on the communication complexity of distributed algebraic computation abstract we consider a situation where two processors p sub 1 and p sub 2 ar e to evaluate a collection of functions function 1 function 8 of two vector variables x y under the assumption that processor p sub 1 respectively p sub 2 has access only to the value of the variable x respectively y and the functional form of function 1 function 8 we provide some new bounds on the communication complexity the amount of information that has to be exchanged between the processors for this problem an almost optimal bound is derived for the case of one way communication when the functions function 1 function 8 are polynomials we also derive some new lower bounds for the case of two way communication which improve on earlier bounds by abelson a 80 as an application we consider the case where x and y are n x n matrices and f x y is a particular entry of the inverse of x y under certain restriction on the class of allowed communication protocols we obtain an omega n squared lower bound in contrast to the omega n lower bound obtained by applying abelson s results our results are based on certain tools from classical algebraic geometry and field extension theory

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

decentralized two filter smoothing algorithms in discrete time systems we develop some decentralized fixed interval smoothing algorithms which are realized by the two filter form in linear discrete time systems where the decentralized estimation structure consists of a central processor and of two local processors two approaches based on local filtering and local smoothing are considered for solving the problems of decentralized smoothing smoothing update and real time smoothing it is then shown that the notion of decentralized kalman filtering plays a significant role in the derivation of the algorithms for the former approach and that the introduction of the hamiltonian system in discrete time immediately gives the solutions of the problems in the latter approach moreover some characteristics of the algorithms arising from each approach are also discussed

a fuzzy set preference model for consumer choice abstract a fuzzy set model for predicting consumer choice is developed by combining the vector conjoint model with fuzzy measurement in a new model that requires only ordinal data fuzzy set measurement of consumer preferences is examined by testing alternative set representations and an interactive set definition method a comparison test of predictive validity using identical data from 139 subjects showed large improvements in rank order prediction validity compared to a non fuzzy approach prediction improvements of 83 are attributable to the use of fuzzy set definitions for subject ratings with the first two of six ordered ranking predicted on average

some aspects of fusion in estimation theory the problem of fusing or combining various estimates to obtain a single good estimate is investigated the problem of fusion in estimation theory is addressed and several examples using common distributions in which virtually any method of fusion would be useless in approximating the random variable of interest are presented a theorem which for a very general situation shows that fusion resulting in an almost surely exact approximation is always possible is presented in particular this result addresses the situation in which the data consists of the random variable of interest corrupted by additive gaussian noise and the random variable of interest could be any second order random variable finally an example which illustrates the utility of this result is presented

pedestrian movement analysis in transfer station corridor velocity based and acceleration based abstract in this paper pedestrians are classified into aggressive and conservative ones by their temper aggressive pedestrians walking through crowd in transfer station corridor is analyzed treating pedestrians as particles this paper uses the modified social force model msfm as the building block where forces involve self driving force repulsive force and friction force the proposed model in this paper is a discrete model combining the msfm and cellular automata ca model where the updating rules of the ca are redefined with msfm due to the continuity of values generated by the msfm we use the fuzzy logic to discretize the continuous values into cells pedestrians can move in one step with the observation that stimulus around pedestrians influences their acceleration directly an acceleration based movement model is presented compared to the generally reviewed velocity based movement model in the acceleration based model a discretized version of kinematic equation is presented based on the acceleration discretized with fuzzy logic in real life some pedestrians would rather keep their desired speed and this is also mimicked in this paper which is called inertia compared to the simple triangular membership function a trapezoidal membership function and a piecewise linear membership function are used to capture pedestrians inertia with the trapezoidal and the piecewise linear membership function many overlapping scenarios should be carefully handled and dubois and prade s four index method is used to completely describe the relative relationship of fuzzy quantities finally a simulation is constructed to demonstrate the effect of our model

toward a conformal field theory for schramm loewner evolutions we discuss the partition function point of view for chordal schramm loewner evolutions and their relationship with correlation functions in conformal field theory both are closely related to crossing probabilities and interfaces in critical models in two dimensional statistical mechanics we gather and supplement previous results with different perspectives point out remaining difficulties and suggest directions for future studies

distributed estimators for nonlinear systems a nonlinear distributed estimation problem is solved by using reduced order local models using local models with lower dimensions than the observed process model will lessen the local processors complexities or computational loads fusion algorithms that combine local densities to construct the centralized density of a nonlinear random process are presented the local densities are generated at each measurement time and communicated to a coordinator the models used to produce these densities are reduced order valid models the validity of the local models guarantees that the coordinator reconstructs exactly the centralized density function

