multiple cumulants based spectrum sensing methods for cognitive radios in cognitive radios energy detector is considered for spectrum sensing in the literature however its performance deteriorates rapidly if the noise power is not known exactly moreover due to the presence of a colored channel interferer or some other reasons the conventional white gaussian noise may become colored in order to solve these problems this paper proposes several multicumulant based spectrum sensing methods generalized likelihood ratio test glrt based multicumulant glrtmc based detection method and multiantenna assisted multicumulant mamc based detection method glrtmc detection method is derived from generalized likelihood ratio test and assumed to be near optimum in theory mamc detection method on the other hand by using multiple antennas is a complexity reduced detector and allows us to make a compromise between performance and complexity it is well known that cumulants higher than second order are zero for gaussian distributions thus glrtmc detection method and mamc detection method can extract a non gaussian signal from gaussian noise even when the noise is colored in addition the proposed methods are nonparametric in the sense that they do not require any exact prior knowledge about the signal or the noise such as noise power or cyclic frequencies hence they are immune from noise uncertainty simulation experiments are provided to show the validity and the superiority over single cumulant based detector of the proposed multicumulant based detectors

neural population densities shape network correlations the way sensory microcircuits manage cellular response correlations is a crucial question in understanding how such systems integrate external stimuli and encode information most sensory systems exhibit heterogeneities in terms of population sizes and features which all impact their dynamics this work addresses how correlations between the dynamics of neural ensembles depend on the relative size or density of excitatory and inhibitory populations to do so we study an apparently symmetric system of coupled stochastic differential equations that model the evolution of the populations activities excitatory and inhibitory populations are connected by reciprocal recurrent connections and both receive different stimuli exhibiting a certain level of correlation with each other a stability analysis is performed which reveals an intrinsic asymmetry in the distribution of the fixed points with respect to the threshold of the nonlinearities based on this we show how the cross correlation between the population responses depends on the density of the inhibitory population and that a specific ratio between both population sizes leads to a state of zero correlation we show that this so called asynchronous state subsists despite the presence of stimulus correlation and most importantly that it occurs only in asymmetrical systems where one population outnumbers the other using linear approximations we derive analytical expressions for the root of the cross correlation function and study how the asynchronous state is impacted by the model s parameters this work suggests a possible explanation for why inhibitory cells outnumber excitatory cells in the visual system

an analysis of band limited communication systems from amplifier efficiency and distortion perspective considering growing concerns toward green communications not only their bandwidth efficiency but also their power consumption is expected to gain increasing importance for future communication systems a power amplifier pa is one of the most power consuming analog devices at the transmitter in communication systems and a precise estimation of the power consumption at the transmitter circuit requires the knowledge of its efficiency that depends on the distribution of input signal envelope and the amount of input back off in this paper we develop a simple analytical model that can be used for estimating achievable efficiency of a linear pa as well as the amount of resulting nonlinear distortion for a given modulated signal exclusively from its envelope distribution based on this model the trade off relationships between the efficiency and signal to distortion power ratio for several spectrally efficient linear modulations are examined it is also shown that in some special cases of gaussian input and memoryless nonlinearity pa models the results can be represented in simple closed form expressions

a bi hamiltonian formulation for triangular systems by perturbations a bi hamiltonian formulation is proposed for triangular systems resulting from perturbations around solutions from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed provided that one operator of the hamiltonian pair is invertible through our formulation four examples of triangular systems are exhibited which also show that bi hamiltonian systems in both lower dimensions and higher dimensions are many and varied two of four examples give local 2 1 dimensional bi hamiltonian systems and illustrate that multiscale perturbations can lead to higher dimensional bi hamiltonian systems

hamiltonian and super hamiltonian systems of a hierarchy of soliton equations abstract by considering an isospectral eigenvalue problem a hierarchy of soliton equations are derived two types of extensions are presented by enlarging the associated spectral problem with the aid of generalized trace identity and the super trace identity the hamiltonian and super hamiltonian structures for the integrable extensions are established

statistical tests for presence of cyclostationarity the presence of kth order cyclostationarity is defined in terms of nonvanishing cyclic cumulants or polyspectra relying upon the asymptotic normality and consistency of kth order cyclic statistics asymptotically optimal spl chi sup 2 tests are developed to detect the presence of cycles in the kth order cyclic cumulants or polyspectra without assuming any specific distribution on the data constant false alarm rate tests are derived in both time and frequency domain and yield consistent estimates of possible cycles present in the kth order cyclic statistics explicit algorithms for k spl les 4 are discussed existing approaches are rather empirical and deal only with k spl les 2 case simulation results are presented to confirm the performance of the given tests

