on the design of multifilter banks and orthonormal multiwavelet bases several forms of parametric expressions for orthogonal multifilter banks are presented the explicit expressions for a group of orthogonal multifilter banks that generate symmetric antisymmetric scaling functions and orthonormal multiwavelets are obtained based on these parametric expressions for orthogonal multifilter banks orthonormal multiwavelet pairs with good time frequency localization are constructed and examples of optimal multifilter banks are provided

armlets and balanced multiwavelets flipping filter construction in the scalar valued setting it is well known that the two scale sequences q sub k of daubechies orthogonal wavelets can be given explicitly by the two scale sequences p sub k of their corresponding orthogonal scaling functions such as q sub k 1 sup k p sub 1 k however due to the noncommutativity of matrix multiplication there is little such development in the multiwavelet literature to express the two scale matrix sequence q sub k of an orthogonal multiwavelet in terms of the two scale matrix sequence p sub k of its corresponding scaling function vector this paper in part is devoted to this study for the setting of orthogonal multiwavelets of dimension r 2 in particular the two lowpass filters are flipping filters whereas the two highpass filters are linear phase these results will be applied to constructing both a family of the most recently introduced notion of armlet of order n and a family of n balanced orthogonal multiwavelets

synchronization of stochastic bistable systems by biperiodic signals we study the nonlinear response of a noisy bistable system to a biperiodic signal through experiments with an electronic circuit schmitt trigger the signal we use is a biharmonic one i e a superposition of low and high frequency harmonic components it is shown that the mean switching frequency msf of the system can be locked at both low and high frequencies moreover the phenomenon of msf locking at the lower frequency can be induced and enhanced by the higher frequency excitation thus high frequency bias can control synchronization at the low frequency

how cells grow and divide mathematical analysis confirms demand for the cell cycle eukaryotes usually grow through cell growth and division how cells grow and divide is essential to life because too small or too large cells cannot function well in order for an organism to survive even under a condition where cell growth and division processes are independent of each other cells must have an appropriate growth factor growth rate and division rate to determine them we derive a time evolution equation for the size distribution of cells from the master equation describing changes in the cell size due to growth and in the total number of cells due to division it is found that long time behaviors of moments of the size distribution divide the parameter space consisting of the growth factor and the ratio of the division rate to the growth rate into infinitely many regions examining the properties of each region we conclude that growth with a small growth factor may be disastrous this demonstrates the demand for the cell cycle consisting of coordinated growth and division processes

weibull type limiting distribution for replicative systems the weibull function is widely used to describe skew distributions observed in nature however the origin of this ubiquity is not always obvious to explain in the present paper we consider the well known galton watson branching process describing simple replicative systems the shape of the resulting distribution about which little has been known is found essentially indistinguishable from the weibull form in a wide range of the branching parameter this can be seen from the exact series expansion for the cumulative distribution which takes a universal form we also find that the branching process can be mapped into a process of aggregation of clusters in the branching and aggregation process the number of events considered for branching and aggregation grows cumulatively in time whereas for the binomial distribution an independent event occurs at each time with a given success probability

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

extreme value statistics and return intervals in long range correlated uniform deviates we study extremal statistics and return intervals in stationary long range correlated sequences for which the underlying probability density function is bounded and uniform the extremal statistics we consider e g maximum relative to minimum are such that the reference point from which the maximum is measured is itself a random quantity we analytically calculate the limiting distributions for independent and identically distributed random variables and use these as a reference point for correlated cases the distributions are different from that of the maximum itself i e a weibull distribution reflecting the fact that the distribution of the reference point either dominates over or convolves with the distribution of the maximum the functional form of the limiting distributions is unaffected by correlations although the convergence is slower we show that our findings can be directly generalized to a wide class of stochastic processes we also analyze return interval distributions and compare them to recent conjectures of their functional form

comment on signal to noise ratio gain in neuronal systems we discuss the gain in signal to noise ratio snr recently reported by liu et al phys rev e 63 051912 2001 in the hodgkin huxley neuronal model we show first that the possibility of signal to noise ratio enhancements can be checked by consideration of the statistical characteristics of switching between the system states and we examine how the snr depends on the shape of a periodic signal second we attempt to verify the snr gain reported by liu et al based on spectral calculations and analyses of switching statistics we are unable to find any snr gain in the hodgkin huxley model

