classification of steady solutions of the full kinematic model abstract the geometric type of kinematic model governs any moving plane curve which propagates in the normal direction in the medium there have appeared some results in the literature via this model however these results are all based upon some simplification on the model or prior phenomenological assumptions on the solutions in this paper we use really full kinematic model to classify steady solutions i e curvature is independent of time with positive or negative curvature various type of solutions have been obtained such as rotating and translating waves especially for the rotating spiral waves spiral waves arise in many biological chemical and physiological systems the kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane in fact using our results theorem 3 8 we can answer the following questions is there any steadily rotating wave for a given weakly excitable medium if yes what kind of information we can know about these rotating waves e g the tip s curvature the tip s tangential velocity and the rotating frequency comparing our results with previous ones in the literature there are some differences between them the only evolving plane curves with positive or negative curvature must have monotonous curvatures via simplified model but full model admits solutions with any given oscillating number of the curvatures

locally optimum detection of signals in a generalized observation model the random signal case locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal dependent and multiplicative noise it is shown that the locally optimum random signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model examples of explicit results for the locally optimum detector test statistics are given for some typical cases both asymptotic and finite sample size performances of the locally optimum detectors are considered and compared with those of other standard detector structures

volume averaging theory for the study of the mechanics of collagen networks abstract a multiscale methodology has been developed for modeling mechanical behavior of collagen fiber networks the methodology addresses scale separation between the macroscopic tissue level scale and the microscopic fiber level scale a three dimensional galerkin finite element model has been employed for the macroscopic scale while the tissue microstructure is represented as a three dimensional fibrillar network the model was applied to a rectangular slab in uniaxial extension a heterogeneous microstructure resulted in a non uniform deformation field and poisson s ratio varied for networks with different alignments the model was also specified and compared to published data relating microstructure to macroscopic behavior of collagen gels

optimal and robust memoryless discrimination from dependent observations discrimination is considered between two possible sources based on dependent observations of their output the discrimination problem is modeled by means of a general binary hypothesis test the main emphasis being on situations that cannot be modeled as signals in additive noise the observations are modeled as stationary m dependent or rho mixing processes the structure of the discriminator is such that the observations are passed through a memoryless nonlinearity summed up to form a test statistic which is then compared to a threshold only fixed sample size tests are considered four different performance measures which resemble the signal to noise ratios encountered in the signal in additive noise problems are derived under different problem formulations the optimal nonlinearities for each of the performance measures are derived as solutions to various integral equations for three of the four performance measures the authors have successfully obtained robust nonlinearities for uncertainty in the marginal and the joint probability density functions of the observations computer simulation results that demonstrate the advantage of using these nonlinearities over the i i d nonlinearity under the probability of error criterion are presented

constitutive equations for fibrous connective tissues a general multiaxial theory for the constitutive relations in fibrous connective tissues is developed on the basis of microstructural and thermodynamic considerations it is compatible with existing general material theories in elastic tissues the theory considers the strain energy function to be the sum of strain energies of the tissue s components the stresses are derived from this strain energy function viscoelastic constitutive relations are obtained in an analogous manner few examples are developed in detail the results of the present strain energy based theory are identical with those of the author s previous structural models lanir 1979a b which are based on detailed equilibrium analysis it turns out however that the analytical work involved in solving boundary value problems is considerably shorter if the present theory is used the advantages of structural theories in avoiding ambiguity in material characterization and in offering an insight into the function structure and mechanics of tissue components are discussed

spiral waves in the belousov zhabotinskii reaction abstract the beautiful spiral waves of oxidation in the belousov zhabotinskii reaction are the source of many interesting and important questions about periods structures in excitable media it has long been known that these spirals are similar to involutes of circles at least some distance from the center but until now no way has been known to determine the correct wavelength and frequency in this paper we show that the parameters of a spiral wave can be viwed s eigenvalues of a problem with unique solution the critical ingredients of the theory are the effects of curvature on the propagation of wavefronts in two dimensional media and the dispersion of plane waves our analytical results are shown to be in good agreement with experimental data for the belousov zhabotinskii reagent

robust detection of signals a large deviations approach robust detection of a signal is considered for the case of independent and identically distributed observations following an asymptotic but nonlocal approach the exponential rates of decrease of the error probabilities are considered as measure of performance under this measure a robust detection structure for the symmetric density case is derived this detection structure is a generalization of an existing result for the local case and is reduced to it when the signal magnitude tends to zero

a maximum variance model for robust detection and estimation with dependent data a model that accounts for uncertain data dependency is developed by generating a large class of stationary stochastic processes each with the same univariate distribution this class can be considered to be a contamination class about the nominal independent and identically distributed i i d process distribution the class is developed specifically for application to robust detector and estimator design based on asymptotic variance application of this dependency class leads to an intuitively pleasing result the minimax variance estimators and the maximin efficacy detectors are the same as obtained using i i d asymptotic estimation and detection theory thus our technique generalizes previously obtained robust design results for i i d data to this dependent data case

excitation wave propagation within narrow pathways geometric configurations facilitating unidirectional block and reentry abstract the propagation of excitation waves in narrow pathways of 2d excitable media through regions of impermeable media and decreased excitability media is investigated as a model of reentrant arrhythmias in the heart arrhythmia occurrences are common in the presence of infarct scars where regions of normal tissue are interspersed with inexcitable ones propagation through narrow pathways with three idealized geometric configurations are considered propagation through narrow paths with either parallel borders tapered borders or a combination of these the focus of this study is on the conditions for unidirectional block and reentry appearance it is shown that in narrow paths with only parallel borders unidirectional block is impossible regardless of the properties of the border media in this case only bidirectional propagation or block is possible depending on the pathway width unidirectional block can occur however when the narrow path has a tapered shape waves propagating from the wide end of the pathway die out at the narrow end while waves propagating in the opposite direction are able to pass through an approximate relationship between the geometry of the pathway and wave front curvature is obtained this provides a simple approach to estimate the critical curvature value in computer simulations of various excitable media or in experiments with real media a new computer simulation approach is proposed to closely approximate the dependence of stationary speed of propagation on wave front curvature in computer simulations of a two dimensional grid of 128 128 membrane segments using the modified fitzhugh nagumo equations the arrangement of two or more pathways in parallel permits reentry if at least one pathway has a configuration causing unidirectional block and the medium at the site of unidirectional block has sufficient time to recover from the previous excitation the latter is facilitated by anisotropic conduction properties of the media especially in the case with impermeable borders thus there exist specific geometric configurations of two dimensional narrow pathways which allow reentry even when the media properties are uniform

