method of speech recognition using time dependent interpolation and hidden dynamic value classes a speech signal is decoded by determining a production related value for a current state based on an optimal production related value at the end of a preceding state the optimal production related value being selected from a set of continuous values the production related value is used to determine a likelihood of a phone being represented by a set of observation vectors that are aligned with a path between the preceding state and the current state the likelihood of the phone is combined with a score from the preceding state to determine a score for the current state the score from the preceding state being associated with a discrete class of production related values wherein the class matches the class of the optimal production related value

modular shimura varieties and forgetful maps in this note we consider several maps that occur naturally between modular shimura varieties hilbert blumenthal varieties and the moduli spaces of polarized abelian varieties when forgetting certain endomorphism structures we prove that up to birational equivalences these forgetful maps coincide with the natural projection by suitable abelian groups of atkin lehner involutions

turing instabilities and patterns near a hopf bifurcation we derive a necessary and sufficient condition for turing instabilities to occur in two component systems of reaction diffusion equations with neumann boundary conditions we apply this condition to reaction diffusion systems built from vector fields with one fixed point and a supercritical hopf bifurcation for the brusselator and the ginzburg landau reaction diffusion equations we obtain the bifurcation diagrams associated with the transition between time periodic solutions and asymptotically stable solutions turing patterns in two component systems of reaction diffusion equations we show that the existence of turing instabilities is neither necessary nor sufficient for the existence of turing pattern type solutions turing patterns can exist on both sides of the hopf bifurcation associated with the local vector field and depending on the initial conditions time periodic and stable solutions can coexist

membrane bound turing patterns motivated by recent observations in biological cells we study turing patterns in bounded regions where the nonlinear chemical reactions occur on the boundary and where reagent transport occurs in the bulk within a generic model we formulate the stability problem and discuss the conditions for the occurrence of a turing instability by choosing other model parameters to be unequal we find that turing patterns exist even in the case of equal diffusion constants finally a recently introduced computation technique is utilized to follow the nascent pattern into the highly nonlinear regime

resonant suppression of turing patterns by periodic illumination we study the resonant behavior of turing pattern suppression in a model of the chlorine dioxide iodine malonic acid reaction with periodic illumination the results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system the resonance in turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force square wave on off periodic forcing is more effective in suppressing turing patterns than sinusoidal forcing we compare the dynamics of periodically forced turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns

riemann roch and abel jacobi theory on a finite graph abstract it is well known that a finite graph can be viewed in many respects as a discrete analogue of a riemann surface in this paper we pursue this analogy further in the context of linear equivalence of divisors in particular we formulate and prove a graph theoretic analogue of the classical riemann roch theorem we also prove several results analogous to classical facts about riemann surfaces concerning the abel jacobi map from a graph to its jacobian as an application of our results we characterize the existence or non existence of a winning strategy for a certain chip firing game played on the vertices of a graph

the stochastic hopf bifurcation analysis in brusselator system with random parameter hopf bifurcation in brusselator system with random parameter is explored in this paper firstly according to the orthogonal polynomial approximation in hilbert space the brusselator system with random parameter can be reduced into the deterministic equivalent system then the hopf bifurcation in deterministic equivalent system is discussed by the mathematical analysis and the first lyapunov coefficient method the studies discovered that different from the deterministic system the critical value of stochastic hopf bifurcation is determined not only by deterministic parameters in stochastic system but also by the intensity of random parameter as the intensity of random parameter is increased the critical value of stochastic hopf bifurcation is decreased at last theoretical results are verified by numerical simulations

congruences between modular forms raising the level and dropping euler factors abstract we discuss the relationship among certain generalizations of results of hida ribet and wiles on congruences between modular forms hida s result accounts for congruences in terms of the value of an l function and ribet s result is related to the behavior of the period that appears there wiles theory leads to a class number formula relating the value of the l function to the size of a galois cohomology group the behavior of the period is used to deduce that a formula at nonminimal level is obtained from one at minimal level by dropping euler factors from the l function

recursive parameter estimation using incomplete data abstract stochastic approximation procedures are considered for the estimation of parameters using incomplete data one procedure is stated and illustrated which often leads to asymptotically efficient estimators others are developed which although possibly not optimal in the above sense will be very much easier to apply this will be particularly advantageous when quick recursive estimates are required examples are given and a link is made between one of the sub optimal methods and the em algorithm author