classification of certain integrable coupled potential kdv and modified kdv type equations in this article we describe the classification of integrable symmetrically coupled potential kdv and modified kdv type equations that possess higher symmetries restricting our attention to the systems that cannot be decoupled by a change of dependent variables we obtain 11 previously unknown classes of integrable equations in some cases we present hamiltonian or bi hamiltonian formulations

an integrable couplings of g wki equations hierarchy with self consistent sources we present a kind of integrable couplings of soliton equations hierarchy with self consistent sources by using the loop algebra sl 4 as an application a new integrable couplings of the generalized wadati konono ichikawa g wki equations hierarchy with self consistent sources is derived through the enlarged loop algebra sl 4

new super integrable hierarchies associated with osp 2 2 and spo 2 2 and their applications abstract based on the lie superalgebras osp 2 2 and spo 2 2 we generate some new super soliton hierarchies these hierarchies can reduce to the akns hierarchy and the super akns hierarchy and by using the supertrace identity on lie superalgebras we construct the super hamiltonian structures of these new super soliton hierarchies then as the applications of spo 2 2 osp 2 2 and spo 2 2 sl 1 2 we obtain the relations of different hierarchies associated with different lie superalgebras

the generalized fractional trace variational identity and fractional integrable couplings of kaup newell hierarchy starting from fractional isospectral problems and general bilinear forms the generalized fractional trace identity is presented then a new explicit lie algebra is introduced for which the fractional integrable couplings of kaup newell hierarchy are derived furthermore we obtained the fractional hamiltonian structures of the fractional integrable couplings of kaup newell hierarchy the methods derived by us can be generalized to other fractional integrable couplings

construction of solutions for an integrable differential difference equation by darboux backlund transformation abstract we first establish a one fold darboux backlund transformation for the integrable differential difference equation which is presented in ref 6 by means of a proper gauge transformation matrix then as a result of the n times one fold darboux backlund transformation we derive n fold darboux backlund transformation finally using the obtained darboux backlund transformation two exact solutions are worked out

nonlinear continuous integrable hamiltonian couplings based on a kind of special non semisimple lie algebras a scheme is presented for constructing nonlinear continuous integrable couplings variational identities over the corresponding loop algebras are used to furnish hamiltonian structures for the resulting continuous integrable couplings the application of the scheme is illustrated by an example of nonlinear continuous integrable hamiltonian couplings of the akns hierarchy of soliton equations

hierarchical digital modulation classification using cumulants a simple method based on elementary fourth order cumulants is proposed for the classification of digital modulation schemes these statistics are natural in this setting as they characterize the shape of the distribution of the noisy baseband i and q samples it is shown that cumulant based classification is particularly effective when used in a hierarchical scheme enabling separation into subclasses at low signal to noise ratio with small sample size thus the method can be used as a preliminary classifier if desired computational complexity is order n where n is the number of complex baseband data samples this method is robust in the presence of carrier phase and frequency offsets and can be implemented recursively theoretical arguments are verified via extensive simulations and comparisons with existing approaches

high order moments and gaussianity of single carrier and ofdm signals this paper analyzes the high order moments of linearly modulated single carrier as well as orthogonal frequency division multiplexing ofdm signals assuming that the modulated symbols that form resulting continuous signal waveform are statistically independent for a single carrier case with the ideal low pass filter used for pulse shaping closed form expressions of the moments with up to the eighth order are derived the proposed approach is then extended to gaussianity assessment of ofdm signals we show how the moments of ofdm signals can approach to those of gaussian distribution as the number of subcarriers increases for a given modulation constraint on each subcarrier also reported is the peculiar nonstationary behavior of the fourth order moments in the case of bpsk modulated ofdm signals

a new loop algebra and a corresponding integrable hierarchy as well as its integrable coupling a type of new interesting loop algebra gm m 1 2 with a simple commutation operation just like that in the loop algebra a1 is constructed with the help of the loop algebra gm a new multicomponent integrable system m akns kn hierarchy is worked out as reduction cases the m akns hierarchy and m kn hierarchy are engendered respectively in addition the system 1 akns kn which is a reduced case of the m akns kn hierarchy above is a unified expressing integrable model of the akns hierarchy and the kn hierarchy obviously the m akns kn hierarchy is again a united expressing integrable model of the multicomponent akns hierarchy m akns and the multicomponent kn hierarchy m kn this article provides a simple method for obtaining multicomponent integrable hierarchies of soliton equations finally we work out an integrable coupling of the m akns kn hierarchy

