multiterminal source channel communication over an orthogonal multiple access channel we consider the problem of multiterminal source channel communication where a number of distributed and possibly correlated sources are transmitted through an orthogonal multiple access channel to a common destination we provide a characterization of the optimal tradeoff between the transmission cost gamma and the distortion vector d as measured against individual sources our approach consists of two steps 1 a multiple letter characterization of the rate distortion region of the multiterminal source coding and 2 a source channel separation theorem ensuring that all achievable pairs of gamma d can be obtained by combining the rate distortion region and the orthogonal multiple access channel capacity region as a corollary we determine the optimal power and distortion tradeoff in a quadratic gaussian sensor network under orthogonal multiple access and show that separate source and channel coding strictly outperforms the uncoded amplify forward transmission and is in fact optimal in this case this result is in sharp contrast to the case of nonorthogonal multiple access for which separate source and channel coding is not only suboptimal but also strictly inferior to uncoded transmission

hydrodynamics of stochastic cellular automata we investigate a stochastic version of cellular automata used for simulating hydrodynamical flows e g the hpp and fhp models the extra stochasticity consists of random exchanges between neighboring cells which conserve momentum we prove that in suitable limits these models satisfy the appropriate continuous boltzmann and hydrodynamic equations the same as those conjectured for the original models except that there is no negative viscosity contribution the results are obtained by proving a very strong form of propagation of chaos and by using hilbert chapman enskog type expansions explicit proofs are presented for the stochastic hpp model

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

combining and updating of local estimates and regional maps along sets of one dimensional tracks in this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates generated at different times of the same process sample path the first of these cases has applications in decentralized estimation while the second has applications in updating maps of spatially distributed random quantities given measurements along several tracks the method of solution for the second problem uses the result of the first and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields

numerical analysis of electric field formulations of the eddy current model this paper deals with finite element methods for the numerical solution of the eddy current problem in a bounded conducting domain crossed by an electric current subjected to boundary conditions involving only data easily available in applications two different cases are considered depending on the boundary data input current intensities or differences of potential weak formulations in terms of the electric field are given in both cases in the first one the input current intensities are imposed by means of integrals on curves lying on the boundary of the domain and joining current entrances and exit in the second one the electric potentials are imposed by means of lagrange multipliers which are proved to represent the input current intensities optimal error estimates are proved in both cases and implementation issues are discussed finally numerical tests confirming the theoretical results are reported

stochastic consensus over noisy networks with markovian and arbitrary switches this paper considers stochastic consensus problems over lossy wireless networks we first propose a measurement model with a random link gain additive noise and markovian lossy signal reception which captures uncertain operational conditions of practical networks for consensus seeking we apply stochastic approximation and derive a markovian mode dependent recursive algorithm mean square and almost sure i e probability one convergence analysis is developed via a state space decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum condition subsequently we consider a model with arbitrary random switching and a common stochastic lyapunov function technique is used to prove convergence finally our method is applied to models with heterogeneous quantizers and packet losses and convergence results are proved

distributed estimation in energy constrained wireless sensor networks in this paper we consider distributed estimation of a noise corrupted deterministic parameter in energy constrained wireless sensor networks from energy distortion perspective given a total energy budget allowable to be used by all sensors there exists a tradeoff between the subset of active sensors and the energy used by each active sensor in order to minimize the estimation mse to determine the optimal quantization bit rate and transmission energy of each sensor a concept of equivalent unit energy mse function is introduced based on this concept an optimal energy constrained distributed estimation algorithm for homogeneous sensor networks and a quasi optimal energy constrained distributed estimation algorithm for heterogeneous sensor networks are proposed moreover the theoretical energy distortion performance bound for distributed estimation is addressed and it is shown that the proposed algorithm is quasi optimal within a factor 2 of the theoretical lower bound simulation results also show that the proposed method can achieve a significant reduction in the estimation mse when compared with other uniform schemes finally the proposed algorithm is easy to implement in a distributed manner and it adapts well to the dynamic sensor environments

microscopic reversibility and the nonlinear einstein onsager relation in macroscopic description of nucleation we investigate the possibility of describing fluctuational decay of a metastable phase macroscopically without a detailed knowledge of the microscopic kinetics using the ideas of microscopic reversibility we construct a hydrodynamic type equation which describes the buildup of fluctuations in the region of subcritical sizes an equation of ornstein uhlenbeck type is used to bridge this equation with the one describing unstable growth of larger overcritical fluctuations an explicit time dependent solution to the proposed system of equations is derived in the spirit of the singular perturbation technique it is shown that this solution also accurately approximates the solution of the farkas becker doring master equation so that the macroscopic level of description is consistent with the underlying models

