wavelet entropy of stochastic processes abstract we compare two different definitions for the wavelet entropy associated to stochastic processes the first one the normalized total wavelet entropy ntws family s blanco a figliola r q quiroga o a rosso e serrano time frequency analysis of electroencephalogram series iii wavelet packets and information cost function phys rev e 57 1998 932 940 o a rosso s blanco j yordanova v kolev a figliola m schurmann e basar wavelet entropy a new tool for analysis of short duration brain electrical signals j neurosci method 105 2001 65 75 and a second introduced by tavares and lucena physica a 357 1 2005 71 78 in order to understand their advantages and disadvantages exact results obtained for fractional gaussian noise 1 1 and fractional brownian motion 1 3 are assessed we find out that the ntws family performs better as a characterization method for these stochastic processes

arithmetic of normal rees algebras two reasons drive this study of the arithmetical properties of blow up like algebras first one still lacks effective criteria for the rees algebra of an ideal to be normal and second there are several new phenomena related to torsionfree symmetric algebras of modules notably bundlesthat need clarification as yet another related question there is the description of the canonical modules of such algebras a necessary step in determining their gorenstein loci the main thread for these questions is the understanding of the divisor class group essentially defined by a pair made up of a morphism and a free subgroup of finite rank the behaviour of the mapping has puzzling

the universal r matrix for u_q rm sl 3 and beyond ther matrices for the quantised lie algebrasa n are constructed through the quantum double procedure given by drinfel d 6 the case ofu q sl 3 is thoroughly analysed initially to demonstrate the more subtle points of the calculation the ease of the calculation fora n is very dependent on a choice of generators for the borel subalgebrau q b and its dual and a certain ordering imposed on these generators which is related to the length of a certain word in the weyl group

unusual solutions to the yang baxter equation the complete list of non symmetric eight vertex constant solutions to the yang baxter equation is obtained and new solutions dependent on more than one variable are presented the corresponding spin hamiltonians are derived by sutherland s method 1970

colored solutions of the yang baxter equation from representations of uqgl 2 we study the hopf algebra structure and the highest weight representation of a multiparameter version of uqgl 2 the hopf algebra maps of this algebra are explicitly given we show that the multiparameter universal r matrix can be constructed directly as a quantum double intertwiner without using reshetikhin s twisting transformation we find there are two types highest weight representations for this algebra type a corresponds to the qeneric q and type b corresponds to the case that q is a root of unity when applying the representation theory to the multi parameter universal r matrix both standard and nonstandard colored solutions of the yang baxter equation are obtained

on the quantum symmetries associated with the two parameter free fermion model the quantum algebras associated with the r matrix obtained from the two parameter free fermion model are examined it is shown that in addition to uq s gl 1 1 there exists another algebra which is isomorphic to uq s gl 1 1 as an algebra but has a different hopf structure it does not have a classical limit and is related to up sl 2 c at a root of unity p i i2 1

duals of colored quantum universal enveloping algebras and colored universal t matrices we extend the notion of dually conjugate hopf super algebras to the colored hopf super algebras hc that we recently introduced we show that if the standard hopf super algebras hq that are the building blocks of hc have hopf duals hq then the latter may be used to construct coloured hopf duals hc endowed with colored algebra and antipode maps but with a standard coalgebraic structure next we review the case where the hq s are quantum universal enveloping algebras of lie super algebras uq g so that the corresponding hq s are quantum super groups gq we extend the fronsdal and galindo universal t matrix formalism to the colored pairs uc g gc by defining colored universal t matrices we then show that together with the colored universal r matrices previously introduced the latter provide an algebraic formulation of the colored rtt relations proposed by basu mallick this establishes a link between the colored extensions of drinfeld jimbo and faddeev reshetikhin takhtajan pictures of quant

stochastic resonance in neuron models periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus they tend to fire at a preferred phase of the stimulus cycle but not at every cycle hence the histogram of interspike intervals isih i e of times between successive firings is multimodal for these neurons with peaks centered at integer multiples of the driving period a particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data in the present paper we show that an excitable cell model the fitzhugh nagumo equations also reproduces these features when driven by additive periodic and stochastic forces this model exhibits its own brand of stochastic resonance as the peaks of the isih successively go through a maximum when the noise intensity is increased further the presence of a noise induced limit cycle introduces a third time scale in the problem this limit cycle is found to modify qualitatively the phase locking picture e g by suppressing certain peaks in the isih finally the role of noise and possibly of stochastic resonance sr in the neural encoding of sensory information is discussed

