hypothesis testing with multiterminal data compression the multiterminal hypothesis testing h xy against h xy is considered where x n x n and y n y n are separately encoded at rates r 1 and r 2 respectively the problem is to determine the minimum beta n of the second kind of error probability under the condition that the first kind of error probability alpha n leq epsilon for a prescribed 0 a good lower bound theta l r 1 r 2 on the power exponent theta r 1 r 2 epsilon lim inf n rightarrow infty 1 n log beta n is given and several interesting properties are revealed the lower bound is tighter than that of ahlswede and csiszar furthermore in the special case of testing against independence this bound turns out to coincide with that given by them the main arguments are devoted to the special case with r 2 infty corresponding to full side information for y n y n in particular the compact solution is established to the complete data compression cases which are useful in statistics from the practical point of view

robust data fusion for multisensor detection systems minimax robust data fusion schemes for multisensor detection systems with discrete time observations characterized by statistical uncertainty are developed and analyzed block sequential and serial fusion rules are considered the performance measures used and made robust with respect to the uncertainties include the error probabilities of the hypothesis testing problem in the block fusion case and the error probabilities and expected numbers of samples or sensors in the sequential and serial fusion cases for different sensor observation statistics the minimax robust fusion rules are derived for two asymptotic cases of interest when the number of sensors is large and when the number of times the fusion center collects the local sensor decisions is large moreover for the case of identical sensor observation statistics and a large number of sensors it is shown that there is no loss in optimality if local tests using likelihood ratios and equal thresholds are used in the sequential fusion rule in all situations the robust decision rules at the sensors and the fusion center are shown to make use of likelihood ratios and thresholds that depend on the least favorable probability distributions of the uncertainty class describing the statistics of sensor observations

optimal linear fusion for distributed detection via semidefinite programming consider the problem of signal detection via multiple distributed noisy sensors we study a linear decision fusion rule of z quan s cui and a h sayed optimal linear cooperation for spectrum sensing in cognitive radio networks ieee j sel topics signal process vol 2 no 1 pp 28 40 feb 2008 to combine the local statistics from individual sensors into a global statistic for binary hypothesis testing the objective is to maximize the probability of detection subject to an upper limit on the probability of false alarm we propose a more efficient solution that employs a divide and conquer strategy to divide the decision optimization problem into two subproblems each subproblem is a nonconvex program with a quadratic constraint through a judicious reformulation and by employing a special matrix decomposition technique we show that the two nonconvex subproblems can be solved by semidefinite programs in a globally optimal fashion hence we can obtain the optimal linear fusion rule for the distributed detection problem compared with the likelihood ratio test approach optimal linear fusion can achieve comparable performance with considerable design flexibility and reduced complexity

a class of nth order impulsive integrodifferential equations in banach spaces abstract by establishing a comparison result and using the monotone iterative technique the author obtains the existence of maximal and minimal solutions of the initial value problem for a class of n th order impulsive integrodifferential equations in a banach space

distributed detection of narrowband signals distributed signal detection schemes have received significant attention but most research has focused on cases with independent observations at the different sensors cases with dependent narrowband signals which are of practical interest in communication radar and sonar problems are studied the focus is on applications where the observations consist of a weak common signal in possibly non gaussian additive noise which is independent from sensor to sensor the author finds that the best locally optimum sensor test statistics for such cases are often different from the best test statistics for cases with isolated sensors and that these sensor test statistics may be nonsymmetric for highly symmetric problems the possible difference between the best weak signal distributed sensor test statistic and the best weak signal test statistic for an isolated sensor can be shown to be due to the distributed sensors attempting to approximate the correlation terms found in the corresponding centralized tests

the suboptimality of randomized tests in distributed and quantized detection systems the design of decentralized or quantized detection systems requires simultaneous optimization of quantizer mappings and ultimate fusion rule it is shown that if the likelihood ratios of the unquantized or raw observations are independent and contain no point masses of probability the optimal test does not randomize this is so despite the fact that the data to be fused can be considered discrete the result is a considerable simplification in the design search

