activities and sensitivities in boolean network models we study how the notions of importance of variables in boolean functions as well as the sensitivities of the functions to changes in these variables impact the dynamical behavior of boolean networks the activity of a variable captures its influence on the output of the function and is a measure of that variable s importance the average sensitivity of a boolean function captures the smoothness of the function and is related to its internal homogeneity in a random boolean network we show that the expected average sensitivity determines the well known critical transition curve we also discuss canalizing functions and the fact that the canalizing variables enjoy higher importance as measured by their activities than the noncanalizing variables finally we demonstrate the important role of the average sensitivity in determining the dynamical behavior of a boolean network

the effect of network topology on the stability of discrete state models of genetic control boolean networks have been proposed as potentially useful models for genetic control an important aspect of these networks is the stability of their dynamics in response to small perturbations previous approaches to stability have assumed uncorrelated random network structure real gene networks typically have nontrivial topology significantly different from the random network paradigm to address such situations we present a general method for determining the stability of large boolean networks of any specified network topology and predicting their steady state behavior in response to small perturbations additionally we generalize to the case where individual genes have a distribution of expression biases and we consider a nonsynchronous update as well as extension of our method to non boolean models in which there are more than two possible gene states we find that stability is governed by the maximum eigenvalue of a modified adjacency matrix and we test this result by comparison with numerical simulations we also discuss the possible application of our work to experimentally inferred gene networks

on the high snr conditional maximum likelihood estimator full statistical characterization in the field of asymptotic performance characterization of the conditional maximum likelihood cml estimator asymptotic generally refers to either the number of samples or the signal to noise ratio snr value the first case has been already fully characterized although the second case has been only partially investigated therefore this correspondence aims to provide a sound proof of a result i e asymptotic in snr gaussianity and efficiency of the cml estimator in the multiple parameters case generally regarded as trivial but not so far demonstrated

joint tdoa and fdoa estimation a conditional bound and its use for optimally weighted localization modern passive emitter location systems are often based on joint estimation of the time difference of arrival tdoa and frequency difference of arrival fdoa of an unknown signal at two or more sensors classical derivation of the associated cramer rao bound crb relies on a stochastic stationary gaussian signal model leading to a diagonal fisher information matrix with respect to the tdoa and fdoa this diagonality implies that under asymptotic conditions the respective estimation errors are uncorrelated however for some specific nonstationary non gaussian signals especially chirp like signals these errors can be strongly correlated in this work we derive a conditional or a signal specific crb modeling the signal as a deterministic unknown given any particular signal our crb reflects the possible signal induced correlation between the tdoa and fdoa estimates in addition to its theoretical value we show that the resulting crb can be used for optimal weighting of tdoa fdoa pairs estimated over different signal intervals when combined for estimating the target location substantial improvement in the resulting localization accuracy is shown to be attainable by such weighting in a simulated operational scenario with some chirp like target signals

on the cramer rao bound for time delay and doppler estimation corresp using a theorem due to whittle simple derivations of the cramer rao lower bound are presented for some delay estimation problems related to a single source multiple sources and multipath the problem of doppler estimation is briefly discussed

broad edge of chaos in strongly heterogeneous boolean networks the dynamic stability of the boolean networks representing a model for the gene transcriptional regulation kauffman model is studied by calculating analytically and numerically the hamming distance between two evolving configurations this turns out to behave in a universal way close to the phase boundary only for in degree distributions with a finite second moment in degree distributions of the form pd k k with 2 3 thus having a diverging second moment lead to a slower increase of the hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite n with decreasing we conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms

synchronization of dynamical hypernetworks dimensionality reduction through simultaneous block diagonalization of matrices we present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems we are able to reduce the dimensionality of the problem by using simultaneous block diagonalization of matrices we obtain necessary and sufficient conditions for stability of the synchronous solution in terms of a set of lower dimensional problems and test the predictions of our low dimensional analysis through numerical simulations under certain conditions this technique may yield a substantial reduction of the dimensionality of the problem for example for a class of dynamical hypernetworks analyzed in the paper we discover that arbitrarily large networks can be reduced to a collection of subsystems of dimensionality no more than 2 we apply our reduction technique to a number of different examples including the class of undirected unweighted hypermotifs with 3 nodes