stability analysis and numerical simulation of gravitactic bioconvection in a rectangular cavity abstract the bioconvection of gravitactic microorganisms through linear analysis and numerical simulation is presented using the basic state as initial condition for both microorganisms and streamlines the critical rayleigh number and the bioconvection are predicted the dynamic microorganisms behavior is influenced by the initial spatial distribution the stability of the system is dependent on the horizontal wave component that is inversely related to wavelength the pattern length and the instability of the process are associated with the horizontal component of the wave number and the characteristic wavelength respectively using complex and real eigenvalues five unstable and three stable rolls are found respectively the three stable rolls is the dominant pattern when varying the principal variables of this bioconvective process

three dimensional dissipative structures in reaction diffusion systems abstract we study analytically and numerically the tridimensional pattern selection problem for reaction diffusion systems qualitative agreement is found with the recent experimental results

method of noise reduction using correction and scaling vectors with partitioning of the acoustic space in the domain of noisy speech a method and apparatus are provided for reducing noise in a training signal and or test signal the noise reduction technique uses a stereo signal formed of two channel signals each channel containing the same pattern signal one of the channel signals is clean and the other includes additive noise using feature vectors from these channel signals a collection of noise correction and scaling vectors is determined when a feature vector of a noisy pattern signal is later received it is multiplied by the best scaling vector for that feature vector and the best correction vector is added to the product to produce a noise reduced feature vector under one embodiment the best scaling and correction vectors are identified by choosing an optimal mixture component for the noisy feature vector the optimal mixture component being selected based on a distribution of noisy channel feature vectors associated with each mixture component

proving the triviality of rational points on atkin lehner quotients of shimura curves in this paper we give a method for studying global rational points on certain quotients of shimura curves by atkin lehner involutions we obtain explicit conditions on such quotients for rational points to be trivial coming from cm points only and exhibit an explicit infinite family of such quotients satisfying these conditions

competition in ramped turing structures abstract stationary pattern selection and competition in the uniform brusselator in two 2d and three 3d dimensions are reviewed including reentrant hexagonal and striped zig zag phases influences of linear or chain like profiles of the pool chemicals on this selection are presented in the form of numerical experiments the relation with the recent experimental patterns obtained with the cima reaction is discussed

numerical studies of turing patterns selection in a two dimensional system abstract the turing bifurcations of the schnackenberg model are studied by numerical simulations the relative stability of the striped and hexagonal patterns are determined for a large range of control parameters we show that the stability of the triangular and honeycomb forms of hexagonal patterns are exchanged at a critical point striped patterns are favoured in the vicinity of this point we also show that one of the hexagonal phase is reentrant far from the bifurcation point finally we show that striped patterns develop preferentially in directions orthogonal to the walls when no flux boundary conditions are applied

qualitative behavior of n dimensional ratio dependent predator prey systems abstract this paper deals with the qualitative properties of an n dimensional autonomous system of differential equations modeling the general ratio dependent predator prey interaction

serre s modularity conjecture ii we provide proofs of theorems 4 1 and 5 1 of khare and wintenberger invent math doi 10 1007 s00222 009 0205 7 2009

special values of anticyclotomic l functions the object of this paper is to extend the results and methods of vat01 where it was shown how cases of a conjecture of mazur on the behavior of l functions in an anticyclotomic zp extension could be deduced by studying the distribution of heegner points associated to definite quaternion algebras the main result of vat01 showed that when the sign in the functional equation is 1 then the special values of the l functions in question are generically nonzero in this paper we propose to study the special values modulo a prime of q and can offer three new theorems in this direction the first result theorem 1 1 determines the iwasawa invariant of the p adic l functions of bertolini and darmon we show that is usually zero but not always when 0 we give a precise formula for the value and an interpretation of the positivity in terms of congruences the second result theorem 1 2 pertains to the case where has residue characteristic p in this case we show that the l values are typically units but again that this is not always the case for technical reasons this theorem applies only to a restricted class of but it seems rather likely that the restrictions can be lifted finally we use the result of theorem 1 2 to transfer our results from the case where the sign in the functional equation is 1 to the case of sign 1 and to derivatives of l functions this is achieved by using congruences and the sign change phenomenon exploited by bertolini darmon namely we prove a jochnowitz congruence which relates the nontriviality of a special value modulo to the nontriviality of a classical heegner point on a modular curve the result is stated in theorem 1 4 to describe these results more precisely let g denote a newform on 0 n let k denote an imaginary quadratic field of discriminant d such that d is prime to n write n n n where n is divisible only by those primes which are split in k whereas n is divisible only by primes

