diagonal plane sections of trivariate copulas we introduce the notion of diagonal plane section of a trivariate copula as an additional tool to describe its tail dependence behavior this notion extends the concept of diagonal section of a bivariate copula we provide existence results for trivariate copulas with a given diagonal plane function related results are discussed especially about extensions to a higher dimensional setting

semilinear copulas a family of copulas called semilinear is constructed starting with some assumptions about the linearity of the copulas along some segments of the unit square this family contains some other known families of copulas e g cuadras auge frechet and has a nice statistical interpretation several construction methods are provided especially concerning aggregation of semilinear copulas and a special form of ordinal sum construction is introduced some results about related families of quasi copulas and semicopulas are hence given

rank minimization code aperture design for spectrally selective compressive imaging a new code aperture design framework for multiframe code aperture snapshot spectral imaging cassi system is presented it aims at the optimization of code aperture sets such that a group of compressive spectral measurements is constructed each with information from a specific subset of bands a matrix representation of cassi is introduced that permits the optimization of spectrally selective code aperture sets furthermore each code aperture set forms a matrix such that rank minimization is used to reduce the number of cassi shots needed conditions for the code apertures are identified such that a restricted isometry property in the cassi compressive measurements is satisfied with higher probability simulations show higher quality of spectral image reconstruction than that attained by systems using hadamard or random code aperture sets

directional dependence of random vectors in this paper we define and study several properties of the concept of multivariate directional dependence and study the new concept in terms of copulas and provide new measures of multivariate association based on directional dependence finally we show the relationships of directional dependence with other dependence concepts such as association and conditional dependence

new constructions of diagonal patchwork copulas we present a method for constructing symmetric copulas which generalizes the diagonal patchwork construction of copulas procedure we also show how it is related to a new construction of a generalized farlie gumbel morgenstern distribution and to the copula transforms

quasi copulas with a given sub diagonal section abstract as is well known the frechet hoeffding bounds are the best possible for both copulas and quasi copulas for every quasi copula q max x y 1 0 q x y min x y for all x y 0 1 sharper bounds hold when the quasi copulas take prescribed values e g along their diagonal or horizontal resp vertical sections here we pursue two goals first we investigate construction methods for quasi copulas with a given sub diagonal section i e with prescribed values along the straight line segment joining the points x 0 0 and 1 1 x 0 for x 0 0 1 then we determine the best possible bounds for sets of quasi copulas with a given sub diagonal section

zero linear copulas abstract we introduce a new method for constructing copulas c a special type of aggregation functions based on the idea that c u v 0 if u g v for any continuous and decreasing function g 0 1 0 1 such that g 1 0 and c is linear if u g v 1 we also study the relationship between these copulas and other known families of copulas we provide some salient properties and measure the dependence and asymmetry in this class of copulas

copulas diagonals and tail dependence we present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence moreover we present the tail concentration function which depends on the diagonal section of a copula as a tool to give a description of tail dependence at finite scale the tail concentration function is hence used to introduce a graphical tool that can help to distinguish different families of copulas in the copula test space moreover it serves as a basis to determine the grouping structure of different financial time series by taking into account their pairwise tail behavior

some results on a transformation of copulas and quasi copulas this paper provides some results including invariance properties dependence measures convexity properties and tail dependence on a transformation of copulas and quasi copulas

the distribution of the probability mass of biconic copulas we study the probability mass distribution of biconic copulas provide a counterexample to a result given in jwaid et al 2012 29 concerning a characterization of singular biconic copulas and provide a new one

all pairs shortest paths using bridging sets and rectangular matrix multiplication we present two new algorithms for solving the all pairs shortest paths apsp problem for weighted directed graphs both algorithms use fast matrix multiplication algorithms the first algorithm solves the apsp problem for weighted directed graphs in which the edge weights are integers of small absolute value in o n2 time where satisfies the equation 1 1 1 2 and 1 1 is the exponent of the multiplication of an n n matrix by an n n matrix currently the best available bounds on 1 1 obtained by coppersmith imply that 0 is an error parameter and w is the largest edge weight in the graph after the edge weights are scaled so that the smallest non zero edge weight in the graph is 1 it returns estimates of all the distances in the graph with a stretch of at most 1 e corresponding paths can also be found efficiently

on a new construction of 1 lipschitz aggregation functions quasi copulas and copulas a new method of constructing 1 lipschitz aggregation functions is proposed and studied as a by product a new method of constructing quasi copulas from a given quasi copula c is obtained newly constructed copulas are negative quadrant dependent for any original copula c the only invariant copula under this construction is the frechet hoffding lower bound w the method preserves several important properties of copulas such as modularity absolute continuity or symmetry and commutes with some other constructions e g the construction of survival copulas

