generalizing capacity new definitions and capacity theorems for composite channels we consider three capacity definitions for composite channels with channel side information at the receiver a composite channel consists of a collection of different channels with a distribution characterizing the probability that each channel is in operation the shannon capacity of a channel is the highest rate asymptotically achievable with arbitrarily small error probability under this definition the transmission strategy used to achieve the capacity must achieve arbitrarily small error probability for all channels in the collection comprising the composite channel the resulting capacity is dominated by the worst channel in its collection no matter how unlikely that channel is we therefore broaden the definition of capacity to allow for some outage the capacity versus outage is the highest rate asymptotically achievable with a given probability of decoder recognized outage the expected capacity is the highest average rate asymptotically achievable with a single encoder and multiple decoders where channel side information determines the channel in use the expected capacity is a generalization of capacity versus outage since codes designed for capacity versus outage decode at one of two rates rate zero when the channel is in outage and the target rate otherwise while codes designed for expected capacity can decode at many rates expected capacity equals shannon capacity for channels governed by a stationary ergodic random process but is typically greater for general channels the capacity versus outage and expected capacity definitions relax the constraint that all transmitted information must be decoded at the receiver we derive channel coding theorems for these capacity definitions through information density and provide numerical examples to highlight their connections and differences we also discuss the implications of these alternative capacity definitions for end to end distortion source channel coding and separation

inference with transposable data modelling the effects of row and column correlations summary we consider the problem of large scale inference on the row or column variables of data in the form of a matrix many of these data matrices are transposable meaning that neither the row variables nor the column variables can be considered independent instances an example of this scenario is detecting significant genes in microarrays when the samples may be dependent because of latent variables or unknown batch effects by modelling this matrix data by using the matrix variate normal distribution we study and quantify the effects of row and column correlations on procedures for large scale inference we then propose a simple solution to the myriad of problems that are presented by unexpected correlations we simultaneously estimate row and column covariances and use these to sphere or decorrelate the noise in the underlying data before conducting inference this procedure yields data with approximately independent rows and columns so that test statistics more closely follow null distributions and multiple testing procedures correctly control the desired error rates results on simulated models and real microarray data demonstrate major advantages of this approach increased statistical power less bias in estimating the false discovery rate and reduced variance of the false discovery rate estimators

the vitali hahn saks theorem for algebras the vitali hahn saks and nikodym theorems are some of the most important and useful theorems in measure theory 8 111 7 2 111 7 4 iv 9 8 5 1 3 1 1 48 1 4 101 there have been many generalizations of these results in various directions for example the values of the measures are assumed to be in a topological vector space or topological group s 4 31 or the domains of the measures are assumed to be special types of algebras which are not necessarily a algebras lo in lo schachermayer has made a detailed study of the vitali hahn saks and nikodym boundedness theorems for scalar valued measures defined on algebras even boolean algebras in particular schachermayer has shown that the vitali hahnsaks vhs property for algebras implies the nikodym boundedness nb property for algebras 10 2 51 and moreover has given a suflicient condition property e of 10 4 21 for an algebra to satisfy the vhs property haydon 9 has considered a property called the sequential completeness property scp which is more general than schachermayer s property e has shown that the grothendieck g property is valid for algebras satisfying scp and has stated that the vhs property holds for algebras which satisfy scp 9 lb the methods of haydon are nontrivial using rosenthal s lemma and stone space methods and yield only the grothendieck property although haydon states that the vhs property for algebras satisfying scp can be obtained by using more care in the arguments in this note we show that the matrix methods employed in 1 see also 2 can be utilized to show that algebras of sets which satisfy scp also satisfy the vhs property it should be noted that these matrix methods are of a significantly simpler nature than the methods employed 116 0022 247x 85 3 00

cafiero approach to the dieudonne type theorems an algebra of subsets of a normal topological space containing the open sets is considered and in this context the uniform exhaustivity and uniform regularity for a family of additive functions are studied based on these results the cafiero convergence theorem with the dieudonne type conditions is proved and in this way also the nikod m dieudonne convergence theorem is obtained