classification error analysis in stereo vision abstract depth perception in humans is obtained by comparing images generated by the two eyes to each other given the highly stochastic nature of neurons in the brain this comparison requires maximizing the mutual information mi between the neuronal responses in the two eyes by distributing the coding information across a large number of neurons unfortunately mi is not an extensive quantity making it very difficult to predict how the accuracy of depth perception will vary with the number of neurons n in each eye to address this question we present a two arm distributed decentralized sensors detection model we demonstrate how the system can extract depth information from a pair of discrete valued stimuli represented here by a pair of random dot matrix stereograms using the theory of large deviations we calculated the rate at which the global average error probability of our detector and the mi between the two arms output vary with n we found that mi saturates exponentially with n at a rate which decays as 1 n the rate function approached the chernoff distance between the two probability distributions asymptotically our results may have implications in computer stereo vision that uses hebbian based algorithms for terrestrial navigation

efficient soft decision fusion rule in cooperative spectrum sensing in cognitive radio cr the soft decision fusion sdf rule plays a critical role in cooperative spectrum sensing css however the computational cost on obtaining efficient sdf rule becomes infeasible even with a small number of cooperative users in this paper the efficiency of sdf rule in inhomogeneous background is studied from the perspective of quantization theory we formulate the calculation of sensing performance including the probabilities of detection and false alarm when regarding both i the quantization impact and ii the inhomogeneous background and then conclude a condition under which the sensing performance can be calculated by the fast fourier transform fft based on this condition two novel quantization schemes with two optimization methods are proposed to guarantee both the quantizer and decision threshold of sdf rule can be obtained efficiently at the same time the sdf can achieve high sensing performance

nonlinear boundary value problem for second order impulsive integro differential equations of mixed type in banach space using the cone theory and lower and upper solutions we investigate the existence of extremal solutions of nonlinear boundary value problem for second order impulsive integro differential equations which involve the derivative x and deviating argument x b t in banach space

new asymptotic results in parallel distributed detection the performance of a parallel distributed detection system is investigated as the number of sensors tends to infinity it is assumed that the i i d sensor data are quantized locally into m ary messages and transmitted to the fusion center for binary hypothesis testing the boundedness of the second moment of the postquantization log likelihood ratio is examined in relation to the asymptotic error exponent it is found that when that second moment is unbounded the neyman pearson error exponent can become a function of the test level whereas the bayes error exponent remains as previously conjectured by j n tsitsiklis 1986 unaffected large deviations techniques are also used to show that in bayes testing the equivalence of absolutely optimal and best identical quantizer systems is not limited to error exponents but extends to the actual bayes error probabilities up to a multiplicative constant

counterexamples in distributed detection specific counterexamples violating three very plausible conjectures about optimal design of distributed detection and decision systems are reported the numerical magnitude of the violation is small in each case

distributed detection with adaptive topology and nonideal communication channels this paper investigates the increase in detection reliability that an adaptive network with adaptive topology and channel dependent decision and fusion rules can provide compared with a fixed topology network we consider a network consisting of n local detectors and a fusion center fc that is tasked with accessing the presence or absence of a phenomenon of interest poi at a specific location the intensity of the signal emitted by the poi when present follows a power law attenuation model assuming that sensors transmit binary modulated local decisions over orthogonal nonideal channels where these channels are modeled as additive white gaussian noise awgn or fading we consider two classes of network topologies 1 sequential topology and 2 parallel topology under bayesian criterion we derive the optimal channel dependent rules and error probabilities for these topologies and establish the dependency of the errors on the received signal to noise ratios snrs of the sensing and communication channels for n 2 our extensive simulation results indicate that the optimality of parallel network is limited and demonstrate the average performance gain of topology adaptation the results also reveal that the performance gain and the optimal topology are dictated by the system parameters e g transmit powers and distances and the design search space i e whether the locations of the local detectors are fixed or optimized

on some unresolved issues in finding optimum distributed detection schemes optimum distributed detection under the neyman pearson np criterion is considered for a general case with possibly dependent observations from sensor to sensor the focus is on the parallel architecture new necessary conditions are presented that relate the threshold used in the np optimum fusion rule to those used in the np optimum sensor rules these results clearly illustrate that the necessary conditions for np optimality have exactly the same form as those for bayes optimality based on these conditions a new algorithm for finding np optimum distributed detection schemes is developed the algorithm allows randomization at the fusion center which we show is generally needed to achieve optimality the algorithm allows one to attempt to optimize the fusion rule along with the sensor rules or to find the best schemes among those using each of a set of fixed possible fusion rules