turing patterns in three dimensions we investigate three dimensional turing patterns in two component reaction diffusion systems the fitzhugh nagumo equation the brusselator and the gray scott model are solved numerically in three dimensions several interconnected structures of domains as well as lamellar hexagonal and spherical domains are obtained as stable motionless equilibrium patterns the relative stability of these structures is studied analytically based on the reduction approximation the relation with the microphase separated structures in block copolymers is also discussed

reaction diffusion patterns in confined chemical systems we review on the effects of the feed mode on pattern selection observed in chemical systems operated in open spatial reactors in two side fed reactors strong parameter ramps naturally confine patterns in a stratum the reactor thickness acts both as a genuine bifurcation parameter and on the pattern dimensionality depending on that thickness standard 2d hexagon and stripe turing patterns or more complex 3d planforms are observed in thin one side fed reactors patterning process must escape the imposed fixed boundary conditions either by devices introducing mixed boundary conditions or by an intrinsic phenomenon dubbed spatial bistability we show that in most cases for a comprehensive understanding of experimental observations the full 3d aspects have to be taken into account

n dimensional ratio dependent predator prey systems with diffusion abstract this paper deals with a ratio dependent predator prey system with diffusion we will investigate under what conditions turing stability or instability occurs in higher dimensions

dynamics of a diffusion reaction prey predator model with delay in prey effects of delay and spatial components abstract we study the complex dynamics of a monod haldane type predator prey interaction model that incorporates 1 a constant time delay in the prey growth and 2 diffusion in both prey and predator we provide the rigorous results of our system including the asymptotic stability of a positive equilibrium hopf bifurcation and the direction of hopf bifurcation and the stability of bifurcated periodic solutions we also perform numerical simulations on the effects of diffusion or and delay when the corresponding ode model has either a unique interior equilibrium with two interior attractors or two interior equilibria our theoretical and numerical results show that diffusion can either stabilize or destabilize the system large delay could destabilize the system and the combination of diffusion and delay could intensify the instability of the system moreover when the corresponding ode system has two interior equilibria diffusion or time delay in prey or both could lead to the extinction of predator our results may provide us useful biological insights on population managements for prey predator interaction systems

spatiotemporal dynamics in a delayed diffusive predator model in this paper we investigate the spatiotemporal dynamics of a delayed reaction diffusion leslie gower model based on the stability analysis we demonstrate that delayed feedback may generate hopf and turing instability under some conditions resulting in spatial patterns one of the most interesting findings is that the model exhibits complex pattern replication pure turing instability gives birth to spots spots stripes mixture stripes stripes holes mixture and holes patterns pure hopf instability to spiral wave pattern and hopf turing instability to chaotic wave pattern our results well extend the findings of spatiotemporal dynamics in the delayed reaction diffusion predator prey model and indicate that time delay play an important roles in pattern formation

the iwasawa main conjectures for gl2 we prove the one two and three variable iwasawa greenberg main conjectures for a large class of modular forms that are ordinary with respect to an odd prime p the method of proof involves an analysis of an eisenstein ideal for ordinary hida families for gu 2 2

on the dynamics of an n dimensional ratio dependent predator prey system with diffusion abstract the main concern of this paper is to study the dynamic of an n dimensional ratio dependent predator prey system with diffusion more concretely we study the dissipativeness the persistence of the system and we obtain condition under which the nontrivial equilibrium is globally asymptotically stable

interconnected turing patterns in three dimensions we study numerically the turing pattern in three dimensions in a fitzhugh nagumo type reaction diffusion system we have found that interconnected periodic domain structures such as a gyroid fddd and perforated lamellar structures appear in three dimensions which never exist in lower dimensions the stability analysis of these structures is also performed by means of a mode expansion

turing models of cortical folding on exponentially and logistically growing domains the brain s cerebral cortex is folded into intricate patterns of gyri hills and sulci valleys the complete biological mechanism underlying the cortical folding process continues to remain elusive to this day one proposed biological mechanism of cortical folding is the intermediate progenitor model which correlates patterns of regional self amplification of neural intermediate progenitor cells with cortical folds we construct mathematical models of cortical folding utilizing a turing reaction diffusion system on an exponentially or logistically growing prolate spheroidal domain patterns generated by our turing system models represent prepatterns for regional activation of self amplification of intermediate progenitor cells which may be correlated with cortical folding patterns according to the intermediate progenitor model we observe that the presence of exponential domain growth generates a turing pattern that is continually transient and evolves from one pattern to another this differs from patterns generated by a static domain turing system which converge to a final pattern we also observe that a logistically growing domain turing system generates a pattern that is transient during the period of rapid domain growth but then converges to a final pattern similar to a static domain turing system our turing models of cortical folding can be used to explain certain diseases of cortical folding

