on the existence of states on mtl algebras the aim of this paper is to investigate the existence of bosbach states and riecan states on mtl algebras we prove that an mtl algebra l has bosbach states if and only if l has an mv filter we also establish that l has a state morphism if and only if l has a maximal mv filter furthermore we obtain the necessary and sufficient condition for an mtl chain having riecan states

iterative image reconstruction algorithms based on cross entropy minimization the related problems of minimizing the functionals f x alpha kl y px 1 alpha kl p x and g x alpha kl px y 1 alpha kl x p respectively over the set of vectors x or 0 are considered kl a b is the cross entropy or kullback leibler distance between two nonnegative vectors a and b iterative algorithms for minimizing both functionals using the method of alternating projections are derived a simultaneous version of the multiplicative algebraic reconstruction technique mart algorithm called smart is introduced and its convergence is proved

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

the radical of a perfect residuated structure in this paper we extend some properties of the radical of an mtl algebra to the non commutative case of a more general residuated structure namely the fl w algebra for the particular case of pseudo mtl algebras some specific results are presented we introduce the notion of a local additive measure on a perfect pseudo mtl algebra and we prove that with some additional conditions every local additive measure can be extended to a riecan state a necessary and sufficient condition is given for such an extension to be a bosbach state

a generalized em algorithm for 3 d bayesian reconstruction from poisson data using gibbs priors a generalized expectation maximization gem algorithm is developed for bayesian reconstruction based on locally correlated markov random field priors in the form of gibbs functions and on the poisson data model for the m step of the algorithm a form of coordinate gradient ascent is derived the algorithm reduces to the em maximum likelihood algorithm as the markov random field prior tends towards a uniform distribution three different gibbs function priors are examined reconstructions of 3 d images obtained from the poisson model of single photon emission computed tomography are presented

stone duality for dedekind σ complete l groups with order unit abstract building on the goodearl handelman lawrence functional representation theorem we provide a purely topological representation specifically a categorical duality for a large class of dedekind complete l groups g with order unit u including all g where u has a finite index of nilpotence our duality is a far reaching generalization of the well known stone duality between complete boolean algebras and basically disconnected compact hausdorff spaces

on the iterative image space reconstruction algorthm for ect the isra of 1 is shown to be an iterative algorithm that aims to converge to the least squares estimates of emission densities convergence is established in the case where a unique least squares estimate exists that is elementwise strictly positive it is pointed out that in terms of asymptotic theory the resulting estimators are inferior to the maximum likelihood estimators for which the em algorithm is a computational procedure potential difficulties with the behavior of the isra are illustrated using very simple examples

an algorithm for maximizing expected log investment return let the random stock market vector x geq 0 be drawn according to a known distribution function f x x in r m a log optimal portfolio b ast is any portfolio b achieving maximal expected log return w ast sup b e ln b t x where the supremum is over the simplex b geq 0 sum i 1 m b i 1 an algorithm is presented for finding b ast the algorithm consists of replacing the portfolio b by the expected portfolio b b i e b i x i b t x corresponding to the expected proportion of holdings in each stock after one market period the improvement in w b after each iteration is lower bounded by the kullback leibler information number d b b between the current and updated portfolios thus the algorithm monotonically improves the return w an upper bound on w ast is given in terms of the current portfolio and the gradient and the convergence of the algorithm is established

parallel application of block iterative methods in medical imaging and radiation therapy some row action algorithms which exploit special objective function and constraints structure have proven advantageous for solving huge and sparse feasibility or optimization problems recently developed block iterative versions of such special purpose methods enable parallel computation when the underlying problem is appropriately decomposed this opens the door for parallel computation in image reconstruction problems of computerized tomography and in the inverse problem of radiation therapy treatment planning all in their fully discretized modelling approach since there is more than one way of deriving block iterative versions of any row action method the choice has to be made with reference to the underlying real world problem

states on finite monoidal t norm based algebras the aim of this paper is to study the existences of bosbach states and riecan states on finite monoidal t norm based algebras mtl algebras for short we give some examples to show that there exist mtl algebras having no bosbach states and riecan states the conditions under which mtl algebras have bosbach states and riecan states are investigated respectively we prove that riecan states on mtl algebras are reduced to states on imtl algebras furthermore the necessary and sufficient conditions for finite linearly ordered locally finite mtl algebras and peculiar mtl algebras having bosbach states and riecan states are obtained respectively in addition the notions of pseudo quasi equivalent and a subalgebra under pseudo quasi equivalent are proposed and some of their properties are investigated

a theoretical study of some maximum likelihood algorithms for emission and transmission tomography this paper has the dual purpose of introducing some new algorithms for emission and transmission tomography and proving mathematically that these algorithms and related antecedent algorithms converge like the em algorithms for positron single photon and transmission tomography the algorithms provide maximum likelihood estimates of pixel concentration or linear attenuation parameters one particular innovation we discuss is a computationally practical scheme for modifying the em algorithms to include a bayesian prior the bayesian versions of the em algorithms are shown to have superior convergence properties in a vicinity of the maximum we anticipate that some of the other algorithms will also converge faster than the em algorithms

