quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

integrable forms of the one dimensional flow equation for unsaturated heterogeneous porous media the equation for the horizontal transport of a liquid in an unsaturated scale heterogeneous porous medium is t x x c x x e x x c e d a systematic search for lie backlund symmetries leads to the requirement that c a b 2 as in the homogeneous 1 case more generally e may be 1 mx 1 3 2 c or exp mx 3c 2 in these cases the transport equation may be linearized and solved exactly examples of more complicated heterogeneous extensions are presented for the integrable nonlinear diffusion equations and for burgers equation

adjoint based predictor corrector sequential convex programming for parametric nonlinear optimization this paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint based predictor corrector sequential convex programming after presenting the algorit

memory effects in fractional brownian motion with hurst exponent h 1 3 we study the regression to the origin of a walker driven by dynamically generated fractional brownian motion fbm and we prove that when the fbm scaling i e the hurst exponent h 1 3 the emerging inverse power law is characterized by a power index that is a compelling signature of the infinitely extended memory of the system strong memory effects leads to the relation h 2 between the hurst exponent and the persistent exponent which is different from the widely used relation h 1 the latter is valid for 1 3 h 1 and is known to be compatible with the renewal assumption

theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average we present a bottom up derivation of fluctuation analysis with detrending for the detection of long range correlations in the presence of additive trends or intrinsic nonstationarities while the well known detrended fluctuation analysis dfa and detrending moving average dma were introduced ad hoc we claim basic principles for such methods where dfa and dma are then shown to be specific realizations the mean squared displacement of the summed time series contains the same information about long range correlations as the autocorrelation function but has much better statistical properties for large time lags however the scaling exponent of its estimator on a single time series is affected not only by trends on the data but also by intrinsic nonstationarities we therefore define the fluctuation function as mean squared displacement with weighting kernel we require that its estimator be unbiased and exhibit the correct scaling behavior for the random component of a signal which is only achieved if the weighting kernel implies detrending we show how dfa and dma satisfy these requirements and we extract their kernel weights

an euler newton continuation method for tracking solution trajectories of parametric variational inequalities a finite dimensional variational inequality parameterized by t in 0 1 is studied under the assumption that each point of the graph of its generally set valued solution mapping is a point of strongly regularity it is shown that there are finitely many lipschitz continuous functions on 0 1 whose graphs do not intersect each other such that for each value of the parameter the set of values of the solution mapping is the union of the values of these functions moreover the property of strong regularity is uniform with respect to the parameter along any such function graph an euler newton continuation method for tracking a solution trajectory is introduced and demonstrated to have l infty accuracy of order o h 4 thus generalizing a known error estimate for equations two examples of tracking economic equilibrium parametrically illustrate the theoretical results a correction is attached

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

a real time iteration scheme for nonlinear optimization in optimal feedback control an efficient newton type scheme for the approximate on line solution of optimization problems as they occur in optimal feedback control is presented the scheme allows a fast reaction to disturbances by delivering approximations of the exact optimal feedback control which are iteratively refined during the runtime of the controlled process the contractivity of this real time iteration scheme is proven and a bound on the loss of optimality compared with the theoretical optimal solution is given the robustness and excellent real time performance of the method is demonstrated in a numerical experiment the control of an unstable system namely an airborne kite that shall fly loops

critical behavior and conservation in directed sandpiles we perform large scale simulations of directed sandpile models with both deterministic and stochastic toppling rules our results show the existence of two distinct universality classes we also provide numerical simulations of directed models in the presence of bulk dissipation the numerical results indicate that the way in which dissipation is implemented is irrelevant for the determination of the critical behavior the analysis of the self affine properties of avalanches shows the existence of a subset of superuniversal exponents whose value is independent of the universality class this feature is accounted for by means of a phenomenological description of the energy balance condition in these models

fractal distribution of floaters on a fluid surface and the transition to chaos for random maps abstract the long time spatial distribution of particles floating on the surface of a confined fluid whose flow velocity has complicated time dependence is considered it is shown that this distribution can be either a fractal or else can clump at several or one discrete points the transition from the latter type of distribution to the former occurs when the lyapunov exponent characterizing the particle motion passes through zero from negative values to positive values the characteristic features of this type of transition are investigated using random maps it is shown that near the transition there are extremely intermittent temporal fluctuations in the particle cloud and their scaling with a parameter is elucidated