on the optimality of the likelihood ratio test for local sensor decision rules in the presence of nonideal channels distributed detection has been intensively studied in the past in this correspondence we consider the design of local decision rules in the presence of nonideal transmission channels between the sensors and the fusion center under the conditional independence assumption among multiple sensor observations we show that the optimal local decisions that minimize the error probability at the fusion center amount to a likelihood ratio test lrt given a particular constraint on the fusion rule this constraint turns out to be quite general and is easily satisfied for most sensible fusion rules a design example using a parallel sensor fusion structure with binary symmetric channels bscs between local sensors and the fusion center is given to illustrate the usefulness of the result in obtaining optimal thresholds for local sensor observations the study that incorporates the transmission channel in the sensor system design may have potential applications in the emerging field of wireless sensor networks

initial value problems for nonlinear second order impulsive integro differential equations in banach spaces in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of initial value problems for nonlinear second order impulsive integro differential equations in banach spaces

detection in sensor networks the saddlepoint approximation this paper presents a computationally simple and accurate method to compute the error probabilities in decentralized detection in sensor networks the cost of the direct computation of these probabilities e g the probability of false alarm the probability of a miss or the average error probability is combinatorial in the number of sensors and becomes infeasible even with small size networks the method is based on the theory of large deviations in particular the saddlepoint approximation and applies to generic parallel fusion sensor networks including networks with nonidentical sensors nonidentical observations and unreliable communication links the paper demonstrates with parallel fusion sensor network problems the accuracy of the saddlepoint methodology 1 computing the detection performance for a variety of small and large sensor network scenarios and 2 designing the local detection thresholds elsewhere we have used the saddlepoint approximation to study tradeoffs among parameters for networks of arbitrary size

a new framework for distributed detection with conditionally dependent observations distributed detection with conditionally dependent observations is known to be a challenging problem in decentralized inference this paper attempts to make progress on this problem by proposing a new framework for distributed detection that builds on a hierarchical conditional independence model through the introduction of a hidden variable that induces conditional independence among the sensor observations the proposed model unifies distributed detection with dependent or independent observations this new framework allows us to identify several classes of distributed detection problems with dependent observations whose optimal decision rules resemble the ones for the independent case the new framework induces a decoupling effect on the forms of the optimal local decision rules for these problems much in the same way as the conditionally independent case this is in sharp contrast to the general dependent case where the coupling of the forms of local sensor decision rules often renders the problem intractable such decoupling enables the use of for example the person by person optimization approach to find optimal local decision rules two classical examples in distributed detection with dependent observations are reexamined under this new framework detection of a deterministic signal in dependent noises and detection of a random signal in independent noises

positive solutions of an infinite boundary value problem for nth order nonlinear impulsive singular integro differential equations in banach spaces abstract in this paper the cone theory and monch fixed point theorem combined with a monotone iterative technique are used to investigate the positive solutions of a class of boundary problems for n th order nonlinear impulsive singular integro differential equations of mixed type on an infinite interval in banach spaces the conditions for the existence of a positive solution are established in addition an explicit iterative approximation of the solution for the boundary value problem is derived

positive solutions for nth order nonlinear impulsive singular integro differential equations on infinite intervals in banach spaces abstract in this paper the cone theory and monch fixed point theorem combined with a monotone iterative technique are used to investigate the positive solutions of a class of boundary problems for n th order nonlinear impulsive singular integro differential equations of mixed type on an infinite interval in banach spaces the conditions for the existence of a positive solution are established in addition an explicit iterative approximation of the solution for the boundary value problem is derived

distributed random signal detection with multibit sensor decisions distributed detection of weak random signals in additive possibly non gaussian noise is considered for cases with multibit sensor decisions signal to noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent analytical expressions are provided that describe the best way to fuse the quantized observations for cases with any given number of sensors the best schemes for originally quantizing the observations at each sensor are also studied for the case of an asymptotically large number of sensors these schemes are shown to minimize the mean squared error between the best weak signal test statistic based on unquantized observations and the best weak signal test statistic based on quantized observations analytical expressions describing optimum sensor quantizers are provided the approach used to obtain these expressions insures these sensor quantizers give good performance for cases with a finite number of sensors a novel iterative technique to search for optimum sensor quantizers efficiently is described numerical solutions are presented some of which involve cases where the best schemes for independent signal observations are shown to be suboptimum

transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations abstract using a new method for dealing with the impulse term of second impulsive differential equations we are concerned with determining values of for which there exist positive solutions of the following boundary value problems in the form of x t f t x t 0 t j t t k x t k x t k c k x t k k 1 2 n a x 0 b x 0 a x 1 b x 1 0 1 h s x t d t where 0 is a positive parameter c k is a real sequence with c k 1 k 1 2 n the dependence of positive solution x t on the parameter is also studied i e lim x or lim x 0 the proof of our main result is based upon transformation techniques and fixed point theories this is probably the first time the existence of positive solutions of second order impulsive differential equations has been studied by applying this technique