algorithms for ambiguity function processing calculation of the complex ambiguity function is viewed as the basis for joint estimation of the differential delay and differential frequency offset between two waveforms that contain a common component plus additive noise in many applications the required accuracy leads to a need for integration over long data sets that can become a challenge for near real time digital processing the nature of the ambiguity processing is interpreted and an algorithm approach is shown that minimizes the processing burden over a broad category of applications without affecting performance

the joint estimation of differential delay doppler and phase corresp in radio and sonar applications it sometimes happens that narrow band signals originated from a remote source and observed at a pair of receivers differ by unknown differential phase and doppler shift in addition to the differential delay corresponding to the range difference the correspondence presents the joint maximum likelihood ml estimate of the differential delay doppler and phase and examines their accuracy by deriving the cramer rao bound it is shown that the joint ml estimators are the values of the delay and doppler that maximize the magnitude of a generalized ambiguity function analogous to the one used in radar it is also shown that for long observation time and high enough signal to noise ratio there is no degradation in the accuracy of the time delay estimator due to the additional phase and doppler uncertainty and that the differential doppler is uncorrelated with the differential delay and phase estimators

improvement of tdoa position fixing using the likelihood curvature a conventional multilateration is a two step process where in the first step the time difference of arrivals tdoa of a signal at multiple sensors are estimated and in the second step these tdoas are used in some position fixing technique to estimate the location of an emitter several estimators have been proposed over the years for the estimation of the tdoas many techniques have been proposed for position fixing as well much of the research on position fixing has been focused on obtaining a simplified closed form solution for the unknown deterministic signal model stein had derived the maximum likelihood estimator mle for the tdoa between two sensors which is the peak location of the cross correlation function since the asymptotic variance of an mle approaches the cramer rao lower bound crlb which is the inverse of the negative of the expected value of the curvature of the log likelihood function using this as a motivation we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log likelihood function

robust matched filtering in ell_ p space a common approach to time delay estimation tde and joint delay doppler estimation jdde for target localization is matched filtering which is equivalent to the cross correlation of the received and transmitted signals the conventional correlation in hilbert space is statistically optimal in white gaussian noise however its performance significantly degrades in the presence of non gaussian noise or clutter in this paper two new concepts called ell p correlation and ell p ambiguity functions which generalize the conventional matched filtering from hilbert space to ell p space are proposed in addition several important mathematical properties of the ell p correlation and ell p ambiguity functions are given and proved compared with conventional ambiguity function the time frequency concentration of the ell p ambiguity function is significantly enhanced i e the delay doppler resolution is improved and the sidelobes are suppressed based on these two newly defined functions a family of tde and jdde algorithms that are robust against impulsive noise or clutter are developed furthermore the cramer rao bounds of tde and jdde for non gaussian noise with arbitrary probability distribution are derived simulation results under several impulsive noise models demonstrate that the performance in terms of robustness resolution and estimation accuracy is substantially improved when compared with the conventional matched filtering and fractional lower order moment based methods

approximating the largest eigenvalue of network adjacency matrices the largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes e g synchronization of oscillators percolation on directed networks and linear stability of equilibria of network coupled systems in this paper we develop approximations to the largest eigenvalue of adjacency matrices and discuss the relationships between these approximations numerical experiments on simulated networks are used to test our results

control of hopf bifurcation in a simple plankton population model with a non integer exponent of closure in this paper control of hopf bifurcation for a plankton population model with a non integer exponent of closure is studied for the plankton model with the closure term varies continuously between the commonly used linear and quadratic forms washout filter aided feedback controllers are employed to control the stability of the hopf bifurcation and thus the chaos could be eliminated by employing the stability theorems derived the stability of a control system is investigated finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods

boolean delay equations ii periodic and aperiodic solutions boolean delay equations bdes areevolution equations for a vector of discrete variables x t the value of each componentx i t 0 or 1 depends on previous values of all componentsx j t t ij x i t f i x1 t t i1 x n t t in bdes model the evolution of biological and physical systems with threshold behavior and nonlinear feedbacks the delays model distinct interaction times between pairs of variables in this paper bdes are studied by algebraic analytic and numerical methods it is shown that solutions depend continuously on the initial data and on the delays bdes are classified intoconservative anddissipative all bdes with rational delays only haveperiodic solutions only but conservative bdes with rationally unrelated delays haveaperiodic solutions of increasing complexity these solutions can be approximated arbitrarily well by periodic solutions of increasing period self similarity andintermittency of aperiodic solutions is studied as a function of delay values and certain number theoretic questions related toresonances and diophantine approximation are raised period length is shown to be a lower semicontinuous function of the delays for a given bde and can be evaluated explicitly for linear equations we prove that a bde isstructurable stable if and only if it has eventually periodic solutions of bounded period and if the length of initial transients is bounded it is shown that for dissipative bdes asymptotic solution behavior is typically governed by areduced bde applications toclimate dynamics and other problems are outlined

