regularity of spike trains and harmony perception in a model of the auditory system spike train regularity of the noisy neural auditory system model under the influence of two sinusoidal signals with different frequencies is investigated for the increasing ratio m n of the input signal frequencies m n are natural numbers the linear growth of the regularity is found at the fixed difference m

linear inviscid damping and enhanced dissipation for the kolmogorov flow abstract in this paper we prove the linear inviscid damping and vorticity depletion phenomena for the linearized euler equations around the kolmogorov flow these results confirm bouchet and morita s predictions based on numerical analysis by using the wave operator method introduced by li wei and zhang we solve beck and wayne s conjecture on the enhanced dissipation rate for the 2 d linearized navier stokes equations around the bar state called kolmogorov flow the same dissipation rate is proved for the navier stokes equations if the initial velocity is included in a basin of attraction of the kolmogorov flow with the size of 2 3 here is the viscosity coefficient

on the resonance structure in a forced excitable system the dynamics of forced excitable systems are studied analytically and numerically with a view toward understanding the resonance or phase locking structure in a singular limit the system studied reduces to a discontinuous flow on a two torus which in turn gives rise to a set valued circle map it is shown how to define rotation numbers for such systems and derive properties analogous to those known for smooth flows the structure of the phase locking regions for a fitzhugh nagumo system in the singular limit is also analyzed a singular perturbation argument shows that some of the general results persist for the nonsingularly perturbed system and some numerical results on phase locking in the forced fitzhugh nagumo equations illustrate this fact the results explain much of the phase locking behavior seen experimentally and numerically in forced excitable systems including the existence of threshold stimuli for phase locking the results are compared with known results for forced oscillatory systems

spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model the phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered two of them here so called sensory neurons are driven by noise and subthreshold periodic signals with different ratio of frequencies and its outputs plus noise are applied synaptically to a third neuron so called interneuron we present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron we find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter firing intervals statistics densities that are very distinctive from densities obtained using tones with ratios that are known to be dissonant in other words at the output of the interneuron inharmonious signals give rise to blurry spike trains while the harmonious signals produce more regular less noisy spike trains theoretical results are compared with numerical simulations

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

equality of norms for a class of bloch and symmetrically weighted lipschitz spaces of vector valued functions and derivation inequalities for pick functions abstract if x and y are banach spaces and f b x y is frechet differentiable on the open unit ball b x of x then for every operator monotone function 1 1 r which satisfies 0 on a b 1 sup a b b x a b f a f b a a b b sup a b x d f a a this generalizes holland walsh pavlovic criterium for the membership in bloch type spaces for functions defined in the unit ball of a banach space and taking values in another banach space we also established relations of the induced bloch and lipschitz spaces with other spaces of vector valued functions

period doubling bifurcations chaos phase locking and devil s staircase in a bonhoeffer van der pol oscillator abstract the effect of a periodic input current a 1 cos t in the bonhoeffer van der pol oscillator along with a bias a 0 is investigated numerically as the parameter a 1 is varied in the absence of bias by holding the other parameters at constant values typical period doubling bifurcation sequence is found to occur leading to chaotic motion in agreement with the feigenbaum scenario when the bias is switched on at the transition to chaos frequency locking is observed in the system the frequency locked intervals exhibit complete devil s staircase similar to the one observed in belousov zhabotinsky reaction

ghost resonance in the chaotic chua s circuit we experimentally investigate the ghost resonance phenomenon in the electronic circuit of chua operating in the chaotic regime the circuit can be stimulated to jump between two single scroll attractors by an external periodic signal with an amplitude above an intrinsic threshold for subthreshold signals jumps between the chaotic attractors can be promoted by a superposed white noise we show that the circuit output can exhibit a well defined ghost resonance signature i e a resonance on a frequency that is absent in a multicomponent input signal when the amplitudes of the input components are properly related further we show that ghost resonance can be induced by the chua s circuit s own chaotic dynamics when it is driven by a suprathreshold multicomponent signal without the need of an external noise source

