diversity induced coherence resonance in spatially extended chaotic systems the effect of parameter diversity on coupled chua systems is investigated in the absence of diversity the systems jump back and forth between two variable domains of a chaotic attractor and the residence times within a single domain are uncertain by introducing parameter diversity a combined numerical and analytical approach indicates that the systems can jump regularly from one domain to another at an intermediate range of diversity a signature of coherence resonance furthermore the influences of coupling strength and the number of units are also considered our results provide a possibility for the control of chaos in spatially extended chaotic systems by the manipulation of parameter diversity

colored noise induced chaotic array synchronization the effect of a time correlated gaussian noise on one dimensional arrays consisting of diffusively coupled chaotic cells is analyzed a resonance effect between the time scale of the chaotic attractor and the colored gaussian noise has been found as well depending on the number of cells coupling and noise strength an improvement of the synchronization or a poor synchronization between cells within the array can occur for some values of the time correlation these nonlinear cooperative effects are studied in terms of a linear stability analysis around the uniform synchronized behavior

witt rings and brauer groups under multiquadratic extensions ii let f be a field of characteristic not 2 and suppose m is a multiquadratic extension of f that is m f is a finite abelian extension of exponent 2 so that m f for some finite subgroup g e f f where f 0 in studying brauer groups and products of quaternion algebras the second author was led to consider the homology groups n m f of a certain complex gm f associated to the extension m f this complex appears in 11 3 1 301 and in 1 1 below the purpose of the present work is to investigate the first homology group n m f and to exhibit its close connections with quadratic form theory the higher homology groups are examined in 11 301 the field f is said to have property pi n if n m f 1 for every multiquadratic extension m f with m f q 2 properties p l and p 2 always hold but there are examples 29 of fields f for which p 3 fails these examples are generalized in section 5

m ary suprathreshold stochastic resonance in multilevel threshold systems with signal dependent noise we investigate multilevel threshold systems with signal dependent noise that transmit a common random input signal we demonstrate the occurrence of m ary suprathreshold stochastic resonance caused by the signal dependent noise and quantify the information enhancement that results relative to the absence of noise we also find that in the case of m ary threshold systems the values of mutual information and signal to quantization noise ratio are larger than the corresponding values in the case of binary threshold systems these results are potentially useful for understanding the encoding mechanism of inner ear hair cells and other biological sensory systems

effect of non gaussian noise sources in a noise induced transition here we study a noise induced transition when the system is driven by a noise source taken as colored and non gaussian we show using both a theoretical approximation and numerical simulations that there is a shift of the transition as the noise departs from the gaussian behavior also we confirm the reentrance effect found for colored gaussian noise and show the behavior of the transition line in the phase like diagram as the noise departs from gaussianity in the large correlation time limit

modified gold codes large families of weakly correlated codes much in the spirit of r gold 1967 and t kasami 1971 are constructed more general codes than those of gold and kasami generated in essentially the same way and with a much simpler method of proof are given

double stochastic resonance in an insect ecosystem with time delays abstract considering additive and multiplicative periodic signals we have investigated the stochastic resonance sr phenomenon in an insect ecosystem with two different types of time delays at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises the signal to noise ratio snr is calculated when two different weak periodic signals are added to the insect system it is shown from the snr that the additive and multiplicative periodic signals can cause the sr and double sr in the case of time delays in the stochastic and deterministic force respectively a detailed study of the snr depending on various noise characteristics is performed and the main results about sr are compared for two different cases of time delays