quaternionic loci in siegel s modular threefold let mathcal q d be the set of moduli points on siegel s modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order mathcal o in an indefinite quaternion algebra of discriminant d over mathbb q such that the rosati involution coincides with a positive involution of the form alpha mapsto mu 1 overline alpha mu on mathcal o for some mu in mathcal o with mu 2 d 0 in this paper we first give a formula for the number of irreducible components in mathcal q d strengthening an earlier result of rotger then for each irreducible component of genus 0 we determine its rational parameterization in terms of a hauptmodul of the associated shimura curve

method of pattern recognition using noise reduction uncertainty a method and apparatus are provided for using the uncertainty of a noise removal process during pattern recognition in particular noise is removed from a representation of a portion of a noisy signal to produce a representation of a cleaned signal in the meantime an uncertainty associated with the noise removal is computed and is used with the representation of the cleaned signal to modify a probability for a phonetic state in the recognition system in particular embodiments the uncertainty is used to modify a probability distribution by increasing the variance in each gaussian distribution by the amount equal to the estimated variance of the cleaned signal which is used in decoding the phonetic state sequence in a pattern recognition task

simple and superlattice turing patterns in reaction diffusion systems bifurcation bistability and parameter collapse abstract we use equivariant bifurcation theory to investigate pattern selection at the onset of a turing instability in a general two component reaction diffusion system the analysis is restricted to patterns that periodically tile the plane in either a square or hexagonal fashion both simple periodic patterns stripes squares hexagons and rhombs and superlattice patterns are considered the latter correspond to patterns that have structure on two disparate length scales the short length scale is dictated by the critical wave number from linear theory while the periodicity of the pattern is on a larger scale analytic expressions for the coefficients of the leading nonlinear terms in the bifurcation equations are computed from the general reaction diffusion system using perturbation theory we show that no matter how complicated the reaction kinetics might be the nonlinear reaction terms enter the analysis through just four parameters moreover for hexagonal problems all patterns bifurcate unstably unless a particular degeneracy condition is satisfied and at this degeneracy we find that the number of effective system parameters drops to two allowing a complete characterization of the possible bifurcation results at this degeneracy for example we find that rhombs squares and superlattice patterns always bifurcate unstably we apply these general results to some specific model equations including the lengyel epstein cima model to investigate the relative stability of patterns as a function of system parameters and to numerically test the analytical predictions

on line estimation of hidden markov model parameters based on the kullback leibler information measure sequential or online hidden markov model hmm signal processing schemes are derived and their performance is illustrated by simulation the online algorithms are sequential expectation maximization em schemes and are derived by using stochastic approximations to maximize the kullback leibler information measure the schemes can be implemented either as filters or fixed lag or sawtooth lag smoothers they yield estimates of the hmm parameters including transition probabilities markov state levels and noise variance in contrast to the offline em algorithm baum welch scheme which uses the fixed interval forward backward scheme the online schemes have significantly reduced memory requirements and improved convergence and they can estimate hmm parameters that vary slowly with time or undergo infrequent jump changes similar techniques are used to derive online schemes for extracting finite state markov chains imbedded in a mixture of white gaussian noise wgn and deterministic signals of known functional form with unknown parameters

bifurcation and turing patterns of reaction diffusion activator inhibitor model abstract gierer meinhardt system is one of prototypical pattern formation models turing instability could induce various patterns in this system hopf bifurcation analysis and its direction are performed on such diffusive model in this paper by employing normal form and center manifold reduction the effects of diffusion on the stability of equilibrium point and the bifurcated limit cycle from hopf bifurcation are investigated it is found that under some conditions diffusion driven instability i e turing instability about the equilibrium point and the bifurcated limit cycle will happen which are stable without diffusion those diffusion driven instabilities will lead to the occurrence of spatially nonhomogeneous solutions as a result some patterns like stripe and spike solutions will form the explicit criteria about the stability and instability of the equilibrium point and the limit cycle in the system are derived which could be readily applied further numerical simulations are presented to illustrate theoretical analysis