trace order and a distortion theorem for linearly invariant families on the unit ball of a finite dimensional jb triple abstract we give a distortion theorem for linearly invariant families on the unit ball b of a finite dimensional jb triple x by using the trace order the exponents in the distortion bounds depend on the bergman metric at 0 further we introduce a new definition for the trace order of a linearly invariant family on b based on a jacobian argument we also construct an example of a linearly invariant family on b which has minimum trace order and is not a subset of the normalized convex mappings of b for dim x 2 finally we prove a regularity theorem for linearly invariant families on b all four types of classical cartan domains are the open unit balls of jb triples and the same holds for any finite product of these domains thus the unit balls of jb triples are natural generalizations of the unit disc in c and we have a setting in which a large number of bounded symmetric homogeneous domains may be studied simultaneously

stochastic resonance in models of neuronal ensembles two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time varying inputs are considered it is shown using theoretical arguments and numerical simulations that the nonmonotonic behavior with increasing noise of the correlation measures used for the so called aperiodic stochastic resonance asr scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems rather asr with slowly varying signals is more properly interpreted as linearization by noise consequently the broadening of the resonance curve in the multineuron stochastic resonance without tuningscenario can also be explained by this linearization computation of the input output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise thus our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals it also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime finally we show that the inclusion of a refractory period in the spike detection scheme produces a better correlation between instantaneous firing rate and input signal s1063 651x 97 01102 1

fredholm composition operators on algebras of analytic functions on banach spaces we prove that fredholm composition operators acting on the uniform algebra h be of bounded analytic functions on the open unit ball of a complex banach space e with the approximation property are invertible and arise from analytic automorphisms of the ball

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

diffusion and mixing in fluid flow we study enhancement of diffusive mixing on a compact riemannian manifold by a fast incompressible flow our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small in an arbitrarily short time provided that the flow amplitude is large enough the necessary and suficient condition on such flows is expressed naturally in terms of the spectral properties of the dynamical system associated with the flow in particular we find that weakly mixing flows always enhance dissipation in this sense the proofs are based on a general criterion for the decay of the semigroup generated by an operator of the form g ial with a negative unbounded self adjoint operator g a self adjoint operator l and parameter a 1 in particular they employ the rage theorem describing evolution of a quantum state belonging to the continuous spectral subspace of the hamiltonian related to a classical theorem of wiener on fourier transforms of measures applications to quenching in reaction diffusion equations are also considered

pseudospectra of linear operators if a matrix or linear operator a is far from normal its eigenvalues or more generally its spectrum may have little to do with its behavior as measured by quantities such as an or exp ta more may be learned by examining the sets in the complex plane known as the pseudospectra of a defined by level curves of the norm of the resolvent zi a 1 five years ago the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications since that time analogous computations have been carried out for differential and integral operators this paper a companion to the earlier one presents ten examples each chosen to illustrate one or more mathematical or physical principles

a uniform algebra of analytic functions on a banach space let a b be the uniform algebra on the unit ball of a dual banach space 2 y generated by the weak star continuous linear functionals we focus on three related problems i to determine when a b is a tight uniform algebra ii to describe which functions in h b are approximable pointwise on b by bounded nets in a b and iii to describe the weak topology of b regarded as a subset of the dual of a b with respect to the second problem we show that any polynomial in elements of 3 can be approximated pointwise on b by functions in a b of the same norm this can be viewed as a generalization of goldstine s theorem in connection with the third problem we introduce a class of banach spaces called a spaces with the property that if xj is a bounded sequence in 2 such that p xj 0 for any mhomogeneous analytic function p on 2 m 1 then xj 0 in norm we show for instance that a banach space has the schur property if and only if it is a a space with the dunford pettis property

distortion of locally biholomorphic bloch mappings on bounded symmetric domains abstract we generalize bonk s distortion theorem on the unit disc in the complex plane to locally biholomorphic mappings on finite dimensional bounded symmetric domains as an application we obtain a lower bound for the bloch constant for various classes of locally biholomorphic bloch mappings