a new construction of noncrossed product algebras new examples of noncrossed product division algebras are obtained using methods different from all previous noncrossed product constructions the examples are division algebras over intersections of henselian valued fields and they have schur index and exponent p for any prime number p and any integers m n 2 n 3if 2 the basic tools used in the construction are valuation theory and galois cohomology no generic methods are applied and there is no p i theory along the way local global principles are proved for central simple algebras over intersections of p henselian valued fields the first examples of central simple division algebras which are not crossed products were obtained by amitsur in am in 1972 amitsur thereby settled a question that had been one of the outstanding open problems in the theory of algebras for at least thirty years his examples were the generic division algebras ud q n of index n over q the rational numbers for any natural number n such that p2 n p an odd prime or 8 all subsequent constructions of noncrossed products in ss 83 883 r r an ti have heretofore been based on amitsur s specialization argument and they are all generic division algebras or extensions of generic division algebras the centers of these noncrossed product algebras are not known nor are the brauer groups nor the absolute galois groups of the centers we present here a new method of constructing noncrossed product algebras in our approach the noncrossed product is realized as the underlying division algebra d of a tensor product of suitably chosen cyclic algebras over a field f l n l2 where each l is a pth root henselian valued field we prove local global principles relating the splitting fields of d to those of d f lt i 1 2 it is shown that the part of the brauer group of f is completely determined by that of ll and l2 computations for central simple f algebras thus become very tractable for exam ple we not only show that d is not a crossed product but also calculate exactly how large r must be so that the matrix ring mr d is a crossed product and how large s must be so that ms d is a tensor product of cyclic algebras indeed the structure of the brauer group of f is so nice that we were somewhat surprised that noncrossed products could possibly exist over f

glassy properties of frustrated arrays of nonlinear devices we study linear arrays of different number of quartic oscillators shaped in the form of a ring when gaussian noise temperature is added frustration is introduced through periodic boundary conditions and repulsive directional interactions between neighboring oscillators we show that these systems have similar dynamic properties than the arrays of fluxgates magnetometers we find that there is a critical number of oscillators separating the regimes arising for systems with few and many oscillators and show that they reach an optimum ordering for a nonvanishing temperature we also find that they have a relaxation process with an infinite mean life that is typical of glassy systems

new designs for signal sets with low cross correlation balance property and large linear span gf p case new designs for families of sequences over gf p with low cross correlation balance property and large linear span are presented the key idea of the new designs is to use short p ary sequences of period spl upsi with the two level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties the resulting sequences are interleaved sequences of period spl upsi sup 2 there are spl upsi cyclically shift distinct sequences in each family the maximal correlation value is 2 spl upsi 3 which is optimal with respect to the welch bound each sequence in the family is balanced and has large linear span in particular for binary case cross out of phase autocorrelation values belong to the set 1 spl upsi spl upsi 2 2 spl upsi 3 2 spl upsi 1 any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span it is shown that some families of these sequences can be implemented efficiently in both hardware and software

on the structure of pythagorean fields abstract in this paper we study in detail the relationship between fans and valuations first uncovered by brocker see 2 our techniques are somewhat different as our valuations are constructed by brute force from the properties of the fields involved this approach has the advantage in that the valuation theory it yields can be directly related to the structure theory for spaces of orderings as developed by murray marshall see 11 14 we also discuss several applications which include results in k theory

binary sequences with gold like correlation but larger linear span a new construction of optimal binary sequences identical to the well known family of gold sequences in terms of maximum nontrivial correlation magnitude and family size but having larger linear span is presented the distribution of correlation values is determined for every odd integer spl tau spl ges 3 the construction provides a family that contains 2 sup spl tau 1 cyclically distinct sequences each of period 2 sup spl tau 1 the maximum nontrivial correlation magnitude equals 2 spl tau 1 sup 2 1 with one exception each of the sequences in the family has linear span at least spl tau sup 2 spl tau 2 compared to 2 spl tau for gold sequences the sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

the graded witt ring and galois cohomology ii a primary problem in the theory of quadratic forms over a field f of characteristic different from two is to prove that the rings hq f and gwf are isomorphic here hqf h gal fq f z 2z where fq is the quadratic closure of f and gwf is the graded witt nrng associated to the fundamental ideal of even dimensional forms in the witt ring wf of f in this paper we assume we are given a field extension k of f such that wk is close to wf or hq k is close to hq f a method is developed to obtain information about these graded rings over f and its 2 extensions from information about the corresponding graded ring of k this relative theory extends and includes the previously developed absolute case where k fq applications are also given to show that hq f and gwf are isomorphic for a collection of fields anrsing naturally from the theory of abstract witt rings