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

differential delay doppler ml estimation with unknown signals previously published analyses on the maximum likelihood estimation of joint frequency and time offsets between two noisy versions of a common signal have assumed a gaussian random signal with a known power spectrum in many applications the common signal is not gaussian and there may be no prior knowledge of its detailed structure instead estimation of a hypothesized common signal can be construed as another element in the estimation process the analysis is straightforward and shows that the complex ambiguity function caf still represents the ml approach when the noise is gaussian and spectrally flat additional interpretation shows that use of interference rejection filtering followed by a caf is an attractive suboptimum approach in an environment of narrowband interferers

collective dynamics in heterogeneous networks of neuronal cellular automata abstract we examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata each automaton has b active states a single silent state and r b 1 refractory states and can show spiking or bursting behavior depending on the values of b we show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of erdos renyi graphs as a function of edge probability different forms of heterogeneity allow distinct structural phase transitions to become relevant we also show that the dynamics on the network can be described by a semi annealed process and as a result can be related to the boolean lyapunov exponent

phase transitions in random networks simple analytic determination of critical points the standard method for determining the critical points in random networks such as boolean nets is based on the derrida approximation this method leads to the critical points based on the so called annealed approximation in this paper we present a very simple annealed approximation based on the study of damage spreading when single elements are modified several examples are analyzed

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

the many proofs and applications of perron s theorem this paper chronicles the wide dispersal of perron s 1907 result on positive matrices into many fields of science the many proofs given during the last 93 years are categorized and critiqued including perron s original two proofs and a more natural proof is presented this simple to understand result of perron provides a unequaled vehicle for taking students on a tour of many applied areas with some depth

iterative constrained weighted least squares source localization using tdoa and fdoa measurements this paper investigates the constrained weighted least squares cwls source localization problem by using time difference of arrival and frequency difference of arrival measurements the problem can be formulated as a quadratic programming with two indefinite quadratic equality constraints which is nonconvex and np hard moreover the weighting matrix is coupled with the unknown source position and velocity we propose an iterative cwls method that can efficiently solve this problem it iteratively performs a linearization procedure on the quadratic equality constraints to obtain an approximate programming with linear constraints which can be analytically solved and the weighting matrix is updated in each iteration theoretical analysis reveals that the proposed method if converges can lead to the global optimal solution of the formulated problem that reaches the crlb accuracy under mild assumptions on the measurement noises the monte carlo simulation results indicate that the percentage of convergence within mathbf 20 iterations is more than mathbf 96 and the localization accuracy is significantly improved over the previous methods with less computation time requirement moreover it is found from simulations that the iterative cwls method retains acceptable performance even under the ill conditioned situation when the sensor geometry is not desirable

random walk networks abstract random boolean networks are among the best known systems used to model genetic networks they show an on off dynamics and it is easy to obtain analytical results with them unfortunately very few genes are strictly on off switched on the other hand continuous methods are in principle more suitable to capture the real behavior of the genome but have difficulties when trying to obtain analytical results in this work we introduce a new model of random discrete network random walk networks where the state of each gene is changed by small discrete variations being thus a natural bridge between discrete and continuous models

complex ambiguity functions using nonstationary higher order cumulant estimates the complex ambiguity function based on second order statistics caf sos has been used to simultaneously estimate the frequency delay of arrival fdoa and time delay of arrival tdoa between two signal measurements its performance however is sensitive to the correlation between two additive noise sources when the noise sources are assumed to be gaussian we develop a new complex ambiguity function based on higher order statistics caf hos that reduces the unknown noise correlation effect the new caf hos algorithm utilizes nonstationary higher order cross cumulant estimates and their fourier transform in fact we suggest a nonstationary estimate of fourth order cross cumulants and obtain the analytical expressions for its mean value and variance we compare the analytical expressions with results obtained by monte carlo runs also we compare the performance of the new complex ambiguity function based on fourth order statistics caf fos against the caf sos algorithm using different gaussian noise sources different signals of interest different signal to noise ratios and different lengths of data