tensor products for non unital operator systems abstract in this short article we study tensor products of not necessarily unital operator systems for short nuos we will define canonical functorial nuos tensor products in a similar fashion to kavruk et al 2011 4 as well as a subclass of them consisting of reduced functorial nuos tensor products that are defined through a unitalization process we show that if a nuos x is min max nuclear in the sense that there is only one nuos tensor product of x with any nuos y then x is trivial however if v is a unital operator system then v is min 0 max 0 nuclear in the sense that there is only one reduced nuos tensor product of v with any nuos y if and only if v is min max nuclear in the sense of han and paulsen 2011 2 i e there is only one unital operator system tensor product of v with any unital operator system w on the other hand a c algebra a is min 0 max 0 nuclear if and only if a is a nuclear c algebra

matrix regular operator space and operator system abstract we establish a relationship between schreiner s matrix regular operator space and werner s nonunital operator system for a matrix ordered operator space v with complete norm we show that v is completely isomorphic and complete order isomorphic to a matrix regular operator space if and only if both v and its dual space v are nonunital operator systems

matrix regular operator spaces the concept of the regular or riesz norm on ordered real banach spaces is generalized to matrix ordered complex operator spaces in a way that respects the matricial structure of the operator space a norm on an ordered real banach spaceeis regular if 1 x y ximplies that y x and 2 y 1 implies the existence ofx esuch that x 1 and x y x a matrix ordered operator space is called matrix regular if at each matrix level the restriction of the norm to the self adjoint elements is a regular norm in such a space elements at each matrix level can be written as linear combinations of four positive elements the concept of the matrix ordered operator space is made specific in such a way as to be a natural generalization of ordered real and complex banach spaces for the case wherevis a matrix ordered operator space a natural cone is defined on the operator spacex hv hx with hindicating the haagerup tensor product so as to make it a matrix ordered operator space exploiting the advantages gained by takingxto be the column hilbert spacehc an equivalence is established between the matrix regularity of a space and that of its operator dual this concept of matrix regularity also provides for more accessible proofs of the christensen sinclair multilinear representation and multilinear decomposition theorems

random field reconstruction with quantization in wireless sensor networks we develop new and novel algorithms for spatial field reconstruction and spatial exceedance level estimation we consider spatial physical phenomena which are partially observed by a wireless sensor network we focus on the practical scenario in which due to bandwidth and power constraints the observations at the sensors are quantized and transmitted over imperfect wireless channels we first develop the spatial best linear unbiased estimator s blue algorithm for the spatial field reconstruction estimation we then develop an algorithm that is based on a multivariate series expansion approach resulting in a saddle point type approximation to solve both problems of spatial field reconstruction and exceedance level estimation we derive the posterior cramer rao lower bound pcrlb and quantify the achievable mse in the estimation the estimation accuracy of the proposed algorithms is quantified via numerical comparisons between the two algorithms and the pcrlb

characterizations of ordered operator spaces abstract we demonstrate new abstract characterizations for unital and non unital operator spaces we characterize unital operator spaces in terms of the cone of accretive operators operators whose real part is positive we show that matrix norms and accretive cones are induced by gauges although inducing gauges are not unique in general finally we show that completely positive completely contractive linear maps on non unital operator spaces extend to any containing operator system if and only if the operator space is induced by a unique gauge

optimal identical binary quantizer design for distributed estimation we consider the design of identical one bit probabilistic quantizers for distributed estimation in sensor networks we assume the parameter range to be finite and known and use the maximum cramer rao lower bound crb over the parameter range as our performance metric we restrict our theoretical analysis to the class of antisymmetric quantizers and determine a set of conditions for which the probabilistic quantizer function is greatly simplified we identify a broad class of noise distributions which includes gaussian noise in the low snr regime for which the often used threshold quantizer is found to be minimax optimal aided with theoretical results we formulate an optimization problem to obtain the optimum minimax crb quantizer for a wide range of noise distributions we demonstrate the superior performance of the new quantizer particularly in the moderate to high snr regime