a distributed m ary hypothesis testing problem with correlated observations the distributed m ary hypothesis testing problem of detecting one of m sub 0 events by an n 1 person hierarchical team when the observations are correlated is examined in this problem each of the n subordinate decision makers dms transmits one of a prespecified set of messages based on their data to a primary decision maker who in turn combines the messages with his or her own data to make the final team decision the necessary conditions for the optimal decision rules of the dms are derived a nonlinear gauss seidel iterative algorithm is developed for the person by person optimal decision rules and its monotonic convergence to the person by person optimum is established a fast approximation algorithm is proposed for computing certain conditional probabilities arising in the person by person optimal decision rules the algorithms are illustrated with several examples and implications for distributed organizational designs are pointed out

on the relationship between circumscription and negation as failure abstract the aim of this paper is to investigate two powerful methods of handling negative information in logic based knowledge representation systems the logical minimization in the form of circumscription and the negation as failure rule formalized by various closures or completions of original theories we suggest a new more powerful form of the negation as failure rule and describe an important class of theories for which this form of negation as failure is equivalent to particular forms of circumscription these results establish a close relationship between the two important formalizations of nonmonotonic reasoning and provide a syntactic characterization of the corresponding circumscriptive theories this allows us to apply existing methods of deduction using various negation as failure rules to answering queries in a broad class of circumscriptive theories

optimum distributed detection of weak signals in dependent sensors locally optimum lo distributed detection is considered for observations that are dependent from sensor to sensor the necessary conditions are presented for lo distributed sensor detector designs and a locally optimum fusion rule for an n sensor parallel distributed detection system with dependent sensor observations is given specific solutions are obtained for a random signal additive noise detection problem with two sensors these solutions indicate that the lo sensor detector nonlinearities in general contain a term proportional to f f where f is the noise probability density function pdf for some non gaussian pdf s the new term is significant and causes the lo sensor detector nonlinearities to be nonsymmetric even for symmetric pdfs lo solutions are presented for finite sample sizes and the solutions for the asymptotic case are discussed these results are extended to yield the form of the solutions for the n sensor lo random signal distributed detection problem that generalize the two sensor results

on the optimality of finite level quantizations for distributed signal detection distributed multiple sensor detection problems with quantized observations are investigated for cases of nonbinary hypothesis and possibly statistically dependent observations from sensor to sensor conditioned on the hypothesis the observations available at each sensor are quantized to produce a multiple digit sensor decision which is sent to a fusion center at the fusion center the sensor decisions are combined to form a final decision using a predetermined fusion rule first it is demonstrated that there is a maximum number of digits that should be used to communicate the sensor decision from a given sensor to the fusion center this maximum is based on the number of digits used to communicate the decisions from all the other sensors to the fusion center if more than this maximum number of digits is used the performance of the optimum scheme will not be improved in some special cases of great interest the upper bound on the number of digits that should be used can be made significantly smaller secondly the optimum way to allocate a fixed overall number of digits across sensors is investigated illustrative numerical results are also presented in this correspondence

locally optimum distributed detection of correlated random signals based on ranks distributed signal detection schemes have received significant attention but most research has focused on cases where the observations at the different sensors are independent and the statistical model for the observations is completely known if the observations at the different sensors consist of noisy versions of random signals which were produced by the same source then these observations may not be independent it is also possible that the noise distribution may not be completely known cases where weak random signals are observed in possibly non gaussian additive noise are considered the focus is on cases where the sensor tests are based only on the ranks and signs of the observations numerical results are provided which indicate that distributed schemes based on ranks and signs are less sensitive to the exact noise statistics when compared to optimum schemes based directly on the observations this is especially true for some cases where the actual noise distribution has heavy tails which can cause the optimum schemes based directly on the observations to perform poorly analytical forms are given for the locally optimum sensor test statistics based on the ranks and signs of the observations and we use these to find the best distributed detection schemes for some cases in the course of obtaining our results a general set of necessary conditions is given which provide the analytical forms of the locally optimum distributed sensor tests for cases where the observations are discrete random variables conditions of this type have not been given previously