generalized bosbach and riecan states based on relative negations in residuated lattices bosbach and riecan states on residuated lattices both are generalizations of probability measures on boolean algebras recently two types of generalized bosbach states on residuated lattices were introduced by georgescu and muresan through replacing the standard mv algebra in the original definition with arbitrary residuated lattices as codomains however several interesting problems there remain still open the first part of the present paper gives positive answers to these open problems it is proved that every generalized bosbach state of type ii is of type i and the similarity cauchy completion of a residuated lattice endowed with an order preserving generalized bosbach state of type i is unique up to homomorphisms preserving similarities where the codomain of the type i state is assumed to be cauchy complete consequently many existing results about generalized bosbach states can be further strengthened the second part of the paper introduces the notion of relative negation with respect to a given element called relative element in residuated lattices and then many issues with the canonical negation such as glivenko property semi divisibility generalized riecan state of residuated lattices can be extended to the context of such relative negations in particular several necessary and sufficient conditions for the set of all relatively regular elements of a residuated lattice to be special residuated lattices are given of which one extends the well known glivenko theorem and it is also proved that relatively generalized riecan states vanishing at the relative element are uniquely determined by their restrictions on the mv algebra consisting of all relatively regular elements when the domain of the states is relatively semi divisible and the codomain is involutive

the primal dual algorithm as a constraint set manipulation device a general primal dual algorithm for linearly constrained optimization problems is formulated in which the dual variables are updated by a dual algorithmic operator convergence is proved under the assumption that the dual algorithmic operator implies asymptotic feasibility of the primal iterates with respect to the linear constraints a general result relating the minimal values of an infinite sequence of constrained problems to the minimal value of a limiting problem constrained by the limit of the sequence of constraints sets is established and invoked the applicability of the general theory is demonstrated by analyzing a specific dual algorithmic operator this leads to the mart algorithm for constrained entropy maximization used in image reconstruction from projections

on fuzzy filters of pseudo bl algebras abstract we introduce the concept of fuzzy filters of pseudo bl algebras and obtain some of their important properties we further give several kinds of fuzzy filters such as fuzzy boolean filter fuzzy normal filter fuzzy prime filter fuzzy ultrafilter and fuzzy obstinate filter and discuss the relations among the above fuzzy filters we establish the prime fuzzy filter theorem in pseudo bl algebras by studying the relation between fuzzy boolean filter and fuzzy normal filter in pseudo bl algebras we solve an open problem that whether or not every boolean filter is normal in pseudo bl algebras

approximation theoretic derivation of logarithmic entropy principles for inverse problems and unique extension of the maximum entropy method to incorporate prior knowledge the minimum distance approach for reconstructing a positive function based on knowledge of finitely many linear functional values is examined two important classes of directed distances for signal processing and statistical inference are discussed by imposing conditions analogous to those satisfied by linear projections in hilbert space two logarithmic entropy principles are derived one of these involves the itakura saito distortion measure of communication theory and uniquely extends burg s maximum entropy method to incorporate prior knowledge the other uses the kullback leibler distance of statistics

states on commutative basic algebras the paper deals with states on commutative basic algebras that are a non associative generalization of mv algebras or in other words the algebraic semantics for a fuzzy logic which generalizes the lukasiewicz logic in that the conjunction is not associative states are defined in the same way as mundici s states on mv algebras as normalized finitely additive 0 1 valued functions and some results analogous to the results that are known from mv algebras are proved

states on semi divisible generalized residuated lattices reduce to states on mv algebras a semi divisible residuated lattice is a residuated lattice l satisfying an additional condition weaker than that of divisibility such structures are related to mathematical fuzzy logic as well as to extended probability theory by the fact that the subset of complemented elements induces an mv algebra we define generalized residuated lattices by omitting commutativity of the corresponding monoidal operation and study semi divisibility in such structures we show that given a good generalized residuated lattice l the set of complemented elements of l denoted by mv l forms a pseudo mv algebra if and only if l is semi divisible maximal filters on a semi divisible generalized residuated lattice l are in one to one correspondence with maximal filters on mv l we study states on semi divisible generalized residuated lattices riecan states on a semi divisible generalized residuated lattice l are determined by riecan states on mv l the same holds true for bosbach states whenever l is a good divisible generalized residuated lattice extremal riecan states on a semi divisible generalized residuated lattice l are in one to one correspondence with maximal and semi normal filters on l

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

properties of positive definite solutions of the equation x a x 2a i abstract in this paper we discuss some properties of a positive definite solution of the matrix equation x a x 2 a i two effective iterative methods for computing a positive definite solution of this equation are proposed necessary and sufficient conditions for existence of a positive definite solution are derived numerical experiments are executed with these methods