every completely polynomially bounded operator is similar to a contraction it is proved that a bounded operator on a hilbert space is similar to a contraction if and only if it is completely polynomially bounded this gives a partial answer to problem 6 of halmos bull amer math soc 76 1970 877 933 the set of completely bounded maps between c algebras is studied to obtain some structure representation and extension theorems for this class of maps these allow a characterization of the completely bounded representations on a hilbert space of any subalgebra of a c algebra to be obtained the result in the title follows by applying this characterization to the disk algebra

minimax estimation of deterministic parameters in linear models with a random model matrix we consider the problem of estimating an unknown deterministic parameter vector in a linear model with a random model matrix with known second order statistics we first seek the linear estimator that minimizes the worst case mean squared error mse across all parameter vectors whose possibly weighted norm is bounded above we show that the minimax mse estimator can be found by solving a semidefinite programming problem and develop necessary and sufficient optimality conditions on the minimax mse estimator using these conditions we derive closed form expressions for the minimax mse estimator in some special cases we then demonstrate through examples that the minimax mse estimator can improve the performance over both a baysian approach and a least squares method we then consider the case in which the norm of the parameter vector is also bounded below since the minimax mse approach cannot account for a nonzero lower bound we consider in this case a minimax regret method in which we seek the estimator that minimizes the worst case difference between the mse attainable using a linear estimator that does not know the parameter vector and the optimal mse attained using a linear estimator that knows the parameter vector for analytical tractability we restrict our attention to the scalar case and develop a closed form expression for the minimax regret estimator

bayesian closed skew gaussian inversion of seismic avo data for elastic material properties bayesian closed skew gaussian inversion is defined as a generalization of traditional bayesian gaussian inversion which is used frequently in seismic amplitude versus offset avo inversion the new model captures skewness in the variables of interest hence the posterior model for log transformed elastic material properties given seismic avo data might be a skew probability density function the model is analytically tractable and this makes it applicable in high dimensional 3d inversion problems assessment of the posterior models in high dimensions requires numerical approximations however the bayesian closed skew gaussian inversion approach has been applied on real elastic material properties from a well in the sleipner field in the north sea a comparison with results from traditional bayesian gaussian inversion shows that the mean square error of predictions of p wave and s wave velocities are reduced by a factor of two although somewhat less for density predictions

spectral truncations in noncommutative geometry and operator systems in this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces i e imposing an ultraviolet cutoff in momentum space and with tolerance relations which provide a coarse grain approximation of geometric spaces at a finite resolution in our new approach the traditional role played by c algebras is taken over by operator systems as part of the techniques we treat c envelopes dual operator systems and stable equivalence we define a propagation number for operator systems which we show to be an invariant under stable equivalence and use to compare approximations of the same space we illustrate our methods for concrete examples obtained by spectral truncations of the circle these are operator systems of finite dimensional toeplitz matrices and their dual operator systems which are given by functions in the group algebra on the integers with support in a fixed interval it turns out that the cones of positive elements and the pure state spaces for these operator systems possess a very rich structure which we analyze including for the algebraic geometry of the boundary of the positive cone and the metric aspect i e the distance on the state space associated to the dirac operator the main property of the spectral truncation is that it keeps the isometry group intact in contrast if one considers the other finite approximation provided by circulant matrices the isometry group becomes discrete even though in this case the operator system is a c algebra we analyze this in the context of the finite fourier transform on the cyclic group the extension of noncommutative geometry to operator systems allows one to deal with metric spaces up to finite resolution by considering the relation d x y varepsilon between two points or more generally a tolerance relation which naturally gives rise to an operator system

multipliers on matrix ordered operator spaces and some k groups abstract matrix ordered operator spaces are non commutative banach spaces equipped with a non commutative order examples include c algebras as well as their duals in this article we define and intrinsically characterize the multiplier algebra for this class of spaces and briefly tackle the problem of extending k theory to this context

