regularity for double phase variational problems we prove sharp regularity theorems for minimisers of a class of variational integrals whose integrand switches between two different types of degenerate elliptic phases according to the zero set of a modulating coefficient a cdot the model case is given by the functional w mapsto int dw p a x dw q rm d x where q p and a cdot geqq 0

nonlinear elliptic systems with general growth we prove local lipschitz continuity and as a consequence c k and c regularity of weak solutions u for a class of nonlinear elliptic differential systems of the formn 1 xi a i du 0 1 2 m the growth conditions on the dependence of functions a i on the gradient du are so mild to allow us to embrace growths between the linear and the exponential cases and they are more general than those known in the literature

regularity for minimizers of integrals with nonstandard growth abstract we deal with variational integrals f x d u x d x and we consider a minimizer u r n r among all functions that agree on the boundary with some fixed boundary value u we assume that the boundary datum u makes the density f x d u x more integrable and we prove that the minimizer u enjoy higher integrability

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

equivalent representations of set functions this paper introduces four alternative representations of a set function the ma bius transformation the co ma bius transformation and the interactions between elements of any subset of a given set as extensions of shapley and banzhaf values the links between the five equivalent representations of a set function are emphasized in this presentation

higher integrability for minimizers of integral functionals with p q growth abstract we prove higher integrability for minimizers u r n of integral functionals f du a x u dx where f satisfies a non standard growth condition of p q type z p f z l 1 z q p

integrability and boundedness of solutions to some anisotropic problems abstract in this article we give a series of results on the improved integrability and boundedness of solutions to several anisotropic problems in particular we consider the nonhomogeneous dirichlet problem for anisotropic elliptic second order equations moreover we study anisotropic variational inequalities with unilateral and bilateral obstacles as well as gradient constraints finally variational problems for integral functionals with anisotropic integrands are considered

pointwise bounds for minimizers of some anisotropic functionals abstract we consider variational integral functionals g x u x d u x d x where is a bounded open subset in r n and the integrand g x s f x b x s is not subjected to any growth condition from above neither satisfies any regularity assumption growing linearly with respect to the s variable their interest relies on the fact that they are strictly connected with optimal transport problems with congestion effects the aim of this paper is to find sufficient conditions on the boundary datum u in order to obtain global and explicit estimates for the solutions of the following minimization problem min g x u x d u x d x u u w 0 1 1

sharp regularity for functionals with p q growth we prove regularity theorems for minimizers of integral functionals of the calculus of variations f x du x dx with non standard growth conditions of p q type z p f x z l z q 1 p q in particular we find that a sufficient condition for minimizers to be regular is qp n n where the function f x z is holder continuous with respect to the x variable and x rn this condition is also sharp we include results in the setting of orlicz spaces moreover we treat certain relaxed functionals too finally we address a problem posed by marcellini in 43 showing a minimizer with an isolated singularity

on deriving the inverse of a sum of matrices available expressions are reviewed and new ones derived for the inverse of the sum of two matrices one of them being nonsingular particular attention is given to text bf a text bf ubv 1 where textbf a is nonsingular and textbf u b and textbf v may be rectangular generalized inverses of textbf a textbf ubv are also considered several statistical applications are discussed

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

regularity of minimizers under limit growth conditions abstract it is well known that an integral of the calculus of variations satisfying anisotropic growth conditions may have unbounded minimizers if the growth exponents are too far apart under sharp assumptions on the exponents we prove the local boundedness of minimizers of functionals with anisotropic p q growth via the de giorgi method as a by product regularity of minimizers of some non coercive functionals is obtained by reduction to coercive ones

harnack inequalities for double phase functionals we prove a harnack inequality for minimisers of a class of non autonomous functionals with non standard growth conditions they are characterised by the fact that their energy density switches between two types of different degenerate phases

scalar minimizers with fractal singular sets lack of regularity of local minimizers for convex functionals with non standard growth conditions is considered it is shown that for every 0 there exists a function ac such that the functional admits a local minimizer uw1 p whose set of non lebesgue points is a closed set with dim n p and where 1 p n n q

statistical regularization of inverse problems in experimental sciences we often need to solve inverse problems that is we want to obtain information about the internal structure of a physical system from indirect noisy observations often the problem is not whether a solution exists on the contrary there are too many solutions that fit the data to a chosen tolerance level the goal is to use prior information to determine a physically meaningful solution here we present some of the basic questions that arise we describe methods that can be used to find inversion estimates as well as ways to assess their performance

