swarm optimization many scientific and engineering applications require optimization methods to find more than one solution to multimodal optimization problems this paper presents a new particle swarm optimization pso technique to locate and refine multiple solutions to such problems the technique nichepso extends the inherent unimodal nature of the standard pso approach by growing multiple swarms from an initial particle population each subswarm represents a different solution or niche optimized individually the outcome of the nichepso algorithm is a set of particle swarms each representing a unique solution experimental results are provided to show that nichepso can successfully locate all optima on a small set of test functions these results are compared with another pso niching algorithm lbest pso and two genetic algorithm niching approaches the influence of control parameters is investigated including the relationship between the swarm size

on the fock space representation of functionals of the occupation field and their renormalization on fournit une representation du champ d occupation et de ses puissances renormalisees dans un bon espace de fock

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

a characterization of the infinitely divisible squared gaussian processes we show that up to multiplication by constants a gaussian process has an infinitely divisible square if and only if its covariance is the green function of a transient markov process

joint density for the local times of continuous time markov chains we investigate the local times of a continuous time markov chain on an arbitrary discrete state space for fixed finite range of the markov chain we derive an explicit formula for the joint density of all local times on the range at any fixed time we use standard tools from the theory of stochastic processes and finite dimensional complex calculus we apply this formula in the following directions 1 we derive large deviation upper estimates for the normalized local times beyond the exponential scale 2 we derive the upper bound in varadhan s lemma for any measurable functional of the local times and 3 we derive large deviation upper bounds for continuous time simple random walk on large subboxes of z d tending to z d as time diverges we finally discuss the relation of our density formula to the ray knight theorem for continuous time simple random walk on z which is analogous to the well known ray knight description of brownian local times

a hybrid particle swarm optimization variable neighborhood search algorithm for constrained shortest path problems abstract in this paper a well known np hard problem the constrained shortest path problem is studied as efficient metaheuristic approaches are required for its solution a new hybridized version of particle swarm optimization algorithm with variable neighborhood search is proposed for solving this significant combinatorial optimization problem particle swarm optimization pso is a population based swarm intelligence algorithm that simulates the social behavior of social organisms by using the physical movements of the particles in the swarm a variable neighborhood search vns algorithm is applied in order to optimize the particles position in the proposed algorithm the particle swarm optimization with combined local and global expanding neighborhood topology psolgent a different equation for the velocities of particles is given and a novel expanding neighborhood topology is used another issue in the application of the vns algorithm in the constrained shortest path problem is which local search algorithms are suitable from this problem in this paper a number of continuous local search algorithms are used the algorithm is tested in a number of modified instances from the tsplib and comparisons with classic versions of pso and with other versions of the proposed method are performed also the results of the algorithm are compared with the results of a number of metaheuristic and evolutionary algorithms the results obtained are very satisfactory and strengthen the efficiency of the algorithm

a ray knight theorem for symmetric markov processes let x be a strongly symmetric recurrent markov process with state space s and let l t x denote the local time of x at x in s for a fixed element 0 in the state space s let tau t inf s l 0 s t the 0 potential density u 0 x y of the process x killed at t 0 inf s x s 0 is symmetric and positive definite let eta eta x x in s be a mean zero gaussian process with covariance e eta eta x eta y u 0 x y the main result of this paper is the following generalization of the classical second ray knight theorem for any b in r and t 0 l x tau t frac 1 2 eta x b 2 x in s frac 1 2 eta x sqrt 2 b 2 2 x in s text in law a version of this theorem is also given when x is transient

vertex reinforced jump processes on trees and finite graphs we study the continuous time process on the vertices of the b ary tree which jumps to each nearest neighbor vertex at the rate of the time already spent at that vertex times plus 1 where is a positive constant we show that for fixed b 1 if is large enough the process is transient and if is close enough to zero it is recurrent related results for some other graphs and trees are also proved