generalized extreme value statistics and sum of correlated variables we show that generalized extreme value statistics the statistics of the kth largest value among a large set of random variables can be mapped onto a problem of random sums this allows us to identify classes of non identical and generally correlated random variables with a sum distributed according to one of the three k dependent asymptotic distributions of extreme value statistics namely the gumbel frechet and weibull distributions these classes as well as the limit distributions are naturally extended to real values of k thus providing a clear interpretation to the onset of gumbel distributions with non integer index k in the statistics of global observables this is one of the very few known generalizations of the central limit theorem to non independent random variables finally in the context of a simple physical model we relate the index k to the ratio of the correlation length to the system size which remains finite in strongly correlated systems

approximation by translates of refinable functions the functions f 1 x dots f r x are refinable if they are combinations of the rescaled and translated functions f i 2x k this is very common in scientific computing on a regular mesh the space v 0 of approximating functions with meshwidth h 1 is a subspace of v 1 with meshwidth h 1 2 these refinable spaces have refinable basis functions the accuracy of the computations depends on p the order of approximation which is determined by the degree of polynomials 1 x dots x p 1 that lie in v 0 most refinable functions such as scaling functions in the theory of wavelets have no simple formulas the functions f i x are known only through the coefficients c k in the refinement equation scalars in the traditional case r times r matrices for multiwavelets the scalar sum rules that determine p are well known we find the conditions on the matrices c k that yield approximation of order p from v 0 these are equivalent to the strang fix conditions on the fourier transforms hat f i omega but for refinable functions they can be explicitly verified from the c k

stochastic resonance nonperturbative calculation of power spectra and residence time distributions we examine the response of a finite temperature two state system to periodic driving using time dependent transition rate theory this system can exhibit the phenomenon of stochastic resonance where raising the temperature increases the signal to noise ratio of the response we obtain the power spectrum and the distribution of residence times nonperturbatively for any transition rates that are periodic in time given the drive period mathit t mathit s the power spectrum is the fourier transform of the sum of signal which is periodic in time with period mathit t mathit s and noise which is the product of an exponential and a function periodic with period mathit t mathit s the residence time distribution is the product of an exponential and a function that is periodic with period mathit t mathit s both the power spectrum and the residence time distribution can be calculated exactly given the dependence of the transition rates on the control parameter e g asymmetry or temperature we calculate the characteristics of stochastic resonance for a two state system with activated transition rates and for a quantum mechanical dissipative two level system

logical response induced by temperature asymmetry it is known that the reliable logical response can be extracted from a noisy bistable system at an intermediate value of noise strength when two random or periodic two level square waveform serve as the inputs the asymmetry of the potential has a very important role and dictates the type of logical operation such as or or and exhibited by the system here we show that one can construct logic gates with symmetric bistable potential if the two states of the double well are thermalized with two different heat baths it has been found that if a given state is kept at a sufficiently low temperature compared to the other the system shows one kind of logic behavior say or interestingly the system s response turns into the other kind say and if the temperature of the initial low temperature well is increased gradually and the quality of the logical response first improves and then weakens after passing through a maximum at a particular value however the reliability of the second kind of logical response and is not as good as the first kind or and depends on the amplitude of the inputs still one can construct both kinds of logic gates with maximum reliability by properly choosing the initial low temperature well

multiwavelet bases with extra approximation properties this paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order because multiwavelet bases normally lack important properties that traditional wavelet bases of equal approximation order possess the associated discrete multiwavelet transform is less useful for signal processing unless it is preceded by a preprocessing step prefiltering this paper examines the properties and design of orthogonal multiwavelet bases with approximation order 1 that possess those properties that are normally absent for these balanced bases so named by lebrun and vetterli see proc ieee int conf acoust speech signal process icassp munich germany vol 3 p 2473 76 1997 and ibid vol 46 p 1119 24 1998 prefiltering can be avoided by reorganizing the multiwavelet filter bank the development in this paper draws from results regarding the approximation order of m band wavelet bases the main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by powers of z sup 2r 1 z sup 1 1 for traditional wavelets r 1 this specializes to the usual factor z 1 sup k

phase synchronization and stochastic resonance effects in the crayfish caudal photoreceptor we study the nonlinear response of the crayfish caudal photoreceptor to periodic mechanical stimuli in terms of stochastic synchronization the amplitude and frequency of the mechanical stimuli and the light level are used as control parameters the system shows multiple locking regions as the stimulus frequency is varied we find that the synchronization index increases as the signal to noise ratio snr of the periodic drive in response to increasing light levels this effect exhibits features similar to stochastic resonance we demonstrate a nonlinear rectification effect in which the snr of the second harmonic of the input stimulus increases as the light level is raised and show that the corresponding synchronization index increases as the snr of the second harmonic