rigid elements valuations and realization of witt rings to the theory over the residue class field of the valuation this theorem generalizes to any 2 henselian valuation cf kl sect 12 21 let v be the valuation let a e k f o 1 be such that v a is not divisible by two the key idea behind the proof is that the quadratic form 1 a only represents elements in u a such an element a is called

powers of totally positive subgroups of fields abstract for a formally real field f a totally positive co torsion subgroup s of f and m 1 we prove that s m s m this extends a result of becker we prove several refinements of this fact related to higher pythagoras numbers real holomorphy rings and sums with mixed powers

frequency sensitivity in weak signal detection the phenomenon of frequency sensitivity in weak signal detection has been studied via numerical simulation in the cases of a single neuron and a neuronal network respectively the membrane potential undergoes a damping oscillation to the quiescent state with a frequency of 11 33 hz under a subthreshold bias in the presence of a subthreshold sinusoidal signal and noise the signal to noise ratio snr of either the single neuron or the network presents the typical characteristic of stochastic resonance in particular there exists a frequency sensitivity range of 15 60 hz over which the snr has a large value implying that the system is more sensitive to signals with these frequencies in signal detection such frequency sensitivity is of functional significance and results from the resonance between the intrinsic oscillation of the system and the input signal in addition two cases where either the values of the bias or the signal strength for neurons may be different are studied respectively the results indicate that the effect of frequency sensitivity generally exists in signal encoding these enable us to interpret the experimental observation

multiplicative characters the weil bound and polyphase sequence families with low correlation power residue and sidelnikov sequences are polyphase sequences with low correlation and variable alphabet sizes represented by multiplicative characters in this paper sequence families constructed from the shift and addition of the polyphase sequences are revisited initially 0 1 is assumed for multiplicative characters to represent power residue and sidelnikov sequences in a simple form the weil bound on multiplicative character sums is refined for the assumption where the character sums are equivalent to the correlations of sequences represented by multiplicative characters general constructions of polyphase sequence families that produce some of known families as the special cases are then presented the refined weil bound enables the efficient proofs on the maximum correlation magnitudes of the sequence families from the constructions it is shown that m ary known sequence families with large size can be partitioned into m 1 disjoint subsequence families with smaller maximum correlation magnitudes more generalized constructions are also considered by the addition of multiple cyclic shifts of power residue and sidelnikov sequences

enhancement of neuronal coherence by diversity in coupled rulkov map models abstract we study the influence of diversity on the dynamics of spiking in spatially extended systems with global or diffusive couplings which is locally modeled by a map based neuron the variance of the system s parameter d is used to measure the diversity it is found that the regularity of spikes reaches a maximum with a variation in d indicating the occurrence of diversity induced coherence resonance moreover diversity induced coherence resonance in this system can be greatly enhanced by increasing the coupling strength our analysis shows that these phenomena have inherent relevance to both the bifurcation feature of a single neuron and interaction through couplings these results may exhibit that diversity plays a constructive role in enhancing the time precision of firing in a neural network

stochastic resonance on weakly paced scale free networks we study the impact of additive gaussian noise and weak periodic forcing on the dynamics of a scale free network of bistable overdamped oscillators the periodic forcing is introduced to a single oscillator and therefore acts as a pacemaker trying to impose its rhythm on the whole ensemble we show that an intermediate intensity of temporally and spatially uncorrelated noise is able to optimally assist the pacemaker in achieving this goal thus providing evidence for stochastic resonance on weakly paced scale free networks because of the inherent degree inhomogeneity of individual oscillators forming the scale free network the placement of the pacemaker within the network is thereby crucial as two extremes we consider separately the introduction of the pacemaker to the oscillator with the highest degree and to one of the oscillators having the lowest degree in both cases the coupling strength plays a crucial role since it determines to what extent the whole network will follow the pacemaker on the expense of a weaker correlation between the pacemaker and the units that are directly linked with the paced oscillator higher coupling strengths facilitate the global outreach of the pacemaker but require higher noise intensities for the optimal response in contrast lower coupling strengths and comparatively low noise intensities localize the optimal response to immediate neighbors of the paced oscillator if the pacemaker is introduced to the main hub the transition between the locally and globally optimal responses is characterized by a double resonance that postulates the existence of an optimal coupling strength for the transmission of weak rhythmic activity across scale free networks we corroborate the importance of the inhomogeneous structure of scale free networks by additionally considering regular networks of oscillators with different degrees of coupling