the universal r matrix and the yang baxter equation with parameters the authors formulate and demonstrate with some examples a method for obtaining solutions of the yang baxter equation with parameters

coloured frt algebra and its yang baxterization leading to integrable models with non additive r matrices a colour representation of faddeev reshetikhin takhtajan frt algebra which in contrast to the standard case is related to the coloured braid group representation with generic values of q is presented explicit realizations of l or matrices occurring in this coloured variant of frt algebra are also obtained for the uq gl 2 quantized algebra though these realizations are found to depend manifestly on the colour parameters the underlying quantum group structure and associated co product are interestingly free from such dependence this allows us to perform the yang baxterization of the coloured frt algebra successfully which leads to the construction of an ancestor law operator associated with a new non additive type quantum r matrix through different realizations of this lax operator a new class of quantum integrable models representing colour generalizations of the well known models such as the lattice sine gordon model the ablowitz ladik model lattice and the derivative nonlinear schrodinger model etc is generated

responses of a hodgkin huxley neuron to various types of spike train inputs numerical investigations have been made of responses of a hodgkin huxley hh neuron to spike train inputs whose interspike interval isi is modulated by deterministic semi deterministic chaotic and stochastic signals as deterministic one we adopt inputs with the time independent isi and with time dependent isi modulated by sinusoidal signal the rossler and lorentz models are adopted for chaotic modulations of isi stochastic isi inputs with the gamma distribution are employed it is shown that distribution of output isi data depends not only on the mean of isis of spike train inputs but also on their fluctuations the distinction of responses to the three kinds of inputs can be made by return maps of input and output isis but not by their histograms the relation between the variations of input and output isis is shown to be different from that of the integrate and fire if model because of the refractory period in the hh neuron

dynamical mean field theory of noisy spiking neuron ensembles application to the hodgkin huxley model a dynamical mean field approximation dma previously proposed by the present author h hasegawa phys rev e 67 041903 2003 has been extended to ensembles described by a general noisy spiking neuron model ensembles of n unit neurons each of which is expressed by coupled k dimensional differential equations des are assumed to be subject to spatially correlated white noises the original mathrm kn dimensional stochastic des have been replaced by k k 2 dimensional deterministic des expressed in terms of means and the second order moments of local and global variables the fourth order contributions are taken into account by the gaussian decoupling approximation our dma has been applied to an ensemble of hodgkin huxley hh neurons k 4 for which effects of the noise the coupling strength and the ensemble size on the response to a single spike input have been investigated numerical results calculated by the dma theory are in good agreement with those obtained by direct simulations although the former computation is about a thousand times faster than the latter for a typical hh neuron ensemble with n 100

dynamical mean field theory of spiking neuron ensembles response to a single spike with independent noises a semianalytical dynamical mean field theory has been developed for a study of dynamics of an ensemble of n unit fitzhugh nagumo neurons subject to white noises assuming weak noises and the gaussian distribution of state variables we have driven equations of motions for moments of local and global variables dynamical mean field approximation dma has replaced original 2n dimensional stochastic differential equations des by eight dimensional deterministic des whereas the conventional moment method yields n 2n 3 dimensional deterministic des for local variables we have discussed the dependence of the spike firing precision and the synchronization on the noise intensity synaptic coupling and the size of the neuron ensemble the spike timing precision is shown to be improved by increasing the size of the neuron ensemble even when there are no couplings among neurons when the coupling is introduced neurons in ensembles respond to an input spike with a partial synchronization results calculated by our dma theory are in good agreement with those obtained by direct simulations dma theory is extended to a large cluster which can be divided into multiple subclusters according to their functions a model calculation has demonstrated that when the noise intensity is moderate the spike propagation with a fairly precise timing is possible among noisy subclusters with feed forward couplings as in the synfire chain we have compared dma theory with the conventional moment method showing that the former may be alternatively derived from the latter by a reduction in the number of moments with the mean field approximation