adaptive l_p norm spectrum sensing for cognitive radio networks in cognitive radio cr systems reliable spectrum sensing techniques are required in order to avoid interference to the primary users of the spectrum whereas most of the existing literature on spectrum sensing considers impairment by additive white gaussian noise awgn only in practice crs also have to cope with various types of non gaussian noise such as man made impulsive noise co channel interference and ultra wideband interference in this paper we propose an adaptive lp norm detector which does not require any a priori knowledge about the primary user signal and performs well for a wide range of circularly symmetric non gaussian noises with finite moments we analyze the probabilities of false alarm and missed detection of the proposed detector in rayleigh fading in the low signal to noise ratio regime and investigate its asymptotic performance if the number of samples available for spectrum sensing is large furthermore we consider the deflection coefficient for optimization of the lp norm parameters and discuss its connection to the probabilities of false alarm and missed detection based on the deflection coefficient an adaptive algorithm for online optimization of the lp norm parameters is developed analytical and simulation results show that the proposed lp norm detector yields significant performance gains compared to conventional energy detection in non gaussian noise and approaches the performance of the locally optimal detector which requires knowledge of the noise distribution

extremal solutions for nth order impulsive integro differential equations on the half line in banach spaces abstract by establishing a comparison result and using the upper and lower solutions the author obtains the existence of maximal and minimal solutions for a boundary value problem of n th order nonlinear impulsive integro differential equations on the half line in banach spaces

multiple positive solutions of a boundary value problem for nth order impulsive integro differential equations in a banach space abstract in this paper the author obtains the existence of multiple positive solutions for a boundary value problem of a class of nth order nonlinear impulsive integro differential equations on an infinite interval in a banach space by means of the fixed point index theory of completely continuous operators

bayesian detection in bounded height tree networks we study the detection performance of large scale sensor networks configured as trees with bounded height in which information is progressively compressed as it moves towards the root of the tree we show that under a bayesian formulation the error probability decays exponentially fast and we provide bounds for the error exponent we then focus on the case where the tree has certain symmetry properties we derive the form of the optimal exponent within a restricted class of easily implementable strategies as well as optimal strategies within that class we also find conditions under which suitably defined majority rules are optimal finally we provide evidence that in designing a network it is preferable to keep the branching factor small for nodes other than the neighbors of the leaves

on cones of nonnegative quadratic functions we derive linear matrix inequality lmi characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co positivity these matrix cones are in fact cones of nonconvex quadratic functions that are nonnegative on a certain domain as a domain we consider for instance the intersection of a upper level set of a quadratic function and a half plane consequently we arrive at a generalization of yakubovich s s procedure result although the primary concern of this paper is to characterize the matrix cones by lmis we show as an application of our results that optimizing a general quadratic function over the intersection of an ellipsoid and a half plane can be formulated as semidefinite programming sdp thus proving the polynomiality of this class of optimization problems which arise e g from the application of the trust region method for nonlinear programming other applications are in control theory and robust optimization

asymptotic locally optimal detector for large scale sensor networks under the poisson regime we consider distributed detection with a large number of identical binary sensors deployed over a region where the phenomenon of interest poi has spatially varying signal strength each sensor makes a binary decision based on its own measurement and the local decision of each sensor is sent to a fusion center using a random access protocol the fusion center decides whether the event has occurred under a global size constraint in the neyman pearson formulation assuming homogeneous poisson distributed sensors we show that the distribution of alarmed sensors satisfies the local asymptotic normality lan we then derive an asymptotically locally most powerful almp detector optimized jointly over the fusion form and the local sensor threshold under the poisson regime we establish conditions on the spatial signal shape that ensure the existence of the almp detector we show that the almp test statistic is a weighted sum of local decisions the optimal weights being the shape of the spatial signal the exact value of the signal strength is not required we also derive the optimal threshold for each sensor for the case of independent identically distributed iid sensor observations we show that the counting based detector is also almp under the poisson regime the performance of the proposed detector is evaluated through analytic results and monte carlo simulations and compared with that of the counting based detector the effect of mismatched signal shapes is also investigated

randomized fusion rules can be optimal in distributed neyman pearson detectors we show that randomized fusion rules can be locally optimal in distributed detection systems under the neyman pearson criterion this result is contrary to common belief we first formulate conditions for a randomized fusion rule to be locally optimal then we present distribution functions of local observations that satisfy these conditions

