generalized blocks for symmetric groups we study via character theoretic methods an l analogue of the modular representation theory of the symmetric group for an arbitrary integer l 2 we find that many of the invariants of the usual block theory ie when l is prime generalize in a natural fashion to this new context

discrete aggregation operators with annihilator abstract mas et al have investigated a special kind of commutative and associative aggregation operators with annihilator on the unit interval 0 1 which includes s uninorms s nullnorms t uninorms t nullnorms bi uninorms and bi nullnorms this paper is devoted to extending this kind of operators from the unit interval 0 1 to a finite chain a characterization of this kind of operators on a finite chain is given including some examples this class of operators can be viewed as a generalization of both uninorms and nullnorms on a finite chain

a disaggregate negative binomial regression procedure for count data analysis various research areas face the methodological problems presented by nonnegative integer count data drawn from heterogeneous populations we present a disaggregate negative binomial regression procedure for analysis of count data observed for a heterogeneous sample of cross sections possibly over some fixed time periods this procedure simultaneously pools or groups cross sections while estimating a separate negative binomial regression model for each group an e m algorithm is described within a maximum likelihood framework to estimate the group proportions the group specific regression coefficients and the degree of overdispersion in event rates within each derived group the proposed procedure is illustrated with count data entailing nonnegative integer counts of purchases events for a frequently bought consumer good

on convergence and parameter selection of the em and da em algorithms for gaussian mixtures abstract the expectation maximization em for gaussian mixtures is popular as a clustering algorithm however the em algorithm is sensitive to initial values and so ueda and nakano 4 proposed the deterministic annealing em da em algorithm to improve it in this paper we investigate theoretical behaviors of the em and da em algorithms we first derive a general jacobian matrix of the da em algorithm with respect to posterior probabilities we then propose a theoretical lower bound for initialization of the annealing parameter in the da em algorithm on the other hand some researches mentioned that the em algorithm exhibits a self annealing behavior that is the equal posterior probability with small random perturbations can avoid the em algorithm to output the mass center for gaussian mixtures however there is no theoretical analysis on this self annealing property since the da em will become the em when the annealing parameter is 1 according to the jacobian matrix of the da em we can prove the self annealing property of the em algorithm for gaussian mixtures based on these results we give not only convergence behaviors of the equal posterior probabilities and initialization lower bound of the temperature parameter of the da em but also a theoretical explanation why the em algorithm for gaussian mixtures exhibits a self annealing behavior

conjugate mixture models for clustering multimodal data the problem of multimodal clustering arises whenever the data are gathered with several physically different sensors observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space a solution may consist in considering multiple clustering tasks independently for each modality the main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent in this letter we show that multimodal clustering can be addressed within a novel framework conjugate mixture models these models exploit the explicit transformations that are often available between an unobserved parameter space objects and each of the observation spaces sensors we formulate the problem as a likelihood maximization task and derive the associated conjugate expectation maximization algorithm the convergence properties of the proposed algorithm are thoroughly investigated several local and global optimization techniques are proposed in order to increase its convergence speed two initialization strategies are proposed and compared a consistent model selection criterion is proposed the algorithm and its variants are tested and evaluated within the task of 3d localization of several speakers using both auditory and visual data

a unified framework and sparse bayesian perspective for direction of arrival estimation in the presence of array imperfections self calibration methods play an important role in reducing the negative effects of array imperfections during direction of arrival doa estimation however the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios such as low signal to noise ratio snr and limited snapshots this paper aims at formulating a unified framework and sparse bayesian perspective for array calibration and doa estimation a comprehensive model of the array output is presented first when a single type of array imperfection is considered with mutual coupling gain phase uncertainty and sensor location error treated as typical examples the spatial sparsity of the incident signals is then exploited and a bayesian method is proposed to realize array calibration and source doa estimation the array perturbation magnitudes are assumed to be small according to most application scenarios and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear cramer rao lower bounds crlbs for the array calibration and doa estimation precisions are also obtained the sparse bayesian method is finally extended to deal with the doa estimation problem when more than one type of array perturbation coexists