tight uniform algebras and algebras of analytic functions abstract a uniform algebra a on a compact space x is tight if for each g c x the hankel type operator f gf a from a to c a is weakly compact two families of uniform algebras are shown to be tight the algebras such as r k that arise in the theory of rational approximation on compact subsets of the complex plane and algebras of analytic functions on domains in c n for which a certain problem is solvable a couple of characterizations of tight algebras are given and one of these is used to show that the property of being tight places severe restrictions on the gleason parts of a and the measures in a

hardy type spaces associated with compact unitary groups abstract we investigate hilbertian hardy type spaces of complex analytic functions of infinite many variables associated with compact unitary groups and the corresponding invariant haar s measures for such analytic functions we establish a cauchy type integral formula and describe natural domains also we show some relations between constructed spaces of analytic functions and the symmetric fock space

distortion theorems for convex mappings on homogeneous balls abstract let b be the open unit ball of a complex banach space x and let b be homogeneous we prove distortion results for normalized convex mappings f b x which generalize various finite dimensional distortion theorems and improve some infinite dimensional ones in particular our results are valid for the open unit balls of complex hilbert spaces and the cartan domains

computation of pseudospectra by continuation the concept of pseudospectrum was introduced by trefethen to explain the behavior of nonnormal operators many phenomena for example hydrodynamic instability and convergence of iterative methods for linear systems cannot be accounted for by eigenvalue analysis but are more understandable by examining the pseudospectra the straightforward way to compute pseudospectra involves many applications of the singular value decomposition svd this paper presents several fast continuation methods to calculate pseudospectra of different types of matrices

universality in three frequency resonances we investigate the hierarchical structure of three frequency resonances in nonlinear dynamical systems with three interacting frequencies we hypothesize an ordering of these resonances based on a generalization of the farey tree organization from two frequencies to three in experiments and numerical simulations we demonstrate that our hypothesis describes the hierarchies of three frequency resonances in representative dynamical systems we conjecture that this organization may be universal across a large class of three frequency systems

pluriharmonic mappings in cn and complex banach spaces abstract in this paper we obtain a sufficient condition for pluriharmonic mappings on the euclidean unit ball b n to be univalent sense preserving quasiconformal and bi lipschitz diffeomorphisms on b n and to have linearly connected images also we give a sufficient condition for pluriharmonic mappings on b n to have quasiconformal extensions to c n next we generalize the harmonic schwarz lemma to pluriharmonic mappings of the unit ball b x of a complex banach space x into the unit ball b n of c n with respect to an arbitrary norm further we obtain a generalization of the harmonic schwarz pick lemma to the case of pluriharmonic mappings of the homogeneous unit ball b x of a complex banach space x into the unit ball b n we also obtain a version of the holomorphic schwarz pick lemma for the jacobian determinant on the euclidean unit ball b n to the case of pluriharmonic mappings of the homogeneous unit ball b x into b n in the case that b x is an open subset of c n finally we obtain the landau and the bloch theorems for pluriharmonic or holomorphic mappings on finite dimensional homogeneous unit balls

subharmonic stochastic synchronization and resonance in neuronal systems we study the response of a model neuron driven simultaneously by noise and at least two weak periodic signals we focus on signals with frequencies components mathrm kf 0 k 1 f 0 dots k n f 0 with kg1 the neuron s output is a sequence of pulses spaced at random interpulse intervals we find an optimum input noise intensity for which the output pulses are spaced ensuremath sim 1 f 0 i e there is a stochastic resonance sr at a frequency missing in the input even higher noise intensities uncover additional but weaker resonances at frequencies present in the input this is a different form of sr whereby the most robust resonance is the one enhancing a frequency which is absent in the input and which is not possible to recover via any linear processing this can be important in understanding sensory systems including the neuronal mechanism for perception of complex tones

two sided polynomial ideals on banach spaces abstract classes of homogeneous polynomials between banach spaces have been studied in the last three decades from the perspective of the stability with respect to the composition of a homogeneous polynomial with linear operators in an attempt to explore the underlying nonlinearity in a more consistent way and to bring the subject closer to its roots in complex analysis and also taking into account recent results in the field in this paper we propose the study of classes of homogeneous polynomials that are stable under the composition with homogeneous polynomials

