ensemble of differential evolution variants abstract differential evolution de is one of the most popular and efficient evolutionary algorithms for numerical optimization and it has gained much success in a series of academic benchmark competitions as well as real applications recently ensemble methods receive an increasing attention in designing high quality de algorithms however previous efforts are mainly devoted to the low level ensemble of mutation strategies of de this study investigates the high level ensemble of multiple existing efficient de variants a multi population based framework mpf is proposed to realize the ensemble of multiple de v ariants to derive a new algorithm named edev for short edev consists of three highly popular and efficient de variants namely jade adaptive differential evolution with optional external archive code differential evolution with composite trial vector generation strategies and control parameters and epsde differential evolution algorithm with ensemble of parameters and mutation strategies the whole population of edev is partitioned into four subpopulations including three indicator subpopulations with smaller size and one reward subpopulation with much larger size each constituent de variant in edev owns an indicator subpopulation after every predefined generations the most efficient constituent de variant is determined and the reward subpopulation is assigned to that best performed de variant as an extra reward through this manner the most efficient de variant is expected to obtain the most computational resources during the optimization process in addition the population partition operator is triggered at every generation which results in timely information sharing and tight cooperation among the component de variants extensive experiments and comparisons have been done based on the cec2005 and cec2014 benchmark suit which shows that the overall performance of edev is superior to several state of the art peer de variants the success of edev reveals that through an appropriate ensemble framework different de variants of different merits can support one another to cooperatively solve optimization problems

disturbed exploitation compact differential evolution for limited memory optimization problems this paper proposes a novel and unconventional memetic computing approach for solving continuous optimization problems characterized by memory limitations the proposed algorithm unlike employing an explorative evolutionary framework and a set of local search algorithms employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators the proposed memetic computing approach is based on a populationless compact evolutionary framework which instead of processing a population of solutions handles its statistical model this evolutionary framework is based on a differential evolution which cooperatively employs two exploitative search operators the first is based on a standard differential evolution mutation and exponential crossover and the second is the trigonometric mutation these two search operators have an exploitative action on the algorithmic framework and thus contribute to the rapid convergence of the virtual population towards promising candidate solutions the action of these search operators is counterbalanced by a periodical stochastic perturbation of the virtual population which has the role of disturbing the excessively exploitative action of the framework and thus inhibits its premature convergence the proposed algorithm namely disturbed exploitation compact differential evolution is a simple and memory wise cheap structure that makes use of the memetic computing paradigm in order to solve complex optimization problems the proposed approach has been tested on a set of various test problems and compared with state of the art compact algorithms and with some modern population based meta heuristics numerical results show that disturbed exploitation compact differential evolution significantly outperforms all the other compact algorithms present in literature and reaches a competitive performance with respect to modern population algorithms including some memetic approaches and complex modern differential evolution based algorithms in order to show the potential of the proposed approach in real world applications disturbed exploitation compact differential evolution has been implemented for performing the control of a space robot by simulating the implementation within the robot micro controller numerical results show the superiority of the proposed algorithm with respect to other modern compact algorithms present in literature

reducing stochasticity in the north atlantic oscillation index with coupled langevin equations we present a critical investigation of the functional relationship between the two pressure time series routinely used to define the index characterizing the north atlantic oscillation nao well known to regulate global climate variability and change first by a standard markov analysis we show that the standard nao index based on the pressure difference is not optimal in the sense of producing sufficiently reliable forecasts because it contains a dominating stochastic term in the corresponding langevin equation then we introduce a variationally optimized markov analysis involving two coupled langevin equations tailored to produce a nao quasi index having the desired minimum possible stochasticity the variationally optimized markov analysis is very general and can be applied in other physical situations involving two or more time series