array shape calibration using sources in unknown locations a maximum likelihood approach sensor location uncertainty can severely degrade the performance of direction finding systems an iterative maximum likelihood method for simultaneously estimating directions of arrival doa and sensor locations is developed to alleviate this problem the case of nondisjoint sources i e sources observed in the same frequency cell and at the same time is emphasized the algorithm converges to the global maximum of the likelihood function if the initial conditions are sufficiently good numerical examples are presented illustrating the performance of the proposed technique a distinctive feature of the algorithm is its ability to locate the sensors accurately without deploying calibration sources at known locations

theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array in array signal processing high resolution direction of arrival doa estimation algorithms are known to be sensitive to system errors in practice the system should be properly calibrated before doa estimation in this paper a calibration method of gain and phase errors of linear equispaced arrays leas is considered a class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed the statistical performance analyses of the calibration algorithms due to finite data perturbations are presented expressions for average bias abias and square root of average variance srav of the calibration algorithms are derived using first order approximation these statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations the more inferior performance that may be obtained based on this conclusion the simple and optimal gain and phase error calibration algorithms for such model are obtained

elementary divisors of the shapovalov form on the basic representation of kac moody algebras we calculate the invariant factors of the standard lattice vz inside the basic representation of untwisted kac moody algebras of ade type this in turn gives the invariant factors of cartan matrices for symmetric groups in prime characteristic as well as for the iwahori hecke algebra at roots of unity

bearing estimation without calibration for randomly perturbed arrays the bearing estimation problem of linearly periodic arrays with the presence of sensor position errors is discussed conventional approaches for solving this problem generally consist of two steps calibrating sensor locations and then performing bearing estimation based on the calibrated sensor locations approaches to carrying out bearing estimation based on the toeplitz and eigenstructure reconstruction of the covariance matrix without the need for calibration are proposed the toeplitz approximation method tam and a modification of it mtam are used to reconstruct a matrix with toeplitz structure to further enhance the capabilities of the tam and mtam an iterative algorithm incorporating with the tam itam and the mtam imtam is proposed to iteratively reconstruct both the toeplitz and the desired eigenstructure from the observed covariance matrix computer simulations show that the mtam is more effective than the tam moreover the iterative methods are superior to the noniterative ones at the price of computations

characterization of idempotent n uninorms abstract the structure of idempotent n uninorms is studied we show that each idempotent 2 uninorm can be expressed as an ordinal sum of an idempotent uninorm possibly also of a countable number of idempotent semigroups with operations min and max and a 2 uninorm from class 1 possibly restricted to open or half open unit square similar results are shown also for idempotent n uninorms further it is shown that idempotent n uninorms are in one to one correspondence with special lower semi lattices defined on the unit interval the z ordinal sum construction for partially ordered semigroups is also defined

sparse power angle spectrum estimation a novel method for estimating the power angle spectrum pas is presented that decomposes the true pas into a small set of basis functions the basis coefficients for this sparse representation are found by enforcing equality to the covariance or bartlett pas subject to a minimum lscr1 norm constraint the method referred to as sparse pas estimation spase can be implemented conveniently using existing linear programming lp solvers further because only a few clusters are required in the representation the method enables reduced complexity stochastic models for the channel and possibly allows reduced overhead in channel feedback schemes application of the method to simulated channels and multiple input multiple output mimo propagation data demonstrates the utility of the method

statistical resolution limits and the complexified crame spl acute r rao bound array resolution limits and accuracy bounds on the multitude of signal parameters e g azimuth elevation doppler range cross range depth frequency chirp polarization amplitude phase etc estimated by array processing algorithms are essential tools in the evaluation of system performance the case in which the complex amplitudes of the signals are unknown is of particular practical interest a computationally efficient formulation of these bounds from the perspective of derivations and analysis is presented for the case of deterministic and unknown signal amplitudes a new derivation is given using the unknown complex signal parameters and their complex conjugates the new formula is readily applicable to obtaining either symbolic or numerical solutions to estimation bounds for a very wide class of problems encountered in adaptive sensor array processing this formula is shown to yield several of the standard crame spl acute r rao results for array processing along with new results of fundamental interest specifically a new closed form expression for the statistical resolution limit of an aperture for any asymptotically unbiased superresolution algorithm e g music esprit is provided the statistical resolution limit is defined as the source separation that equals its own crame spl acute r rao bound providing an algorithm independent bound on the resolution of any high resolution method it is shown that the statistical resolution limit of an array or coherent integration window is about 1 2 spl middot snr sup 1 4 relative to the fourier resolution limit of 2 spl pi n radians large number n of array elements that is the highest achievable resolution is proportional to the reciprocal of the fourth root of the signal to noise ratio snr in contrast to the square root snr sup 1 2 dependence of standard accuracy bounds these theoretical results are consistent with previously published bounds for specific superresolution algorithms derived by other methods it is also shown that the potential resolution improvement obtained by separating two collinear arrays synthetic ultra wideband each with a fixed aperture b wavelengths by m wavelengths assumed large is approximately m b sup 1 2 in contrast to the resolution improvement of m b for a full aperture exact closed form results for these problems with their asymptotic approximations are presented