higher dimensional localized patterns in excitable media abstract the excitable reaction diffusion equation model of the form e u t e 2 2 u u v v t 2 v u v is considered when u is assumed to be of mckean s piecewise linear type the interfacial approach can be applied to the stability of various localized patterns in higher dimensional spaces it is shown that a band shaped localized pattern is destabilized into a zig zag mode or a varicose mode and that a disk shaped localized pattern is destabilized into static modes and when is small into an oscillatory mode like a breather motion numerical simulations are performed to confirm such destabilizations for more general nonlinear functions u

effect of diffusion on patterns in excitable belousov zhabotinskii systems travelling wave patterns occur frequently in chemically reacting systems these include planar fronts target patterns and spiral structures we review the dispersion relation for planar waves including the effects of diffusion in the slow field for a simplified piecewise linear model with a focus on the scaling behavior with respect to the relative rate of the fast and slow reactions we discuss the implications of these results for spirals showing the origins of fife scaling and deriving a boundary integral formulation of the spiral equations we discuss the generalization to more realistic models in particular the popular oregonator model for belousov zhabotinskii reactions

symmetric spirals in media with relaxation kinetics and two diffusing species abstract we find an approximate solution for the shape and rotation frequency of spirals in excitable media with anti symmetric kinetics and diffusion in both species using singular perturbation theory we approximate the governing diffusion reaction system with a free boundary problem and then map this free boundary problem onto a fixed domain problem the resulting fixed domain problem is viewed as a nonlinear eigenvalue problem which can be solved iteratively using a numerical shooting algorithm solutions of the approximate free boundary problem are compared with numerical solutions of the full system of diffusion reaction equations and shown to be in good agreement

min max detection of weak signals in phi mixing noise detection of weak signals in a special varphi mixing noise class is considered the detector structure is restricted to sums of memoryless nonlinear transformations of the observations correlated with the data sequence and compared to a fixed threshold using the efficacy to measure performance the nonlinearity that has min max performance is derived

continuum and discrete models for structures including quasi inextensible elasticae with a view to the design and modeling of composite reinforcements abstract inspired by some composite fiber reinforcements used in aeronautical engineering and by the need of conceiving new metamaterials some discrete models including quasi inextensible elasticae are considered a class of continuum models approximately describing the macroscopic mechanical behavior of introduced structures is then heuristically proposed some of these continuum models can be regarded as a special kind of second gradient elastic media in which the higher gradient elasticity is conferred by the flexural stiffnesses of elasticae constituting the microscopic lattice the discrete models are studied by means of suitably tailored numerical codes designed to avoid numerical instabilities and locking and a comparison of discrete versus continuum models is attempted the obtained results show that the theory of generalized continua may be useful in some engineering applications and it plays a relevant role in the mechanics of woven composites the introduced discrete and continuum models are used to describe the so called bias extension test on woven fabrics and it is shown that a good choice to correctly reproduce the targeted phenomenology is to use a second gradient continuum theory however as discussed throughout the paper in the context of rigorous micro macro identification procedures there still remain many open problems to be solved especially when dealing with systems subjected to particular constraints such as inextensibility

on signal detection in the presence of weakly correlated noise over fading channels in cognitive radio networks in order to avoid interference form secondary users to the primary license holders of the spectrum reliable spectrum sensing is necessary in scenarios where the noise samples are correlated the spectrum sensing methods optimized considering impairment by independent noise samples will not provide optimum performances to address this issue a locally optimum detection method for random signals under a weakly correlated noise model over fading channels is proposed the probabilities of false alarm and detection of the proposed detector in the low signal to noise ratio regime are analyzed the average probabilities are calculated over different channel gains numerical and simulation results demonstrate the superiority of the proposed method over the known energy detection method with comparable complexities furthermore we consider the scenario where the estimated correlation is different from the real correlation and investigate the effect of this correlation mismatch on the probabilities of false alarm and detection of the proposed method

geometrical properties of optimal volterra filters for signal detection linear quadratic filters are a special example of volterra filters that are limited to the second order it is shown that all the results recently published which are valid in the linear quadratic case can be extended with the appropriate notations to volterra filters of arbitrary order particularly the optimum volterra filter giving the maximum of the deflection for detecting a signal in noise is wholly calculated in addition several geometrical properties of optimal volterra filters are investigated by introducing appropriate scalar products in particular the concept of space orthogonal to the signal and the noise alone reference nar property are introduced allowing a decomposition of the optimal filter that exhibits a relation between detection and estimation extensions to the infinite case and relations with the likelihood ratio are also investigated

a mixture approach to the mechanics of skin skin can be considered to be a mixture of a solid and a fluid a general theory for the description of the behaviour of mixtures is presented and applied to a mixture of a solid and a fluid a numerical procedure is presented to solve the non linear field equations describing such a mixture the abilities of the procedure are demonstrated by means of a confined compression test

on an alternative modelling of distributed fibre directions abstract the main contribution of this work is the introduction of an alternative approach for the fast and accurate modelling of distributed fibre directions this method employs a quadrature rule which uses the sample vectors of the fibre orientation distribution function as integration points thus the computation time is drastically reduced compared to the classic angular integration method whereas the accuracy remains the same the effective stress converges with increasing numbers of integration further studies on different sets of sample vectors reveal a dependency of the effective second and fourth moment of the orientation distribution function on the choice of the integration points and their initial position by means of two example deformations with two different free energy densities the accuracy of the alternative method is clearly depicted over the complete range of fibre distributions it is worth mentioning that the method is not restricted to rotationally symmetric distributions and it is able to incorporate all five irreducible invariants of transverse isotropy the application of the alternative method to the numerical example of an arterial layer simulation by means of the fe method reveals drastic differences to the established modelling approaches