inter particle communication and search dynamics of lbest particle swarm optimizers an analysis particle swarm optimization pso is arguably one of the most popular nature inspired algorithms for real parameter optimization at present the existing theoretical research on pso focuses on the issues like stability convergence and explosion of the swarm however all of them are based on the gbest global best communication topology which usually is susceptible to false or premature convergence over multi modal fitness landscapes the present standard pso spso 2007 uses an lbest local best topology where a particle is stochastically attracted not towards the best position found in the entire swarm but towards the best position found by any particle in its topological neighborhood this article presents a first step towards a probabilistic analysis of the particle interaction and information exchange in an lbest pso with variable random neighborhood topology as found in spso 2007 it addresses issues like the distribution of particles over neighborhoods the probability distributions of the social and cognitive terms in lbest model and the explorative power of the lbest pso it also presents a state space model of the lbest pso and draws important conclusions regarding the stability and convergence of the particle dynamics in the light of control theory

a penalty function heuristic for the resource constrained shortest path problem abstract the resource constrained shortest path problem rcsp consists of finding the shortest path between two nodes of an assigned network with the constraint that traversing an arc of the network implies the consumption of certain limited resources in this paper we propose a new heuristic for the solution of the rcsp problem in medium and large scale networks it is based on the extension to the discrete case of the penalty function heuristic approach for the fast e approximate solution of difficult large scale continuous linear programming problems computational experience on test instances has shown that the proposed penalty function heuristic pfh is very effective in the solution of medium and large scale rcsp instances for all the tests reported it provides very good upper bounds in many cases the optimal solution in less than 26 iterations where each iteration requires only the computation of a shortest path

unit dual quaternion based feedback linearization tracking problem for attitude and position dynamics abstract this paper provides a unified solution for the attitude and position tracking problem of a rigid body in 3 dimensional space using the concept of the unit dual quaternion the error dynamics described by a unit dual quaternion are deduced after the dual quaternion based dynamics of a single rigid body are given then by utilizing the feedback linearization principle a unit dual quaternion based tracker is proposed based on the error dynamics which is proven to render the equilibrium point of the closed loop system asymptotically stable and includes the attitude and position regulation problems as particular cases furthermore to solve the two equilibria problem a switching parameter is introduced to improve the tracker which causes the system to converge to the nearer equilibrium with a shorter path both the trackers uniquely deal with the rotational and translational dynamics simultaneously with non singularity and maintain the interconnection between rotation and translation finally the proposed control schemes with applications to the regulation problem and the tracking problem are simulated to illustrate the theoretical results

continuous time vertex reinforced jump processes we study the continuous time integer valued process which jumps to each of its two nearest neighbors at the rate of one plus the total time the process has previously spent at that neighbor we show that the proportion of the time before t which this process spends at integers j converges to positive random variables v j which sum to one and whose joint distribution is explicitly described we also show

further passivity results for the attitude control problem in this paper we establish passivity for the system which describes the attitude motion of a rigid body in terms of minimal three dimensional kinematic parameters in particular we show that linear asymptotically stabilizing controllers and control laws without angular velocity measurements follow naturally from these passivity properties the results of this paper extend similar results for the case of the nonminimal euler parameters

unit quaternion based output feedback for the attitude tracking problem in this note we propose a quaternion based dynamic output feedback for the attitude tracking problem of a rigid body without velocity measurement our approach consists of introducing an auxiliary dynamical system whose output which is also a unit quaternion is used in the control law together with the unit quaternion representing the attitude tracking error roughly speaking the necessary damping that would have been achieved by the direct use of the angular velocity can be achieved in our approach by the vector part mathtilde q of the error signal between the output of the auxiliary system and the unit quaternion tracking error the resulting velocity free control scheme guarantees almost global asymptotic stability which is as strong as the topology of the motion space can permit in the regulation case our control law is a pure quaternion feedback i e consisting of two terms that are vector parts of unit quaternion and hence the control torques are naturally bounded by the control gains simulation results are provided to show the effectiveness of the proposed control scheme

inverting ray knight identity we provide a short proof of the ray knight second generalized theorem using a martingale which can be seen on the positive quadrant as the radon nikodym derivative of the reversed vertex reinforced jump process measure with respect to the markov jump process with the same conductances next we show that a variant of this process provides an inversion of that ray knight identity we give a similar result for the ray knight first generalized theorem