class of cellular automata for reaction diffusion systems finite difference methods for solving the pde s finite difference methods then proceed to solve the resulting coupled system of n s ordinary differential equations n points in space s equations in the pde system by any of a number of numerical methods operating on floating point numbers the use of floating point numbers on computers implies a discretization of the continuous variables the errors introduced by this discretization and the ensuing roundoff errors are often not considered explicitly but assumed to be small because the precision is rather high 8 decimal digits for usual floating point numbers in contrast in the ca approach all variables are explicitly discretized into relatively small integers this discretization allows the use of lookup tables to replace the evaluation of the nonlinear rate functions it is this table lookup combined with the fact that all calculations are performed using integers instead of floating point variables that accounts for an improvement in speed of orders of magnitude on a conventional multi purpose computer the undesirable effects of discretization are overcome by using probabilistic rules for the updating of the ca the state of the ca is given by a regular array of concentration vectors y residing on a d dimensional lattice each y r is a s vector of integers s is the number of reactive species for reasons of efficiency and to fulfill the finiteness condition of the definition of cellular automata each component yi r can only take integer values between 0 and bi where the bi s can be different for each species i the position index r is a d dimensional vector in the ca lattice for cubic lattices r is a d vector of integers the central operation of the automaton consists of calculating the sum

a parametric nonconvex decomposition algorithm for real time and distributed nmpc a novel decomposition scheme to solve parametric nonconvex programs as they arise in nonlinear model predictive control nmpc is presented it consists of a fixed number of alternating proximal gradient steps and a dual update per time step hence the proposed approach is attractive in a real time distributed context assuming that the nonlinear program nlp is semi algebraic and that its critical points are strongly regular contraction of the sequence of primal dual iterates is proven implying stability of the sub optimality error under some mild assumptions moreover it is shown that the performance of the optimality tracking scheme can be enhanced via a continuation technique the efficacy of the proposed decomposition method is demonstrated by solving a centralized nmpc problem to control a dc motor and a distributed nmpc program for collaborative tracking of unicycles both within a real time framework furthermore an analysis of the sub optimality error as a function of the sampling period is proposed given a fixed computational power

d map distributed maximum a posteriori probability estimation of dynamic systems this paper develops a framework for the estimation of a time varying random signal using a distributed sensor network given a continuous time model sensors collect noisy observations and produce local estimates according to the discrete time equivalent system defined by the sampling period of observations estimation is performed using a maximum a posteriori probability estimator map within a given window of interest to mediate the incorporation of information from other sensors we introduce lagrange multipliers to penalize the disagreement between neighboring estimates we show that the resulting distributed d map algorithm is able to track dynamical signals with a small error this error is characterized in terms of problem constants and vanishes with the sampling time as long as the log likelihood function which is assumed to be log concave satisfies a smoothness condition we implement the d map algorithm for a linear and a nonlinear system model to show that the performance corroborates with theoretical findings

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

scaling properties and entropy of long range correlated time series we calculate the shannon entropy of a time series by using the probability density functions of the characteristic sizes of the long range correlated clusters introduced in a carbone g castelli h e stanley phys rev e 69 2004 026105 we define three different measures of the entropy related respectively to the length the duration and the area of the clusters for all the three cases the entropy increases as the logarithm of a power of the size with exponents equal to the fractal dimension of the cluster length duration and area respectively r 2007 elsevier b v all rights reserved

scaling of swimming sequences in copepod behavior data analysis and simulation abstract we consider symbolic sequences of copepod behavior classified as break and slow swimming states successive residence times for each state have been recorded for 327 symbolic times series obtained from 52 different trajectories we performed a symbolic dynamics analysis of the succession of states and showed that the probability densities of the duration of each state obey power laws for large times we analyzed the transition between states and showed as expected the non markovian properties of this dynamics we further simulate a copepod trajectory using an alternate renewal process for the generation of the sequence time series and using a brownian motion for the copepod motion during swimming periods