size independence of the strength of snow the mechanical reliability of 600 randomly taken snow samples follows weibull distributions if sigma max is the maximum stress present in a specimen of given density the fraction of specimens that fail at stresses below sigma max is p 1 exp sigma max sigma 0 m the scale parameter sigma 0 evaluated by the maximum likelihood method increases nearly quadratically with the density rho of snow but unlike predicted by the weakest link model is independent of size and shape of the specimen there is no size dependence of the strength of snow the weibull parameter m is independent of density size and shape of the snow sample m 1 5 0 5 this implies on the one hand that the results of laboratory scale tests can be used for avalanche prediction but on the other hand that these predictions remain contaminated with large statistical errors snow is a fragile weak and unreliable material

array enhancement of stochastic synchronization and signal to noise ratio gain in the nonlinear regime of signal transmission the nonlinear transformation of an external noisy signal by an array of noninteracting elements with internal noise is considered the array simulates a neuronal system that processes spike trains it is shown that increasing the number of array elements entails significant extending of the stochastic synchronization region and improvement of the signal to noise ratio snr the effects are demonstrated for arrays of triggers overdamped bistable oscillators and fitzhugh nagumo systems the interrelation between snr improvement and the efficiency of information processing is discussed

discriminating between weibull distributions and log normal distributions emerging in branching processes we consider the yule type multiplicative growth and division process and describe the ubiquitous emergence of weibull and log normal distributions in a single framework with the help of the integral transform and series expansion we show that both distributions serve as asymptotic solutions of the time evolution equation for the branching process in particular the maximum likelihood method is employed to discriminate between the emergence of the weibull distribution and that of the log normal distribution further the detailed conditions for the distinguished emergence of the weibull distribution are probed it is observed that the emergence depends on the manner of the division process for the two different types of distribution numerical simulations are also carried out confirming the results obtained analytically

oscillatory systems driven by noise frequency and phase synchronization the phenomenon of effective phase synchronization in stochastic oscillatory systems can be quantified by an average frequency and a phase diffusion coefficient a different approach to compute the noise averaged frequencyis put forward the method is based on a threshold crossing rate pioneered by rice after the introduction of the rice frequency for noisy systems we compare this quantifier with those obtained in the context of other phase concepts such as the natural and the hilbert phase respectively it is demonstrated that the average rice frequency r typically supersedes the hilbert frequency h i e r h we investigate next the rice frequency for the harmonic and the damped bistable kramers oscillator both without and with external periodic driving exact and approximative analytic results are corroborated by numerical simulation results our results complement and extend previous findings for the case of noise driven inertial systems

a method of construction for biorthogonal multiwavelets system with 2r multiplicity biorthogonal multiwavelets systems are consisted of a pair of biorthogonal multiscaling functions and the corresponding a pair of multiwavelets a method for constructing biorthogonal multiwavelets systems with multiplicity 2r was derived in particular hermite interpolation mask was considered as primal masks a pair of primal and dual masks with high order of sum rules should be firstly designed in order to obtain a biorthogonal multiwavelet with high vanishing moment concretely starting from a short sequence primal masks possessing hermite interpolation properties a necessary and sufficient conditions such that primal masks satisfies the preassigned order of sum rules are established then a dual masks with short support symmetry and any preassigned order of sum rules is constructed it follows that two multiscaling functions are obtained and then multiwavelets and dual multiwavelets are derived from which a general design framework is obtained for constructing biorthogonal multiwavelets system with multiplicity 2r associated with hermite interpolation functions the biorthogonal multiwavelets constructed by our design framework has desirable properties such as symmetry short support high vanishing moments and simple structures with explicit expressions finally an example is given

multivariate matrix refinable functions with arbitrary matrix dilation characterizations of the stability and orthonormality of a multivariate matrix refinable function d with arbitrary matrix dilation m are provided in terms of the eigenvalue and 1 eigenvector properties of the restricted transition operator under mild conditions it is shown that the approximation order of d is equivalent to the order of the vanishing moment conditions of the matrix refinement mask pa the restricted transition operator associated with the matrix refinement mask pa is represented by a finite matrix ami j i j with a idet m i 1 e p j q3 p e and p j q3 p being the kronecker product of matrices p j and p the spectral properties of the transition operator are studied the sobolev regularity estimate of a matrix refinable function 4 is given in terms of the spectral radius of the restricted transition operator to an invariant subspace this estimate is analyzed in an example

quantifying stochastic resonance in bistable systems response vs residence time distribution functions a wealth of research on stochastic resonance sr during the past decade has led to different ways of defining this phenomenon most prominent are measures based on the response function and on the residence time distribution function while the theory for the response functions is well developed a first fully systematic theory for the residence time distribution functions is developed in this paper subsequently we reconsider formerly introduced measures of sr based on the residence time distribution and compare with those based on the response function