application of the volterra functional expansion in the detection of nonlinear functions of gaussian processes detection of a memoryless nonlinear functional of a gaussian process in additive gaussian white noise is considered the volterra functional expansion for the likelihood ratio and two examples of calculating the kernels are presented it is shown that kernels up to third order can be obtained for a hard limited gaussian process and for the absolute value of a gaussian process for the case of hard limiting the kernels are nonlinear functions of the autocorrelation of the gaussian process for the absolute value case the kernels are nonlinear functions of the kernel derived for the linear problem a monte carlo simulation of receiver performance is presented for the case of detection of the absolute value of a first order butterworth process in additive gaussian white noise the suboptimal detector is obtained by truncating the log likelihood ratio to second order

a heuristic description of spiral wave instability in discrete media abstract a set of simple low dimensional differential equations representing a chain of coupled oscillators is suggested as a model for explaining the instability of a rigidly rotating spiral wave that has been observed in spatially discrete and continuous models bifurcation to an invariant circle on a torus appears to be the mechanism responsible for this instability in the discrete case and is thus in agreement with barkley s assertion of an instability due to a hopf bifurcation

signal detection in the presence of weakly dependent noise i optimum detection the problem of designing robust systems for detecting constant signals in the presence of weakly dependent noise with uncertain statistics is considered as in part i of this study which treated optimum detection in weakly dependent noise a moving average representation is used to model the dependence structure of the noise process with the degree of dependence being parameterized by the averaging weights weak dependence is then modeled as the situation in which quantities depending to second or higher order on the averaging weights can be considered to be negligible uncertainty in the noise statistics is introduced within this framework by allowing a general type of uncertainty in the univariate statistics of the independent sequence that drives the moving average to find robust detectors for signals in this type of weakly dependent noise environment related results concerning robust location estimation in an analogous dependent situation are applied to modify a robust detection system for the corresponding independent noise case it is argued here that a robust detector for this dependent noise model is characterized by a least favorable noise distribution which coincides with the distribution that is least favorable for the corresponding independent noise case however the resulting detector design for dependent noise differs from that for independent noise in particular the robust detector for dependent noise is based on a linearly corrected version of the influence curve that defines the independent noise robust detector the worst case performance of the proposed robust detector relative to that of the independent noise robust detector is also analyzed with the conclusion that the performance of the proposed technique is better to first order in the averaging weights in this respect a modification of this robust detector is also proposed which eliminates some practical disadvantages of this system while retaining equivalent performance to first order the specific situation of contaminated gaussian noise is treated in order to illustrate the analysis

the eikonal equation stability of reaction diffusion waves on a sphere abstract the eikonal approach to excitable reaction diffusion systems provides an analytical hold on the phenomenon of wave propagation on curved surfaces and the evolution of toroidal scroll structures in the neighbourhood of organising filaments the extent to which the eikonal equation contains information on the stability of these wave solutions is important from a theoretical and experimental point of view we initiated this study in 1987 by demonstrating the stability of an expanding spherical wave recent experiments on wave propagation on a sphere encouraged us further to investigate stability of waves on surfaces we analyse in this paper the geometrical stability of symmetric counter rotating spiral waves propagating on the unit sphere we demonstrate that these solutions are stable under small perturbations normal to the wave fron lying on the unit sphere

singular perturbation theory of traveling waves in excitable media a review abstract waves of chemical or electrical activity traveling through space have been observed in several contexts chemical reaction mixtures in non convecting liquid phase cell suspensions nerve axons and neuromuscular tissues typically wave supporting preparations are excitable that is they respond and sensitivity to perturbations are rapidly damped out but suprathreshold disturbances trigger an abrupt and substantial response the abruptness of the response can be exploited by the methods of singular perturbation theory to obtain a mathematical description of wave propagation in spatially distributed excitable media singular perturbation analysis of propagating waves in one spatial dimension is straightforward and uncontentious but the analysis of propagating waves in one spatial dimension is straightforward and several fundamentally different ways we compare and contrast the approaches taken by greenberg zykov fife krinskii and his collaborators and ourselves with particular emphasis on the case of rotating spiral waves our intention is to bring some order to the important but difficult theory of propagating waves in two dimensional excitable media in conclusion we discuss briefly some possible extensions of the singular perturbation approach to propagating wave surfaces in three dimensional space

stability in linear detection the stability of linear detectors for signals nominally known except for amplitude in correlated nominally gaussian noise is considered stability is defined in terms of bounds on the distribution of the test statistic as the true probability measure on the observation space varies in a prokhorov neighborhood of the nominal the derived stability index is independent of the neighborhood size an optimization problem is formulated and solved to give the most stable linear detector meeting a constraint on the nominal level of detectability

alternative stable rotors in an excitable medium abstract a given excitable medium continuous uniform isotropic simply connected two or three dimensional may support alternative types of vortex like solution radiating from a rotor these have distinct periods wavelengths behaviors near interfaces and in rotationally symmetric vortex rings different contraction or expansion rates and drift rates initial conditions select among the discrete alternatives rotors of different types may coexist within one medium until the interface between their domains encroaches upon the rotor of longer period examples are given using the fitzhugh nagumo model they are interpreted in terms of the measured dispersion curve for one dimensional propagation and a hypothetical curvature relation with one undetermined parameter

a cellular automaton model of excitable media ii curvature dispersion rotating waves and meandering waves abstract a cellular automaton model of excitable media recently introduced by the authors is examined in more detail here we show that i the model is consistent with a linear dependence of wave speed on wave front curvature in two dimensional space ii the model exhibits a stepwise increasing relation between wave speed and temporal period the dispersion relation whose precise shape can be controlled by parameter settings iii the model generates rigidly rotating spiral waves whose frequency speed and core size are consistent with theoretical expectations and iv spiral waves rotate non rigidly showing short term flowerlet meandering which seems to arise by bifurcation from the rigidly rotating solution and long term irregular wandering over large distances these observations are consistent with many known features of wave propagation in two dimensional continuous excitable media governed by reaction diffusion equations suggesting that our cellular automaton model is not only a fast but also a reliable method for investigating the behavior of excitable media