detrending fluctuation analysis based on high pass filtering abstract detrended fluctuation analysis dfa is a scaling method commonly used for detecting long range correlations in non stationary time series the dfa method uses a trend based on polynomial fitting to extract and quantify fluctuations at different time scales basically such procedure acts as a non dynamical high pass filter that removes time series components below a given time scale as an alternative to the polynomial fitting approach this paper proposes a dfa method based on well known high pass filters e g butterworth elliptic etc numerical results show that the proposed dfa approach yields results similar to traditional dfa method maybe the main advantage of the proposed dfa method is that efficient implementations of high pass filters are available commercially

economic fluctuations and statistical physics quantifying extremely rare and less rare events in finance one challenge of economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture crystalline or otherwise nonetheless as if by magic out of nothing but randomness one finds remarkably fine tuned processes in time we present an overview of recent research joining practitioners of economic theory and statistical physics to try to better understand puzzles regarding economic fluctuations one of these puzzles is how to describe outliers phenomena that lie outside of patterns of statistical regularity we review evidence consistent with the possibility that such outliers may not exist this possibility is supported by recent analysis of databases containing information about each trade of every stock r 2007 elsevier b v all rights reserved

the level crossing and inverse statistic analysis of german stock market index dax and daily oil price time series a b s t r a c t the level crossing and inverse statistics analysis of dax and oil price time series are given we determine the average frequency of positive slope crossings where t 1 is the average waiting time for observing the level again we estimate the probability p k which provides us the probability of observing k times of the level with positive slope in time scale t for analyzed time series we found that maximum k is about 6 we show that by using the level crossing analysis one can estimate how the dax and oil time series will develop we carry out the same analysis for the increments of dax and oil price log returns which is known as inverse statistics and provide the distribution of waiting times to observe some level for the increments 2011 elsevier b v all rights reserved stochastic processes occur in many natural and man made phenomena ranging from various indicators of economic activities in the stock market velocity fluctuations in turbulent flows and heartbeat dynamics etc 1 the level crossing analysis of stochastic processes has been introduced by rice 1944 1945 2 26 and used to describe the turbulence 16 rough surfaces 27 stock markets 28 burgers turbulence and kardar parisi zhang equation 29 30 the level crossing analysis of the data set has the advantage that it gives important global properties of the time series and do not need the scaling feature the almost of the methods in time series analysis are using the scaling features of time series and their applications are restricted to the time series with scaling properties our goal with the level crossing analysis is to characterize the statistical properties of the data set with the hope to better understand the underlying stochastic dynamics and provide a possible tool to estimate its dynamics the level crossing and inverse statistics analysis can be viewed as the complementary method to the other well known methods such as detrended fluctuation analysis dfa 31 detrended moving average dma 32 wavelet transform modulus maxima wtmm 33 rescaled range analysis r s 34 scaled windowed variance swv 35 langevin dynamics 36 detrended cross correlation analysis 37 multifactor analysis of

on the scaling ranges of detrended fluctuation analysis for long term memory correlated short series of data abstract we examine the scaling regime for the detrended fluctuation analysis dfa the most popular method used to detect the presence of long term memory in data and the fractal structure of time series first the scaling range for dfa is studied for uncorrelated data as a function of time series length l and the correlation coefficient of the linear regression r 2 at various confidence levels next a similar analysis for artificial short series of data with long term memory is performed in both cases the scaling range is found to change linearly both with l and r 2 we show how this dependence can be generalized to a simple unified model describing the relation l r 2 h where h 1 2 h 1 stands for the hurst exponent of the long range autocorrelated signal our findings should be useful in all applications of dfa technique particularly for instantaneous local dfa where a huge number of short time series has to be analyzed at the same time without possibility of checking the scaling range in each of them separately

a mixed gh2 h approach for stabilization and accurate trajectory tracking of unicycle like vehicles the control problem of unicycle like vehicles such as mobile robots is considered more exactly we propose the use of a linear parameter varying lpv approach to obtain both stabilization of the kinematic model together with high accuracy in trajectory tracking this objective has been achieved by exploiting the advantages offered by linear matrix inequality lmi theory and by introducing in the synthesis phase a tight limit on the peak value of control signals

general four step discrete time zeroing and derivative dynamics applied to time varying nonlinear optimization abstract time varying nonlinear optimization tvno problems are considered as important issues in various scientific disciplines and industrial applications in this paper the continuous time derivative dynamics ctdd model is developed for obtaining the real time solutions of tvno problems furthermore aiming to remedy the weaknesses of ctdd model a continuous time zeroing dynamics ctzd model is presented and investigated for potential digital hardware realization by using bilinear transform a general four step zhang et al discretization zead formula is proposed and applied to the discretization of both ctdd and ctzd models a general four step discrete time derivative dynamics general four step dtdd model and a general four step discrete time zeroing dynamics general four step dtzd model are proposed on the basis of this general four step zead formula further theoretical analyses indicate that the general four step dtzd model is zero stable consistent and convergent with the truncation error of o g 4 which denotes a vector with every entries being o g 4 with g denoting the sampling period theoretical analyses also indicate that the maximal steady state residual error mssre has an o g 4 pattern confirmedly the efficacy and accuracy of the general four step dtdd and dtzd models are further illustrated by numerical examples

directed self organized critical patterns emerging from fractional brownian paths abstract we discuss a family of clusters c corresponding to the region whose boundary is formed by a fractional brownian path y i and by the moving average function y n i 1 n k 0 n 1 y i k our model generates fractal directed patterns showing spatio temporal complexity and we demonstrate that the cluster area length and duration exhibit the characteristic scaling behavior of soc clusters the function cn i acts as a magnifying lens zooming in or out the avalanches formed by the cluster construction rule where the magnifying power of the zoom is set by the value of the amplitude window n on the basis of the construction rule of the clusters c n i y i y n i and of the relationship among the exponents we hypothesize that our model might be considered to be a generalized stochastic directed model including the dhar ramaswamy dr model and the stochastic models as particular cases as in the dr model the growth and annihilation of our clusters are obtained from the set of intersections of two random walk paths and we argue that our model is a variant of the directed self organized criticality scheme of the dr model

a class of prediction correction methods for time varying convex optimization this paper considers unconstrained convex optimization problems with time varying objective functions we propose algorithms with a discrete time sampling scheme to find and track the solution trajectory based on prediction and correction steps while sampling the problem data at a constant rate of 1 h where h is the sampling period the prediction step is derived by analyzing the iso residual dynamics of the optimality conditions the correction step adjusts for the distance between the current prediction and the optimizer at each time step and consists either of one or multiple gradient steps or newton steps which respectively correspond to the gradient trajectory tracking gtt or newton trajectory tracking ntt algorithms under suitable conditions we establish that the asymptotic error incurred by both proposed methods behaves as o h 2 and in some cases as o h 4 which outperforms the state of the art error bound of o h for correction only methods in the gradient correction step moreover when the characteristics of the objective function variation are not available we propose approximate gradient and newton tracking algorithms agt and ant respectively that still attain these asymptotical error bounds numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude

parameter estimation for the generalized fractional element network zener model based on the bayesian method abstract in the present study an inverse problem to estimate parameters in the zener model of viscoelasticity based on the generalized fractional element gfe network is studied the bayesian method is proposed to obtain the optimal estimation of the viscoelastic parameters three examples are performed to certify the validity of the method all numerical results lead to an excellent fitting between the calculative results and experimental data it is shown that the bayesian method is feasible in the inverse problem of parameter estimation for the fractional constitutive equation and the gfe network zener model is efficient in the modeling of the viscoelastic behavior

real time nonlinear optimization as a generalized equation we establish results for the problem of tracking a time dependent manifold arising in real time optimization by casting this as a parametric generalized equation we demonstrate that if points along a solution manifold are consistently strongly regular it is possible to track the manifold approximately by solving a single linear complementarity problem lcp at each time step we derive sufficient conditions guaranteeing that the tracking error remains bounded to second order with the size of the time step even if the lcp is solved only approximately we use these results to derive a fast augmented lagrangian tracking algorithm and demonstrate the developments through a numerical case study

lifetime distributions for adjacency relationships in a vicsek model we investigate the statistical properties of adjacency relationships in a two dimensional vicsek model we define adjacent edges for all particles at every time step by a delaunay triangulation and b euclidean distance and obtain cumulative distributions p ensuremath tau of lifetime ensuremath tau of the edges we find that the shape of p ensuremath tau changes from an exponential to a power law depending on the interaction radius which is a parameter of the vicsek model we discuss the emergence of the power law distribution from the viewpoint of first passage time problem for a fractional brownian motion

decentralized dynamic optimization through the alternating direction method of multipliers this paper develops the application of the alternating direction method of multipliers admm to optimize a dynamic objective function in a decentralized multi agent system at each time slot agents in the network observe local functions and cooperate to track the optimal time varying argument of the sum objective this cooperation is based on maintaining local primal variables that estimate the value of the optimal argument and auxiliary dual variables that encourage proximity with neighboring estimates primal and dual variables are updated by an admm iteration that can be implemented in a distributed manner whereby local updates require access to local variables and the most recent primal variables from adjacent agents for objective functions that are strongly convex and have lipschitz continuous gradients the distances between the primal and dual iterates to their corresponding time varying optimal values are shown to converge to a steady state gap this gap is explicitly characterized in terms of the condition number of the objective function the condition number of the network that is defined as the ratio between the largest and smallest nonzero laplacian eigenvalues and a bound on the drifts of the optimal primal variables and the optimal gradients numerical experiments corroborate theoretical findings and show that the results also hold for non differentiable and non strongly convex primal objectives

analysis of clusters formed by the moving average of a long range correlated time series we analyze the stochastic function c n i ensuremath equiv y i ensuremath y n i where y i is a long range correlated time series of length n mathrm max and y n i ensuremath equiv 1 n ensuremath sum k 0 n ensuremath 1 y i ensuremath k is the moving average with window n we argue that c n i generates a stationary sequence of self affine clusters mathcal c with length mathcal l lifetime ensuremath tau and area s the length and the area are related to the lifetime by the relationships mathcal l ensuremath sim ensuremath tau ensuremath psi mathcal l and s ensuremath sim ensuremath tau ensuremath psi s where ensuremath psi mathcal l 1 and ensuremath psi s 1 h we also find that mathcal l ensuremath tau and s are power law distributed with exponents depending on h p mathcal l ensuremath sim mathcal l ensuremath ensuremath alpha p ensuremath tau ensuremath sim ensuremath tau ensuremath ensuremath beta and p s ensuremath sim s ensuremath ensuremath gamma with ensuremath alpha ensuremath beta 2 ensuremath h and ensuremath gamma 2 1 h these predictions are tested by extensive simulations on series generated by the midpoint displacement algorithm of assigned hurst exponent h ranging from 0 05 to 0 95 of length up to n mathrm max 2 21 and n up to 2 13

some results and a conjecture for manna s stochastic sandpile model we present some analytical results for the stochastic sandpile model studied earlier by manna in this model the operators corresponding to particle addition at different sites commute the eigenvalues of operators satisfy a system of coupled polynomial equations for an l l square we construct a nontrivial toppling invariant and hence a ladder operator which acting on eigenvectors of the evolution operator gives new eigenvectors with different eigenvalues for periodic boundary conditions in one direction one more toppling invariant can be constructed we show that there are many forbidden subconfigurations and only an exponentially small fraction of all stable configurations are recurrent we obtain rigorous lower and upper bounds for the minimum number of particles in a recurrent configuration and conjecture a formula for its exact value for finite size rectangles

exactly solved model of self organized critical phenomena we define a variant of the model of bak tang and wiesenfeld of self organized critial behavior by introducing a preferred direction we characterize the critical state and by establishing equivalence to a voter model determine the critical exponents exactly in arbitrary dimension d the upper critical dimension for this model is three in two dimensions the model is equivalent to an earlier solved special case of directed percolation