decomposable measures and nonlinear equations abstract using integrals based on decomposable measures with respect to a pseudo addition related to a semiring a b a b a unified method is given for solving some nonlinear differential ordinary and partial difference and optimization equations for that purpose important tools as pseudo superposition principle and pseudolaplace transform are used

semiconormed possibility integrals and multi feature pattern classification abstract the semiconormed possibility integrals are proposed as a multi feature pattern classification model a semiconormed possibility integral is a nonlinear integration of a function and its corresponding non normalized possibility measures over feature space the function of an object s feature vector represents the possibilities with uncertainty that the object belongs to a class the uncertainty is due to the similar characteristics of objects from different classes and the distortion of the original characteristic information caused by feature data acquisition systems the uncertainty is assessed by the non normalized possibility measures a possibility measure of a feature is considered as the credibility of the feature to provide reliable information for pattern classification integration of a function and the possibility measures effectively reduces the uncertainty and improves the pattern classification results a pattern classification algorithm based on the semiconormed possibility integrals was used to classify a set of ellipse data and the well known iris data the classification results were compared with those obtained by using bayes classifier

channel state feedback over the mimo mac in order to exploit the full multiplexing gain of multi antenna multi user downlink schemes accurate channel state information at the transmitter i e at the base station is required we consider the design of a closed loop channel state information feedback scheme where user terminals feed back their channel state information simultaneously to a multi antenna base station the underlying information theoretic problem consists of lossy source channel coding of multiple independent analog sources i e the users channel coefficients over a gaussian multiple input multiple output multi access channel mimo mac unlike the classical source channel coding setting this application requires low latency otherwise the channel state information would be outdated hence source channel codewords can span only a single fading state of the uplink feedback channel furthermore the transmitters are ignorant of the realization of the uplink channel coefficients in this scenario the scaling of the maximum of the estimated downlink channel mean square errors with the snr dominates the performance of the multiuser downlink this scaling is described by the distortion snr exponent previously introduced in a single user mimo setting this paper analyzes the max min distortion snr exponent of the mimo mac for both separated source channel coding and a particular hybrid digital analog joint source channel coding scheme for the case of single antenna users we prove that the distortion snr exponent of separated source channel coding can be achieved by the concatenation of scalar quantization and uncoded quadrature amplitude modulation qam transmission with lattice decoding at the base station receiver the resulting scheme has very low encoding latency only a few symbols of the uplink slot and generally outperforms currently proposed channel state feedback schemes based on analog unquantized transmission or vector quantization with fixed codebooks

matrix completion and low rank svd via fast alternating least squares the matrix completion problem has attracted a lot of attention largely as a result of the celebrated net flix competition two popular approaches for solving the problem are nuclear norm regularized matrix approximation candes and tao 2009 mazumder et al 2010 and maximum margin matrix factorization srebro et al 2005 these two procedures are in some cases solving equivalent problems but with quite different algorithms in this article we bring the two approaches together leading to an efficient algorithm for large matrix factorization and completion that outperforms both of these we develop a software package softimpute in r for implementing our approaches and a distributed version for very large matrices using the spark cluster programming environment

the range of null additive fuzzy and non fuzzy measures abstract in this paper a wide class of non additive set functions is investigated for finite null additive fuzzy and non fuzzy measures saks decomposition type theorem theorem on darboux property and lyapunov s type theorems are proved

on the distortion snr exponent of some layered transmission schemes we consider the problem of joint source channel coding for transmitting k samples of a complex gaussian source overt bk uses of a block fading multiple input multiple output mimo channel with m transmit and n receive antennas we consider the case when we are allowed to code over l blocks the channel gain is assumed to be constant over a block and channel gains for different blocks are assumed to be independent the performance measure of interest is the rate of decay of the expected mean squared error with the signal to noise ratio snr called the distortion snr exponent we first show that using a broadcast strategy similar to that of gunduz and erkip but with a different power and rate allocation policy the optimal distortion snr exponent can be achieved for 0 les b les n m 1 min m n and for b mnl2 this is the first time the optimal exponent is characterized for 1 min m n b n m 1 min m n then we propose a digital layered transmission scheme that uses both time layering and superposition the new scheme is at least as good as currently known schemes for the entire range of bandwidth expansion factors b whereas at least for some m n and b it is strictly better than the currently known schemes