distributed multisensor parameter estimation in dependent noise the problem of distributed estimation of a weak nonrandom location parameter theta in additive stationary dependent noise is addressed multisensor configurations with and without a coordinator are considered dependence in the sensor observations is described by m dependent phi mixing and p mixing models two cases of interest are addressed one in which sensor observations are dependent across time but independent across sensors and one in which sensor observations are dependent across both time and sensors numerical results on the performance evaluation of the various estimation schemes derived are presented and the relative performances of the various schemes are compared

curvature dependence of a model for calcium wave propagation abstract the propagation of a two dimensional wave front in an excitable medium is dependent on the curvature of the front current theories of excitable reaction diffusion models predict that when reaction is much faster than diffusion the normal wave speed n is approximately related to the curvature of the wave front the plane wave speed c and the diffusion coefficient of the propagator variable d by the eikonal equation n c d we show that a simple model for intracellular calcium ca2 wave propagation does not obey the eikonal equation and postulate an alternative curvature equation that is dependent on the parameter values used in the model this new curvature relation is confirmed by numerical simulations we raise the possibility that different models for ca2 wave propagation will have qualitatively different spiral wave patterns providing a new way of distinguishing between proposed models the theory developed here also necessitates a reconsideration of methods previously used to measure the intracellular diffusion coefficient of ca2

spiral wave solutions for reaction diffusion equations in a fast reaction slow diffusion limit abstract a two species reaction diffusion equation is studied in a distinguished limit of fast reaction and slow diffusion asymptotic matching yields a spiral solution whose rotation frequency is a unique function of the physical parameters and the constant pitch of the spiral using an idea of fife the problem is first reduced to a free boundary problem the solution is obtained by matching the core where diffusion balances the curvature of the free boundary to the far field where the effects of diffusion are small the equations of motion are averaged over the rotation frequency to yield steady equations in the two regions helically symmetric solutions to the averaged equation reduce to solving a fourth order ode in the core region matched to a second order ode in the far field speculations on the dynamics of the system and coupling between the core and far field are presented

one step memory nonlinearities for signal detection and discrimination from correlated observations detectors based on one step memory nonlinearities are introduced problems of discrimination between two arbitrary stationary m dependent or mixing sequences of observations and problems of detecting a weak signal in additive stationary m dependent or mixing noise are considered in this context for each problem the nonlinearity is optimized for performance criteria such as the generalized signal to noise ratio snr and the efficacy and is obtained as the solution to an appropriate linear integral equation the schemes considered can be made robust to statistical uncertainties determined by two alternating capacity classes for the second order joint pdfs probability distribution functions of the observations and by bounds on the correlation coefficients of time shifts of the observation sequence for the third and fourth order joint pdfs evaluation of the performance of the schemes via simulation reveals significant gains over that of detectors employing memoryless nonlinearities or the independent and identically distributed nonlinearity

application of cumulant method in performance evaluation of turbo like codes in this paper a new method for performance evaluation of turbo like codes is presented this is based on estimating the probability density function of the bit log likelihood ratio using higher order statistics we do not restrict ourselves to any specific model for the pdf and try to estimate it directly using a cumulant matching method numerical results show a close agreement between the proposed method and the simulations the complexity of this method is similar to the monte carlo simulation with the advantage of providing similar accuracy using significantly fewer samples

singularities in a modified kuramoto sivashinsky equation describing interface motion for phase transition abstract phase transitions can be modeled by the motion of an interface between two locally stable phases a modified kuramoto sivashinsky equation h t 2 h 4 h 1 h 2 2 h 2 h xx h yy h xy 2 describes near planar interfaces which are marginally long wave unstable we study the question of finite time singularity formation in this equation in one and two space dimensions on a periodic domain such singularity formation does not occur in the kuramoto sivashinsky equation 0 for all 1 0 we provide sufficient conditions on the initial data and size of the domain to guarantee a finite time blow up in which a second derivative of h becomes unbounded using a bifurcation theory analysis we show a parallel between the stability of steady periodic solutions and the question of finite time blow up in one dimension finally we consider the local structure of the blow up in the one dimensional case via similarity solutions and numerical simulations that employ a dynamically adaptive self similar grid the simulations resolve the singularity to over 25 decades in h xx l and indicate that the singularities are all locally described by a unique self similar profile in h xx we discuss the relevance of these observations to the full intrinsic equations of motion and the associated physics

robust locally optimum detection of signals in dependent noise a robust locally optimum detector of a signal embedded in additive dependent nongaussian noise is presented the performance criterion is bayes risk the sample size is finite and the uncertainty class of multivariate inputs is the in contamination model the locally optimum detector is shown to be a censored version of the nominal likelihood ratio

insight into detection of deterministic and gaussian signals in correlated plus impulsive noise environments the authors present a different view of the discrete time detection problem in impulsive noise the approach used is to examine the geometry from a subspace viewpoint of two detectors the clairvoyant matched filter and the clairvoyant power detector they are clairvoyant in that the locations of the impulses in the received data sample are assumed known in the presence of impulses both detectors use this knowledge for properly weighting these samples to reduce the effects of the impulses unfortunately since it is never reasonable to assume that the impulse locations are known these are unrealizable detectors however these clairvoyant detectors provide insight into the problem of detection in an impulsive environment when the nominal component is correlated and suggest detectors which are realizable the results can be used as a theoretical justification of preprocessing the data to eliminate impulsive samples prior to detection