on maximal tensor products and quotient maps of operator systems abstract we introduce quotient maps in the category of operator systems and show that the maximal tensor product is projective with respect to them whereas the maximal tensor product is not injective which makes the el max nuclearity distinguish a class in the category of operator systems we generalize lance s characterization of c algebras with the wep by showing that el max nuclearity is equivalent to the weak expectation property applying werner s unitization to the dual spaces of operator systems we consider a class of completely positive maps associated with the maximal tensor product and establish the duality between quotient maps and complete order embeddings

bayesian linearized rock physics inversion abstractthe estimation of rock and fluid properties from seismic attributes is an inverse problem rock physics modeling provides physical relations to link elastic and petrophysical variables most of these models are nonlinear therefore the inversion generally requires complex iterative optimization algorithms to estimate the reservoir model of petrophysical properties we have developed a new approach based on the linearization of the rock physics forward model using first order taylor series approximations the mathematical method adopted for the inversion is the bayesian approach previously applied successfully to amplitude variation with offset linearized inversion we developed the analytical formulation of the linearized rock physics relations for three different models empirical granular media and inclusion models and we derived the formulation of the bayesian rock physics inversion under gaussian assumptions for the prior distribution of the model the application of the inversion to real

on distributed linear estimation with observation model uncertainties we consider distributed estimation of a gaussian source in a heterogenous bandwidth constrained sensor network where the source is corrupted by independent multiplicative and additive observation noises we assume the additive observation noise is zero mean gaussian with known variance however the system designer is unaware of the distribution of multiplicative observation noise and only knows its first and second order moments for multibit quantizers we derive an accurate closed form approximation for the mean square error mse of the linear minimum mse estimator at the fusion center for both error free and erroneous communication channels we propose several rate allocation methods named as longest root to leaf path greedy integer relaxation and individual rate allocation to minimize the mse given a network bandwidth constraint and minimize the required network bandwidth given a target mse we also derive the bayesian cramer rao lower bound crlb for an arbitrarily distributed multiplicative observation noise and compare the mse performance of our proposed methods against the crlb our results corroborate that for the low power multiplicative observation noise and adequate network bandwidth the gaps between the mse of greedy and integer relaxation methods and the crlb are negligible while the mse of individual rate allocation and uniform methods is not satisfactory through analysis and simulations we also explore why maximum likelihood and maximum a posteriori estimators based on one bit quantization perform poorly for the low power additive observation noise

linear regression with gaussian model uncertainty algorithms and bounds in this paper we consider the problem of estimating an unknown deterministic parameter vector in a linear regression model with random gaussian uncertainty in the mixing matrix we prove that the maximum likelihood ml estimator is a de regularized least squares estimator and develop three alternative approaches for finding the regularization parameter that maximizes the likelihood we analyze the performance using the cramer rao bound crb on the mean squared error and show that the degradation in performance due the uncertainty is not as severe as may be expected next we address the problem again assuming that the variances of the noise and the elements in the model matrix are unknown and derive the associated crb and ml estimator we compare our methods to known results on linear regression in the error in variables eiv model we discuss the similarity between these two competing approaches and provide a thorough comparison that sheds light on their theoretical and practical differences

parameter estimation from quantized observations in multiplicative noise environments the problem of distributed parameter estimation from binary quantized observations is studied when the unquantized observations are corrupted by combined multiplicative and additive gaussian noise these results are applicable to sensor networks where the sensors observe a parameter in combined additive and nonadditive noise and to a case where dispersed receivers are employed with analog communication over fading channels where the receivers employ binary quantization before noise free digital communications to a fusion center we first discuss the case in which all the quantizers use an identical threshold the parameter identifiability condition is given and surprisingly it is shown that unless the common threshold is chosen properly and the parameter lies in an open interval the parameter will not generally be identifiable in contrast to the additive noise case the best achievable mean square error mse performance is characterized by deriving the corresponding cramer rao lower bound crlb a closed form expression describing the corresponding maximum likelihood ml estimator is presented the stability of the performance of the ml estimators is improved when a nonidentical threshold strategy is utilized to estimate the unknown parameter the thresholds are designed by maximizing the minimum asymptotic relative efficiency are between quantized and unquantized ml estimators although the ml estimation problem is nonconvex it is shown that one can relax the optimization to make it convex the solution to the relaxed problem is used as an initial solution in a gradient algorithm to solve the original problem next the case where both the variances of the additive noise and multiplicative noise are unknown is studied the corresponding crlb is obtained and the ml estimation problem is transformed to a convex optimization which can be solved efficiently finally numerical simulations are performed to substantiate the theoretical analysis