a trace identity and its applications to the theory of discrete integrable systems a general theory for studying discrete integrable systems is developed based on a trace identity that the author previously proposed a scheme for generating hierarchies of discrete integrable systems is presented under broad assumptions the resulting hierarchies are shown to consist of liouville integrable hamiltonian systems

constructing nonlinear discrete integrable hamiltonian couplings beginning with lax pairs from special non semisimple matrix lie algebras we establish a scheme for constructing nonlinear discrete integrable couplings discrete variational identities over the associated loop algebras are used to build hamiltonian structures for the resulting integrable couplings we illustrate the application of the scheme by means of an enlarged volterra spectral problem and present an example of nonlinear discrete integrable hamiltonian couplings for the volterra lattice equations

theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback a network of leaky integrate and fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied we calculate the spectral statistics of the network power spectrum of the population activity cross spectrum between spike trains of different neurons as well as of a single neuron power spectrum of spike train cross spectrum between external noise and spike train within the network as shown by comparison with numerical simulations our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise by means of our analytical results we discuss the quality of the correlation induced oscillation in a large network as a function of the transmission delay and the internal noise intensity it is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay i e the delay period is longer than any other time scale in the system for a neuron with a strong intrinsic frequency the oscillation becomes strongly anharmonic in the case of a long delay time we also discuss briefly the kind of synchrony introduced by the feedback induced oscillation

restricted flows of the ablowitz ladik hierarchy and their continuous limits it is studied here how the ablowitz ladik al hierarchy and their restricted flows are related to the akns hierarchy and to their restricted flows in the continuous limit it is shown that restricted flows of the al hierarchy yield discrete maps approximating restricted flows of the akns hierarchy integrals of motion and lax representation for restricted flows of the al hierarchy as well as a discrete zero curvature representation for the al hierarchy with sources are given

the cumulant theory of cyclostationary time series ii development and applications for pt i see ibid vol 42 no 12 p 3387 3408 1994 the development of the theory of nonlinear processing of cyclostationary time series that is initiated in part i is continued a new type of cumulant for complex valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time series from real valued to complex valued time series the relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined formulas for the temporal and spectral cumulants of complex valued pulse amplitude modulated time series are derived estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed the performance of these estimators is illustrated by several computer simulation examples for pulse amplitude modulated time series the theory is applied to the problems of weak signal detection and interference tolerant time delay estimation

how effective delays shape oscillatory dynamics in neuronal networks abstract synaptic dendritic and single cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons previous work has shown that such effective delays can be taken into account with a rate model through the addition of an explicit fixed delay roxin et al 2005 2006 29 30 here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions specifically we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the asynchronous state in this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity we arrive at two general observations of physiological relevance that could not be explained in previous work these are 1 fast oscillations are always supercritical for realistic transfer functions and 2 traveling waves are preferred over standing waves given plausible patterns of local connectivity we finally demonstrate that these results show good agreement with those obtained performing numerical simulations of a network of hodgkin huxley neurons

time domain tests for gaussianity and time reversibility statistical signal processing algorithms often rely upon gaussianity and time reversibility two important notions related to the probability structure of stationary random signals and their symmetry parametric models obtained via second order statistics sos are appropriate when the available data is gaussian and time reversible on the other hand evidence of nonlinearity non gaussianity or time irreversibility favors the use of higher order statistics hos in order to validate gaussianity and time reversibility and quantify the tradeoffs between sos and hos consistent time domain chi squared statistical tests are developed exact asymptotic distributions are derived to estimate the power of the tests including a covariance expression for fourth order sample cumulants a modification of existing linearity tests in the presence of additive gaussian noise is discussed briefly the novel gaussianity statistic is computationally attractive leads to a constant false alarm rate test and is well suited for parametric modeling because it employs the minimal hos lags which uniquely characterize arma processes simulations include comparisons with an existing frequency domain approach and an application to real seismic data time reversibility tests are also derived and their performance is analyzed both theoretically and experimentally

integrable semi discretization of the coupled modified kdv equations the discrete version of the inverse scattering method proposed by ablowitz and ladik is extended to solve multi component systems the extension enables one to solve the initial value problem which proves directly the complete integrability of a semi discrete version of the coupled modified korteweg de vries kdv equations and their hierarchy it also provides a procedure to obtain conservation laws and multi soliton solutions of the hierarchy