new hierarchy of colored braid group representations novel solutions of the yang baxter relation for a series of multistate vertex models are presented in the braid group limit the obtained family of solutions gives a sequence of colored braid group representations possible generalizations of the multivariable alexander polynomial are discussed

universal r matrix of reductive lie algebras and quantum integrable systems from its colour representation the universal r matrix intertwining between the coproduct structures related to the universal deformations of reductive lie algebras has been found in an explicit form using twisting a possible colour representation of this r matrix and its application to the integrable systems are shown using the example of a deformed gl n algebra

wavelet analysis of discharge dynamics of fusimotor neurons abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the wavelet transform analysis and confirm the existence of the white noise characteristics of the isi time series this means that the neuron activity may serve as the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles besides we apply the multifractal formalism adapted for the wavelet transform time series analysis thus we have established the multifractality of the isi data and achieved an additional insight into fusimotor discharge dynamics

yang baxterization of braid group representations for a given braid group representation bgr a process of the yang baxterization is formulated to generate solutions of the yang baxter equation ybe when a bgr admits the birman wenzl bw algebraic structure this process can be explicitly passed through and two types of trigonometric solutions of ybe are generated from such a bgr these two solutions have the essential difference to each other and both of them preserve the crossing symmetry property if the given bgr has by taking certain reduction on the bw algebra the rational solution is also generated a practical condition to judge whether a bgr satisfies the bw algebra is given from which one finds that not only the familiar bgrs of 5 7 9 but also some new ones obtained recently in 12 have the bw structure thus they can be explicitly yang baxterized to solutions of the ybe

information transmission in parallel threshold arrays suprathreshold stochastic resonance the information transmitted through a parallel summing array of noisy threshold elements with a common threshold is considered in particular using theoretical and numerical analysis a recently reported n g stocks phys rev lett 84 2310 2000 form of stochastic resonance termed suprathreshold stochastic resonance ssr is studied in detail ssr is observed to occur in arrays with two or more elements and unlike stochastic resonance sr in a single element gives rise to noise induced information gains that occur independent of the setting of the threshold or the size of the signal the transmitted information is maximized when all thresholds are set to coincide with the signal mean in this situation and for large arrays the noise can enhance performance up to approximately half the theoretical noiseless channel capacity the theory is tested against digital simulation

theoretical analysis of array enhanced stochastic resonance in the diffusively coupled fitzhugh nagumo equation the array enhanced stochastic resonance aesr in the diffusively coupled fitzhugh nagumo equation is investigated the two properties of aesr namely the scaling of the optimal noise intensity and the enhancement of the maximum value of the correlation coefficient as a function of the coupling strength are analyzed theoretically by transforming the dynamics of n elements into that of the mean and the deviation from it it is found that aesr is caused by the correlation between them a low dimensional model that reproduces the above properties is constructed

universal r matrix for a two parametric quantization of gl 2 for the two parametric quantized group glq s 2 the authors calculate the explicit form of the universal r matrix

stochastic resonance of ensemble neurons for transient spike trains wavelet analysis by using the wavelet transformation wt i have analyzed the response of an ensemble of n 1 10 100 and 500 hodgkin huxley neurons to transient m pulse spike trains m i to 3 with independent gaussian noises thecross correlation between the input and output signals is expressed in terms of the wt expansion coefficients the signal to noise ratio snr is evaluated by using the denoising method within the wt by which the noise contribution is extracted from the output signals although the response of a single n 1 neuron to subthreshold transient signals with noises is quite unreliable the transmission fidelity assessed by the cross correlation and snr is shown to be much improved by increasing the value of n a population of neurons plays an indispensable role in the stochastic resonance sr for transient spike inputs it is also shown that in a large scale ensemble the transmission fidelity for suprathreshold transient spikes is not significantly degraded by a weak noise which is responsible to sr for subthreshold inputs

rees algebras of f regular type abstract we study the f regularity of rees algebras r i a it in terms of the global f regularity of the blowing up x proj r i of spec a as it reads global f regularity is a global analog of strong f regularity defined via splitting of frobenius maps in prime characteristic and these notions are extended to characteristic zero by reduction modulo p 0 we study in detail the case where a m is a two dimensional local ring and i is an m primary ideal in characteristic zero the condition for r i to have f regular type is described in terms of the dual graph of a resolution x on which i o x is invertible we also prove some miscellaneous results concerning singularities of rees algebras and extended rees algebras of higher dimension