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

quantization in multisensor random signal detection optimum detection schemes based on quantized data are of great interest in radar and sonar applications the design and properties of multisensor schemes are considered here for detection of weak random signals in additive possibly non gaussian noise signal to noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent analytical expressions describing the best way to fuse the quantized observations for cases with any given observation sample size are provided the best schemes for originally quantizing the observations are also studied for the case of asymptotically large observation sample sizes these schemes are shown to minimize the mean squared error between the best weak signal test statistic based on unquantized observations and the best weak signal test statistic based on quantized observations under signal absent numerical results indicate it is sometimes best for each quantizer to use different size alphabets when a quantizer is located at each sensor

fundamental structures and asymptotic performance criteria in decentralized binary hypothesis testing two fundamental distributed decision network structures are considered the first system consists of finite number of sensors each collecting asymptotically many data while the second one employs asymptotically many sensors each collecting a single datum for binary hypothesis testing the neyman pearson criterion is utilized and justified via information theoretic arguments an asymptotic relative efficiency performance measure is used to establish tradeoffs between the two structures by comparing the performance characteristics of the decentralized detection systems to their centralized counterparts

distributed signal detection under the neyman pearson criterion a procedure for finding the neyman pearson optimum distributed sensor detectors for cases with statistically dependent observations is described this is the first valid procedure we have seen for this case this procedure is based on a theorem proven in this paper these results clarify and correct a number of possibly misleading discussions in the existing literature cases with networks of sensors in fairly general configurations are considered along with cases where the sensor detectors make multiple bit sensor decisions

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

saturation nonmonotonic reasoning and the closed world assumption abstract to deal with the problem of implicit negative information in databases it is necessary to use a nonmonotonic form of reasoning the form of reasoning described in this paper uses an ordering relation on interpretations of the type i is inferior to j if every elementary fact true in i is true in j in simple cases this rule may be defined by a set p of formulas implies a formula q if every minimal model of p satisfies q in more general cases this definition leads to paradox if p is consistent and has no minimal model p must not imply q and its negation we have 1 1 carefully formulated the definition of a special type of implication called sub implication to avoid this type of paradox 2 2 proved that if p is a set of clauses then p has a minimal model and more generally that every model of a set of clauses is minored by one of its minimal models 3 3 developed in this last case subject to certain conditions such as the use of a particular set of clauses called groundable clauses or g clauses a decidable algorithm to compute whether p implies q q being practically any formula

necessary conditions for optimum distributed sensor detectors under the neyman pearson criterion distributed signal detection schemes that are optimum under the neyman pearson criterion continue to be of interest the functional forms of these schemes can be difficult to specify especially for cases with dependent observations from sensor to sensor for cases with dependent observations from sensor to sensor the optimum sensor test statistics are generally not the likelihood ratios of the sensor observations equations expressing the forms of the optimum sensor test statistics in terms of the other optimum test statistics and the optimum fusion rule are given detailed proofs of these results are given in this correspondence and have not been given previously in some communication radar and sonar system problems the amplitude of the received signal may be unknown but the signal may be known to be weak equations expressing the forms of the optimum sensor test statistics for such cases are given these expressions have already been shown to be useful for interpreting and finding optimum distributed detection schemes but detailed proofs of the type given here have not yet been given

on well posedness of an initial value problem for nonlinear second order impulsive integro differential equations of volterra type in banach spaces in this paper we develop an existence and uniqueness theorem of the solution to an initial value problems for a class of second order impulsive integro differential equations of volterra type in a real banach space by using the generalized banach fixed point theorem an explicit iterative scheme for the solution and an error estimate of the approximation sequence for the initial value problem are also derived two examples are presented to demonstrate the application of our results

new results on quadratic minimization in this paper we present several new results on minimizing an indefinite quadratic function under quadratic linear constraints the emphasis is placed on the case in which the constraints are two quadratic inequalities this formulation is termed the extended trust region subproblem in this paper to distinguish it from the ordinary trust region subproblem in which the constraint is a single ellipsoid the computational complexity of the extended trust region subproblem in general is still unknown in this paper we consider several interesting cases related to this problem and show that for those cases the corresponding semidefinite programming relaxation admits no gap with the true optimal value and consequently we obtain polynomial time procedures for solving those special cases of quadratic optimization for the extended trust region subproblem itself we introduce a parameterized problem and prove the existence of a trajectory that will lead to an optimal solution combining this with a result obtained in the first part of the paper we propose a polynomial time solution procedure for the extended trust region subproblem arising from solving nonlinear programs with a single equality constraint