on the structure of 2 uninorms abstract in this paper we describe the structure of 2 uninorms defined on the unit interval we divide the class of 2 uninorms into five mutually exclusive subclasses based on their boundary behaviour as determined by the absorbing element and the conjunctive disjunctive nature of the underlying uninorms which every 2 uninorm is known to have for each of these subclasses we fully characterize the structure of its members albeit for two subclasses only under an additional continuity assumption a common practice in the study of associative operations

a novel online mutual coupling compensation algorithm for uniform and linear arrays in this paper a novel online mutual coupling compensation algorithm especially tailored to uniform and linear arrays is presented it is conceived to simultaneously compensate for mutual coupling and estimate the direction of arrivals doas of signals impinging on the array since the estimated calibration matrix can be embedded within any classical super resolution direction finding method an alternating minimization procedure based on closed form solutions is performed to estimate the mutual coupling matrix in the field of complex symmetric toeplitz matrices unlike many existing array calibration methods it requires neither the presence of calibration sources nor previous calibration information as initialization computer simulations show the effectiveness of the proposed technique and prove that the nice statistical properties of classical super resolution doa estimation algorithms can be restored despite the presence of mutual coupling

weak uninorm aggregation operators abstract by weakening the identity condition of uninorm a general class of associative aggregation operators called weak uninorm is introduced it is proved that continuous weak uninorms are the combination of continuous t norm and continuous t conorm through a median operator the representation theorem for archimedean weak uninorm is also given finally the counting number of the identity elements of weak uninorm is also investigated

on graded cartan invariants of symmetric groups and hecke algebras we consider graded cartan matrices of the symmetric groups and the iwahori hecke algebras of type a at roots of unity these matrices are mathbb z v v 1 valued and may also be interpreted as gram matrices of the shapovalov form on sums of weight spaces of a basic representation of an affine quantum group we present a conjecture predicting the invariant factors of these matrices and give evidence for the conjecture by proving its implications under a localization and certain specializations of the ring mathbb z v v 1 this proves and generalizes a conjecture of ando suzuki yamada on the invariants of these matrices over mathbb q v v 1 and also generalizes the first author s recent proof of the kulshammer olsson robinson conjecture over mathbb z

bayesian and regularization methods for hyperparameter estimation in image restoration in this paper we propose the application of the hierarchical bayesian paradigm to the image restoration problem we derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori map analysis within the hierarchical bayesian paradigm we show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the map approach for the image restoration problem we furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters or their ratio defined as the regularization parameter finally the proposed algorithms are tested experimentally

van melle s combining function in mycin is a representable uninorm an alternative proof abstract recently tsadiras and margaritis have shown that the function implemented in the expert system mycin for combining certainty factors is a uninorm in this paper we present a compact alternative to the given direct and lengthy proof based on the construction of representable uninorms by means of an additive generator consequently we show that van melle s combining function is a representable uninorm in fact it is a rescaled version of the representable uninorm on the unit interval constructed from the algebraic product and the probabilistic sum

an eigenstructure method for estimating doa and sensor gain phase errors in this paper we consider the problem of direction of arrival doa estimation in the presence of sensor gain phase errors under some mild assumptions we propose a new doa estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate by combining the new doa estimation with the conventional gain phase error estimation a method is proposed to simultaneously estimate the doa and gain phase errors without joint iteration theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors however the resolution capability of the proposed method is lower than that of the method in a j weiss and b friedlander eigenstructure methods for direction finding with sensor gain and phase uncertainties circuits systems signal process vol 9 no 3 pp 271 300 1990 named as the wf method in order to improve the resolution capability and maintain phase error independence a combined strategy is developed using the proposed and wf methods the advantage of the proposed methods is that they are independent of phase errors leading to the cancellation of phase error calibration during the operation life of an array moreover the proposed methods avoid the problem of suboptimal convergence which occurs in the wf method the drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other and they are not applicable to a linear array simulation results verify the effectiveness of the proposed methods