spirals in excitable media the free boundary limit with diffusion abstract we solve numerically for the steady state spiral in the thin interface limit including the effects of diffusion of the slow field the calculation is performed using a generalization of the hybrid scheme of keener in this method the diffusion equation is solved on a suitable mapped lattice while the eikonal equation relating the field on the interface to the interfacial velocity and curvature is solved independently we present results for the selected frequency and tip radius as a function of the various parameters we note that a stability analysis based on these results may be performed

a free boundary problem arising in some reacting diffusing system we prove the well posedness for a one dimensional free boundary problem arising from some reaction diffusion system the interfacial point hits a boundary point in finite time or remains inside for all time in the large diffusion limit the system is reduced to ordinary differential equations of finite dimension

dynamics of wave fronts in excitable media abstract the dynamics of wave fronts in two dimensional excitable media is analytically studied by means of the asymptotic perturbation method for wave fronts in reaction diffusion systems we derive a space derivative burgers equation which governs the shape of boundary layers and their propagation application of lie group analysis of differential equations yields group invariant solutions of this equation and their classification some classes of the group invariant solutions determine the remarkable patterns expanding circle waves rotating spiral waves initial value problems for the burgers equation are also studied and a spiral wave is shown to be asymptotically realized under some proper boundary conditions

theory of the spiral core in excitable media abstract a rigorous asymptotic spiral solution to an excitable reaction diffusion system is found by separating space into two scaling regions an outer region having the same spatial scaling as the overall spiral structure which exhibits a singularity at the spiral tip and a core region around the spiral tip where space is scaled so as to resolve the tip singularity the stability of the spiral structure is investigated for both the outer region which is found to possess no intrinsic instability and the core region which is found to be unstable both the zero and small diffusion systems are found to exhibit qualitatively similar behaviour the implication of these results for both experiment and simulation in particular within the context of the observed meandering instability are addressed

on the robust estimation of the autocorrelation coefficients of stationary sequences this paper discusses methods for the estimation of the autocorrelation coefficients of a finite dependent stationary random sequence three estimators are examined the sample average and two proposed approaches namely the pseudo maximum likelihood pseudo ml estimator and the pseudo m estimator the latter scheme is found as a solution of a fredholm integral equation all three estimators are first studied for specific distribution models then the existence of a minimax robust design is proved and a suboptimally robust scheme is proposed simulation results illustrate the theoretical foundations of the methods and indicate that the pseudo m estimator achieves significantly better performance than the other two schemes when tested against dependent data and in the presence of outliers finally the results may also be applied to the estimation of a location parameter of a dependent random sequence

the change of variance function for dependent data the infinitesimal stability of the asymptotic variance is considered form estimators of a location parameter when the nominal sample with i i d data is contaminated by a possibly dependent process it is shown that the resulting change of variance function can be expressed as a sum of two terms one corresponding contamination of the univariate distribution and one to contamination of the bivariate distributions a change of variance sensitivity is introduced the form of which is closely related to the average patch length of the outliers finally optimalv robust and mostv robust score functions are derived the resulting family of estimators is the same as for independent data in the general case but the truncation point approaches zero when dependency is accounted for for redescending score functions the family of estimators is changed

a nonlinear optimum detection problem i theory an approximate log likelihood ratio for detecting a deterministic signal in linear and nonlinear gaussian noise is derived the new aspect of this detection problem is the inclusion of a nonlinear form of gaussian noise and a certain interaction between the signal and the linear noise such as modulation of the signal by the noise the derived log likelihood ratio consists of a modified version of the classical correlation detector and a new processor where the latter is an order of magnitude smaller than the former in the absence of the signal noise interaction the modification consists of subtracting the estimate of the nonlinear noise from the input to the correlation detector the nonlinear processor is a quadratic correlation processor where the correlation is not against the transformed signal but against the difference of two estimates of the nonlinear noise under the two hypotheses signal presence and signal absence presence of the signal noise interaction introduces further modification and complication on both processors

stable particle like solutions to the nonlinear wave equations of three dimensional excitable media so called excitable media support nonlinear waves that propagate as pulses e g the action potential in nerve fibers and heart muscle and the oxidation pulse in certain chemical reactions in two dimensional media the right stimulus will also create rotating vortices which radiate such pulses periodically in every direction their investigation in diverse excitable media has dramatically expanded in the usa and ussr since their discovery in both countries in 1970 in three dimensional media the pivot of the rotating structure is not a point but a curved line generically a closed ring rings linked together and knotted constitute topologically distinctive organizing centers for periodic activity throughout the medium it is of interest to understand how stimuli create organizing centers and how organizing centers persist or decay the numerically discovered stable organizing centers exhibit enough symmetries to encourage mathematical attention this paper illustrates organizing centers by computer g

an optimum strategy for detection in the presence of random transient disturbance and white gaussian noise detection of a deterministic signal is considered because of the presence of the transient disturbance the traditional totally probabilistic criteria are no longer appropriate since they cannot be related to the physical reality as in the case of stationary ergodic noise only a mixed strategy is proposed for the detection where the disturbance is treated as a semideterministic object while white gaussian noise is treated as a genuinely random object specifically the author uses as the detection statistic the log likelihood ratio of two conditional probability measures corresponding to the signal presence and the signal absence hypotheses given the disturbance in which the disturbance is replaced by its maximum a posteriori likelihood estimate the detection statistic takes the generalized in function space form of a soft limiter or a blanker followed by the matched filter it is an explicit detection algorithm though improvement in computational efficiency is much desired

locally optimum detection in moving average non gaussian noise detection algorithms that are locally optimum bayes and also asymptotically optimum are developed for both coherent and incoherent signaling for arbitrary interference and signal waveforms when the dependence in the noise samples is represented by a moving average model this leads to receiver structures which are prewhitened versions of the locally optimum detectors in the independent case a probability of error expression in the ideal observer symmetric case the processing gain and the minimum detectable signal are derived in both cases these demonstrate by means of an expression comparing performance between this and the independent case that for the same large sample size n 1 an improvement in performance is always achieved when the noise samples are dependent without any additional complexity in receiver structure