swarm intelligence and evolutionary algorithms the popularity of metaheuristics especially swarm intelligence and evolutionary algorithms has increased rapidly over the last two decades numerous algorithms are proposed each year and progressively more novel applications are being found however different metaheuristics are often compared by their performance on problems with an arbitrarily fixed number of allowed function calls there are surprisingly few papers that explore the relationship between the relative performance of numerous metaheuristics on versatile numerical real world problems and the number of allowed function calls in this study the performance of 33 various metaheuristics proposed between 1960 and 2016 have been tested on 22 numerical real world problems from different fields of science with the maximum number of function calls varying between 5000 and 500 000 it is confirmed that the algorithms that succeed in comparisons when the computational budget is low are among the poorest performers when the computational budget is high and vice versa among the tested variants particle swarm optimization algorithms and some new types of metaheuristics perform relatively better when the number of allowed function calls is low whereas differential evolution and genetic algorithms perform better relative to other algorithms when the computational budget is large it is difficult to find any metaheuristic that would perform adequately over all of the numbers of function calls tested it was also found that some algorithms may become completely unreliable on specific real world problems even though they perform reasonably on others

cluster based population initialization for differential evolution frameworks this article proposes a procedure to perform an intelligent initialization for population based algorithms the proposed pre processing procedure namely cluster based population initialization cbpi consists of three consecutive stages at the first stage the individuals belonging to a randomly sampled population undergo two subsequent local search algorithms i e a simple local search that performs moves along the axes and rosenbrock algorithm at the second stage the solutions processed by the two local searches undergo the k means clustering algorithm and are grouped into sets on the basis of their euclidean distance at the third stage the best individuals belonging to each cluster are saved into the initial population of a generic optimization algorithm if the population has not been yet filled the other individuals of the population are sampled within the clusters by using a fitness based probabilistic criterion this three stage procedure implicitly performs an initial screening of the problem features in order to roughly estimate the most interesting regions of the decision space the proposed cbpi has been tested on multiple classical and modern differential evolution variants on a wide array of test problems and dimensionality values as well as on a real world problem the proposed intelligent sampling appears to have a significant impact on the algorithmic functioning as it consistently enhances the performance of the algorithms with which it is integrated

on the scattering length spectrum for real analytic obstacles abstract it follows trivially from old results of majda and lax phillips that connected obstacles k with real analytic boundary in r n are uniquely determined by their scattering length spectrum in this paper we prove a similar result in the general case i e k may be disconnected imposing some non degeneracy conditions on k and assuming that its trapping set does not topologically divide s c where c is a sphere containing k it is shown that the conditions imposed on k are fulfilled for instance when k is a finite disjoint union of strictly convex bodies

stochastic heart rate model can reveal pathologic cardiac dynamics a simple one dimensional langevin type stochastic difference equation can simulate the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical of gaussian noise and both parts can be directly determined from measured heart rate data data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points studies of 15 congestive heart failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects results directly indicate that pathologic situations simplify the heart rate control system

how novel is the novel black hole optimization approach due to abundance of novel optimization algorithms in recent years the problem of large similarities among methods that are named differently is becoming troublesome and general the question arises if the novel source of inspiration is sufficient to breed an optimization algorithm with a novel name even if its search properties are almost the same as or are even a simplified variant of the search properties of an older and well known method in this paper it is rigidly shown that the recently proposed heuristic approach called the black hole optimization is in fact a simplified version of particle swarm optimization with inertia weight additionally because a large number of metaheuristics developed during the last decade is claimed to be nature inspired a short discussion on inspirations of optimization algorithms is presented

langevin equations from time series we discuss the link between the approach to obtain the drift and diffusion of one dimensional langevin equations from time series and pope and ching s relationship for stationary signals the two approaches are based on different interpretations of conditional averages of the time derivatives of the time series at given levels the analysis provides a useful indication for the correct application of pope and ching s relationship to obtain stochastic differential equations from time series and shows its validity in a generalized sense for nondifferentiable processes originating from langevin equations