on a b transformations of conjunctive functions we introduce and study transformations that assign to each conjunctive real valued function f 0 1 2 r and any pair of parameters a b 0 1 2 a function fa b 0 1 2 r that is shown to be conjunctive too in more details we study the proposed transformations in the classes of all binary copulas quasi copulas conjunctive k lipschitz functions and the class of all conjunctive lipschitz functions we discuss the invariance of these classes with respect to all possible transformations an interesting result is that although the class of all copulas is invariant with respect to all considered transformations the only copula that is not changed by any of them is the product copula we also show that a b transformations of copulas yield the same results as constructions of copulas based on special measure preserving transformations and using measure preserving transformations we extend the studied binary constructions to n dimensional copulas finally we focus our attention on consecutive realization of the proposed transformations in the class of binary copulas and we also show several properties of a b transforms of the basic copulas including some dependence parameters

sharing information for the all pairs shortest path problem we improve the time complexity of the all pairs shortest path apsp problem for special classes of directed graphs one is a nearly acyclic directed graph and the other is a directed graph with limited edge costs the common idea for speed up is information sharing by n single source shortest path sssp problems that are solved for apsp we measure the degree of acyclicity by the size r of a given set of feedback vertices if r is small the given graph can be considered to be nearly acyclic we consider this parameter r in addition to the traditional parameters of the number of vertices n and that of edges m in the first part we improve the existing time complexity of o mn r 3 for the all pairs shortest path problem to o mn rnlogn this complexity is equal to or better than the previous one for all values of r under a reasonable assumption of m n in the second part we deal with a directed graph with non negative integer edge costs bounded by c we show the all pairs shortest path apsp problem can be solved in o mn n 2log c n time with the data structure of cascading bucket system we use the traditional computational model such that comparison addition operations on distance data and random access with o logn bits can be done in o 1 time also the graph is not separated meaning m n 1

bivariate copulas generated by perturbations in this paper we provide a family of bivariate copulas based on a perturbation of a given copula by a factor term the new class generalizes well known families of copulas and allows to describe a wide range of possible dependencies

on the relationship between modular functions and copulas copulas are nothing else but supermodular functions with absorbing element 0 and neutral element 1 although a copula c cannot be modular on the unit square itself it is effectively so on every rectangle with zero c volume in this paper we show that an appropriate modular function on the unit square can be transformed into a copula by performing a simple truncation operation either from below or above to ensure the compatibility with the frechet hoeffding bounds modular functions on the unit square admit an additive representation in terms of two univariate functions we specifically focus on cases where these univariate functions are sections horizontal vertical diagonal of a given copula ample illustrations are provided

semi copulas capacities and families of level sets we point out how capacities non additive measures can be used to provide explanations about the concept of bivariate ageing function the latter had been introduced to describe the family of the level sets of a survival function and motivated the interest toward the concept of semi copula

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

characterization of copulas with given diagonal and opposite diagonal sections in recent years special attention has been devoted to the problem of finding a copula the diagonal section and opposite diagonal section of which are known for given diagonal function and opposite diagonal functions we provide necessary and sufficient conditions for the existence of a copula to have these functions as diagonal and opposite diagonal sections we make use of techniques related to interpolation between the diagonals the construction of checkerboard copulas and linear programming this result allows us to solve two open problems to characterize the class of copulas where the knowledge of diagonal and opposite diagonal sections determines the copula in a unique way and to formulate necessary and sufficient conditions for each pair of such functions to be the diagonal and opposite diagonal sections of a unique copula

2 increasing binary aggregation operators abstract in this work we investigate the class of binary aggregation operators agops satisfying the 2 increasing property obtaining some characterizations for agops having other special properties e g quasi arithmetic mean choquet integral based modularity and presenting some construction methods in particular the notion of p increasing function is used in order to characterize the composition of 2 increasing agops the lattice structure with respect to the pointwise order of some subclasses of 2 increasing agops is presented finally a method is given for constructing copulas beginning from 2 increasing and 1 lipschitz agops

optimal transforms for multispectral and multilayer image coding multispectral images are composed of a series of images at differing optical wavelengths since these images can be quite large they invite efficient source coding schemes for reducing storage and transmission requirements because multispectral images include a third spectral dimension with nonstationary behavior these multilayer data sets require specialized coding techniques the authors develop both a theory and specific methods for performing optimal transform coding of multispectral images the theory is based on the assumption that a multispectral image may be modeled as a set of jointly stationary gaussian random processes therefore the methods may be applied to any multilayer data set which meets this assumption although the authors do not assume the autocorrelation has a separable form they show that the optimal transform for coding has a partially separable structure in particular they prove that a coding scheme consisting of a frequency transform within each layer followed by a separate kl transform across the layers at each spatial frequency is asymptotically optimal as the block size becomes large two simplifications of this method are also shown to be asymptotically optimal if the data can be assumed to satisfy additional constraints the proposed coding techniques are then implemented using subband filtering methods and the various algorithms are tested on multispectral images to determine their relative performance characteristics