theory of frequency and phase synchronization in a rocked bistable stochastic system we investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked overdamped bistable potential driven by white gaussian noise the archetype description of stochastic resonance we present an approach to the stochastic counting process of noise induced switching events starting from the markovian dynamics of the nonstationary continuous particle dynamics one finds upon contraction onto two states a non markovian renewal dynamics a proper definition of an output discrete phase is given and the time rate of change of its noise average determines the corresponding output frequency the phenomenon of noise assisted phase synchronization is investigated in terms of an effective instantaneous phase diffusion the theory is applied to rectangular shaped rocking signals versus increasing input noise strengths in this case for an appropriate choice of the parameter values the system exhibits a noise induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal precise numerical simulations corroborate very favorably our analytical results the novel theoretical findings are also compared with prior ones

balanced multi wavelets in ℝ the notion of k balancing was introduced a few years ago as a condition for the construction of orthonormal scaling function vectors and multi wavelets to ensure the property of preservation annihilation of scalarvalued discrete polynomial data of order k or degree k 1 when decomposed by the corresponding matrix valued low pass high pass filters while this condition is indeed precise to the best of our knowledge only the proof for k 1 is known in addition the formulation of the k balancing condition for k 2 is so prohibitively difficult to satisfy that only a very few examples for k 2 and vector dimension 2 have been constructed in the open literature the objective of this paper is to derive various characterizations of the k balancing condition that include the polynomial preservation property as well as equivalent formulations that facilitate the development of methods for the construction purpose these results are established in the general multivariate and bi orthogonal settings for any k 1

an algorithm for matrix extension and wavelet construction this paper gives a practical method of extending an n x r matrix p z r n with laurent polynomial entries in one complex variable z to a square matrix also with laurent polynomial entries if p z has orthonormal columns when z is restricted to the torus t it can be extended to a paraunitary matrix if p z has rank r for each z t it can be extended to a matrix with nonvanishing determinant on t the method is easily implemented in the computer it is applied to the construction of compactly supported wavelets and prewavelets from multiresolutions generated by several univariate scaling functions with an arbitrary dilation parameter

on a family of biorthogonal armlets with prescribed properties abstract the notion of armlets analysis ready multiwavelets was introduced and studied by jian ao lian most recently as a precise formulation of orthonormal multiwavelets that guarantee wavelet decomposition with highpass output not being effected by polynomial perturbation of the input in this paper we first extend this concept to the biorthogonal setting and then we concern ourselves about a particular construction of biorthogonal multiscaling function and multiwavelets with multiplicity r 2 in particular we consider the two pairs of lowpass filters are flipped and the two pairs of highpass filters are linearphase respectively and we also give several equivalent forms of flipping property in terms of symbols and filters associated with multiscaling functions and multiwavelets by requiring flipping property we can represent all the entries of the matrix symbols p z q z p z q z of a biorthogonal multiwavelet using p11 z and p 11 z which are the first row and first column entries of p z and p z respectively these results will lead to a procedure for the construction of biorthogonal armlets with prescribed properties consequently a family of biorthogonal multiscaling functions which are mirrored copies each other and biorthogonal multiwavelets which are armlets of higher order with symmetry and antisymmetry are constructed explicitly

a new prefilter design for discrete multiwavelet transforms in conventional wavelet transforms prefiltering is not necessary due to the lowpass property of a scaling function this is no longer true for multiwavelet transforms a few research papers on the design of prefilters have appeared but the existing prefilters are usually not orthogonal which often causes problems in coding moreover the condition on the prefilters was imposed based on the first step discrete multiwavelet decomposition we propose a new prefilter design that combines the ideas of the conventional wavelet transforms and multiwavelet transforms the prefilters are orthogonal but nonmaximally decimated they are derived from a very natural calculation of multiwavelet transform coefficients in this new prefilter design multiple step discrete multiwavelet decomposition is taken into account our numerical examples by taking care of the redundant prefiltering indicate that the energy compaction ratio with the geronimo hardin massopust 1994 2 wavelet transform and our new prefiltering is better than the one with daubechies d sub 4 wavelet transform

balanced multiwavelets theory and design this article deals with multiwavelets which are a generalization of wavelets in the context of time varying filter banks and with their applications to signal processing and especially compression by their inherent structure multiwavelets are fit for processing multichannel signals this is the main issue in which we are interested first we review material on multiwavelets and their links with multifilter banks and especially time varying filter banks then we have a close look at the problems encountered when using multiwavelets in applications and we propose new solutions for the design of multiwavelets filter banks by introducing the so called balanced multiwavelets