stochastic resonance and generalized information measures abstract we use tsallis information measure and the recently advanced escort tsallis one in order to investigate the stochastic resonance sr phenomenon in particular on the basis of these generalized information measures gim both characterized by a non extensivity parameter q we study the effect of modifying the type of noise the gim are used to measure sr phenomenon comparing the input and output probability distributions finding that for the range of noise intensities enhancing sr q 0 gives the optimum measure an important advantage of using gim instead of shannon s measure is the possibility of detecting smaller signal amplitudes with the former than with the latter one

witt rings and almost free pro 2 groups let f be a field of characteristic not 2 wf the witt ring of quadratic forms over f if the maximal ideal consisting of even dimensional forms and i f its square let g 2 gal f 2 f where f 2 is the maximal 2 extension quadratic closure of f in this note we prove a decomposition theorem for wf in the case that z f is torsion free and use it to obtain a new proof of a theorem of ershov on the structure of almost free pro a groups e theorem 41 in what follows w f denotes the torsion subgroup of wf and wredf wf w f is the reduced witt ring the set of orderings on f will be denoted by x and will be given the harrison topology with subbasis consisting of the sets h a e x 1 0 a f is called a sap field if every open and closed clopen subset of x is equal to some h a if r r are abstract witt rings then r x r denotes their product in the category of witt rings ml all unexplained notations and terminology about quadratic forms and witt rings can be found in l and m for elementary facts about profinite groups the reader is referred to ri following kijima and nishi kn the field f is called quasi pythugorean if z f is torsion free i e u f d 2 equivalently if the kaplansky radical of f consists of all nonzero sums of two squares ell corollary 2 91 compare el2 classification theorem 23 examples of these fields include formally real generalized hilbert fields k pseudo real closed fields p and fields satisfying the strong hasse principle h4 every totally indefinite quadratic form of dimension 4 over f is isotropic i e ii f 2 a formally real field satisfies h if and only if it is a quasi pythagorean sap field elp in ko koziol gives a criterion characterizing the class of quasi pythagorean algebraic extensions of q such fields necessarily satisfy h the best known examples of fields satisfying h are formally real

a generalization of marshall s equivalence relation for p prime and for a field f containing a root of unity of order p we generalize marshall s equivalence relation on orderings to arbitrary subgroups of f of index p the equivalence classes then correspond to free pro p factors of the maximal pro p galois group of f we generalize to this setting results of jacob on the maximal pro 2 galois group of a pythagorean field

demuskin fields with valuations we study the arithmetic structure of fields f of characteristic neq p containing a primitive pth root of unity for which the maximal pro p galois group of f is a finitely generated demuskin group

bent function sequences in this paper we construct a new family of nonlinear binary signal sets which achieve welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes given a parameter n with n 0 pmod 4 the period of the sequences is 2 n 1 the number of sequences in the set is 2 n 2 and the cross auto correlation function has three values with magnitudes leq 2 n 2 1 the equivalent linear span of the codes is bound above by sum i 1 n 4 left stackrel n i right these new signal sets have the same size and correlation properties as the small set of kasami codes but they have important advantages for use in spread spectrum multiple access communications systems first the sequences are balances which represents only a slight advantage second the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly hopped from sequence to sequence for code division multiple access operation most importantly the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it this high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing

a recursive description of pro p galois groups abstract in this note we study a modified version of the elementary type conjecture for pro p galois groups to be precise let g p f be the galois group of the maximal galois p extension of a field f containing a primitive p th root of unity under some natural assumptions concerning valuation rings of f and also orderings of f when p 2 we prove that g p f can be obtained from suitable closed subgroups using a finite number of free pro p products and semidirect products