travelling times in scattering by obstacles abstract the paper deals with some problems related to recovering information about an obstacle in a euclidean space from certain measurements of lengths of generalised geodesics in the exterior of the obstacle the main result is that if two obstacles satisfy some generic regularity conditions and have almost the same travelling times then the generalised geodesic flows in their exteriors are conjugate on the non trapping part of their phase spaces with a time preserving conjugacy apart from that a constructive procedure is described that shows how to recover an obstacle consisting of two convex domains in the plane from travelling times

travelling times in scattering by obstacles in curved space abstract we consider travelling times of billiard trajectories in the exterior of an obstacle k on a two dimensional riemannian manifold m we prove that given two obstacles with almost the same travelling times the generalised geodesic flows on the non trapping parts of their respective phase spaces will have a time preserving conjugacy moreover if m has non positive sectional curvature we prove that if k and l are two obstacles with strictly convex boundaries and almost the same travelling times then k and l are identical

some metaheuristics should be simplified abstract users have a large and constantly increasing number of optimization metaheuristics at their disposal in pursuit of ever better approaches popular and successful methods are often improved a number of times in a row or various methods are hybridized one should however pay attention to whether such deliberately improved or hybridized methods do not become unnecessarily complicated or if some of their elements do not introduce a structural bias in the first case the algorithm should be simplified by eliminating the unneeded elements this will make it more clear to the users and as shown in this study may even improve the results in the second case operators that are responsible for over frequent sampling of some part of the search space have to be removed in this study we address the problem of over complexity of metaheuristics focusing on two joint winners of the cec2016 competition on single objective numerical optimization l shade epsin and umoea ii algorithms it is shown that each of them includes a procedure which introduces a structural bias by attracting population towards the origin o as discussed in the text in the case of seven out of 30 benchmark problems considered in the cec2016 competition the objective function values in the origin o are better than those found by the vast majority of algorithms hence structural bias affects the results obtained by l shade epsin and umoea ii in this work we simplify both algorithms by removing operators that are the main cause of structural bias further we show that in the l shade epsin algorithm the ensemble sinusoidal adaptation mechanism of control parameter f that is used during the first half of the search is not needed slightly better results on both artificial benchmarks used in the cec2016 competition and on a wide set of real world problems may be obtained if during that period of the search the value of f is simply set to 0 5 such a simplified algorithm is competitive against a large number of metaheuristics and may be much easier for the users to understand

on a general link between anomalous diffusion and nonextensivity stochastic processes of systems with composable entropy measures are studied the processes are described by fokker planck equations which are nonlinear with respect to their probability densities and whose diffusion coefficients are derived from the entropy measures in questions in nonextensive extensive systems anomalous normal diffusion is found

on the marked length spectrum of generic strictly convex billiard tables in this paper we show that for a generic strictly convex domain one can recover the eigendata corresponding to aubry mather periodic orbits of the induced billiard map from the maximal marked length spectrum of the domain

santalo s formula and stability of trapping sets of positive measure abstract billiard trajectories broken generalised geodesics are considered in the exterior of an obstacle k with smooth boundary on an arbitrary riemannian manifold we prove a generalisation of the well known santalo s formula as a consequence it is established that if the set of trapped points has positive measure then for all sufficiently small smooth perturbations of the boundary of k the set of trapped points for the new obstacle obtained in this way also has positive measure more generally the measure of the set of trapped points depends continuously on perturbations of the obstacle k some consequences are derived in the case of scattering by an obstacle k in i r n for example it is shown that for a large class of obstacles k the volume of k is uniquely determined by the average travelling times of scattering rays in the exterior of k