phase transition for the once reinforced random walk on mathbb z d like trees in this short paper we consider the once reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk on each of these trees we prove that there exists an explicit critical parameter a 0 such that the once reinforced random walk is almost surely recurrent if a a 0 and almost surely transient if a a 0 this provides the first examples of phase transition for the once reinforced random walk

markov loops and renormalization we study the poissonnian ensembles of markov loops and the associated renormalized self intersection local times

cover times blanket times and majorizing measures we exhibit a strong connection between cover times of graphs gaussian processes and talagrand s theory of majorizing measures in particular we show that the cover time of any graph g is equivalent up to universal constants to the square of the expected maximum of the gaussian free field on g scaled by the number of edges in g this allows us to resolve a number of open questions we give a deterministic polynomial time algorithm that computes the cover time to within an o 1 factor for any graph answering a question of aldous and fill 1994 we also positively resolve the blanket time conjectures of winkler and zuckerman 1996 showing that for any graph the blanket and cover times are within an o 1 factor the best previous approximation factor for both these problems was o loglogn 2 for n vertex graphs due to kahn kim lovasz and vu 2000

random interlacements and the gaussian free field we consider continuous time random interlacements on zd d 3 and characterize the distribution of the corresponding stationary random field of occupation times when d 3 we relate this random field to the two dimensional gaussian free field pinned at the origin by looking at scaled differences of occupation times of long rods by random interlacements at appropriately tuned levels in the main asymptotic regime a scaling factor appears in the limit which is independent of the free field and distributed as the time marginal of a zero dimensional bessel process for arbitrary d 3 we also relate the field of occupation times at a level tending to infinity to the d dimensional gaussian free field

on the transience of processes defined on galton watson trees we introduce a simple technique for proving the transience of certain processes defined on the random tree mathcal g generated by a supercritical branching process we prove the transience for once reinforced random walks on mathcal g that is a generalization of a result of durrett kesten and limic probab theory related fields 122 2002 567 592 moreover we give a new proof for the transience of a family of biased random walks defined on mathcal g other proofs of this fact can be found in ann probab 16 1988 1229 1241 and ann probab 18 1990 931 958 as part of more general results a similar technique is applied to a vertex reinforced jump process a by product of our result is that this process is transient on the 3 ary tree davis and volkov probab theory related fields 128 2004 42 62 proved that a vertex reinforced jump process defined on the b ary tree is transient if b 4 and recurrent if b 1 the case b 2 is still open

the attitude control problem a general framework for the analysis of the attitude tracking control problem for a rigid body is presented a large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body the controllers share the common structure of a proportional derivative feedback plus some feedforward which can be zero the model independent case the coriolis torque compensation or an adaptive compensation these controller structures are compared in terms of the requirement on the a priori model information guaranteed transient performance and robustness the global stability of the luh walker paul robot end effector controller is also analyzed in this framework

random point fields associated with certain fredholm determinants i fermion poisson and boson point processes we introduce certain classes of random point fields including fermion and boson point processes which are associated with fredholm determinants of certain integral operators and study some of their basic properties limit theorems correlation functions palm measures etc also we propose a conjecture on an analogue of the determinant and permanent

new perspectives on ray s theorem for the local times of diffusions a new global isomorphism theorem is obtained that expresses the local times of transient regular diffusions under px y in terms of related gaussian processes this theorem immediately gives an explicit description of the local times of diffusions in terms of 0th order squared bessel processes similar to that of eisenbaum and ray s classical description in terms of certain randomized fourth order squared bessel processes the proofs given are very simple they depend on a new version of kac s lemma for h transformed markov processes and employ little more than standard linear algebra the global isomorphism theorem leads to an elementary proof of the markov property of the local times of diffusions and to other recent results about the local times of general strongly symmetric markov processes the new version of kac s lemma gives simple short proofs of dynkin s isomorphism theorem and an unconditioned isomorphism theorem due to eisenbaum