pseudo analysis and its applications in railway routing using as a base the pseudo analysis the problem of railway routing is treated first a deterministic approach is applied on three and four stations these problems are treated also with a stochastic approach when one variable is randomized

successive normalization of rectangular arrays standard statistical techniques often require transforming data to have mean 0 and standard deviation 1 typically this process of standardization or normalization is applied across subjects when each subject produces a single number high throughput genomic and financial data often come as rectangular arrays where each coordinate in one direction concerns subjects who might have different status case or control say and each coordinate in the other designates outcome for a specific feature for example gene polymorphic site or some aspect of financial profile it may happen when analyzing data that arrive as a rectangular array that one requires both the subjects and features to be on the same footing thus there may be a need to standardize across rows and columns of the rectangular matrix there arises the question as to how to achieve this double normalization we propose and investigate the convergence of what seems to us a natural approach to successive normalization which we learned from colleague bradley efron we also study the implementation of the method on simulated data and also on data that arose from scientific experimentation

on achievable distortion exponents for a gaussian source transmitted over parallel gaussian channels with correlated fading and asymmetric snrs this paper considers the end to end mean squared error distortion in reconstructing a memoryless proper complex gaussian source transmitted over a set of parallel block fading gaussian noise channels where the fading gains are modeled as correlated rayleigh distributed random variables with different average powers thus resulting in asymmetric average received signal noise ratios snrs the distortion exponent i e how fast the average distortion decays to zero as the average received snr increases of several coding strategies based on separate source and channel coding is characterized the definition of distortion exponent commonly used in the literature for snr symmetric channels is generalized to the case of snr asymmetric channels it is shown that fading correlation degrades the achievable mean squared error distortion but does not affect the distortion exponent in the analyzed achievable schemes the logarithm of the determinant of the fading correlation matrix is found to be a proxy for measuring the performance degradation due to correlation as compared with the case of independent fading the proposed framework allows one to study any number of correlated parallel channels contrary to the most of the literature that restricts attention to two channels only with the same received snr and with independent fading in particular a scheme based on the multiple description coding with more than two descriptions is analyzed it is shown that determining the distortion exponent in this setting reduces to solving a linear program which can be done numerically very efficiently the proposed methodology relies on combining the ideas from linear innovation sequences and properties of determinant of sub matrices interestingly it is found that snr asymmetry is beneficial for multiple description coding when the total average received snr in decibel is held constant even in the snr symmetric case asymmetry in the compression rates is shown to lead to a larger distortion exponent than symmetric rates

a note on the optimality of variant i permutation modulation codes in this correspondence the optimality of variant i permutation codes initially proposed by slepian see proc ieee vol 53 no 3 p 228 236 mar 1965 is shown in a simple way

possibility measures integration and fuzzy possibility measures abstract non negative measurable functions integrals based on possibility measures and max measures including sugeno integral and shilkret integral are introduced possibility measures of fuzzy events are studied and their integral representation is investigated a key role is played by possibility measures fulfilling the countable chain condition whose structure is investigated too

distortion minimization in gaussian layered broadcast coding with successive refinement a transmitter without channel state information wishes to send a delay limited gaussian source over a slowly fading channel the source is coded in superimposed layers with each layer successively refining the description in the previous one the receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion the expected distortion is minimized by optimally allocating the transmit power among the source layers for two source layers the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution all remaining power if any is allocated to the lower layer for convex distortion cost functions with convex constraints the minimization is formulated as a convex optimization problem in the limit of a continuum of infinite layers the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution as the number of channel uses per source symbol tends to zero the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity

finitely maxitive conditional possibilities bayesian like inference disintegrability and conglomerability the aim of the paper is to study bayesian like inference processes involving coherent finitely maxitive t conditional possibilities assessed on infinite sets of conditional events coherence of an assessment consisting of an arbitrary possibilistic prior and an arbitrary possibilistic likelihood function is proved thus a closed form expression for the envelopes of the relevant joint and posterior possibilities is given when t is the minimum or a strict t norm the notions of disintegrability and conglomerability are also studied and their relevance in the infinite version of the possibilistic bayes formula is highlighted