rigidity of the scattering length spectrum in this paper we consider properties of obstacles satisfying some non degeneracy conditions that can be recovered from the scattering length spectrum sls clearly the latter tells us whether the obstacle k is trapping or non trapping if the set of trapped points is relatively small then the sls also determines the volume of the obstacle the number of its connected components and whether its boundary is convex everywhere or it has non trivial concavities under the additional assumption that the curvature of the obstacle does not vanish of infinite order it is proved that from the sls one can recover certain information about the number of reflection points of any simply reflecting ray in the exterior of the obstacle finally for some special classes of obstacles e g star shaped ones it is shown that the sls completely determines the obstacle

qualitative and quantitative analysis of stochastic processes based on measured data i theory and applications to synthetic data analysis of stochastic processes governed by the langevin equation is discussed the analysis is based on a general method for non parametric estimation of deterministic and random terms of the langevin equation directly from given data separate estimation of the terms corresponds to decomposition of process dynamics into deterministic and random components such decomposition provides a basis for qualitative and quantitative analysis of process dynamics in part i the following analysis possibilities are described and illustrated using various synthetic datasets 1 qualitative inspection of the estimated terms presented as fields 2 reconstruction of the deterministic and stochastic evolution of the process and 3 approximation of the deterministic term by an analytical function and quantitative treatment of the equations obtained in part ii these analysis possibilities are applied to experimental datasets from metal cutting and laser beam welding

regarding the rankings of optimization heuristics based on artificially constructed benchmark functions novel evolutionary algorithms are usually tested on sets of artificially constructed benchmark problems such problems are often created to make the search of one global extremum usually minimum tricky in this paper it is shown that benchmarking heuristics on either minimization or maximization of the same set of artificially created functions with equal bounds and number of allowed function calls may lead to very different ranking of tested algorithms as evolutionary algorithms and other heuristic optimizers are developed in order to be applicable to real world problems such result may raise doubts on the practical meaning of benchmarking them on artificial functions as there is little reason that searching for the minimum of such functions should be more important than searching for their maximum thirty optimization heuristics including a number of variants of differential evolution as well as other kinds of evolutionary algorithms particle swarm optimization direct search methods and following the idea borrowed from no free lunch pure random search are tested in the paper some discussion regarding the choice of the mean or the median performance for comparison is addressed and a short debate on the overall performance of particular methods is given

region based memetic algorithm for real parameter optimisation memetic algorithms with an appropriate trade off between the exploration and exploitation can obtain very good results in continuous optimisation that implies the evolutionary algorithm should be focused in exploring the search space while the local search method exploits the achieved solutions to tackle this issue we propose to maintain a higher diversity in the evolutionary algorithm s population by including a niching strategy in the memetic algorithm framework in this work we design a novel niching strategy where the niches divide the search space into hypercubes of equal size called regions forbidding the presence of two solutions in each region the objective is to avoid the competition between the local search and the evolutionary algorithm we tested this niching strategy in a memetic algorithm with local search chaining and obtained significant improvements the resulting model also appeared to be very competitive with state of the art algorithms

the differential ant stigmergy algorithm ant colony optimization aco is a popular swarm intelligence scheme known for its efficiency in solving combinatorial optimization problems however despite some extensions of this approach to continuous optimization high dimensional problems remain a challenge for aco this paper presents an aco based algorithm for numerical optimization capable of solving high dimensional real parameter optimization problems the algorithm called the differential ant stigmergy algorithm dasa transforms a real parameter optimization problem into a graph search problem the parameters differences assigned to the graph vertices are used to navigate through the search space we compare the algorithm results with the results of previous studies on recent benchmark functions and show that the dasa is a competitive continuous optimization algorithm that solves high dimensional problems effectively and efficiently