distributed estimation and detection for sensor networks using hidden markov random field models we develop a hidden markov random field hmrf framework for distributed signal processing in sensor network environments under this framework spatially distributed observations collected at the sensors form a noisy realization of an underlying random field that has a simple structure with markovian dependence we derive iterated conditional modes icm algorithms for distributed estimation of the hidden random field from the noisy measurements we consider both parametric and nonparametric measurement error models the proposed distributed estimators are computationally simple applicable to a wide range of sensing environments and localized implying that the nodes communicate only with their neighbors to obtain the desired results we also develop a calibration method for estimating markov random field model parameters from training data and discuss initialization of the icm algorithms the hmrf framework and icm algorithms are applied to event region detection numerical simulations demonstrate the performance of the proposed approach

distributed estimation algorithms for nonlinear systems in this paper we consider the problem of combining the local conditional distributions of a random variable which have been generated by local observers having access to their private information sufficient statistics for the local distributions are communicated to a coordinator who attempts to reconstruct the global centralized distribution using only the communicated statistics we obtain a distributed processing algorithm which recovers exactly the centralized conditional distribution the results can be applied in designing distributed hypothesis testing algorithms for event driven systems

stochastic least action principle for the incompressible navier stokes equation abstract we formulate a stochastic least action principle for solutions of the incompressible navier stokes equation which formally reduces to hamilton s principle for the incompressible euler solutions in the case of zero viscosity we use this principle to give a new derivation of a stochastic kelvin theorem for the navier stokes equation recently established by constantin and iyer which shows that this stochastic conservation law arises from particle relabelling symmetry of the action we discuss issues of irreversibility energy dissipation and the inviscid limit of navier stokes solutions in the framework of the stochastic variational principle in particular we discuss the connection of the stochastic kelvin theorem with our previous martingale hypothesis for fluid circulations in turbulent solutions of the incompressible euler equations

linear coherent decentralized estimation we consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center due to power and bandwidth limitations each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center in this context we study the linear decentralized estimation of the source vector where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages we adopt the mean squared error mse as the performance criterion when the channels between sensors and the fusion center are orthogonal it has been shown previously that the complexity of designing the optimal encoding matrices is np hard in general in this paper we study the optimal linear decentralized estimation when the multiple access channel mac is coherent for the case when the source and observations are scalars we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation simulations show that the proposed power scheduling improves the mse performance by a large margin when compared to the uniform power scheduling we also show that under a finite network power budget the asymptotic mse performance when the total number of sensors is large critically depends on the multiple access scheme for the case when the source and observations are vectors we study the optimal linear decentralized estimation under both bandwidth and power constraints we show that when the mac between sensors and the fusion center is noiseless the resulting problem has a closed form solution which is in sharp contrast to the orthogonal mac case while in the noisy mac case the problem can be efficiently solved by semidefinite programming sdp

power scheduling of universal decentralized estimation in sensor networks we consider the optimal power scheduling problem for the decentralized estimation of a noise corrupted deterministic signal in an inhomogeneous sensor network sensor observations are first quantized into discrete messages then transmitted to a fusion center where a final estimate is generated supposing that the sensors use a universal decentralized quantization estimation scheme and an uncoded quadrature amplitude modulated qam transmission strategy we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power while ensuring a given mean squared error mse performance the proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power for the remaining active sensors their optimal quantization and transmit power levels are determined jointly by individual channel path losses local observation noise variance and the targeted mse performance numerical examples show that in inhomogeneous sensing environment significant energy savings is possible when compared to the uniform quantization strategy

decentralized estimation in an inhomogeneous sensing environment we consider decentralized estimation of a noise corrupted deterministic parameter by a bandwidth constrained sensor network with a fusion center the sensor noises are assumed to be additive zero mean spatially uncorrelated but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment the classical best linear unbiased estimator blue linearly combines the real valued sensor observations to minimize the mean square error mse unfortunately such a scheme cannot be implemented in a practical bandwidth constrained sensor network due to its requirement to transmit real valued messages in this paper we construct a decentralized estimation scheme des where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal to noise ratio snr the resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter the proposed des is universal in the sense that each sensor compression scheme requires only the knowledge of local snr rather than the noise probability distribution functions pdf while the final fusion step is also independent of the local noise pdfs we show that the mse of the proposed des is within a constant factor of 25 8 of that achieved by the classical centralized blue estimator