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

bandwidth constrained distributed estimation for wireless sensor networks part i gaussian case we study deterministic mean location parameter estimation when only quantized versions of the original observations are available due to bandwidth constraints when the dynamic range of the parameter is small or comparable with the noise variance we introduce a class of maximum likelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the clairvoyant sample mean estimator when the dynamic range is comparable or larger than the noise standard deviation we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint we will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons we finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave

distributed adaptive quantization for wireless sensor networks from delta modulation to maximum likelihood we consider distributed parameter estimation using quantized observations in wireless sensor networks wsns where due to bandwidth constraint each sensor quantizes its local observation into one bit of information a conventional fixed quantization fq approach which employs a fixed threshold for all sensors incurs an estimation error growing exponentially with the difference between the threshold and the unknown parameter to be estimated to address this difficulty we propose a distributed adaptive quantization aq approach which with sensors sequentially broadcasting their quantized data allows each sensor to adaptively adjust its quantization threshold three aq schemes are presented 1 aq fs that involves distributed delta modulation dm with a fixed stepsize 2 aq vs that employs dm with a variable stepsize and 3 aq ml that adjusts the threshold through a maximum likelihood ml estimation process the ml estimators associated with the three aq schemes are developed and their corresponding cramer rao bounds crbs are analyzed we show that our 1 bit aq approach is asymptotically optimum yielding an asymptotic crb that is only pi 2 times that of the clairvoyant sample mean estimator using unquantized observations

multitrace impedance inversion with lateral constraints abstractwe have developed a lateral constraint to the inversion of 1d seismic impedance models to suppress the effect of data noise and improve the fidelity of formation boundaries in 2d models for situations with dips of less than 20 typical inversion frameworks rely on a 1d forward model with each 1d trace being inverted independently adjacent inversion models are combined together to form a 2d impedance model adding a lateral constraint improves the fidelity of the 2d impedance models while retaining much of the advantage of the low computational cost associated with typical 1d inversion schemes solving the 1d lateral constraint inversion 1d lci problem involves the simultaneous inversion of multiple 1d traces producing layered sections with lateral smoothed transition in addition to enforcing lateral continuity in the inversion model this algorithm allows for the inclusion of a priori knowledge from boreholes we determined the effectiveness of this algorithm on two synthetic models as well

applications of model theory to c dynamics we initiate the study of compact group actions on c algebras from the perspective of model theory and present several applications to c dynamics firstly we prove that the continuous part of the central sequence algebra of a strongly self absorbing action is indistinguishable from the continuous part of the sequence algebra and in fact equivariantly isomorphic under the continuum hypothesis as another application we present a unified approach to several dimensional inequalities in c algebras which is done through the notion of order zero dimension for an equivariant homomorphism finiteness of the order zero dimension implies that the dimension of the target algebra can be bounded by the dimension of the domain the dimension can be among others decomposition rank nuclear dimension or rokhlin dimension as a consequence we obtain new inequalities for these quantities as a third application we obtain the following result if a c algebra a absorbs a strongly self absorbing c algebra d and is an action of a compact group g on a with finite rokhlin dimension with commuting towers then absorbs any strongly self absorbing action of g on d this has a number of interesting consequences already in the case of the trivial action on d for example we deduce that d stability passes from a to the crossed product additionally in many cases of interest our result restricts the possible values of the rokhlin dimension to and showing a striking parallel to the behavior of the nuclear dimension for simple c algebras we also show that an action of a finite group with finite rokhlin dimension with commuting towers automatically has the rokhlin property if the algebra is uhf absorbing

matrix convexity operator analogues of the bipolar and hahn banach theorems abstract several basic results of convexity theory are generalized to the quantized matrix convex sets of wittstock these include the bipolar theorem a gauge version of the hahn banach theorem and the existence theorem for support functionals

fast sampling of gaussian markov random fields this paper demonstrates how gaussian markov random fields conditional autoregressions can be sampled quickly by using numerical techniques for sparse matrices the algorithm is general and efficient and expands easily to various forms for conditional simulation and evaluation of normalization constants we demonstrate its use by constructing efficient block updates in markov chain monte carlo algorithms for disease mapping