bloch functions on bounded symmetric domains we introduce and characterize bloch functions on bounded symmetric domains which may be infinite dimensional by extending several well known equivalent conditions for bloch functions on the open unit disc u in cc we also generalize a number of results concerning bloch functions on u to bounded symmetric domains given a holomorphic mapping between bounded symmetric domains bxbx and byby we derive criteria for boundedness and compactness of the composition operator c c between the bloch spaces b by b by and b bx b bx extending several known results for finite dimensional domains

compact composition operators on the bloch space of the unit ball abstract in this paper we give several new necessary and sufficient conditions for the compactness of the composition operator c on the bloch space of the unit ball b n

linear inviscid damping for a class of monotone shear flow in sobolev spaces in this paper we prove the decay estimates of the velocity and h1 scattering for the two dimensional linearized euler equations around a class of monotone shear flow in a finite channel our result is consistent with the decay rate predicted by case in 1960 2016 wiley periodicals inc

polynomial properties of banach spaces abstract several properties defined by polynomials on a banach space are introduced and briefly studied we apply them to give necessary and sufficient conditions for the non containment of l 1 in a symmetric projective tensor product of banach spaces

polynomial sequential continuity on c k e spaces we show that for bounded sequences in c k e the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence we introduce several conditions on e under which different versions of the result are true when k is a scattered compact space these conditions are related with some others appeared in the literature and they seem to be of independent interest

bloch functions on the unit ball of an infinite dimensional hilbert space the bloch space has been studied on the open unit disk of c and some ho mogeneous domains of c n we dene bloch functions on the open unit ball of a hilbert space e and prove that the corresponding space b be is invariant under composition with the automorphisms of the ball leading to a norm that modulo the constant functions is automorphism invariant as well all bounded analytic functions on be are also bloch functions ones resulting the fact that if for a given n the restrictions of the function to the n dimensional subspaces have their bloch norms uniformly bounded then the function is a bloch one and conversely we also introduce an equivalent norm forb be obtained by replacing the gradient by the radial derivative we exhibit in section 3 another equivalent norm forb be which is invariant modulo the constant functions under the action of the automorphisms of the ball this is achieved without appealing to the invariant laplacian and relying only on properties of automorphisms of be further we are able to show that the space h 1 be of bounded analytic functions is contractively embedded in b be as it occurs in the nite dimensional case examples of unbounded bloch functions are also shown

growth and distortion theorems for linearly invariant families on homogeneous unit balls in cn abstract let b be a homogeneous unit ball in x c n in this paper we obtain growth and distortion theorems for linearly invariant families f of locally biholomorphic mappings on the unit ball b with finite norm order ord e 1 f we use the euclidean norm for the target space instead of the norm of x because we are able to obtain lower bounds in the two point distortion theorems for linearly invariant families on any homogeneous unit ball in c n we also obtain similar results for affine and linearly invariant families a l i f s of pluriharmonic mappings of the unit ball b into c n again in most of these results we use the euclidean norm for the target space to obtain lower bounds in the two point distortion theorems for a l i f s on b these results are generalizations to homogeneous unit balls of recent results due to graham kohr and pfaltzgraff the authors of this paper and duren hamada and kohr in the last section we consider two point distortion theorems for l i f s and a l i f s on the unit polydisc u n in c n

linear inviscid damping for monotone shear flows recently there has been much interest in damping phenomena for kinetic equations following the seminal works of mouhot villani on landau damping and of bedrossian masmoudi on inviscid damping around couette flow in this talk i present a proof of linear inviscid damping for the 2d euler equations around general monotone shear flows in the framework of sobolev regularity here i consider both the settings of an infinite periodic and a finite periodic channel with impermeable walls in the latter case i explain the non negligible effect of boundary conditions on the attainable regularity and stability results speaker sciencesconf org equadiff2015 64596