stochastic resonance in an activator inhibitor system through adiabatic and quasi variational approaches abstract we study the phenomenon of stochastic resonance in a spatially extended system an activator inhibitor reaction diffusion model is analyzed through two different approximations an adiabatic one leading to a known form of the graham s nonequilibrium potential and a quasi variational approach that allows to obtain an approximated form of graham s potential for a different parameter region those potentials have been exploited to obtain firstly the probability for the decay of the metastable extended states and secondly expressions for the correlation function and for the signal to noise ratio within the framework of a two state description the analytical results show how this ratio depends on both local and nonlocal coupling parameters

generators and irreducible polynomials over finite fields weil s character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field an application to the distribution of irreducible polynomials is given which confirms an asymptotic version of a conjecture of hansen mullen

prime phase sequences with periodic correlation properties better than binary sequences for the case where p is an odd prime n or 2 is an integer and omega is a complex primitive pth root of unity a construction is presented for a family of p sup n p phase sequences symbols of the form omega sup i where each sequence has length p sup n 1 and where the maximum nontrivial correlation value c sub max does not exceed 1 square root p sup n a complete distribution of correlation values is provided as a special case of this construction a previous construction due to sidelnikov 1971 is obtained the family of sequences is asymptotically optimum with respect to its correlation properties and in comparison with many previous nonbinary designs the present design has the additional advantage of not requiring an alphabet of size larger than three the new sequences are suitable for achieving code division multiple access and are easily implemented using shift registers they wee discovered through an application of deligne s bound 1974 on exponential sums of the weil type in several variables the sequences are also shown to have strong identification with certain bent functions

optimal range of a nonlocal kernel for stochastic resonance in extended systems abstract here we study stochastic resonance sr in a spatially extended system described by a reaction diffusion equation for a scalar activator like field including a nonlocal contribution we assume that such a contribution arises from an effective adiabatic elimination of an auxiliary inhibitor like field our aim is to study the role played by the range of the nonlocal kernel on the sr phenomena we have found that increasing the nonlocal coupling reduces the system s response and that similar to the so called system size sr there is an optimal value of the kernel s range yielding a maximum in the system s response

fault tolerance in noise enhanced propagation as a mock up of synaptic transmission between neurons we revisit a problem that has recently risen the interest of several authors the propagation of a low frequency periodic signal through a chain of one way coupled bistable oscillators subject to uncorrelated additive noise on a numerical study performed in the optimal range of noise intensity for which essentially undamped transmission along the chain has been reported we focus on the outcome of feeding with noise all the nodes but the central one a moderate critical value of the coupling between oscillators is found such that whereas below it the propagation can be considered to be interrupted at the dead neuron it is reestablished above it thus one of the distinguishing features of synaptic transmission namely a fault tolerant behavior that enhances reliability at the expense of efficiency arises here as an emergent property of the system

stochastic resonance with spatiotemporal signal controlled by time delays stochastic resonance in two coupled threshold elements with input periodic signals shifted in phase is studied for fixed phase shift and coupling strength the signal to noise ratio at the output of each element can be maximized by introducing proper time delays in the coupling terms which cancel the effect of the phase shift this shows that in systems of coupled elements driven by spatiotemporal periodic signals stochastic resonance can be controlled by delayed coupling

cross correlation of sidel nikov sequences and their constant multiples in this correspondence we prove that the complex cross correlation of a k ary sidel nikov sequence of period q 1 and its constant multiple sequence is upper bounded by radicq 3 where q pm and here p is an odd prime and m is a positive integer

stochastic resonance in coupled threshold elements on a barabasi albert network abstract stochastic resonance is investigated in a system of threshold elements located at nodes and coupled along edges of a barabasi albert network driven by a common subthreshold periodic signal and independent noises array enhanced stochastic resonance is observed i e increase of the spectral power amplification evaluated from the mean output of the network due to proper coupling this enhancement occurs though the response of individual threshold elements to the periodic signal is very diverse due to a power law distribution of their connectivity numerical results are qualitatively explained using simple linear response theory in the mean field approximation

compatible valuations and generalized milnor k theory given a field and a subgroup of there is a minimal group for which there exists an compatible valuation whose units are contained in assuming that has finite index in and contains for prime we describe in computable theoretic terms