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

ordered c ast modules in this first part of a study of ordered operator spaces we develop the basic theory of ordered c bimodules a crucial role is played by open tripotents a jb triple variant of akemann s notion of open projection

quantizer precision for distributed estimation in a large sensor network we investigate the design of simple noncooperative quantizers for distributed estimation of a common random variable it is assumed that there is a budget of aggregate rate a criterion of fisher information and a large population of sensors it is further assumed that sensor quantizers are uniform and that rate is determined by the entropy of the outputs of these the key question asked is whether it is better to quantize a relatively few sensors finely or as many as possible coarsely

rate distortion theory for gaussian multiterminal source coding systems with several side informations at the decoder in this paper we consider the separate coding problem for l 1 correlated gaussian memoryless sources we deal with the case where l sources work as partial side information at the decoder for the reconstruction of the remaining source the determination problem of the rate distortion region for this system is the so called many help one problem and it has been known as a highly challenging problem for almost 20 years in this paper we give a partial solution to this problem we determine the rate distortion region in the case where the l sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given the additive white gaussian noise ceo problem is a special case of this we also discuss the relation of the result previous results of ours

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

bayesian linearized avo inversion a new linearized avo inversion technique is developed in a bayesian framework the objective is to obtain posterior distributions for p wave velocity s wave velocity and density distributions for other elastic parameters can also be assessed for example acoustic impedance shear impedance and p wave to s wave velocity ratio the inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the zoeppritz equation the solution is represented by a gaussian posterior distribution with explicit expressions for the posterior expectation and covariance hence exact prediction intervals for the inverted parameters can be computed under the specified model the explicit analytical form of the posterior distribution provides a computationally fast inversion method tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero with realistic noise levels acoustic impedance was the best determined parameter

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

uncertainty in inverted elastic properties resulting from uncertainty in the low frequency model a bayesian linearized inversion bli framework is used to analyze how uncertainty in the low frequency model lfm affects the solution in prestack seismic inversion two related effects are considered sensitivity addresses how a change in the lfm changes the inversion solution whereas uncertainty addresses how uncertainty in the lfm is propagated into the inversion results the posterior covariance matrix in the bli equations does not depend on the lfm and it can be concluded mistakenly that uncertainty in the inversion result is independent of uncertainty in the lfm instead a broader characterization of uncertainty can be made by using a hierarchical bli framework that includes uncertainties in the lfm the standard bli equations are adequate to describe uncertainty in relative rock property inversion which can be obtained by subtracting the logarithm of the lfm from the logarithm of the inversion solution uncertainty in relative rock property inversion is independent of both the particular lfm used in the solution and the uncertainty associated with the lfm on the other hand uncertainty in absolute rock property inversion is independent of the particular lfm used but does depend on the uncertainty of that lfm the uncertainty of absolute rock property inversion is always greater than the uncertainty of the associated relative rock property inversion

rapid spatially coupled avo inversion in the fourier domain spatial coupling of the model parameters in an inversion problem provides lateral consistency and robust solutions we have defined the inversion problem in a bayesian framework where the solution is represented by a posterior distribution obtained from a prior distribution and a likelihood model for the recorded data the spatial coupling of the model parameters is imposed via the prior distribution by a spatial correlation function in the fourier domain the spatially correlated model parameters can be decoupled and the inversion problem can be solved independently for each frequency component for a spatial model parameter represented on n grid nodes the computing time for the inversion in the fourier domain follows a linear function of the number of grid nodes while the computing time for the fast fourier transform follows an n log n function we have developed a 3d linearized amplitude variation with offset avo inversion method with spatially coupled model parameters where the objective is to