sensor array calibration using a maximum likelihood approach high resolution array processing algorithms for source localization are known to be sensitive to errors in the model for the sensor array spatial response in particular unknown gain phase and mutual coupling as well as errors in the sensor positions can seriously degrade the performances of array processing algorithms this paper describes a calibration algorithm that estimates the calibration matrix consisting of the unknown gain phase and mutual coupling coefficients as well as the sensor positions using a set of calibration sources in known locations the estimation of the various parameters is based on a maximum likelihood approach cramer rao lower bound crb expressions for the sensor positions and the calibration matrix parameters are also derived numerical results are shown to illustrate the potential usefulness of the proposed calibration algorithm toward better accuracy and resolution in parametric array processing algorithms

roughness penalties on finite domains a class of penalty functions for use in estimation and image regularization is proposed these penalty functions are defined for vectors whose indexes are locations in a finite lattice as the discrepancy between the vector and a shifted version of itself after motivating this class of penalty functions their relationship to markov random field priors is explored one of the penalty functions proposed a divergence roughness penalty is shown to be a discretization of a penalty proposed by good and gaskins 1971 for use in density estimation one potential use in estimation problems is explored an iterative algorithm that takes advantage of induced neighborhood structures is proposed and convergence of the algorithm is proven under specified conditions examples in emission tomographic imaging and radar imaging are given

an advanced interpretable fuzzy neural network model based on uni nullneuron constructed from n uninorms abstract this paper formulates a fuzzy logic neuron that uses n uninorms to construct uni nullneurons a fuzzy neural network fnn composed of these neurons is easy to operate with nullnorms and uninorms at different times which results in high accuracy of the model outputs and increases the flexibility in connecting the rule antecedents enabling and and or connections within one rule this in turn may allow experts operators to extract more knowledge from data the fnn uses a one versus rest classifier learning scheme for multi class classification problems where neuron activation levels construct the indicator regression matrix this results in a non linear regression by indicator which can resolve the inherent class masking problem apparent in the linear case we propose a specific neuron selection strategy in the learning stage that applies lasso to bootstrap replications in order to ensure that the rule base is as compact as possible and induced by a low number of neurons to evaluate the new neuron acting in fnns we performed pattern classification and regression tests compared with traditional fnn in the literature our variant showed improved model accuracies for several high dimensional real world datasets in binary and multi class classification and regression problems combined with the ability to generate human readable rules this offers the ability to generate parsimonious responses with a high degree of confidence

generalized perfect isometries in some groups of lie rank one abstract in a recent paper b kulshammer j b olsson and g r robinson introduced notions of generalized blocks and generalized perfect isometries and studied them in the case of the symmetric group s n it is the purpose of this paper to investigate some families of groups of lie rank one exhibiting generalized perfect isometries where there are none in the sense given by m broue and thus proving a weaker analogue of one of broue s conjectures in these cases

direction of arrival estimation using a sparse representation of array covariance vectors a new direction of arrival doa estimation method is proposed based on a novel data model using the concept of a sparse representation of array covariance vectors sracv in which doa estimation is achieved by jointly finding the sparsest coefficients of the array covariance vectors in an overcomplete basis the proposed method not only has high resolution and the capability of estimating coherent signals based on an arbitrary array but also gives an explicit error suppression criterion that makes it statistically robust even in low signal to noise ratio snr cases simulation experiments are conducted to validate the effectiveness of the proposed method the performance is compared with several existing doa estimation methods and the cramer rao lower bound crlb