r matrix approach to lattice integrable systems an r matrix formalism is applied to the construction of the integrable lattice systems and their bi hamiltonian structure miura like gauge transformations between the hierarchies are also investigated in the end the ladder of linear maps between generated hierarchies is established and described

two integrable couplings of the tu hierarchy and their hamiltonian structures the double integrable couplings of the tu hierarchy are worked out by use of vector loop algebras g 6 and g 9 respectively also the hamiltonian structures of the obtained system are given by the quadratic form identity

a discrete variational identity on semi direct sums of lie algebras the discrete variational identity under general bilinear forms on semi direct sums of lie algebras is established the constant involved in the variational identity is determined through the corresponding solution to the stationary discrete zero curvature equation an application of the resulting variational identity to a class of semi direct sums of lie algebras in the volterra lattice case furnishes hamiltonian structures for the associated integrable couplings of the volterra lattice hierarchy

cumulant based approach to harmonic retrieval and related problems a frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored gaussian noise in practice the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density a cumulant based approach to these problems is proposed the cumulants of complex processes are defined and it is shown that specific 1 d slices of the fourth order cumulant of the noisy signal for the direction of arrival doa and retrieval of harmonics in noise rhn problems are identical to the autocorrelation of a related noiseless signal hence correlation based high resolution methods may be used with fourth order cumulants as well the effectiveness of the proposed methods is demonstrated through standard simulation examples

integrable couplings of vector akns soliton equations by enlarging the associated matrix spectral problems two specific classes of multicomponent integrable couplings of the physically important vector akns soliton equations are constructed which can be linked to each other by a backlund transformation the resulting two hierarchies of integrable couplings possess the enlarged zero curvature representations and recursion structures and thus each system in the two hierarchies has infinitely many commuting symmetries

algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations an algebraic structure related to discrete zero curvature equations is established it is used to give an approach for generating master symmetries of the first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries the key of the theory is to generate nonisospectral flows t l l 0 from the discrete spectral problem associated with a given system of discrete evolution equations three examples are given

a family of liouville integrable lattice equations with a parameter and its two symmetry constraints a two by two matrix spectral problem with an arbitrary constant is introduced a family of integrable lattice equations involving a parameter is derived by the technique of lax pairs the typical lattice equation in the obtained family is a deformed toda lattice system the bi hamiltonian structure of the obtained family of integrable lattice equations is established by using the discrete trace identity and we prove the liouville integrability of obtained family of integrable lattice equations then bargmann symmetry constraint and an implicit symmetry constraint of the obtained family are presented by binary nonlinearization method under these two symmetry constraints we obtain two series of integrable symplectic maps and two sequences of completely integrable finite dimensional hamiltonian systems in liouville sense and every integrable lattice equation in the obtained family is decomposed by an integrable symplectic map and a completely integrable finite dimensional hamiltonian system as a specia

a deformed reduced semi discrete kaup newell equation the related integrable family and darboux transformation we propose a deformed reduced semi discrete kaup newell equation we derive the related integrable family through discrete zero curvature equation we establish a darboux transformation of lax pair of the proposed equation three exact solutions are given a deformed reduced semi discrete kaup newell equation and its related integrable family are derived from discrete zero curvature equation a darboux transformation of lax pair of this equation is established with the help of gauge transformation by means of the resulting darboux transformation three exact solutions are given

a non isospectral integrable couplings of volterra lattice hierarchy with self consistent sources a kind of non isospectral integrable couplings of discrete soliton equations hierarchy with self consistent sources associated with email protected 4 y f zhang e g fan characteristic numbers of matrix lie algebras commun theor phys china 49 2008 845 is presented as an application example the hierarchy of non isospectral cubic volterra lattice hierarchy with self consistent sources is derived furthermore we construct a non isospectral integrable couplings of cubic volterra lattice hierarchy with self consistent sources by using the loop algebra email protected 4

complexiton solutions of the toda lattice equation a set of coupled conditions consisting of differential difference equations is presented for casorati determinants to solve the toda lattice equation one class of the resulting conditions leads to an approach for constructing complexiton solutions to the toda lattice equation through the casoratian formulation an analysis is made for solving the resulting system of differential difference equations thereby providing the general solution yielding eigenfunctions required for forming complexitons moreover a feasible way is presented to compute the required eigenfunctions along with examples of real complexitons of lower order