log spectral compensation of pmc gaussian mean vectors for noisy speech recognition using log max assumption reducing mismatch between hmms trained with clean speech and speech signals recorded under background noise can be approached by distribution adaptation using parallel model combination pmc accurate pmc has no closed form expression therefore simplification assumptions must be made in implementation under a new log max assumption adaptation formula for log spectral parameters are presented both for static and dynamic parameters the system takes the mean vector 41 made up of the static part 41 a and the dynamic part 41 b and the noise vector 43 made up of the static part 43 a and dynamic part 43 b and applies to a decision circuit 45 to determine if the quiet vector plus the gain of speech produced in noise with respect to clean speech is greater than the noisy mean vector and if so the static part is equal to the gain plus the clean speech vector and the dynamic part is the change in the the quiet speech vector and if not greater than the noise vector then the static part equals the noise vector and the dynamic part is zero

method of reducing index sizes used to represent spectral content vectors a method identifies a codeword to represent a vector derived from an audio signal by applying the vector to first and second decision trees the first decision tree is associated with a first type of audio sound and produces a first codeword the second decision tree is associated with a second type of audio sound and produces a second codeword one of the first and second codewords is then selected as the codeword for the vector in further embodiments the vector describes the spectral content of the audio signal and a linear prediction value is generated for the vector the difference between the linear prediction value and the vector is used to identify the codeword

the effect of boundary conditions on the mesoscopic lattice boltzmann method case study of a reaction diffusion based model for min protein oscillation abstract min protein oscillation in escherichia coli has an essential role in controlling the accurate placement of the cell division septum at the middle cell zone of the bacteria this biochemical process has been successfully described by a set of reaction diffusion equations at the macroscopic level the lattice boltzmann method lbm has been used to simulate min protein oscillation and proved to recover the correct macroscopic equations in this present work we studied the effects of lbm boundary conditions bc on min protein oscillation the impact of diffusion and reaction dynamics on bcs was also investigated it was found that the mirror image bc is a suitable boundary treatment for this min protein model the physical significance of the results is extensively discussed

method of determining uncertainty associated with acoustic distortion based noise reduction a method and apparatus are provided for determining uncertainty in noise reduction based on a parametric model of speech distortion the method is first used to reduce noise in a noisy signal in particular noise is reduced from a representation of a portion of a noisy signal to produce a representation of a cleaned signal by utilizing an acoustic environment model the uncertainty associated with the noise reduction process is then computed in one embodiment the uncertainty of the noise reduction process is used in conjunction with the noise reduced signal to decode a pattern state

on modular representations of bar q q arising from modular forms where g is the galois group gai i q and f is a finite field of characteristic i 3 suppose that p is modular of level n i e that it arises from a weight 2 newform of level dividing n and trivial nebentypus character then p is an odd representation the matrix p c where c is a complex conjugation in g has eigenvalues 1 1 since 1 and 1 are distinct in f p is absolutely irreducible and has a model over every subfield of f containing the set trace p we assume that f has been chosen so that it is generated by this set assume that p is a prime which exactly divides n we write p i n and restrict p to a decomposition group of g for the prime p view the restriction as a representation p p of gal t p qp we say that p is finite at p 34 or 35 w if there is a finite flat f vector space scheme h over zp for which the action of gal t p qp on the f vector space h 1 p gives pp i f p 9 is finite at p if and only if pp is unramified it is clear that p is finite at p whenever p is already modular of level n p in w of 34 cf 35 serre conjectured the converse i e that if p is finite then p is modular of level n p soon thereafter mazur 1 20 proved this conjecture in the case

pattern formation in the three dimensional reaction diffusion systems existing group theoretic analysis of pattern formation in three dimensions t k callahan e knobloch symmetry breaking bifurcations on cubic lattices nonlinearity 10 1997 1179 1216 is used to make specific predictions about the formation of three dimensional patterns in two models of the turing instability the brusselator model and the lengyel epstein model spatially periodic patterns having the periodicity of the simple cubic sc face centered cubic fcc or body centered cubic bcc lattices are considered an efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellae sc fcc double diamond hexagonal prism bcc and bcci states both models possess a special wavenumber k at which the normal form coefficients take on fixed model independent ratios and both are described by identical bifurcation diagrams this property is generic for two species chemical reaction diffusion models with a single activator and inhibitor 1999 elsevier science b v all rights reserved