parallel memetic structures memetic computing mc structures are algorithms composed of heterogeneous operators memes for solving optimization problems in order to address these problems this study investigates and proposes a simple yet extremely efficient structure namely parallel memetic structure pms pms is a single solution optimization algorithm composed of tree operators the first one being a stochastic global search which explores the entire decision space searching for promising regions in analogy with electrical networks downstream of the global search component there is a parallel of two alternative elements i e two local search algorithms with different features in terms of search logic whose purpose is to refine the search in the regions detected by the upstream element the first local search explores the space along the axes while the second performs diagonal movements in the direction of the estimated gradient the pms algorithm despite its simplicity displays a respectable performance compared to that of popular meta heuristics and modern optimization algorithms representing the state of the art in the field thanks to its simple structure pms appears to be a very flexible algorithm for various problem features and dimensionality values unlike modern complex algorithm that are specialized for some benchmarks and some dimensionality values pms achieves solutions with a high quality in various and diverse contexts for example both on low dimensional and large scale problems an application example in the field of magnetic sensors further proves the potentials of the proposed approach this study confirms the validity of the ockham s razor in mc efficiently designed simple structures can perform as well as if not better than complex algorithms composed of many parts

adaptive memetic differential evolution with global and local neighborhood based mutation operators differential evolution de is one of the most popular optimization methods for real valued problems and a large number of its variants have been proposed so far however bringing together different ideas that already led to successful de versions is rare in the literature in the present paper a novel de algorithm is proposed in which three among the most efficient concepts already applied separately within de framework are gathered together namely 1 the adaptation of algorithm control parameters and probabilities of using different mutation strategies 2 the use of nelder mead algorithm as a local search method hybridized with de and 3 the splitting mutation into global and local models when local mutation model is based on the concept of neighborhood of individuals organized on a ring topology the performance of the novel algorithm called adaptive memetic de with global and local neighborhood based mutation operators is compared with 13 different de variants on a set of 25 popular problems which include rotated shifted and hybrid composition functions it is found that although none de algorithm outperforms all the others for the majority of problems on average the proposed approach perform better than all 13 de algorithms selected for comparison the proposed algorithm is another heuristic approach developed to solve optimization problems the question may arise whether proposing novel methods is useful as no free lunch theorems for optimization state that the expected performance of all possible heuristics on all possible problems is equal in the last section of the paper the limitations and implications of no free lunch theorems are discussed based on rich but unfortunately frequently neglected literature a very simple continuous and differentiable minimization problem is proposed for which it is empirically verified that each among considered 14 de algorithms perform poorer than random sampling it is also empirically shown that when all considered de algorithms search for the maximum of the proposed problem they found lower minimum than de algorithms searching for the minimum such result is not unexpected according to no free lunch theorems and should be considered as a precaution from generalization of good performance of heuristic optimization methods

chatter onset in non regenerative cutting a numerical study a non linear model of non regenerative cutting is analyzed when damped the model has a stable fixed point for small values of chip thickness as chip thickness is increased the fixed point becomes unstable via a sub critical hopf bifurcation this transition corresponds to the onset of chatter when dynamic noise is added to the system chatter onset can occur in the sub critical parameter region although chatter free cutting is predicted by the stability analysis of the fixed point a noisy bifurcation diagram is compared qualitatively to a diagram obtained experimentally in regenerative cutting similar features regarding the onset of chatter are observed in both diagrams

self adaptive multi objective evolutionary algorithm based on decomposition for large scale problems large scale multi objective optimization problems ls mop are complex problems with a large number of decision variables due to its high dimensional decision space ls mop poses a significant challenge to multi objective optimization methods including multi objective evolutionary algorithms moeas following the algorithmic framework of multi objective evolutionary algorithm based on decomposition moea d an enhanced algorithm with adaptive neighborhood size and genetic operator selection named self adaptive moea d samoea d is developed for solving ls mop in this work learning from the search history each scalar optimization subproblem in samoea d varies its neighborhood size and selects a genetic operator adaptively the former determines the size of the search scope while the latter determines the search behavior and as a result the newly generated solution experimental results on 20 ls mop benchmarks have demonstrated that samoea d outperforms or performs similarly to the other four state of the art moeas the effectiveness of the self adaptive strategies has also been experimentally verified furthermore samoea d and the comparing algorithms are then applied to solve a challenging real world problem the multi objective reservoir flood control operation problem optimization results illustrate the superiority of samoea d