on quantizer design for distributed bayesian estimation in sensor networks we consider the problem of distributed estimation under the bayesian criterion and explore the design of optimal quantizers in such a system we show that for a conditionally unbiased and efficient estimator at the fusion center and when local observations have identical distributions it is optimal to partition the local sensors into groups with all sensors within a group using the same quantization rule when all the sensors use identical number of decision regions use of identical quantizers at the sensors is optimal when the network is constrained by the capacity of the wireless multiple access channel over which the sensors transmit their quantized observations we show that binary quantizers at the local sensors are optimal under certain conditions based on these observations we address the location parameter estimation problem and present our optimal quantizer design approach we also derive the performance limit for distributed location parameter estimation under the bayesian criterion and find the conditions when the widely used threshold quantizer achieves this limit we corroborate this result using simulations we then relax the assumption of conditionally independent observations and derive the optimality conditions of quantizers for conditionally dependent observations using counter examples we also show that the previous results do not hold in this setting of dependent observations and therefore identical quantizers are not optimal index terms

joint bayesian wavelet and well path estimation in the impedance domain abstractwe addressed the problem of the well to seismic tie as a bayesian inversion for the wavelet and well path in the impedance domain the result of the joint inversion is a set of wavelets for multiple angle stacks and a corresponding well path the wavelet optimally links the impedance data along the well to the seismic data along the optimized well path in the seismic time domain starting with prior distribution for wavelet and well path the method calculates the posterior distribution of conditioning the prior distributions with the seismic and well log data this is done by iteratively inverting the seismic data with the current wavelet to obtain an impedance cube around the well in a second step the seismic impedances are projected onto the well path by minimizing the misfit between the inverted seismic impedances and the impedances derived from the well log the wavelet and well path are optimized comparing the well and seismic data in the impedance domain enables the method to work on

operator algebras with contractive approximate identities ii abstract we make several contributions to our recent program investigating structural properties of algebras of operators on a hilbert space for example we make substantial contributions to the noncommutative peak interpolation program begun by hay and the first author hay and neal another sample result an operator algebra has a contractive approximate identity iff the linear span of the elements with positive real part is dense we also extend the theory of compact projections to the most general case despite the title our algebras are often allowed to have no approximate identity

robust mean squared error estimation in the presence of model uncertainties we consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties where the vector x is known to satisfy a weighted norm constraint we first assume that the model is known exactly and seek the linear estimator that minimizes the worst case mean squared error mse across all possible values of x we show that for an arbitrary choice of weighting the optimal minimax mse estimator can be formulated as a solution to a semidefinite programming problem sdp which can be solved very efficiently we then develop a closed form expression for the minimax mse estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of mayer and willke with a specific choice of shrinkage factor that explicitly takes the prior information into account next we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst case mse across all possible values of x and all possible values of the model matrix as we show the robust minimax mse estimator can also be formulated as a solution to an sdp finally we demonstrate through several examples that the minimax mse estimator can significantly increase the performance over the conventional least squares estimator and when the model matrix is subject to uncertainties the robust minimax mse estimator can lead to a considerable improvement in performance over the minimax mse estimator

multilinear maps and tensor norms on operator systems abstract we extend work of christensen and sinclair on completely bounded multilinear forms to the case of subspaces of c algebras and obtain a representation theorem and a hahn banach extension theorem for such maps in the second part of the paper the haagerup norms on tensor products are investigated and we obtain new characterizations of these quantities

subspaces of l h that are invariant abstract a result of choi and effros says how invariant spaces of bounded operators on hilbert space that contain the identity can be abstractly characterized in terms of their order structure the aim here is to dispose of the identity and to prove a similar theorem for spaces of bounded operators that are merely invariant absence of a unit will also permit to deal with duals in a satisfactory way

subspaces of c algebras abstract basic properties of matricially normed spaces are considered and a simple matrix norm characterization of the subspaces of c algebras is given the latter result is used to study the haagerup tensor products and quotients of such subspaces