a nonlinear deformed su 2 algebra with a two color quasitriangular hopf structure nonlinear deformations of the enveloping algebra of su 2 involving two arbitrary functions of j0 and generalizing the witten algebra were introduced some time ago by delbecq and quesne in the present paper the problem of endowing some of them with a hopf algebraic structure is addressed by studying in detail a specific example referred to as aq 1 this algebra is shown to possess two series of n 1 dimensional unitary irreducible representations where n 0 1 2 to allow the coupling of any two such representations a generalization of the standard hopf axioms is proposed by proceeding in two steps in the first one a variant and extension of the deforming functional technique is introduced variant because a map between two deformed algebras suq 2 and aq 1 is considered instead of a map between a lie algebra and a deformed one and extension because use is made of a two valued functional whose inverse is singular as a result the hopf structure of suq 2 is carried over to aq 1 ther

multi symbolic rees algebras and strong f regularity let i be a divisorial ideal of a strongly f regular ring a k i watanabe raised the question whether the symbolic rees algebra mathcal r s i oplus n ge 0 i n is cohen macaulay whenever it is noetherian we develop the notion of multi symbolic rees algebras and use this to show that mathcal r s i is indeed cohen macaulay whenever a certain auxiliary ring is finitely generated over a

f rational rings have rational singularities it is proved that an excellent local ring of prime characteristic in which a single ideal generated by any system of parameters is tightly closed must be pseudorational a key point in the proof is a characterization of f rational local rings as those cohen macaulay local rings r m in which the local cohomology module h d m r where d is the dimension of r have no submodules stable under the natural action of the frobenius map an analog for finitely generated algebras over a field of characteristic zero is developed which yields a reasonably checkable tight closure test for rational singularities of an algebraic variety over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i without reference to a desingularization

aperiodic stochastic resonance stochastic resonance sr is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise recently we presented a method and theory for characterizing sr type behavior in excitable systems with aperiodic i e broadband input signals phys rev e 52 r3321 1995 we coined the term aperiodic stochastic resonance asr to describe this general type of behavior in that earlier study we demonstrated asr in the fitzhugh nagumo neuronal model here we demonstrate asr in three additional systems a bistable well system an integrate and fire neuronal model and the hodgkin huxley hh neuronal model we present computational and theoretical results for each system in the context of the hh model we develop a general theory for asr in excitable membranes this work clearly shows that sr type behavior is not limited to systems with periodic inputs thus in general noise can serve to enhance the response of a nonlinear system to a weak input signal regardless of whether the signal is periodic or aperiodic textcopyright 1996 the american physical society

nonstationary stochastic resonance it is by now established that remarkably the addition of noise to a nonlinear system may sometimes facilitate rather than hamper the detection of weak signals this phenomenon usually referred to as stochastic resonance was originally associated with strictly periodic signals but it was eventually shown to occur for stationary aperiodic signals as well however in several situations of practical interest the signal can be markedly nonstationary we demonstrate that the phenomenon of stochastic resonance extends to nonstationary signals as well and thus could be relevant to a wider class of biological and electronic applications building on both nondynamic and aperiodic stochastic resonance our scheme is based on a multilevel trigger mechanism which could be realized as a parallel network of differentiated threshold sensors we find that optimal detection is reached for a number of thresholds of order 10 and that little is gained by going much beyond that number we raise the question of whether this is related to the fact that evolution has favored some fixed numbers of precisely this order of magnitude in certain aspects of sensory perception

f rationality of rees algebras in this paper using the notion of the tight integral closure we will give a criterion for f rationality of rees algebras of m primary ideals in a cohen macaulay local ring as its application we prove the following results 1 in dimension two if a is f rational and i is integrally closed then the rees algebra r i is f rational on the other hand in higher dimensions we construct many examples of cohen macaulay normal rees algebras which are not f rational 2 if both a and r i are f rational then so is the extended rees algebra r i 3 if r i is f rational and a g i 1 then a is f rational on the other hand using resolution of singularities we will prove that a two dimensional rational singularity always admits f rational rees algebras in particular this theorem gives another way than that devised by watanabe 1997 j pure appl algebra122 323 328 to construct counterexamples to the boutot type theorem for f rational rings