a robust nonparametric framework for reconstruction of stochastic differential equation models abstract in this paper we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series the proposed method significantly improves the accuracy of the parameter estimation in this framework drift and diffusion coefficients are modeled through orthogonal legendre polynomials we employ the least squares regression approach along with the euler maruyama approximation method to learn coefficients of stochastic model next a numerical discrete construction of mean squared prediction error mspe is established to calculate the order of legendre polynomials in drift and diffusion terms we show numerically that the new method is robust against the variation in sample size and sampling rate the performance of our method in comparison with the kernel based regression kbr method is demonstrated through simulation and real data in case of real dataset we test our method for discriminating healthy electroencephalogram eeg signals from epilepsy ones we also demonstrate the efficiency of the method through prediction in the financial data in both simulation and real data our algorithm outperforms the kbr method

statistics of the stochastically forced lorenz attractor by the fokker planck equation and cumulant expansions we investigate the fokker planck description of the equal time statistics of the three dimensional lorenz attractor with additive white noise the invariant measure is found by computing the zero or null mode of the linear fokker planck operator as a problem of sparse linear algebra two variants are studied a self adjoint construction of the linear operator and the replacement of diffusion with hyperdiffusion we also access the low order statistics of the system by a perturbative expansion in equal time cumulants a comparison is made to statistics obtained by the standard approach of accumulation via direct numerical simulation theoretical and computational aspects of the fokker planck and cumulant expansion methods are discussed

may the same numerical optimizer be used when searching either for the best or for the worst solution to a real world problem over the last two decades numerous metaheuristics have been proposed and it seems today that nobody is able to understand evaluate or compare them all in principle optimization methods including the recently popular evolutionary computation or swarm intelligence based ones should be developed in order to solve real world problems yet the vast majority of metaheuristics are tested in the source papers on artificial benchmarks only so their usefulness for various practical applications remains unverified as a result choosing the proper method for a particular real world problem is a difficult task this paper shows that such a choice is even more complicated if one wishes with good reason to use metaheuristics twice once to find the best and then to find the worst solutions for the specific numerical real world problem it often occurs that for either case different optimizers are to be recommended the above finding is based on testing 30 metaheuristics on numerical real world problems from cec2011 first we solve 22 minimization problems as defined for cec2011 then we reverse the objective function for each problem and search for its maximizing solution we also observe that algorithms that are highly ranked on average may not perform best for any given specific problem rather the highest average ranking may be achieved by methods that are never among the poorest ones in other words occasional winners may get less attention than rare losers

ensemble of niching algorithms although niching algorithms have been investigated for almost four decades as effective procedures to obtain several good and diverse solutions of an optimization problem no effort has been reported on combining different niching algorithms to form an effective ensemble of niching algorithms in this paper we propose an ensemble of niching algorithms ena and illustrate the concept by an instantiation which is realized using four different parallel populations the offspring of each population is considered by all parallel populations the instantiation is tested on a set of 16 real and binary problems and compared against the single niching methods with respect to searching ability and computation time results confirm that ena method is as good as or better than the best single method in it on every test problem moreover comparison with other state of the art niching algorithms demonstrates the competitiveness of our proposed ena

memetic binary particle swarm optimization for discrete optimization problems in recent decades many researchers have been interested in algorithms inspired by the observation of natural phenomena to solve optimization problems among them meta heuristic algorithms have been extensively applied in continuous real and discrete binary search spaces such algorithms are appropriate for global searches because of their global exploration and local exploitation abilities in this study a memetic binary particle swarm optimization bpso scheme is introduced based on hybrid local and global searches in bpso the algorithm binary hybrid topology particle swarm optimization bhtpso is used to solve the optimization problems in the binary search spaces in addition a variant of the proposed algorithm binary hybrid topology particle swarm optimization quadratic interpolation bhtpso qi is proposed to enhance the global searching capability these algorithms are tested on two set of problems in the binary search space several nonlinear high dimension functions and benchmarks for the 0 1 multidimensional knapsack problem mkp are employed to evaluate their performances their results are compared with some well known modified binary pso and binary gravitational search algorithm bgsa the experimental results showed that the proposed methods improve the performance of bpso in terms of convergence speed and solution accuracy