driving neural oscillations with correlated spatial input and topographic feedback we consider how oscillatory activity in networks of excitable systems depends on spatial correlations of random inputs and the spatial range of feedback coupling analysis of a neural field model with topographic delayed recurrent feedback reveals how oscillations in certain frequency bands including the gamma band are enhanced by increases in the input correlation length further the enhancement is maximal when this length exceeds the feedback coupling range suppression of oscillatory power occurs concomitantly in other bands these effects depend solely on the ratio of input and feedback length scales the precise positions of these bands are determined by the synaptic constants and the delays the results agree with numerical simulations of the model and of a network of stochastic spiking neurons and are expected for any noise driven excitable element networks

a new hierarchy of integrable differential difference equations and darboux transformation a new discrete isospectral problem and the corresponding hierarchy of nonlinear differential difference equations are proposed it is shown that the hierarchy of differential difference equations possesses the hamiltonian structures a darboux transformation for the discrete spectral problem is found as an application two soliton solutions for the first system of differential difference equations in the hierarchy are given

what is the relativistic volterra lattice we develop a systematic procedure of finding integrable 6ldquo relativistic regular one parameter deformations for integrable lattice systems our procedure is based on the integrable time discretizations and consists of three steps first for a given system one finds a local discretization living in the same hierarchy second one considers this discretization as a particular cauchy problem for a certain 2 dimensional lattice equation and then looks for another meaningful cauchy problem which can be in turn interpreted as a new discrete time system third one has to identify integrable hierarchies to which these new discrete time systems belong these novel hierarchies are called then relativistic the small time step h playing the role of inverse speed of light we apply this procedure to the toda lattice and recover the well known relativistic toda lattice as well as to the volterra lattice and a certain bogoyavlensky lattice for which the relativistic deformations were not known previously

a modified toda spectral problem and its hierarchy of bi hamiltonian lattice equations starting from a modified toda spectral problem a hierarchy of generalized toda lattice equations with two arbitrary constants is constructed through discrete zero curvature equations it is shown that the hierarchy possesses a bi hamiltonian structure and a hereditary recursion operator which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals two cases of the involved constants present two specific integrable sub hierarchies one of which is exactly the toda lattice hierarchy

nonlinearization of spectral problems for the perturbation kdv systems abstract the theory of nonlinearization of spectral problems is developed for investigating the perturbation kdv systems and a kind of finite dimensional integrable hamiltonian systems is generated from spectral problems of the perturbation kdv systems to establish the liouville integrability of the obtained hamiltonian systems we identify them with the perturbation systems of the garnier system which can be directly proved to be integrable a useful formula to compute the functional gradient of the spectral parameter with respect to the potential is also presented for arbitrary order matrix spectral problems

integrable couplings of relativistic toda lattice systems in polynomial form and rational form their hierarchies and bi hamiltonian structures integrable couplings of relativistic toda lattice systems in polynomial form and rational form and their hierarchies are derived from a four by four discrete matrix eigenvalue problem the bi hamiltonian structure for every integrable coupling in the two hierarchies obtained is established by means of the discrete variational identity ultimately liouvolle integrability of the obtained integrable couplings is demonstrated

hamiltonian structure of discrete soliton systems we describe an approach for investigating the hamiltonian structures of the lattice isospectral evolution equations associated with a general discrete spectral problem by using the so called implicit representations of the isospectral flows we demonstrate the existence of the recursion operator l which is a strong and hereditary symmetry of the flows it is then proven that every equation in the isospectral hierarchy possesses the hamiltonian structure if l has a skew symmetric factorization and the first equation ut k 0 in the hierarchy satisfies some simple condition we obtain related properties such as the implectic symplectic factorization of l the liouville complete integrability and the multi hamiltonian structures of the isospectral hierarchy four examples are given

semidirect sums of lie algebras and discrete integrable couplings a relation between semidirect sums of lie algebras and integrable couplings of lattice equations is established and a practicable way to construct integrable couplings is further proposed an application of the resulting general theory to the generalized toda spectral problem yields two classes of integrable couplings for the generalized toda hierarchy of lattice equations the construction of integrable couplings using semidirect sums of lie algebras provides a good source of information on complete classification of integrable lattice equations

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

hamiltonian and quasi hamiltonian structures associated with semi direct sums of lie algebras the trace variational identity is generalized to zero curvature equations associated with non semi simple lie algebras or equivalently lie algebras possessing degenerate killing forms an application of the resulting generalized variational identity to a class of semi direct sums of lie algebras in the akns case furnishes hamiltonian and quasi hamiltonian structures of the associated integrable couplings three examples of integrable couplings for the akns hierarchy are presented one hamiltonian and two quasi hamiltonian

relativistic toda systems we present and study poincare invariant generalizations of the galilei invariant toda systems the classical nonperiodic systems are solved by means of an explicit action angle transformation