smoothing error dynamics and their use in the solution of smoothing and mapping problems martingale decomposition techniques are used to derive markovian models for the error in smoothed estimates of processes described by linear models driven by white noise these models together with some simple hilbert space decomposition ideas provide a simple unified framework for examining a variety of problems involving the efficient assimilation of spatial data which we refer to as mapping problems algorithms for several different mapping problems are derived a specific example of map updating for a two dimensional random field is included

on conformally invariant cle explorations we study some conformally invariant dynamic ways to construct the conformal loop ensembles with simple loops introduced in earlier papers by sheffield and by sheffield and werner one outcome is a conformally invariant way to measure a distance of a cle4 loop to the boundary within the cle4 when one identifies all points of each loop

a hybrid approach to combine fuzziness and randomness in travel choice prediction abstract several approaches have been developed in order to deal with uncertainty in the prediction of travellers choices uncertainty almost always affects travel alternatives in several different choice contexts however the way in which this uncertainty affects choice options may consistently vary two main types of uncertainty can be identified randomness and fuzziness this paper discusses the use of a hybrid approach for choice modelling of travellers behaviour in choice contexts that involve conditions of high variability and uncertainty the aim of the work is to implement a hybrid methodology based on the use of a two term hybrid utility which allows taking into account at the same time the effects of both random and fuzzy uncertainty on travellers choice behaviour an application of the proposed methodology to a transit choice context is then presented

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

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

three dimensional reconstruction from projections with incomplete and noisy data by object estimation an estimation approach to three dimensional reconstruction from parallel ray projections with incomplete and very noisy data is described using a stochastic dynamic model for an object of interest in a probed domain of known background density the reconstruction problem is reformulated as a n onlinear state estimation problem an approximate minimum mean square error globally optimal algorithm for the solution of this problem is presented the algorithm which is recursive in a hybrid frequency space domain operates directly on the fourier transformed projection data eliminating altogether the attempt to invert the projection integral equation the simulation example considered in this paper demonstrates that good object estimates may be obtained with as few as five views in a limited sector of 90 and at a signal to noise ratio as low as 0 db

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

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

construction and applications of discrete time smoothing error models we present a unified perspective on techniques for constructing both forward and backward markovian realizations of the error process associated with discrete time fixed interval smoothing several alternative approaches are presented each of which provides additional insight and connections with other results in linear estimation theory in addition two applications of such models are described the first is a problem in the validation of an error model for a measurement system while the second concerns the problems of updating and combining smoothed estimates we also present an example of the use of our updating solution for the mapping of random fields based on several sets of data tracks

data fusion with minimal communication two sensors obtain data vectors x and y respectively and transmit real vectors m spl i oarr sub 1 x and m spl i oarr sub 2 y respectively to a fusion center the authors obtain tight lower bounds on the number of messages the sum of the dimensions of m spl i oarr sub 1 and m spl i oarr sub 2 that have to be transmitted for the fusion center to be able to evaluate a given function f spl i oarr x y when the function f spl i oarr is linear they show that these bounds are effectively computable certain decentralized estimation problems can be cast in the framework and are discussed in some detail in particular the authors consider the case where x and y are random variables representing noisy measurements and f spl i oarr x y e z x y where z is a random variable to be estimated furthermore it is established that a standard method for combining decentralized estimates of gaussian random variables has nearly optimal communication requirements

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

ordering for estimation and optimization in energy efficient sensor networks a discretized version of a continuous optimization problem is considered for the case where data is obtained from a set of dispersed sensor nodes and the overall metric is a sum of individual metrics computed at each sensor an example of such a problem is maximum likelihood estimation based on statistically independent sensor observations by ordering transmissions from the sensor nodes a method for achieving a saving in the average number of sensor transmissions is described while the average number of sensor transmissions is reduced the approach always yields the same solution as the optimum approach where all sensor transmissions occur the approach is described first for a general optimization problem a maximum likelihood target location and velocity estimation example for a multiple node noncoherent multiple input multiple output mimo radar system is later described in particular for cases with n good quality sensors with ideal signals and sufficiently large signal to interference plus noise ratio sinr the average percentage of transmissions saved approaches 100 as the number of discrete grid points in the optimization problem q becomes significantly large in these same cases the average percentage of transmissions saved approaches q 1 q 100 as the number of sensors n in the network becomes significantly large similar savings are illustrated for general optimization or estimation problems with some sufficiently well designed sensors savings can be even larger in some cases for systems with some poor quality sensors

on the quasi decentralized estimation and control of linear stochastic systems abstract it is shown that the quasi decentralized estimation and control of linear stochastic systems have extremely simple and computationally very efficient solutions in the domain of nonoptimal local filters these solutions reduce both off line and on line computation requirements the optimal global estimate is obtained simply by the addition of nonoptimal local estimates

multistage linear estimation using partitioning the estimation algorithm described in this note solves the linear estimation problem as a two stage estimator consisting of two consecutive kalman filters the interconnections between this estimator structure and the more familiar one stage optimal kalman filter are discussed applications to decentralized estimation bias estimation and parameter identification are described