dieudonne s theorem for non additive set functions a cafiero type criterion and an extension of the classical dieudonne s theorem for a class of non additive set functions valued into a complete hausdorff uniform space are established

lebesgue and saks decompositions of b decomposable measures abstract the properties of decomposable measures are investigated for t conorms which are more general than archimedean t conorms the continuity of such set functions with respect to suitably chosen submeasures is proved as an important consequence a lebesgue type decomposition theorem is obtained a version of saks decomposition for order continuous decomposable measures with respect to arbitrary t conorms is proved

joint source channel codes for mimo block fading channels we consider transmission of a continuous amplitude source over an l block rayleigh fading mt x mr multiple input multiple output mimo channel when the channel state information is only available at the receiver since the channel is not ergodic shannon s source channel separation theorem becomes obsolete and the optimal performance requires a joint source channel approach our goal is to minimize the expected end to end distortion particularly in the high signal to noise ratio snr regime the figure of merit is the distortion exponent defined as the exponential decay rate of the expected distortion with increasing snr we provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths for the lower bounds we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital analog transmission in each case by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio we prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom that is l 1 and min mt mr 1 when we have more degrees of freedom our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio we demonstrate that our results which were derived for a complex gaussian source can be extended to more general source distributions as well

t evaluators and s evaluators the scalar evaluation of the aggregation of elements from a complete lattice via the operation meet join is compared with the aggregation of scalar evaluations of these elements via a t norm t conorm based on this comparison the notion of a t evaluator s evaluator is introduced and its basic properties are studied the relationship between t s evaluators fuzzy measures and generalized filters is investigated an application of t evaluators in fuzzy preference modelling is presented

diversity effects in kalman filtering over rayleigh fading channels a scalar first order gauss markov signal is sent over d parallel i i d rayleigh fading channels using uncoded transmission assuming perfect channel estimation at the receiver the optimal mmse estimator is the kalman filter with random instantaneous estimation error variance statistical characteristics of the instantaneous estimation error variance are studied to characterize the estimation quality one such characteristic is the estimation error outage which probabilistically depicts how often the value of the instantaneous estimation error variance exceeds a certain threshold in this paper we study the effect of channel diversity on the estimation error outage probability we show that for a certain range of outage thresholds the estimation error outage probability decreases with inverse of d th power of the average signal to noise ratio at the receiver side this means that analogous to the context of digital communication over fading channels our result implies a diversity order of d in estimating the input process

hybrid digital analog hda joint source channel codes for broadcasting and robust communications we consider the problem of transmitting a band limited gaussian source on an additive band limited gaussian noise channel the well known threshold effect dictates that the more powerful a code is the more sensitive it is to the exact knowledge of the channel noise a code is said to be robust if it is asymptotically optimal for a wide range of channel noise thus robust codes have a graceful degradation characteristic and are free of the threshold effect it is demonstrated that robust codes exist whenever the source and channel bandwidths are equal in the unequal bandwidth case a collection of nearly robust joint source channel codes is constructed using a hybrid digital analog hda coding technique for designing nearly robust codes a matched tandem code whose channel encoder s output is partially fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown the nearly robust codes achieve the shannon limit theoretically optimum distortion and have a less severe threshold effect finally for the case of two different noise conditions the distortion regions of these codes are determined

successive refinement of information the successive refinement of information consists of first approximating data using a few bits of information then iteratively improving the approximation as more and more information is supplied the goal is to achieve an optimal description at each stage in general an ongoing description which is rate distortion optimal whenever it is interrupted is sought it is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a markov chain in particular all finite alphabet signals with hamming distortion satisfy these requirements it is also shown that the same is true for gaussian signals with squared error distortion and for laplacian signals with absolute error distortion a simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented

conditional measures based on archimedean semigroups abstract the starting point of our measure theory are decomposable measures m for crisp events i e those characterized by the property with respect to an archimidean t conorm in the present paper we pay attention to the nsa case i e where the measures can be transformed into probabilities a generalized bayesian model will be presented based on inconditional and conditional decomposable measures section 1 conditional measures as functions of the condition can be interpreted as fuzzy sets crisp and fuzzy valued measures for such fuzzy sets will be discussed section 2 the model and the measures will be applied to sugeno s problem of buying residences section 3 the model will be generalized section 4

multiple description analog joint source channel coding to exploit the diversity in parallel channels the complexity and delay introduced by efficient digital coding strategies may be a barrier in some real time communications in this sense these last years joint source channel coding schemes based on analog mappings have gained prominence precisely for their simplicity and their implicit low delay in this work analog mappings originally designed for point to point communications are adapted to the case of parallel channels by following the multiple description strategy traditionally used in source coding in principle the coding scheme is designed to transmit over parallel awgn on off channels which are characterized by the possibility of having failures we also show that our scheme performs satisfactorily over slow rayleigh fading parallel channels

analog multiple description joint source channel coding based on lattice scaling joint source channel coding schemes based on analog mappings for point to point channels have recently gained attention for their simplicity and low delay in this paper these schemes are extended either to scenarios with or without side information at the decoders to transmit multiple descriptions of a gaussian source over independent parallel channels they are based on a lattice scaling approach together with bandwidth reduction analog mappings adapted for this multiple description scenario the rationale behind lattice scaling is to improve performance through bandwidth expansion another important contribution of this paper is the proof of the separation theorem for the communication scenario of multiple description with side information at the decoders this proof allows us to compare the performance of the proposed schemes with the theoretical limits when considering awgn channels finally when the channels are parallel slow fading rayleigh the proposed schemes are optimal in terms of distortion exponent

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

on the distributivity between t norms and t conorms the main result presented here concerns the distributivity between triangular norms and conorms understood in an extended meaning that is maps defined on an interval a b instead of the classical interval 0 1 as a secondary result the bidistributivity has been used to characterize the union and the intersection of fuzzy sets by means of algebraic conditions

possibility and necessity integrals abstract in this paper we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures these confidence measures have a field of sets as their domain and a complete lattice as their codomain in introducing these integrals the analogy with the classical introduction of lebesgue integrals is explored and exploited it is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties in this way our dual classes of fuzzy integrals constitute a significant generalization of sugeno s fuzzy integrals a large number of important general properties of these integrals is studied furthermore and most importantly the combination of seminormed fuzzy integrals and possibility measures on the one hand and semiconormed fuzzy integrals and necessity measures on the other hand is extensively studied it is shown that these combinations are very natural and have properties which are analogous to the combination of lebesgue integrals and classical measures using these results the very basis is laid for a unifying measure and integral theoretic account of possibility and necessity theory in very much the same way as the theory of lebesgue integration provides a proper framework for a unifying and formal account of probability theory

fast super paramagnetic clustering abstract we map stock market interactions to spin models to recover their hierarchical structure using a simulated annealing based super paramagnetic clustering spc algorithm this is directly compared to a modified implementation of a maximum likelihood approach we call fast super paramagnetic clustering f spc the methods are first applied to standard toy test case problems and then to a data set of 447 stocks traded on the new york stock exchange nyse over 1249 days the signal to noise ratio of stock market correlation matrices is briefly considered our result recover approximately clusters representative of standard economic sectors and mixed ones whose dynamics shine light on the adaptive nature of financial markets and raise concerns relating to the effectiveness of industry based static financial market classification in the world of real time data analytics a key result is that we show that f spc maximum likelihood solutions converge to ones found within the super paramagnetic phase where the entropy is maximum and those solutions are qualitatively better for high dimensionality data sets