method of upper and lower solutions for second order impulsive integro differential equations in a banach space abstract this paper discusses the initial value problem for second order nonlinear impulsive integro differential equations of volterra type in a banach space by means of upper and lower solutions by establishing a comparison result criteria on the existence of maximal and minimal solutions are obtained

the good bad and ugly distributed detection of a known signal in dependent gaussian noise most results about quantized detection rely strongly on an assumption of independence among random variables with this assumption removed little is known thus in this paper bayes optimal binary quantization for the detection of a shift in mean in a pair of dependent gaussian random variables is studied this is arguably the simplest meaningful problem one could consider if results and rules are to be found they ought to make themselves plain in this problem for certain problem parametrizations meaning the signals and correlation coefficient optimal quantization is achievable via a single threshold applied to each observation the same as under independence in other cases one observation is best ignored or is quantized with two thresholds neither behavior is seen under independence further and again in distinction from the case of independence it is seen that in certain situations an xor fusion rule is optimal and in these cases the implied decision rule is bizarre the analysis is extended to the multivariate gaussian problem

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

target location estimation in sensor networks with quantized data a signal intensity based maximum likelihood ml target location estimator that uses quantized data is proposed for wireless sensor networks wsns the signal intensity received at local sensors is assumed to be inversely proportional to the square of the distance from the target the ml estimator and its corresponding crameacuter rao lower bound crlb are derived simulation results show that this estimator is much more accurate than the heuristic weighted average methods and it can reach the crlb even with a relatively small amount of data in addition the optimal design method for quantization thresholds as well as two heuristic design methods are presented the heuristic design methods which require minimum prior information about the system prove to be very robust under various situations

quantization for decentralized hypothesis testing under communication constraints in a decentralized hypothesis testing network several peripheral nodes observe an environment and communicate their observations to a central node for the final decision the presence of capacity constraints introduces theoretical and practical problems the following problem is addressed given that the peripheral encoders that satisfy these constraints are scalar quantizers how should they be designed in order that the central test to be performed on their output indices is most powerful the scheme is called cooperative design separate encoding since the quantizers process separate observations but have a common goal they seek to maximize a system wide performance measure the bhattacharyya distance of the joint index space as such a criterion is suggested and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed a simplified version of the algorithm namely an independent design separate encoding scheme where the correlation is either absent or neglected for the sake of simplicity is outlined performances are compared through worked examples

the semantics of incomplete databases as an expression of preferences abstract we address the problem of incomplete information in deductive databases from a semantic point of view we want to treat the problem in a homogeneous way using a formalism which can handle different types of incompleteness we argue that it is convenient to define an incomplete database as a double entity an underlying incomplete database together with selection criteria formally some preference relation on the set of models of the underlying database intended to reduce the incompleteness such an idea has been already exploited in the perfect model semantics of negation as failure in the stratified databases we propose another notion of preference which induces a stronger selection of models and captures an intuitive process of making choices in disjunctive databases we study both the declarative and the operational semantics for this notion of preference

error probability bounds for balanced binary relay trees we study the detection error probability associated with a balanced binary relay tree where the leaves of the tree correspond to n identical and independent sensors the root of the tree represents a fusion center that makes the overall detection decision each of the other nodes in the tree is a relay node that combines two binary messages to form a single output binary message only the leaves are sensors in this way the information from the sensors is aggregated into the fusion center via the relay nodes in this context we describe the evolution of the type i and type ii error probabilities of the binary data as it propagates from the leaves toward the root tight upper and lower bounds for the total error probability at the fusion center as functions of n are derived these characterize how fast the total error probability converges to 0 with respect to n even if the individual sensors have error probabilities that converge to 1 2

decentralized estimation with dependent gaussian observations this paper considers decentralized estimation with correlated noises under the bayesian framework for a tandem network with correlated additive gaussian noises we establish that threshold quantizers on local observations are optimal in the sense of maximizing fisher information at the fusion center this is true despite the fact that subsequent estimators may differ at the fusion center depending on the statistical distribution of the parameter to be estimated in addition it is always beneficial to have the better sensor i e the one with higher signal to noise ratio serve as the fusion center in a tandem network finally we identify different correlation regimes in terms of their impact on the estimation performance these include the well known case where negatively correlated noise benefits estimation performance as it facilitates noise cancellation as well as two distinct regimes with positively correlated noises