method and apparatus for denoising and deverberation using variational inference and strong speech models a probability distribution for speech model parameters such as auto regression parameters is used to identify a distribution of denoised values from a noisy signal under one embodiment the probability distributions of the speech model parameters and the denoised values are adjusted to improve a variational inference so that the variational inference better approximates the joint probability of the speech model parameters and the denoised values given a noisy signal in some embodiments this improvement is performed during an expectation step in an expectation maximization algorithm the statistical model can also be used to identify an average spectrum for the clean signal and this average spectrum may be provided to a speech recognizer instead of the estimate of the clean signal

qualitative stability of linear systems abstract this paper provides a finitely computable graph theoretic answer to the following question concerning linear dynamical systems when given only the signs of entries or 0 in a real square matrix a can one be certain that all positive trajectories of the system ax are bounded matrices having such sign patterns are called sign quasistable with bounded replaced by convergent to the origin the matrices are called sign stable and were fully described in earlier papers however when a s digraph has several strong components so that the system is actually a hierarchy of subsystems and when some of those subsystems fail to be sign stable the recognition of sign quasistability is a very delicate matter by means of certain graph color tests it is possible to identify the system variables that are capable for some choice of matrix entry magnitudes and initial conditions of emitting nonzero constant

necessary condition of the turing instability a reaction diffusion system in any number of spatial variables consisting of an arbitrary number of chemical species cannot exhibit turing instability if none of the reaction steps expresses cross inhibition a corollary of this result underlines the importance of nonlinearity in the formation of stationary spatial structures a kind of self organization on a chemical basis

morphological transitions and bistability in turing systems it is well known that in two dimensions turing systems produce spots stripes and labyrinthine patterns and in three dimensions lamellar and spherical structures or their combinations are observed in this paper we study transitions between these states in both two and three dimensions first we derive the regions of stability for different patterns using nonlinear bifurcation analysis then we apply large scale computer simulations to analyze the pattern selection in a bistable system by studying the effect of parameter selection on morphological clustering and the appearance of topological defects the method elaborated in this paper presents a probabilistic approach for studying pattern selection in a bistable reaction diffusion system

turing model for the patterns of lady beetles in 1952 turing proposed a general model for generating biological patterns 1 the model was realized in some definite forms and has been used successfully to produce patterns in various biological cases such as seashells fish zebras leopards giraffes etc 2 the formation of patterns and their stabilities in these kinds of reaction diffusion model are well studied and understood in the general sense 3 4 however a specific pattern cannot be predicted this is because there are several parameters that can be adjusted to produce all kinds of possibilities in any of these models in most of these systems calculations are done on a flat surface that is the reaction diffusion equations in the model are solved on a surface of zero curvature the curvature of the geometry of the system is not taken into consideration recently varea aragon and barrio solved a turing model on a spherical surface 5 in their work they produced symmetric spot patterns on a sphere which can be considered as a first step toward simulating the patterns of some microscopic organisms such as radiolarians and viruses in this work we consider a different type of turing model on a spherical surface a portion of a spherical surface is used to approximate the shape of the hard wings of lady beetles we demonstrate that the model we use can yield patterns similar to those of the lady beetles

noise compensation in speech recognition apparatus a method and apparatus for noise suppression for speech recognition systems which employs the principle of a least means square estimation which is implemented with conditional expected values essentially according to this method one computes a series of optimal estimators which estimators and their variances are then employed to implement a noise immune metric this noise immune metric enables the system to substitute a noisy distance with an expected value which value is calculated according to combined speech and noise data which occurs in the bandpass filter domain thus the system can be used with any set of speech parameters and is relatively independent of a specific speech recognition apparatus structure

a new dimension to turing patterns abstract it is well known that simple reaction diffusion systems can display very rich pattern formation behaviour here we have studied two examples of such systems in three dimensions first we investigate the morphology and stability of a generic turing system in three dimensions and then the well known gray scott model in the latter case we added a small number of morphogen sources in the system in order to study its robustness and the formation of connections between the sources our results raise the question of whether turing patterning can produce an inductive signalling mechanism for neuronal growth

turing patterns with pentagonal symmetry we explore numerically the formation of turing patterns in a confined circular domain with small aspect ratio our results show that stable fivefold patterns are formed over a well defined range of disk sizes offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids using this pattern as a seed more complex biological structures can be mimicked such as the pigmentation pattern of sea urchins and the plate arrangements of the calyxes of primitive camerate crinoids

the arithmetic of qm abelian surfaces through their galois representations abstract this note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields we study the fields of definition of the endomorphisms on these abelian varieties and the images of the galois representations on their tate modules we illustrate our results with an explicit example