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

a unified approach to define fuzzy integrals recently the two most general and well known fuzzy integrals sugeno s integral and choquet s integral were characterized it was also shown how both integrals fitted the same formal model and they only differed in the operators used in this paper we try to analyze whether it is possible to improve those characterization theorems and we also study the possibility of defining other fuzzy integrals following the same model but using other operators in a recent paper campos and bolafios 6 characterized two general and well known fuzzy integrals sugeno s integral 11 and choquet s integral 7 the last one also called monotone expectation 2 4 5 6 the two characterization theorems are based on the same formal model of four properties which only differ in the operators used sum and product for choquet s integral maximum and minimum for sugeno s integral two important questions remained open one involved the characterization theorems of these integrals in an attempt to further refine them the second question was to investigate the possibility of defining other fuzzy integrals using different operators but following the same model in this paper we give answers to those problems section 2 is devoted to describing fuzzy integrals defined on sugeno s fuzzy measures particularly sugeno s and choquet s integrals and their characterizations in section 3 we show how the characterization of choquet s integral can be refined whereas the same cannot be made for sugeno s integral finally other fuzzy integrals fitting our formal model are obtained in section 4

decomposable and k additive multi capacities and multi polar capacities extensions of several concepts for definition of capacities given by a small number of parameters in the unipolar and bipolar framework to the case of multi polar input spaces are studied the paper covers decomposable symmetric category symmetric additive reduced additive and k additive multi polar capacities and discusses its properties the multi polar mobius transform of multi polar capacities is introduced and its properties for coordinate wisely given additive and k additive multi polar capacities are described

q scale measures of fuzzy sets abstract in an attempt to generalize nahmias scale measure to apply to fuzzy sets in this paper we introduce the notion of q scale measure a q scale measure is slightly different from a crisp valued possibility measure in several ways we use a number of examples to demonstrate the validity of the notion of q scale measure in various circumstances and give preliminary discussions on basic properties of q scale measure induced q scale measure semigroup of q scale measures q scale measure of probabilistic sets and q scale measure of l fuzzy sets

the streaming dmt of fading channels we study sequential transmission of a stream of messages over a block fading multi input multi output mimo channel a new message arrives in each coherence block and the decoder is required to output each message after a delay of t coherence blocks we establish the optimal diversity multiplexing tradeoff dmt and show that it can be achieved using a simple interleaving of messages the converse is based on an outage amplification technique which appears to be new we also discuss another coding scheme based on a sequential tree code this coding scheme only requires the knowledge of delay at the decoder and yet realizes the optimal dmt we finally discuss some extensions when multiple messages at uniform intervals arrive within each coherence period

integrals based on monotone set functions an overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set called here monotone measures our survey includes not only the choquet integral 1954 10 the shilkret integral 1971 66 and the sugeno integral 1974 71 and some of their properties but also some more general and more recent concepts as universal integrals klement et al 2010 27 and decomposition integrals even 2014 13 together with some of their properties such as integral inequalities and convergence theorems

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

on source transmission over mimo channels with limited feedback the problem of source channel coding over a multiple antenna mimo channel with quantized channel state information at the transmitter csit is considered upper bounds on the distortion exponents achieved with partial csit under a long term power constraint are developed it is shown that the distortion exponent with perfect csit grows unbounded as the ratio between the channel and source bandwidth increases while the exponent achieved with any feedback link of fixed finite resolution is bounded above by a polynomial of the product between the number of transmit and number of receive antennas the resolution of the feedback link should grow with the bandwidth ratio to make the distortion exponent scale as fast as that in the perfect csit case we show that in order to achieve the optimal scaling the csit feedback resolution must grow logarithmically with the bandwidth ratio for mimo channels and faster than linear for the single input single output channel the achievable distortion exponent of some hybrid schemes with heavily quantized feedback is also derived the results demonstrate that dramatic performance improvement over the case of no csit can be achieved by combining simple schemes with a very coarse csit feedback

a heuristic simulated annealing algorithm of learning possibility measures for multisource decision making abstract in multisource decision making non normalized possibility measures are used to gauge the credibilities of each subset of information sources in order to reduce the uncertainty introduced by the sources and minimize decision error the credibility of individual information source i e the possibility density is objectively learned from subjectively chosen training data a learning algorithm of the possibility measures is constructed based on the ideas of simulated annealing and feasible direction the algorithm is designed for large training data set two multifeature image segmentation experiments and a comparison of learning speed are presented

on pseudo metric spaces induced by σ decomposable measures in this paper we study the relationship between the pseudo metric and decomposable measures with respect to a triangular conorm decomposable measures for short we first construct a pseudo metric on the measurable sets of a given decomposable measure and then discuss several properties such as completeness and continuity of the constructed pseudo metric space finally we show that the separability and nonatom of the decomposable measure can be characterized in the constructed pseudo metric space our results suggest that the standard approach for obtaining a metric from a given probability measure can be generalized to the setting of decomposable measure