data fusion trees for detection does architecture matter we consider the problem of decentralized detection in a network consisting of a large number of nodes arranged as a tree of bounded height under the assumption of conditionally independent and identically distributed i i d observations we characterize the optimal error exponent under a neyman pearson formulation we show that the type ii error probability decays exponentially fast with the number of nodes and the optimal error exponent is often the same as that corresponding to a parallel configuration we provide sufficient as well as necessary conditions for this to happen for those networks satisfying the sufficient conditions we propose a simple strategy that nearly achieves the optimal error exponent and in which all non leaf nodes need only send 1 bit messages

error exponents for the detection of gauss markov signals using randomly spaced sensors we derive the neyman pearson error exponent for the detection of gauss markov signals using randomly spaced sensors we assume that the sensor spacings d 1 d 2 are drawn independently from a common density fd and we treat both stationary and nonstationary markov models error exponents are evaluated using specialized forms of the strong law of large numbers and are seen to take on algebraically simple forms involving the parameters of the markov processes and expectations over fd of certain functions of d 1 these expressions are evaluated explicitly when fd corresponds to i exponentially distributed sensors with placement density lambda ii equally spaced sensors and iii the proceeding cases when sensors fail or equivalently are asleep with probability q many insights follow for example we determine the optimal lambda as a function of q in the nonstationary case numerical simulations show that the error exponent predicts trends of the simulated error rate accurately even for small data sizes

theory of the stochastic resonance effect in signal detection part ii variable detectors in part i of this paper ldquotheory of the stochastic resonance effect in signal detection part i fixed detectors rdquo ieee transactions on signal processing vol 55 no 7 pt 1 pp 3172 3184 the mechanism of the stochastic resonance sr effect for a fixed detector has been examined this paper analyzes the stochastic resonance sr effect under the condition that the detector structure or its parameters can also be changed the detector optimization problem with sr noise under both neyman pearson and bayesian criteria is examined in the bayesian approach when the prior probabilities are unknown the minimax approach is adopted the form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined the developed theory is then applied to a general class of weak signal detection problems under the assumptions that the sample size n is large enough and the test statistics satisfies the conditions of central limit theorem the optimal sr noise is shown to be a constant vector and independent of the signal strength for both neyman pearson and bayesian criteria illustrative examples are presented where performance comparisons are made between the original detector and the optimal sr noise modified detector for different types of sr noise

robustness of decentralized tests with spl epsiv contamination prior we consider a decentralized detection problem where the prior density is not completely known but is assumed to belong to an spl epsiv contamination class the expressions for the infimum and the supremum of the posterior probability that the parameter under question is in a given region as the prior varies over the spl epsiv contamination class are derived numerical results are obtained for a specific case of an exponentially distributed observation and an exponentially distributed nominal prior asymptotic as number of sensors tends to a large value results are also obtained the results illustrate the degree of robustness achieved with quantized observations as compared to unquantized observations

an algorithm to compute circumscription abstract mccarthy s theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems in this paper we describe a query answering algorithm for circumscriptive theories the closed world assumption cwa and its generalizations the generalized closed world assumption gcwa and the extended closed world assumption ecwa can be considered as special forms of circumscription consequently our algorithm also applies to answering queries in theories using the closed world assumption and its generalizations similarly since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription

comparison results for initial value problems of second order impulsive integro differential inclusions abstract in this paper we present new maximum and minimum principles for the initial value problem for a class of second order nonlinear impulsive integro differential inclusions with discontinuous multivalued functions on the right hand side in a real banach space this allows us to lead on to the development of the comparison principle and monotone iterative technique for a nonlinear second order impulsive integro differential inclusion

massive mimo for wireless sensing with a coherent multiple access channel we consider the detection and estimation of a zero mean gaussian signal in a wireless sensor network with a coherent multiple access channel when the fusion center fc is configured with a large number of antennas and the wireless channels between the sensor nodes and fc experience rayleigh fading for the detection problem we study the neyman pearson np detector and energy detector ed and find optimal values for the sensor transmission gains for the np detector which requires channel state information csi we show that detection performance remains asymptotically constant with the number of fc antennas if the sensor transmit power decreases proportionally with the increase in the number of antennas performance bounds show that the benefit of multiple antennas at the fc disappears as the transmit power grows the results of the np detector are also generalized to the linear minimum mean squared error estimator for the ed which does not require csi we derive optimal gains that maximize the deflection coefficient of the detector and we show that a constant deflection can be asymptotically achieved if the sensor transmit power scales as the inverse square root of the number of fc antennas unlike the np detector for high sensor power the multi antenna ed is observed to empirically have significantly better performance than the single antenna implementation a number of simulation results are included to validate the analysis