detection in multivariate non gaussian noise the applications of multivariate edgeworth series and higher order statistics to the discrete time detection of a known constant signal in multivariate non gaussian noise are considered a technique to derive suboptimum detectors from the neyman pearson optimum and locally optimum detectors is described a numerical algorithm based on knowledge of the noise cumulants is presented in order to analyze the finite sample size performance of the suboptimum detectors as an example the performance of the detectors as compared with the linear detector in multivariate gaussian gaussian mixture noise is presented via receiver operating characteristic curves numerical results indicate that the suboptimum detectors when exploiting knowledge of the dependence structure of the noise can have very good performance with respect to the linear detector

spirals in excitable media ii meandering transition in the diffusive free boundary limit abstract in this paper we present a numerical stability calculation for steadily rotating spirals in an excitable medium while experiments as well as numerical simulations of two field reaction diffusion models have shown the existence of a hopf bifurcation from steady rotations to a meandering state all the analytical approaches so far have failed to predict this transition this mismatch between analysis and simulations raises the question whether meandering critically depends on the finite diffusivity of the interface separating between the excited and the refractory phases our calculations show that this is not the case the meandering transition takes place even in the limit of an infinitely sharp interface the boundaries of the meandering transition as function of the model parameters are traced we discuss possible explanations for the failure of previous analytical approaches

expansions of the likelihood ratio and applications the likelihood ratio receiver although optimal is oftentimes difficult to realize to overcome this difficulty suboptimal approximations have been studied in the past one of the simplest approaches is to expand the likelihood ratio and truncate this expansion under the weak signal assumption in this paper we first study the relations between the taylor expansion and the volterra expansion under a weak signal assumption we emphasize the links between the taylor expansion with respect to the snr and the detection criteria on one hand and with robustness on the other in particular using two criteria derived from deflection we show that the minimax robust filter is the matched filter finally an application to underwater signal detection is studied showing that the degradation resulting from the use of the locally optimal receiver is small

partial update lms algorithms partial updating of lms filter coefficients is an effective method for reducing computational load and power consumption in adaptive filter implementations this paper presents an analysis of convergence of the class of sequential partial update lms algorithms s lms under various assumptions and shows that divergence can be prevented by scheduling coefficient updates at random which we call the stochastic partial update lms algorithm spu lms specifically under the standard independence assumptions for wide sense stationary signals the s lms algorithm converges in the mean if the step size parameter spl mu is in the convergent range of ordinary lms relaxing the independence assumption it is shown that s lms and lms algorithms have the same sufficient conditions for exponential stability however there exist nonstationary signals for which the existing algorithms s lms included are unstable and do not converge for any value of spl mu on the other hand under broad conditions the spu lms algorithm remains stable for nonstationary signals expressions for convergence rate and steady state mean square error of spu lms are derived the theoretical results of this paper are validated and compared by simulation through numerical examples

a geometrical approach to wave type solutions of excitable reaction diffusion systems we formulate the eikonal equation approximation for travelling waves in excitable reaction diffusion systems which have been proposed as models for a large number of biomedical situations this formulation is particularly suited in a natural way to numerical solution by finite difference methods we show how this solution is independent of the parametric variable used for expressing the eikonal equation and how a reduction of dimensionality implies a major saving over the time taken to solve the original reaction diffusion system neumann boundary conditions on reactants in the original system translate into a geometric constraint on the wave boundary itself we show how this leads to geometrically stable stationary wave boundaries in appropriately shaped non convex domains this analytical prediction is verified by numerical solution of the eikonal equation on a domain which supports geometrically stable stationary wave boundary configurations we show how the concepts of geometrical stability and wave front stability relate to a problem where a bi stable reaction diffusion system has a stable stationary wave front configuration

a model for fast computer simulation of waves in excitable media abstract starting from a two variable system of reaction diffusion equations an algorithm is devised for efficient simulation of waves in excitable media the spatio temporal resolution of the simulation can be varied continuously for fine resolutions the algorithm provides accurate solution of the underlying reaction diffusion equations for coarse resolutions the algorithm provides qualitative simulations at small computational cost

optimal linear quadratic systems for detection and estimation the problem of linear quadratic systems for detection has long been solved by assuming the deflection criterion and gaussian noise it is shown here that the gaussian assumption can be removed and a complete solution is presented for an arbitrary probability distribution with finite fourth order moments the optimal solution can always be obtained by solving a linear system of equations some properties of the optimal systems are developed for particular examples of nongaussian noise it is shown that there is a strong relationship between linear quadratic optimal detection and optimal estimation which extends results known for the purely linear case

a nonlocal approach for asymptotic memoryless detection theory corresp previous literature on detector design has presented many tractable results using efficacy as a performance functional which is a small signal or local approach some nonlocal issues of memoryless detection are considered we argue that the asymptotic exponential rate of decrease of error probabilities or bayes risk provides the appropriate asymptotic measure of performance a main contribution is the development of an approximation for nonlocal design that retains the tractability of the efficacy approach we have proved the local consistency of our approximation also as a consequence of the analysis new proofs for pitman noether like theorems have been obtained

shaping wave patterns in reaction diffusion systems we present a method to control the two dimensional shape of traveling wave solutions to reaction diffusion systems such as interfaces and excitation pulses control signals that realize a pregiven wave shape are determined analytically from nonlinear evolution equation for isoconcentration lines as the perturbed nonlinear phase diffusion equation or the perturbed linear eikonal equation while the control enforces a desired wave shape perpendicular to the local propagation direction the wave profile along the propagation direction itself remains almost unaffected provided that the one dimensional wave profile of all state variables and its propagation velocity can be measured experimentally and the diffusion coefficients of the reacting species are given the new approach can be applied even if the underlying nonlinear reaction kinetics are unknown

the dynamics of three dimensional scroll waves in excitable media abstract we investigate the motion of the central filament of a scroll wave in excitable medium we assume that two dimensional spiral solutions are known and use these solutions to produce slowly varying scroll waves in three dimensional space using standard ideas from perturbation theory multiscale techniques we find equations governing the motion of the central filament of the scroll and the twist of the scroll wave these equations are specialized to the case of a circular filament with uniformly distributed twist to determine the collapse or expansion and vertical drift of the spiral filament and to a helical filament with drift the predictions of these equations are in good qualitative agreement with the numerical experiments