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

on the distortion snr exponent of hybrid digital analog space time coding we consider the transmission of a real independent and identically distributed i i d analog source over a quasi static m input n output multiple input multiple output mimo block fading channel the relevant performance criterion is end to end average quadratic distortion d versus channel signal to noise ratio snr for given spectral efficiency eta defined as the ratio of the source bandwidth over the channel bandwidth in the limit of high snr we define the distortion snr exponent a eta as the largest a such that d esdot snr a over all possible source channel coding schemes of spectral efficiency eta we find a simple upper bound on a eta an achievable lower bound asep eta achievable by separated tandem source channel coding and a tighter lower bound ahybrid eta achievable by new hybrid digital analog space time coding schemes as a corollary we have that a eta is completely determined for the scalar case m n 1 and for the bandwidth compression case eta ges 2 min m n expiicit and simple construction of hybrid space time codes achieving ahybrid eta are also given

delay limited source and channel coding of quasi stationary sources over block fading channels design and scaling laws in this paper delay limited transmission of quasi stationary sources over block fading channels is considered considering distortion outage probability as the performance measure two source and channel coding schemes with power adaptive transmission are presented the first one is optimized for fixed rate transmission and hence enjoys simplicity of implementation the second one is a high performance scheme which also benefits from optimized rate adaptation with respect to source and channel states in high snr regime the performance scaling laws in terms of outage distortion exponent and asymptotic outage distortion gain are derived where two schemes with fixed transmission power and adaptive or optimized fixed rates are considered as benchmarks for comparisons various analytical and numerical results are provided which demonstrate a superior performance for source and channel optimized rate and power adaptive scheme it is also observed that from a distortion outage perspective the fixed rate adaptive power scheme substantially outperforms an adaptive rate fixed power scheme for delay limited transmission of quasi stationary sources over wireless block fading channels the effect of the characteristics of the quasi stationary source on performance and the implication of the results for transmission of stationary sources are also investigated

different interpretations of triangular norms and related operations triangular norms and triangular conorms and uni norms can be treated as semigroup two place function also as commutative semiring multiplications it can also be derived from the difference operation in a difference poset we discuss here these different interpretations and their consequences

a broadcast approach for a single user slowly fading mimo channel a broadcast transmission strategy for the slowly fading gaussian multiple input multiple output mimo channel is introduced this broadcast strategy is an extension of the single input single output siso broadcast approach perfect channel state information csi is assumed known at the receiver end only this strategy facilitates to adapt the reliably decoded rate to the actual channel state without having any feedback link to the transmitter transmission of layered coded information is motivated by the theory of majorization we derive the basic equations characterizing achievable rates of the strategy several ad hoc approximations to the achievable region are considered and their performance is compared with the siso setting and the ergodic capacity it has been demonstrated that a single layer outage approach is reasonably efficient in the mimo setting in terms of the average reliably decoded rate a multiple access channel mac broadcast approach is also applied for the mimo case and demonstrated to be relatively efficient

dominance in the family of sugeno weber t norms the dominance relationship between two members of the family of sugeno weber t norms is proven by using a quantifier elimination algorithm further it is shown that dominance is a transitive and therefore also an order relation on this family of t norms

on the convex combination of td and continuous triangular norms the problem of when t l 1 l t d lt l 0 1 is a triangular norm where t d is the drastic product and t is a continuous triangular norm is studied it is shown that t l cannot be a triangular norm when t is nilpotent it is also shown that t l is a triangular norm if t is strict and its additive generator f satisfies f lx f x f l for all x 0 1 the cases that t t m and t is the ordinal sum of continuous archimedean summands are also discussed some left continuous t norms which can be combined with each other are given