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

generalised cartan invariants of symmetric groups kulshammer olsson and robinson developed an analogue of modular representation theory of symmetric groups where is not necessarily a prime they gave a conjectural combinatorial description for invariant factors of the cartan matrix in this context we confirm their conjecture by proving a more precise blockwise version of the conjecture due to bessenrodt and hill

asymptotically optimal blind calibration of uniform linear sensor arrays for narrowband gaussian signals an asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband gaussian signals is proposed rather than taking the direct maximum likelihood ml approach for joint estimation of all the unknown model parameters which leads to a multi dimensional optimization problem with no closed form solution we revisit paulraj and kailath s p k s classical approach in exploiting the special toeplitz structure of the observations covariance however we offer a substantial improvement over p k s ordinary least squares ls estimates by using asymptotic approximations in order to obtain simple non iterative quasi linear optimally weighted ls owls estimates of the sensors gains and phases offsets with asymptotically optimal weighting based only on the empirical covariance matrix of the measurements moreover we prove that our resulting estimates are also asymptotically optimal w r t the raw data and can therefore be deemed equivalent to the ml estimates mle which are otherwise obtained by joint ml estimation of all the unknown model parameters after deriving computationally convenient expressions of the respective cramer rao lower bounds we also show that our estimates offer improved performance when applied to non gaussian signals and or noise as quasi mle in a similar setting the optimal performance of our estimates is demonstrated in simulation experiments with a considerable improvement reaching an order of magnitude and more in the resulting mean squared errors w r t p k s ordinary ls estimates we also demonstrate the improved accuracy in a multiple sources directions of arrivals estimation task

an em algorithm for fitting two level structural equation models maximum likelihood is an important approach to analysis of two level structural equation models different algorithms for this purpose have been available in the literature in this paper we present a new formulation of two level structural equation models and develop an em algorithm for fitting this formulation this new formulation covers a variety of two level structural equation models as a result the proposed em algorithm is widely applicable in practice a practical example illustrates the performance of the em algorithm and the maximum likelihood statistic

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

minimum mean square distance estimation of a subspace we consider the problem of subspace estimation in a bayesian setting since we are operating in the grassmann manifold the usual approach which consists of minimizing the mean square error mse between the true subspace u and its estimate u may not be adequate as the mse is not the natural metric in the grassmann manifold gn p i e the set of p dimensional subspaces in rn as an alternative we propose to carry out subspace estimation by minimizing the mean square distance between u and its estimate where the considered distance is a natural metric in the grassmann manifold viz the distance between the projection matrices we show that the resulting estimator is no longer the posterior mean of u but entails computing the principal eigenvectors of the posterior mean of uut derivation of the minimum mean square distance mmsd estimator is carried out in a few illustrative examples including a linear gaussian model for the data and bingham or von mises fisher prior distributions for u in all scenarios posterior distributions are derived and the mmsd estimator is obtained either analytically or implemented via a markov chain monte carlo simulation method the method is shown to provide accurate estimates even when the number of samples is lower than the dimension of u an application to hyperspectral imagery is anally investigated

nullnorms on bounded lattices derived from t norms and t conorms abstract nullnorms with an annihilator a in any point of a bounded lattice are generalizations and unifications of t norms and t conorms this study continues to investigate the construction of nullnorms on bounded lattices we propose some methods to construct nullnorms derived from t norms and t conorms on bounded lattices where some sufficient and necessary conditions on theirs annihilator are required as a by product of these constructions idempotent nullnorms on bounded lattices are obtained further we provide some illustrative examples of the new classes of nullnorms idempotent nullnorms on bounded lattices

cartan determinants and shapovalov forms we compute the determinant of the gram matrix of the shapovalov form on weight spaces of the basic representation of an affine kac moody algebra of ade type possibly twisted as a consequence we obtain explicit formulae for the determinants of the cartan matrices of p blocks of the symmetric group and its double cover and of the associated hecke algebras at roots of unity

on generalized blocks for alternating groups abstract in a recent paper kulshammer olsson robinson gave a d analogue for the nakayama conjecture for symmetric groups where d 2 is an arbitrary integer we prove that there is a natural d analogue of the nakayama conjecture for alternating groups whenever d is 2 or an arbitrary odd integer greater than 1 this generalizes an old result of kerber