estimation of particle swarm distribution algorithms combining the benefits of pso and edas this paper presents a novel framework of the estimation of particle swarm distribution algorithms epsdas the aim is to effectively combine particle swarm optimization pso with the estimation of distribution algorithms edas without losing their unique features this aim is achieved by incorporating the following mechanisms 1 selection is applied to the local best solutions in order to obtain more promising individuals for model building 2 a probabilistic model of the problem is built from the selected solutions and 3 new individuals are generated by a stochastic combination of the eda s model sampling method and the pso s particle moving mechanism to exhibit the utility of the epsda framework an extended compact particle swarm optimization ecpso is developed by combining the strengths of the extended compact genetic algorithm ecga with binary pso bpso along the lines of the suggested framework due to its effective nature of harmonizing the global search of ecga with the local search of bpso ecpso is able to discover the optimal solution in a fast and reliable manner experimental results on artificial to real world problems have adduced grounds for the effectiveness of the proposed approach

heuristic space diversity control for improved meta hyper heuristic performance this paper expands on the concept of heuristic space diversity and investigates various strategies for the management of heuristic space diversity within the context of a meta hyper heuristic algorithm in search of greater performance benefits evaluation of various strategies on a diverse set of floating point benchmark problems shows that heuristic space diversity has a significant impact on hyper heuristic performance an exponentially increasing strategy eihh obtained the best results the value of a priori information about constituent algorithm performance on the benchmark set in question was also evaluated finally eihh demonstrated good performance when compared to a popular population based algorithm portfolio algorithm and the best performing constituent algorithm

parametric estimation from approximate data non gaussian diffusions we study the problem of parameters estimation in indirect observability contexts where x t in r r is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an approximating process y varepsilon t which is close to x t in l 4 norm we construct consistent parameter estimators which are smooth functions of the sub sampled empirical mean and empirical lagged covariance matrices computed from the observable data we derive explicit optimal sub sampling schemes specifying the best paired choices of sub sampling time step and number of observations we show that these choices ensure that our parameter estimators reach optimized asymptotic l 2 convergence rates which are constant multiples of the l 4 norm y varepsilon t x t

boundary rigidity with partial data we study the boundary rigidity problem with partial data consisting of determining locally the riemannian metric of a riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the boundary we show that one can recover uniquely and in a stable way a conformal factor near a strictly convex point where we have the information in particular this implies that we can determine locally the isotropic sound speed of a medium by measuring the travel times of waves joining points close to a convex point on the boundary the local results lead to a global lens rigidity uniqueness and stability result assuming that the manifold is foliated by strictly convex hypersurfaces

stochastic model for heart rate fluctuations a normal human heart rate shows complex fluctuations in time which is natural because the heart rate is controlled by a large number of different feedback control loops these unpredictable fluctuations have been shown to display fractal dynamics long term correlations and 1 f noise these characterizations are statistical and they have been widely studied and used but much less is known about the detailed time evolution dynamics of the heart rate control mechanism here we show that a simple one dimensional langevin type stochastic difference equation can accurately model the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical to gaussian noise and both parts can be directly determined from the measured heart rate data studies of 27 healthy subjects reveal that in most cases the deterministic part has a form typically seen in bistable systems there are two stable fixed points and one unstable one

analysis of time series from stochastic processes analysis of time series from stochastic processes governed by a langevin equation is discussed several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the fokker planck equation the coefficients are estimated directly from a time series the applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting