correlation structure of fractional pearson diffusions the stochastic solution to a diffusion equations with polynomial coefficients is called a pearson diffusion if the first time derivative is replaced by a caputo fractional derivative of order less than one the stochastic solution is called a fractional pearson diffusion this paper develops an explicit formula for the covariance function of a fractional pearson diffusion in steady state in terms of mittag leffler functions that formula shows that fractional pearson diffusions are long range dependent with a correlation that falls off like a power law whose exponent equals the order of the fractional derivative

transient and cyclic behavior of cellular automata with null boundary conditions one dimensional cellular automata ca over finite fields are studied in which each interior cell is updated to contain the sum of the previous values of its two nearest neighbors boundary cells are updated according to null boundary conditions for a given initial configuration the ca evolves through transient configurations to an attracting cycle the dependence of the maximal transient length and maximal cycle length on the number of cells is investigated both can be determined from the minimal polynomial of the update matrix which in this case satisfies a useful recurrence relation with cell values from a field of characteristic two the explicit dependence of the maximal transient length on the number of cells is determined extensions and directions for future work are presented

stable continuous time autoregressive process driven by stable subordinator abstract in this paper we examine the continuous time autoregressive moving average process driven by stable levy motion delayed by inverse stable subordinator this process can be applied to high frequency data with visible jumps and so called trapping events those properties are often visible in financial time series but also in amorphous semiconductors technical data describing the rotational speed of a machine working under various load regimes or data related to indoor air quality we concentrate on the main characteristics of the examined subordinated process expressed in the language of the measures of dependence which are main tools used in statistical investigation of real data however because the analyzed system is based on the stable distribution therefore we cannot consider here the correlation or covariance as a main measure which indicates at the dependence inside the process in the paper we examine the codifference the more general measure of dependence defined for wide class of processes moreover we present the simulation procedure of the considered system and indicate how to estimate its parameters the theoretical results we illustrate by the simulated data analysis

on behavior of two dimensional cellular automata with an exceptional rule several studies a r khan p p choudhury k dihidar s mitra p sarkar vlsi architecture of a cellular automata comput math appl 33 1997 79 94 a r khan p p choudhury k dihidar r verma text compression using two dimensional cellular automata comput math appl 37 1999 115 127 k dihidar p p choudhury matrix algebraic formulae concerning some exceptional rules of two dimensional cellular automata inf sci 165 2004 91 101 have explored a new rule convention for two dimensional 2 d nearest neighborhood linear cellular automata ca with null and periodic boundary conditions a variety of applications of the rule convention have been illustrated and the vlsi architecture of cellular automata machine cam has been proposed however most of the studies address the issue of the kernel dimension of 2 d ca and many other important characteristics of ca such as garden of eden goe maximal transient length maximal cycle length etc have not been explored in this paper by exploiting matrix algebra in gf 2 the galois field with two elements we attempt to characterize the behavior of a specific rule which is not covered in existing work but accords with the same convention a necessary and sufficient condition is given to ensure that a given configuration is a goe meanwhile we propose some algorithms to determine the number of goes the maximal transient length and the maximal cycle length in a 2 d ca

a characterization of important algorithms for quantum dot cellular automata abstract feature sizes in chip manufacturing are becoming so small that quantum mechanical behavior will soon have a deleterious effect on the function of devices quantum dot cellular automata qdca have been proposed as computing devices which are helped rather than hindered by the quantum behavior of electrons qdca compute by relaxing to a configuration of minimal energy previously it has been shown that a quantum dot device may not compute properly if all of its relaxed configurations are not equal in energy level such an automation is termed unbalanced a necessary condition for an automaton to be balanced is that the number of distinguished configurations with minimum energy should equal the number of input combinations the automaton handles does an efficient algorithm for determining the number of distinguished ground states exist if so it will be difficult to find as such an algorithm is shown to be np hard furthermore the related problem of determining the minimum energy level of arbitrary automata is also shown to be np hard these results have important implications for simulating and analyzing qdca on conventional computers

garden of eden configurations for 2 d cellular automata with rule 2460n an important problem in cellular automata theory is the reversibility of a cellular automaton which is related to the existence of garden of eden configurations in cellular automata in this paper we study new local rules for two dimensional cellular automata over the ternary field z 3 the set of integers modulo three with some of their important characteristics we obtain necessary and sufficient conditions for the existence of garden of eden configurations for two dimensional ternary cellular automata also by making use of the matrix representation of two dimensional cellular automata we provide an algorithm to obtain the number of garden of eden configurations for two dimensional cellular automata defined by rule 2460n we present an application of the reversible two dimensional ternary cellular automata to cryptography

fluctuation driven computing on number conserving cellular automata a number conserving cellular automaton ncca is a cellular automaton in which the states of cells are denoted by integers and the sum of all of the numbers in a configuration is conserved throughout its evolution nccas have been widely used to model physical systems that are ruled by conservation laws of mass or energy imai et al 13 showed that the local transition function of ncca can be effectively translated into the sum of a binary flow function over pairs of neighboring cells in this paper we explore the computability of nccas in which the pairwise number flows are performed at fully asynchronous timings despite the randomness that is associated with asynchronous transitions useful computation still can be accomplished efficiently in the cellular automata through the active exploitation of fluctuations 18 specifically certain numbers may flow randomly fluctuating between forward and backward directions in the cellular space as if they were subject to brownian motion because random fluctuations promise a powerful resource for searching through a computational state space the brownian like flow of the numbers allows for efficient embedding of logic circuits into our novel asynchronous ncca

subordinated continuous time ar processes and their application to modeling behavior of mechanical system abstract many real data exhibit behavior adequate to subdiffusion processes very often it is manifested by so called trapping events the visible evidence of subdiffusion we observe not only in financial time series but also in technical data in this paper we propose a model which can be used for description of such kind of data the model is based on the continuous time autoregressive time series with stable noise delayed by the infinitely divisible inverse subordinator the proposed system can be applied to real datasets with short time dependence visible jumps and mentioned periods of stagnation in this paper we extend the theoretical considerations in analysis of subordinated processes and propose a new model that exhibits mentioned properties we concentrate on the main characteristics of the examined subordinated process expressed mainly in the language of the measures of dependence which are main tools used in statistical investigation of real data we present also the simulation procedure of the considered system and indicate how to estimate its parameters the theoretical results we illustrate by the analysis of real technical data

codifference as a practical tool to measure interdependence abstract correlation and spectral analysis represent the standard tools to study interdependence in statistical data however for the stochastic processes with heavy tailed distributions such that the variance diverges these tools are inadequate the heavy tailed processes are ubiquitous in nature and finance we here discuss codifference as a convenient measure to study statistical interdependence and we aim to give a short introductory review of its properties by taking different known stochastic processes as generic examples we present explicit formulas for their codifferences we show that for the gaussian processes codifference is equivalent to covariance for processes with finite variance these two measures behave similarly with time for the processes with infinite variance the covariance does not exist however the codifference is relevant we demonstrate the practical importance of the codifference by extracting this function from simulated as well as real data taken from turbulent plasma of fusion device and financial market we conclude that the codifference serves as a convenient practical tool to study interdependence for stochastic processes with both infinite and finite variances as well

geometric brownian motion with tempered stable waiting times one of the earliest system that was used to asset prices description is black scholes model it is based on geometric brownian motion and was used as a tool for pricing various financial instruments however when it comes to data description geometric brownian motion is not capable to capture many properties of present financial markets one can name here for instance periods of constant values therefore we propose an alternative approach based on subordinated tempered stable geometric brownian motion which is a combination of the popular geometric brownian motion and inverse tempered stable subordinator in this paper we introduce the mentioned process and present its main properties we propose also the estimation procedure and calibrate the analyzed system to real data

structure and reversibility of 2d hexagonal cellular automata cellular automata are used to model dynamical phenomena by focusing on their local behavior which depends on the neighboring cells in order to express their global behavior the geometrical structure of the models suggests the algebraic structure of cellular automata after modeling the dynamical phenomena it is sometimes an important problem to be able to move backwards in order to understand it better this is only possible if cellular automata is reversible in this paper 2d finite cellular automata defined by local rules based on hexagonal cell structure are studied rule matrix of the hexagonal finite cellular automaton is obtained the rank of rule matrices representing the 2d hexagonal finite cellular automata via an algorithm is computed it is a well known fact that determining the reversibility of a 2d cellular automata is a very difficult problem in general here the reversibility problem of this family of 2d hexagonal cellular automata is also resolved completely

numerical approach to the fractional klein kramers equation subdiffusion in the presence of an external force field can be described in phase space by the fractional klein kramers equation in this paper we explore the stochastic structure of this equation using a subordination method we define a random process whose probability density function is a solution of the fractional klein kramers equation the structure of the introduced process agrees with the two stage scenario underlying the anomalous diffusion mechanism in which trapping events are superimposed on the langevin dynamics we develop an efficient computer algorithm for visualization of fractional klein kramers dynamics and present some simulation results based on monte carlo techniques

computing with random quantum dot repulsion quantum dot cellular automata qca show great promise for fast computation with larger integration density and lower power consumption unfortunately previous research has shown that qca are likely to be extremely sensitive to placement error during an investigation into placement sensitivity it was discovered that completely random quantum dot structures have the ability to compute simple binary functions in this paper we further explore the random structures in an idealized way looking for higher order functions an example of one bit full adder is shown in the paper moreover a new structure the semi random structure is introduced to alleviate some but not all difficulties in connecting disparate random structures the difficulties arise from the fact that inputs and outputs to and from a purely random structure may not reside at the edges of the structure in the semi random structure the inputs and outputs are localized to the edges it is demonstrated that semi random structures like random structures can almost assuredly compute simple boolean functions

arithmetic brownian motion subordinated by tempered stable and inverse tempered stable processes abstract in the last decade the subordinated processes have become popular and have found many practical applications therefore in this paper we examine two processes related to time changed subordinated classical brownian motion with drift called arithmetic brownian motion the first one so called normal tempered stable is related to the tempered stable subordinator while the second one to the inverse tempered stable process we compare the main properties such as probability density functions laplace transforms ensemble averaged mean squared displacements of such two subordinated processes and propose the parameters estimation procedures moreover we calibrate the analyzed systems to real data related to indoor air quality

discriminating between normal and anomalous random walks commonly normal diffusive behavior is characterized by a linear dependence of the second central moment on time x 2 t ensuremath propto t while anomalous behavior is expected to show a different time dependence x 2 t ensuremath propto t ensuremath delta with ensuremath delta l1 for subdiffusive and ensuremath delta g1 for superdiffusive motions here we explore in details the fact that this kind of qualification if applied straightforwardly may be misleading there are anomalous transport motions revealing perfectly normal diffusive character x 2 t ensuremath propto t yet being non markov and non gaussian in nature we use recently developed framework of monte carlo simulations which incorporates anomalous diffusion statistics in time and space and creates trajectories of such an extended random walk for special choice of stability indices describing statistics of waiting times and jump lengths the ensemble analysis of anomalous diffusion is shown to hide temporal memory effects which can be properly detected only by examination of formal criteria of markovianity fulfillment of the chapman kolmogorov equation

comment on fractional fokker planck equation with space and time dependent drift and diffusion the purpose of this paper is to correct errors presented recently in the paper lv et al j stat phys 149 619 628 2012 where the authors analyzed fractional fokker planck equation ffpe with space time dependent drift f x t f x f t and diffusion d x t d x tilde d t coefficients in the factorized form we show an important drawback in the derivation of the stochastic representation of ffpe presented in the aforementioned paper which makes the whole proof wrong moreover we present a correct proof of their result in even more general case when both drift and diffusion can have any not necessarily factorized form

fokker planck type equations associated with fractional brownian motion controlled by infinitely divisible processes abstract in this paper we study the anomalous diffusion process driven by fractional brownian motion delayed by general infinitely divisible subordinator we show the analyzed process is the stochastic representation of the fokker planck type equation that describes the probability density function of an introduced model moreover we study main characteristics of the examined process the first two moments that allow us in special cases for classification of it as a system with accelerating subdiffusion property

the nonlinear programming method of wilson han and powell with an augmented lagrangian type line search function the paper represents an outcome of an extensive comparative study of nonlinear optimization algorithms this study indicates that quadratic approximation methods which are characterized by solving a sequence of quadratic subproblems recursively belong to the most efficient and reliable nonlinear programming algorithms available at present the purpose of this paper is to analyse the theoretical convergence properties and to investigate the numerical performance in more detail in part 1 the exactl 1 penalty function of han and powell is replaced by a differentiable augmented lagrange function for the line search computation to the able to prove the global convergence and to show that the steplength one is chosen in the neighbourhood of a solution in part 2 the quadratic subproblem is exchanged by a linear least squares problem to improve the efficiency and to test the dependence of the performance from different solution methods for the quadratic or least squares subproblems

text compression using two dimensional cellular automata abstract this paper presents an elegant mathematical model using simple matrix algebra for characterising the behaviour of two dimensional nearest neighbourhood linear cellular automata with periodic boundary conditions based on this mathematical model the vlsi architecture of a cellular automata machine cam has been proposed for text compression experimental results of comparisons with adaptive huffman coding scheme also presented

subordinated α stable ornstein uhlenbeck process as a tool for financial data description abstract the classical financial models are based on the standard brownian diffusion type processes however in the exhibition of some real market data like interest or exchange rates we observe characteristic periods of constant values moreover in the case of financial data the assumption of normality is often unsatisfied in such cases the popular vasicek model that is a mathematical system describing the evolution of interest rates based on the ornstein uhlenbeck process seems not to be applicable therefore we propose an alternative approach based on a combination of the popular ornstein uhlenbeck process with a stable distribution and subdiffusion systems that demonstrate such characteristic behavior the probability density function of the proposed process can be described by a fokker planck type equation and therefore it can be examined as an extension of the basic ornstein uhlenbeck model in this paper we propose the parameters estimation method and calibrate the subordinated vasicek model to the interest rate data

restoring and non restoring array divider designs in quantum dot cellular automata quantum dot cellular automata qca is a very high speed extra low power and extremely dense technology for implementing computing architectures which encodes binary logics through configuration of charges amongst quantum dots several studies of adders and multipliers in qca have been proposed whereas qca divider design and implementation is a rather unexplored research area in this paper the earliest designs for qca dividers which explore the restoring and non restoring array dividers considered as the best possible dividers are introduced these designs use well organized arithmetic components as their basic construction parts and take some design rules into consideration which make them reliable and more robust against noise these dividers with their design considerations and constraints are introduced step by step moreover these designs are probed in terms of complexity clocking and latency qcadesigner a simulation tool for qca circuits is used to check circuits layout and functionality

parameter estimation for arma models with infinite variance innovations abstract we consider a standard arma process of the form phi b xt theta b zt where the innovations zt belong to the domain of attraction of a stable law so that neither the zt nor the xt have a finite variance our aim is to estimate the coefficients of phi and theta since maximum likelihood estimation is not a viable possibility due to the unknown form of the marginal density of the innovation sequence we adopt the so called whittle estimator based on the sample periodogram of the x sequence despite the fact that the periodogram does not a priori seem like a logical object to study in this non l situation we show that our estimators are consistent obtain their asymptotic distributions and show that they converge to the true values faster than in the usual l2 case

vlsi architecture of a cellular automata machine abstract in the past cellular automata based models and machines 1 have been proposed for simulation of physical systems without any analytical insight into the behaviour of the underlying simulation machine this paper makes a significant departure from this traditional approach an elegant mathematical model using simple matrix algebra is reported in this paper for characterizing the behaviour of two dimensional nearest neighbourhood linear cellular automata with null and periodic boundary conditions based on this mathematical model a vlsi architecture of a cellular automata machine cam has been proposed interesting applications of cam in the fields of image analysis and fractal image generation are also reported

on the augmented lagrangian it is well known that for a nonlinear program any karush kuhn tucker point that satisfies the second order sufficient condition is also a strict local minimum of the augmented lagrangian with an underlying penalty parameter sufficiently large a main theme of the paper is to strengthen the theorem and bring to light an interesting connection among general critical points of a nonlinear program and its augmented lagrangian when a penalty parameter is sufficiently large it will be shown that a karush kuhn tucker point of a nonlinear program is also a critical point of its augmented lagrangian with the same index and the same nullity the aforementioned theorem is just the special case when the index and the nullity are zeros this result is established through an extension of a lemma due to finsler and debreu which is interesting in its own right consequently under a constraint qualification any karush kuhn tucker point can also be shown to satisfy a second order necessary condition for a local maximum of the generalized wolfe dual induced from the augmented lagrangian interestingly this relation holds without requiring the karush kuhn tucker point itself to satisfy any second order optimality condition

predecessors of cellular automata states iii garden of eden classification of cellular automata abstract a procedure is given which determines all finite sequences without pre images for any one dimensional cellular automata with entries in z 2 on this basis we determine some properties of such sequences and classify all three site rules categories defined by this classification are compared to other phenomenological classifications introduced by wolfram gutowitz and jen