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

structure of n uninorms in this paper we study binary operators on 0 1 which are associative monotone non decreasing in both variables and commutative amc with neutral element in this work we generalize the concept of neutral element and this generalization gives rise to a new class of amc binary operators on 0 1 called n uninorms n uninorms are denoted as u n where n comes from the generalization of the neutral element we study the structure of n uninorms the structure resembles an ordinal sum structure made up of n uninorms we characterize some special cases of them based on some continuity considerations and show that t norms t conorms uninorms and nullnorms t operators are special cases of n uninorms we also show that given n there are n 1 classes of operators in u n and each of them has many subclasses we also study the frank equation involving n uninorms and show that we need to consider only n uninorms for the study finally we show that the total number of subclasses of operators in u n follows the famous series called catalan numbers

isometries and extra special sylow groups of order p3 abstract a new type of isometry between the sets of irreducible characters of blocks is introduced and a conjecture is stated using the classifications of finite simple groups and saturated fusion systems over an extra special group p of order p 3 and exponent p we check that the conjecture is affirmatively answered for the principal blocks of finite groups with sylow p subgroup p

cs decomposition based bayesian subspace estimation in numerous applications it is required to estimate the principal subspace of the data possibly from a very limited number of samples additionally it often occurs that some rough knowledge about this subspace is available and could be used to improve subspace estimation accuracy in this case this is the problem we address herein and in order to solve it a bayesian approach is proposed the main idea consists of using the cs decomposition of the semi orthogonal matrix whose columns span the subspace of interest this parametrization is intuitively appealing and allows for non informative prior distributions of the matrices involved in the cs decomposition and very mild assumptions about the angles between the actual subspace and the prior subspace the posterior distributions are derived and a gibbs sampling scheme is presented to obtain the minimum mean square distance estimator of the subspace of interest numerical simulations and an application to real hyperspectral data assess the validity and the performances of the estimator

a single point characterization of representable uninorms we study uninorms of which both the underlying t norm and underlying t conorm are strict such uninorms are the only candidates for being representable by an additive generator we prove that the representability of such a uninorm depends solely on its value at a single arbitrary point in the remaining open part of the unit square more explicitly such a uninorm turns out to be representable if and only if this single value is located strictly between the minimum and the maximum of the corresponding arguments if this single value coincides with one of these bounds then the value of the uninorm at any point in the remaining open part is determined by the same bound

accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation the em method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography pet the result is an iterative algorithm for image reconstruction that is finding increasing use in pet due to its attractive theoretical and practical properties its major disadvantage is the large amount of computation that is often required due to the algorithm s slow rate of convergence this paper presents an accelerated form of the em algorithm for pet in which the changes to the image as calculated by the standard algorithm are multiplied at each iteration by an overrelaxation parameter the accelerated algorithm retains two of the important practical properties of the standard algorithm namely the selfnormalization and nonnegativity of the reconstructed images experimental results are presented using measured data obtained from a hexagonal detector system for pet the likelihood function and the norm of the data residual were monitored during the iterative process according to both of these measures the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm for two different sets of data important theoretical properties remain to be investigated namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator

convergence theorems for generalized alternating minimization procedures the em algorithm is widely used to develop iterative parameter estimation procedures for statistical models in cases where these procedures strictly follow the em formulation the convergence properties of the estimation procedures are well understood in some instances there are practical reasons to develop procedures that do not strictly fall within the em framework we study em variants in which the e step is not performed exactly either to obtain improved rates of convergence or due to approximations needed to compute statistics under a model family over which e steps cannot be realized since these variants are not em procedures the standard g em convergence results do not apply to them we present an information geometric framework for describing such algorithms and analyzing their convergence properties we apply this framework to analyze the convergence properties of incremental em and variational em for incremental em we discuss conditions under these algorithms converge in likelihood for variational em we show how the e step approximation prevents convergence to local maxima in likelihood

perfect isometries and murnaghan nakayama rules acknowledgement the authors wish to thank the referee for a very careful and precise reading of several earlier versions of this manuscript they are grateful for the number quality and helpfulness of comments and suggestions received

uninorms on bounded lattices with the underlying t norms and t conorms abstract uninorms are a generalization of the concepts of triangular norms t norms and triangular conorms t conorms that admit a neutral element as any element in a bounded lattice in this study we discuss the characterization of uninorms on bounded lattices we introduce some new constructions for uninorms on bounded lattices which are derived from both t norms and t conorms in particular two idempotent uninorms on bounded lattices are obtained we also provide some corresponding examples to help understand the structure of these new classes of uninorms in addition we provide an answer to the open problem proposed by cayli 2019 14