distributed kalman filtering with quantized sensing state this paper studies a quantized gossip based interactive kalman filtering qgikf algorithm implemented in a wireless sensor network where the sensors exchange their quantized states with neighbors via inter sensor communications we show that in the countable infinite quantization alphabet case the network can still achieve weak consensus with the information loss due to quantization i e the estimation error variance sequence at a randomly selected sensor can converge weakly in distribution to a unique invariant measure to prove the weak convergence we first interpret error variance sequences as interacting particles then model each sequence evolution as a random dynamical system rds and further prove its stochastically bounded nature moreover based on the analysis for the countable infinite quantization alphabet case we also prove that under certain conditions the network can also achieve weak consensus when the quantization alphabet is finite which is more restricted and practical

power constrained linear estimation in wireless sensor networks with correlated data and digital modulation we study the problem of joint quantization and power allocation in wireless sensor networks where spatially distributed sensors observe a gaussian random source quantize the resulting noisy observations and transmit over orthogonal fading channels to a remote fusion center fc the role of the fc is to reconstruct the source with minimal distortion using linear minimum mean square error estimation rule in this paper we undertake the design of joint quantization and power allocation based on the following optimization problem minimize the reconstruction distortion for a given total network power consumption to address this problem at each sensor node uniform scalar quantization is assumed moreover assuming pseudo quantization noise model we show that the problem can be solved using a block coordinate descent type algorithm which iteratively optimizes the quantization bits and the power allocations the algorithm takes into account the spatial correlation the observation noise and the channel quality of the sensors numerical and simulation examples corroborate the analytical results the examples illustrate that the proposed design holds a considerable performance gain compared to a quantization scheme based on uniform power allocation to the sensors

universal decentralized estimation in a bandwidth constrained sensor network consider a situation where a set of distributed sensors and a fusion center wish to cooperate to estimate an unknown parameter over a bounded interval u u each sensor collects one noise corrupted sample performs a local estimation and transmits a message to the fusion center while the latter combines the received messages to produce a final estimate this correspondence investigates optimal local estimation and final fusion schemes under the constraint that the communication from each sensor to the fusion center must be a one bit message such a binary message constraint is well motivated by the bandwidth limitation of the communication links fusion center and by the limited power budget of local sensors in the absence of bandwidth constraint and assuming the noises are bounded to the interval u u additive independent but otherwise unknown the classical estimation theory suggests that a total of o u2 epsi2 sensors are necessary and sufficient in order for the sensors and the fusion center to jointly estimate the unknown parameter within epsi root mean squared error mse it is shown in this correspondence that the same remains true even with the binary message constraint furthermore the optimal decentralized estimation scheme suggests allocating 1 2 of the sensors to estimate the first bit of the unknown parameter 1 4 of the sensors to estimate the second bit and so on

constrained decentralized estimation over noisy channels for sensor networks decentralized estimation of a noise corrupted source parameter by a bandwidth constrained sensor network feeding through a noisy channel a fusion center is considered the sensors due to bandwidth constraints provide binary representatives of a noise corrupted source parameter recently proposed decentralized distributed estimation and power scheduling methods do no consider errors occurring during the transmission of binary observations from the sensors to fusion center in this paper we extend the decentralized estimation model to the case where imperfect transmission channels are considered the proposed estimator which operates on additive channel noise corrupted versions of quantized noisy sensor observations is approached from maximum likelihood ml perspective the resulting ml estimate is a root in the region of interest roi of a derivative polynomial function we analyze the natural logarithm of the polynomial within the roi showing that the function is log concave thereby indicating that numerical methods such as newton s algorithm can be utilized to obtain the optimal solution due to complexity and implementation issues associated with the numerical methods we derive and analyze simpler suboptimal solutions i e the two stage and mean estimators the two stage estimator first estimates the binary observations from noisy fusion center observations utilizing a threshold operation followed by an estimate of the source parameter the optimal threshold is the maximum a posteriori map detector for binary detection and minimizes the probability of binary observation estimation error optimal threshold expressions for commonly utilized light gaussian and heavy tailed cauchy channel noise models are derived the mean estimator simply averages the noisy fusion center observations the output variances of means of the proposed suboptimal estimators are derived in addition a computational complexity analysis is presented comparing the proposed ml optimal and suboptimal two stage and mean estimators numerical examples evaluating and comparing the performance of proposed ml two stage and mean estimators are also presented