travelling waves and static structures in a two dimensional exactly solvable reaction diffusion system exact travelling wave solutions of a fisher type reaction diffusion equation in two spatial dimensions are obtained the waves have nontrivial geometries and possess velocities smaller and larger than that of a plane wave the dispersion relationship and velocity curvature dependence generated by these solutions are characterized static structures with and without circular symmetry are constructed

winding numbers for the supercritical sine circle map abstract the dependence of the winding number on the initial value and on the nonlinearity for the supercritical sine circle map is discussed analytical investigations and numerical results show that some scaling behavior for the winding number can be extracted

the existence of spiral waves in an oscillatory reaction diffusion system rotating waves are proven to exist on the unit disk for an oscillatory reaction diffusion equation with neuman boundary conditions the method of proof relies on a two parameter shooting argument for the ensemble frequency and the radial derivative of the magnitude numerical solutions indicate that the waves are stable if the diffusion is sufficiently small it is also shown that these solutions cease to exist for large diffusion the origin of the rotating waves is discussed key words reaction diffusion equations spiral waves oscillatory media

robust detection of signals in dependent noise the robust detection of signals in additive dependent noise is considered the solution to the finite sample problem is obtained when the bayes risk is used as the performance measure for the multivariate densities involved we assume that they belong to an e contamination model the robust detection structure is shown to be optimum for the least favorable density and is a censored version of the nominal likelihood ratio

diffusion and wave propagation in cellular automaton models of excitable media in this paper the authors 1 examine general masks as discrete approximations to the diffusion equation showing how to calculate the diffusion coefficient from the elements of the mask 2 combine the mask with a thresholding operation to simulate the propagation of waves in excitable media showing that for well chosen masks the waves obey a linear speed curvature relation with slope given by the predicted diffusion coefficient and 3 assess the utility of different masks in terms of computational efficiency and adherence to a linear speed curvature relation

numerical integration on the sphere and its effect on the material symmetry of constitutive equations a comparative study in the present paper we consider a class of constitutive models based on numerical integration on the unit sphere the directional behaviour of the quadrature schemes and its effect on the symmetry properties of these constitutive models are studied by subjecting the set of integration points on the sphere to arbitrary rigid rotations we investigate a number of recently proposed integration schemes in application to a full network model of rubber elasticity and to an exponential model for soft tissues in order to assess and compare these schemes statistical methods are presented and applied the analysis discloses a number of integration schemes that offer a good compromise between the numerical error and the number of integration points however as a general result it turns out that numerical integration is prone to introduce strong anisotropy into originally isotropic constitutive equations in particular for highly non linear integrand functions the consequences for application of the investigated class of constitutive models in finite element calculations are highlighted in a benchmark like numerical example copyright 2009 john wiley sons ltd

a cumulant based adaptive technique for coherent radar detection in a mixture of k distributed clutter and gaussian disturbance in this paper we consider the problem of radar signal detection in the presence of disturbance which is assumed to be a mixture of coherent k distributed and gaussian distributed clutter besides thermal noise which is always present in the radar receiver has been considered the optimum detector is determined by thresholding an appropriate likelihood ratio test to properly operate in an interference environment of unknown correlation the optimum detector needs to adaptively estimate from the data the statistical properties of the interferences second order spectral analysis is unable to separately estimate the correlation structure of k distributed and gaussian distributed clutter sources their separate estimation can be accomplished only in higher order spectrum domain to reach this goal an adaptive algorithm based on second and higher order cumulants is proposed that removes these drawbacks and is able to operate in an environment of unknown correlation structure the performance of the adaptive processing scheme has been evaluated by means of monte carlo simulations

optimum detection of a weak signal with minimal knowledge of dependency the optimum nonlinearity is defined for detection of a weak signal when minimal knowledge of the dependency structure of the observations is available specifically it is assumed that the observations form a one dependent strictly stationary sequence of random variables and that only a finite number of moments of the marginal density and the correlation coefficient between consecutive observations are known it is assumed that the bivariate densities involved can be represented as diagonal series using orthonormal polynomials using efficacy as a performance measure the optimum nonlinearity is required to satisfy a saddle point condition over this class of bivariate densities

a geometrical theory for spiral waves in excitable media in this paper we develop a geometrical theory for waves in excitable reacting media using singular perturbation arguments and dispersion of traveling plane wave trains we derive an approximate theory of wave front propagation which has strong resemblance to the geometrical diffraction theory of high frequency waves in hyperbolic systems governed by the eikonal equation using this theory we study the effect of curvature on waves in excitable media specifically rotating spiral patterns in planar regions from this theory we are able to determine the frequency and wavelength for spiral patterns in excitable nonoscillatory media

spread spectrum multiple access performance of orthogonal codes impulsive noise a direct sequence spread spectrum multiple access ssma communication system that assigned a set of m orthogonal sequences to each user is analyzed an accurate model is incorporated for the impulsive noise that characterizes the lf and mf bands so that the ssma receiver operates in a combination of multiple access interference and impulsive atmospheric noise the performance of a linear receiver operating in such an environment is analyzed and probability of error curves are presented the presence of impulsive noise motivates the derivation and analysis of a nonlinear receiver that use a variable gain stage to suppress noise impulses this receiver is effectively optimum when the signal amplitudes are below a certain bound and when the noise and interference samples are independent or nearly so however the gain stage of this nearly optimum receiver depends on the noise model parameters including the various user delays consequently a nonparametric receiver that incorporates a simple clipper is also analyzed the asymptotic relative efficiency of both receivers is determined

the dynamics of scroll waves in excitable media an overview is given of the attempts to understand the behavior of scroll waves in three dimensional excitable media using analytical methods and these results are compared with recent numerical and experimental results the behavior of untwisted planar scroll rings twisted rings and helices and knotted scroll wave filaments is discussed