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 e equilibrium in transportation networks abstract the principle of traffic equilibrium wardrop 1952 demands that the trip makers have enough knowledge of transportation networks which needs to be attained by accumulating experiences for a long time because of the complexity of traffic situation in the networks the route choice decisions for trip makers are however not always optimal objectively as a consequence it is impossible to strictly attain wardrop equilibrium in this paper a new concept of equilibrium equilibrium is proposed under the realistic assumption i e the fuzzy road information and random route choices equilibrium in the network is discussed by adopting fuzzy set theory mixed stochastic games and brouwer fixed point theorem in topological space the conclusion is that there is equilibrium in the real transportation network and this equilibrium has some deviations from the strict wardrop equilibrium the notion of equilibrium extends the traditional notion of network equilibrium it shows that traffic flow in the network converges to a region rather than to the points

distributing the kalman filter for large scale systems this paper presents a distributed kalman filter to estimate the state of a sparsely connected large scale n dimensional dynamical system monitored by a network of n sensors local kalman filters are implemented on nl dimensional subsystems nl lt n obtained by spatially decomposing the large scale system the distributed kalman filter is optimal under an lth order gauss markov approximation to the centralized filter we quantify the information loss due to this lth order approximation by the divergence which decreases as l increases the order of the approximation l leads to a bound on the dimension of the subsystems hence providing a criterion for subsystem selection the approximated centralized riccati and lyapunov equations are computed iteratively with only local communication and low order computation by a distributed iterate collapse inversion dici algorithm we fuse the observations that are common among the local kalman filters using bipartite fusion graphs and consensus averaging algorithms the proposed algorithm achieves full distribution of the kalman filter nowhere in the network storage communication or computation of n dimensional vectors and matrices is required only nl lt n dimensional vectors and matrices are communicated or used in the local computations at the sensors in other words knowledge of the state is itself distributed

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

fuzzy route choice model for traffic assignment abstract in order to represent traffic assignment on a road network we propose a new route choice model taking account of the imprecisions and the uncertainties lying in the dynamic choice process this model makes possible a more accurate description of the process than those deterministic or stochastic used in the literature we assume that drivers choose a path all the more than it is foreseen to have a lesser cost the predicted cost for each path is modelled by a fuzzy subset which can represent imprecision on network knowledge e g length of links as well as uncertainty on traffic conditions e g congested or uncongested network incident the costs of all possible paths are compared and result in an attractiveness degree for each path various comparison indices can be used to represent the different possible natures of drivers when making their decisions pessimistic optimistic risk taking risk averting the fuzzy choice model was compared with the logit model a widely used stochastic discrete choice model and has been proved to be able to find the same results the effect of advanced travellers information systems atis on drivers is modeled as a modification of the imprecision or the uncertainty of the predicted cost of a route

handling uncertainty in route choice models from probabilistic to possibilistic approaches abstract in order to design effective advanced traffic information systems atis suitable mathematical models have to be defined to simulate the effects of information on users route choice behaviour and then to incorporate it into traffic assignment models to estimate how traffic demand loads the roads network to face this problem it is necessary to deal with uncertainty that plays a crucial role in the users decision making processes to this purpose this paper first analyses how uncertainty affects users route choice process and how traffic assignment models may take it into account in literature route choice behaviour modelling is widely solved within the random utility theory framework but we show in this paper that such an approach only considers one type of uncertainty more precisely the consideration of randomness of traffic by drivers is for example hardly ever represented in classical models in spite of its importance in the management of information by drivers starting from the presented analysis a new route choice model is also proposed to represent explicitly the uncertainty lying in users route choice behaviour it is based on recent developments in possibility theory which is an alternate way to probability theory in order to represent or measure uncertainty

partition functions loop measure and versions of sle we discuss the partition function view of the schramm loewner evolution after reviewing a number of known results in the framework of brownian loop measures and scaling rules for partition functions we give some speculation about multiply connected domains

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

distributed estimation constraints on the choice of the local models the following estimation problem is considered a coordinator must reconstruct the global probability density of a nonlinear random process conditioned on the noise corrupted observation history the coordinator can only access the local probability density produced by local processing of the observation history using a local model different from the process model it is shown that if the local model satisfies an algebraic constraint the coordinator can reconstruct the same conditional density of the state process as the one obtained if the observations were processed using the coordinator process model it is assumed that the random process is a nonlinear stochastic differential equation driven by a brownian motion and the observation process is corrupted by additive brownian motion which is identically modeled by the coordinator and the local processor