fractal heterogeneous media a method is presented for generating compact fractal disordered media by generalizing the random midpoint displacement algorithm the obtained structures are invasive stochastic fractals with the hurst exponent varying as a continuous parameter as opposed to lacunar deterministic fractals such as the menger sponge by employing the detrending moving average algorithm a carbone phys rev e 76 056703 2007 the hurst exponent of the generated structure can be subsequently checked the fractality of such a structure is referred to a property defined over a three dimensional topology rather than to the topology itself consequently in this framework the hurst exponent should be intended as an estimator of compactness rather than of roughness applications can be envisaged for simulating and quantifying complex systems characterized by self similar heterogeneity across space for example exploitation areas range from the design and control of multifunctional self assembled artificial nanostructures and microstructures to the analysis and modeling of complex pattern formation in biology environmental sciences geomorphological sciences etc

distribution of the first return time in fractional brownian motion and its application to the study of on off intermittency herein the term fractional brownian motion is used to refer to a class of random walks with long range correlated steps where the mean square displacement of the walker at large time t is proportional to mathit t 2 mathit h with 0h1 for ordinary brownian motion we obtain h 1 2 let t denote the time at which the random walker starting at the origin first returns to the origin the purpose of this paper is to show that the probability distribution of t scales with t as p t ensuremath sim mathit t mathit h mathrm ensuremath 2 theoretical arguments and numerical simulations are presented to support the result additional issues explored include modification to the power law distribution when the random walk is biased and the application of the result to the characterization of on off intermittency a recently proposed mechanism for bursting

immiscible two phase flow in a porous medium utilization of a laplace transform boost a boost operator is defined for the laplace transform it is used in conjunction with the laplace transform to solve the diffusion equation on a domain with multiple moving boundaries this problem arises in the study of immiscible multiphase flow in a finite medium including end effects extensions of this method to the solution of other linear differential equations are conceivable

a two phase free boundary problem for a nonlinear diffusion convection equation a two phase free boundary problem associated with a diffusion convection equation is considered the problem is reduced to a system of nonlinear integral equations which admits a unique solution for small times the system admits an explicit two component solution corresponding to a two component shock wave of the burgers equation the stability of such a solution is also discussed

time optimal path tracking for robots a convex optimization approach this paper focuses on time optimal path tracking a subproblem in time optimal motion planning of robot systems through a nonlinear change of variables the time optimal path tracking problem is transformed here into a convex optimal control problem with a single state various convexity preserving extension are introduced resulting in a versatile approach for optimal path tracking a direct transcription method is presented that reduces finding the globally optimal trajectory to solving a second order cone program using robust numerical algorithms that are freely available validation against known examples and application to a more complex example illustrate the versatility and practicality of the new method

on the exactly solvable equation s_t beta s gamma 2 s_x _x alpha beta s gamma 2 s_x occurring in two phase flow in porous media the symmetry approach of fokas j math phys 21 1980 pp 1318 1325 is used to show that the most general equation of the form s t g s s xx f s s x dg ds ne 0 which is exactly solvable is equivalent to the equation s t beta s gamma 2 s x x alpha beta s gamma 2 s x this equation is then mapped to the linear heat equation through a series of backlund transformations the above result is used to solve an initial boundary value problem modeling the process of waterflooding i e the displacement of oil initially in a porous reservoir by continuously injected water

detrending fluctuation analysis based on moving average filtering abstract detrended fluctuation analysis dfa is a scaling method commonly used for detecting long range correlations in nonstationary time series applications range from financial time series to physiological data however as the removal of trends in dfa is based on discontinuous polynomial fitting oscillations in the fluctuation function and significant errors in crossover locations can be introduced to reduce the problems induced by discontinuous fitting moving average ma methods have been proposed previously by alesio et al eur j phys b 27 2002 197 in this work a variant of such ma methods is studied specifically the performance and characteristics of a ma method based on central differences is studied some important properties of this ma method are analyzed and illustrated with several artificial and real time series

universality in sandpiles we perform extensive numerical simulations of different versions of the sandpile model we find that previous claims about universality classes are unfounded since the method previously employed to analyze the data suffered from a systematic bias we identify the correct scaling behavior and provide evidences suggesting that sandpiles with stochastic and deterministic toppling rules belong to the same universality class