the effect of correlated observations on the performance of distributed estimation estimating unknown signal in wireless sensor networks wsns requires sensor nodes to transmit their observations of the signal over a multiple access channel to a fusion center fc the fc uses the received observations which is corrupted by observation noise and both channel fading and noise to find the minimum mean square error mse estimate of the signal in this paper we investigate the effect of the source node correlation the correlation between sensor node observations and the source signal and the inter node correlation the correlation between sensor node observations on the performance of the linear minimum mean square error lmmse estimator for three correlation models in the presence of channel fading first we investigate the asymptotic behavior of the achieved distortion i e mse resulting from both the observation and channel noise in a non fading channel then the effect of channel fading is considered and the corresponding distortion outage probability the probability that the distortion exceeds a certain value is found by representing the distortion as a ratio of indefinite quadratic forms a closed form expression is derived for the outage probability that shows its dependency on the correlation finally the new representation of the outage probability allows us to propose an iterative solution for the power allocation problem to minimize the outage probability under total and individual power constraints numerical simulations are provided to verify our analytic results

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

optimal periodic transmission power schedules for remote estimation of arma processes we consider periodic sensor transmission power allocation with an average energy constraint the sensor sends its kalman filter based state estimate to the remote estimator through an unreliable link dropout probabilities depend on the power level used to encompass applications where the estimator needs to attend to multiple tasks we allow for irregular sampling following a periodic pattern using properties of an underlying markov chain model we derive an explicit expression for the estimation error covariance the results are then used to study optimal sensor power scheduling which minimizes the average error covariance

on infinite horizon sensor scheduling in this paper we consider the problem of infinite horizon sensor scheduling for estimation in linear gaussian systems due to possible channel capacity energy budget or topological constraints it is assumed that at each time step only a subset of the available sensors can be selected to send their observations to the fusion center where the state of the system is estimated by means of a kalman filter several important properties of the infinite horizon schedules will be presented in this paper in particular we prove that the infinite horizon average estimation error and the boundedness of a schedule are independent of the initial covariance matrix we further provide a constructive proof that any feasible schedule with finite average estimation error can be arbitrarily approximated by a bounded periodic schedule we later generalized our result to lossy networks these theoretical results provide valuable insights and guidelines for the design of computationally efficient sensor scheduling policies

hydrodynamics for an ideal fluid hamiltonian formalism and liouville equation abstract a hamiltonian formalism for hydrodynamics of ideal fluids is developed with the help of seliger and whitham s variational principle it is shown that a density distribution function in the phase space of the mass density momentum density and energy density fields obeys a liouville equation

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

trace formula for noisy flows a trace formula is derived for the fokker planck equation associated with ito stochastic differential equations describing noisy time continuous nonlinear dynamical systems in the weak noise limit the trace formula provides estimations of the eigenvalues of the fokker planck operator on the basis of the pollicott ruelle resonances of the noiseless deterministic system which is assumed to be non bifurcating at first order in the noise amplitude the effect of noise on a periodic orbit is given in terms of the period and the derivative of the period with respect to the pseudo energy of the onsager machlup freidlin wentzell scheme

dissipation and large thermodynamic fluctuations the results of recent work of kipnis olla and varadhan on the dynamic large deviations from a hydrodynamic limit for some interacting particle models are formally extended to a general hydrodynamic situation including non equilibrium steady states as a fluctuation dissipation hypothesis the basic conjecture is that the exponent of decay in the probability of a large thermodynamic fluctuation is given by the dissipation of the force required to produce the fluctuation it is shown that this hypothesis leads to a nonlinear version of onsager machlup fluctuation theory that had previously been proposed by graham a direct consequence of the theory is a dynamic variational principle for the most probable thermodynamic history subject to imposed constraints onsager s principle of least dissipation following graham the theory leads also to a generalized potential analogous to an equilibrium free energy for the nonequilibrium steady state and an associated static variational principle finally a formulation of nonlinear fluctuating hydrodynamics is proposed in which the noise enters multiplicatively so as to reproduce the conjectured large deviations theory on a formal analogy with the results of freidlin and wentzell for finite dimensional systems