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

interaction indices for games on combinatorial structures with forbidden coalitions abstract the notion of interaction among a set of players has been defined on the boolean lattice and cartesian products of lattices the aim of this paper is to extend this concept to combinatorial structures with forbidden coalitions the set of feasible coalitions is supposed to fulfil some general conditions this general representation encompasses convex geometries antimatroids augmenting systems and distributive lattices two axiomatic characterizations are obtained they both assume that the shapley value is already defined on the combinatorial structures the first one is restricted to pairs of players and is based on a generalization of a recursivity axiom that uniquely specifies the interaction index from the shapley value when all coalitions are permitted this unique correspondence cannot be maintained when some coalitions are forbidden from this a weak recursivity axiom is defined we show that this axiom together with linearity and dummy player are sufficient to specify the interaction index the second axiomatic characterization is obtained from the linearity dummy player and partnership axioms an interpretation of the interaction index in the context of surplus sharing is also proposed finally our interaction index is instantiated to the case of games under precedence constraints

a unified approach to statistical tomography using coordinate descent optimization over the past years there has been considerable interest in statistically optimal reconstruction of cross sectional images from tomographic data in particular a variety of such algorithms have been proposed for maximum a posteriori map reconstruction from emission tomographic data while map estimation requires the solution of an optimization problem most existing reconstruction algorithms take an indirect approach based on the expectation maximization em algorithm we propose a new approach to statistically optimal image reconstruction based on direct optimization of the map criterion the key to this direct optimization approach is greedy pixel wise computations known as iterative coordinate decent icd we propose a novel method for computing the icd updates which we call icd newton raphson we show that icd newton raphson requires approximately the same amount of computation per iteration as em based approaches but the new method converges much more rapidly in our experiments typically five to ten iterations other advantages of the icd newton raphson method are that it is easily applied to map estimation of transmission tomograms and typical convex constraints such as positivity are easily incorporated

convergent incremental optimization transfer algorithms application to tomography no convergent ordered subsets os type image reconstruction algorithms for transmission tomography have been proposed to date in contrast in emission tomography there are two known families of convergent os algorithms methods that use relaxation parameters and methods based on the incremental expectation maximization em approach this paper generalizes the incremental em approach by introducing a general framework incremental optimization transfer the proposed algorithms accelerate convergence speeds and ensure global convergence without requiring relaxation parameters the general optimization transfer framework allows the use of a very broad family of surrogate functions enabling the development of new algorithms this paper provides the first convergent os type algorithm for nonconcave penalized likelihood pl transmission image reconstruction by using separable paraboloidal surrogates sps which yield closed form maximization steps we found it is very effective to achieve fast convergence rates by starting with an os algorithm with a large number of subsets and switching to the new transmission incremental optimization transfer triot algorithm results show that triot is faster in increasing the pl objective than nonincremental ordinary sps and even os sps yet is convergent

bounded minimisers of double phase variational integrals bounded minimisers of the functional w mapsto int dw p a x dw q rm d x where 0 leqq a cdot in c 0 alpha and 1 p q are c 1 beta regular provided the sharp bound q leqq p alpha holds

axioms for the shapley value on convex geometries the purpose of this article is an extension of shapley s value for games with restricted cooperation the classical model of cooperative game where every subset of players is a feasible coalition may be unrealistic the feasible coalitions in our model will be the convex sets i e those subsets of players belonging to a convex geometry l in the last section we apply this model to several examples about the power in the council of ministers of the european union

calderon zygmund estimate for asymptotically regular non uniformly elliptic equations abstract we prove a global calderon zygmund estimate for the distributional solution to non uniformly elliptic equation with an asymptotically regular nonlinearity in a c 1 domain for some 0 here a key ingredient of our proof is to make use of approximating the solution of asymptotically regular problem by the solution of regular problem while the gradient of its solution close to infinity

interior behaviour of minimizers for certain functionals with nonstandard growth for all t e 0 00 for example we see that f t2 atp btq a o b o l p 1 satisfy the ellipticity condition 2 recently a number of authors have considered regularity questions of minimizers for z under nonstandard growth conditions onf see l 7 indeed in the scalar cases choe 3 has already obtained c regularity result for minimizers of z when f t2 tp log 1 t p 1 using lewis method 8 in this paper we prove that a locally bounded minimizer u is c f under the assumption that l prq p l 3

block iterative fisher scoring algorithms for maximum penalized likelihood image reconstruction in emission tomography this paper introduces and evaluates a block iterative fisher scoring bfs algorithm the algorithm provides regularized estimation in tomographic models of projection data with poisson variability regularization is achieved by penalized likelihood with a general quadratic penalty local convergence of the block iterative algorithm is proven under conditions that do not require iteration dependent relaxation we show that when the algorithm converges it converges to the unconstrained maximum penalized likelihood mpl solution simulation studies demonstrate that with suitable choice of relaxation parameter and restriction of the algorithm to respect nonnegative constraints the bfs algorithm provides convergence to the constrained mpl solution constrained bfs often attains a maximum penalized likelihood faster than other block iterative algorithms which are designed for nonnegatively constrained penalized reconstruction