kinematical theory of spiral waves in excitable media comparison with numerical simulations abstract the kinematical theory of spiral waves is compared with the data of numerical simulations using complete partial differential equations of a reaction diffusion model we find good agreement for temporal periods of spiral waves which rotate around minimal holes and in the free medium no adjustable parameters were used in the calculations

large excitability asymptotics for scroll waves in three dimensional excitable media three dimensional scroll waves are considered in a reaction diffusion model of excitable media in the large excitability limit coordinates based on the scroll filament are defined and shown to provide a natural extension of the coordinates used for two dimensional spiral waves the leading order free boundary equations for interface motion in three dimensions are explicitly derived in these coordinates three specific examples are considered straight twisted scroll waves axisymmetric scroll waves and helical scroll waves the equations for the fields at leading and first order in the core region are given

detection in impulsive noise based on robust whitening despite the widespread use of the additive gaussian noise model it has long been recognized that many important environments are distinctly nongaussian the authors present a detector which is designed to operate in a correlated plus impulsive noise environment the detector robustly whitens the data and then uses a two sided threshold test to determine the presence of impulsive samples the impulsive samples are discarded and the remaining samples are used to detect the presence or absence of a signal using a matched filter an approximate analysis is presented and simulations are used to demonstrate the effectiveness of this approach

asymptotically robust detection and estimation for very heavy tailed noise the asymptotically robust detection of signals and the analogous problem of estimation of location are considered for noise distributions with heavier than exponential tails the solution to both problems is identical and is obtained when using efficacy or asymptotic variance as the performance measure the density of the noise is assumed to belong to a e contamination class where the contaminant is either 1 from the class of unimodal densities 2 from the class of densities limited in support to an interval about the mode of the nominal density or 3 a mixture of a member of 1 with a member of 2 the robust detector or estimator is similar to a censored version of the nonlinearity used for maximum likelihood estimation or locally optimal detection in the presence of noise with the nominal distribution

noise benefits to robust m estimation of location in dependent observations abstract in the presence of weakly dependent noise we analyze the asymptotic efficiency of robust maximum likelihood type estimators m estimators for location estimation we observe the noise enhanced asymptotic efficiency effect by tuning the background noise level for a single m estimator we also theoretically derive the asymptotic efficiency of a parallel array of m estimators and illustrate the possibility of the noise enhancement of the asymptotic efficiency by injecting extra additive noise components these obtained results enrich the research of noise benefits for the robust estimation of location from the dependent observations

robust hypothesis testing for bounded classes of probability densities corresp least favorable pairs of probability density functions and robust tests are obtained for classes of density functions specified as bands with upper and lower bounds the results are shown to extend huber s solution for the epsilon contaminated classes which is contained as a special case a minimum distance property of the least favorable density pair is also made explicit

on the p point uncertainty class corresp the p point uncertainty class also known as sakrison s class b is considered although the p point class is not a 2 alternating choquet capacity class it is shown how many of the robust signal processing and communication theory results which have been developed for capacity classes can be applied to the p point class by embedding it in a slightly larger extended p point class

locally optimal detection in multivariate non gaussian noise the detection of a vanishingly small known signal in multi variate noise is considered efficacy is used as a criterion of detector performance and the locally optimal detector lod for multivariate noise is derived it is shown that this is a generalization of the well known lod for independent identically distributed i i d noise several characterizations of multivariate noise are used as examples these include specific examples and some general methods of density generation in particular the class of multivariate densities generated by a zero memory nonlinear transformation of a correlated gaussian source is discussed in some detail the detector structure is derived and practical aspects of obtaining detector subsystems are considered through the use of monte carlo simulations the performance of this system if compared to that of the matched filter and of the i i d lod finally the class of multivariate densities generated by a linear transformation of an i i d noise source is described and its lod is shown to be a form frequently suggested to deal with multivariate non gaussian noise a linear filter followed by a memoryless nonlinearity and a correlator

the core of the spiral the problem of finding the unique frequency and shape including the core of spirals in excitable media is studied a leading order approximation of the problem is formulated as a nonlinear eigenvalue problem involving only ordinary differential equations odes shooting and comparison arguments are used to show why solutions of the leading order approximate problem exist and some of their quantitative features are explored numerically because of inaccuracies of the results in certain parameter ranges an improved formulation of the problem is proposed when solved numerically as in the special case of symmetric spirals solutions of the improved formulation differ significantly from solutions of the leading order problem but agree closely with the numerical solution of the full partial differential equation pde system

the effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex ginzburg landau equation abstract in this paper we consider an oscillatory medium whose dynamics are modeled by the complex ginzburg landau equation in particular we focus on n armed spiral wave solutions of the complex ginzburg landau equation in a disk of radius d with homogeneous neumann boundary conditions it is well known that such solutions exist for small enough values of the twist parameter q and large enough values of d we investigate the effect of boundaries on the rotational frequency of the spirals which is an unknown of the problem uniquely determined by the parameters d and q we show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak we use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q

postfiltering versus prefiltering for signal recovery from noisy samples we consider the extension of the whittaker shannon ws reconstruction formula to the case of signals sampled in the presence of noise and which are not necessarily band limited observing that in this situation the classical sampling expansion yields inconsistent reconstruction we introduce a class of signal recovery methods with a smooth correction of the interpolation series two alternative data smoothing methods are examined based either on a global postfiltering or a local data presmoothing we assess the accuracy of the methods by the global l sub 2 error both band limited and non band limited signals are considered a general class of correlated noise processes is taken into account the weak and strong rates of convergence of the algorithms are established and their relative efficiency is discussed the influence of noise memory and its moment structure on the accuracy is thoroughly examined

dispersion of traveling waves in the belousov zhabotinskii reaction abstract we use perturbation and numerical methods to calculate the dispersion relation for periodic wave train solutions of diffusion reaction equations modeling the belousov zhabotinskii reaction these results are compared with experimental data for the belousov zhabotinskii reagent and shown to be in good agreement