quadratic constructions of copulas in the paper we introduce and study quadratic constructions of copulas based on composition of a copula and some quadratic polynomial we characterize all quadratic polynomials whose composition with an arbitrary copula always results in a copula due to this result we can assign a two parametric class k c c d of copulas with parameters c d in a certain subset r 2 to each copula c moreover we also determine all copulas invariant with respect to the quadratic constructions presented this investigation brings two interesting parametric classes of copulas we show that the union of these two classes is equal to the so called plackett family of copulas we add some properties of these copulas and their statistical consequences

on copulas and their diagonals we formulate the necessary and sufficient conditions for a function d 0 1 0 1 to be the diagonal section of a multivariate absolutely continuous copula moreover we provide some simple analytic formulas for copulas having given diagonal section or given distribution functions of order statistics

coperm transform domain energy compaction by optimal permutation compaction by optimal permutation coperm is a tool for transform domain energy compaction of broadband signals whose foundation is a simple but powerful idea any signal can be transformed to resemble a more desirable e g from a transform domain compaction viewpoint signal from a class of target signals e g dct basis functions by means of a suitable permutation of its samples one application of transform domain energy compaction is in lossy compression we pursue one possible thread in detail and demonstrate some interesting broadband image compression results

absolutely continuous copulas with given sub diagonal section abstract recently durante and jaworski 2008 6 have proved that the class of absolutely continuous copulas with a given diagonal section is non empty in case that the diagonal function is such that the set of points where this coincides with the identity function has null measure in this paper we show that if we consider sub diagonals or super diagonals then the framework changes concretely for each sub diagonal function there exists an absolutely continuous copula having this function as sub diagonal section

shock models with recovery option via the maxmin copulas ever since the historical sklar s theorem in 1959 copulas have been one of the main tools in modelling dependence of random variables with the range of applications in applied mathematics expanding and varying from mathematics of finance through system theory to fuzzy set theory there is a growing need for new types of copulas that could serve as appropriate models in these applications it is our aim to turn a new page in constructing copulas by setting a counterpart to the famous marshall copulas an extension of marshall olkin copulas that are typically applied to model lifetime of a two component system even a small but essential change of assumptions that the model is applied to such a system with one of the components having a recovery option turns into a substantially different problem on the level of copulas we give a full study of the augmented case by introducing a new type of copulas called maxmin together with concrete applications in server side web framework in an economic model and in fuzzy set theory

orthogonal grid constructions of copulas we establish a general framework for constructing copulas that can be regarded as a patchwork like assembly of arbitrary copulas with nonoverlapping rectangles as patches we derive a family of construction methods that require the choice of a single background copula when this background copula is the greatest copula we retrieve the well known ordinal sum construction while in the case of the smallest copula we obtain a construction method that is dual to the ordinal sum construction also nonsingular background copulas lead to suitable construction methods

multichannel image compression by bijection mappings onto zero trees a new approach to multichannel image compression is introduced where the intra and cross band correlations are jointly exploited in a surprisingly simple yet very effective manner the key component of the algorithm is a bijection mapping of the original multichannel image into a virtual two dimensional 2 d scalar image by optimally mapping the multichannel image set into a 2 d array and by subsequently applying a scalar image coding algorithm the spatial correlation and the spectral correlation of the multichannel data set are jointly exploited based on the statistical characteristics of the multichannel data the bijection mapping can be optimized to minimize the distortion introduced by the compression algorithm the optimization reduces to the maximization of a function of the second order statistics of the multichannel data at high compression rates the new algorithm outperforms traditional compression algorithms whenever the cross band correlation is high and it yields comparable performance at low compression rates

band ordering in lossless compression of multispectral images in this paper we consider a model of lossless image compression in which each band of a multispectral image is coded using a prediction function involving values from a previously coded band of the compression and examine how the ordering of the bands affects the achievable compression we present an efficient algorithm for computing the optimal band ordering for a multispectral image this algorithm has time complexity o n sup for an n band image while the naive algorithm takes time spl omega n a slight variant of the optimal ordering problem that is motivated by some practical concerns is shown to be np hard and hence computationally infeasible in all cases except for the most trivial possibility in addition we report on our experimental findings using the algorithms designed in this paper applied to real multispectral satellite data the results show that the techniques described here hold great promise for application to real world compression needs

algebraic theory on shortest paths for all flows abstract we consider a shortest path problem for a directed graph with edges labeled with a cost and a capacity the problem is to push flow f from a specified source to all other vertices with the minimum cost for all f values if there are t capacity values we can solve the single source shortest path problem t times for all capacity values in o t m t n log n time which is o m 2 when t m we improve this time to o c m n if edge costs are non negative integers bounded by c for the all pairs problem we give a simple floyd like algorithm with complexity o min t c n n 3 better than the best known o t c 1 843 n 2 843 for certain ranges of t and c

on a family of multivariate copulas for aggregation processes we introduce a family of multivariate copulas a special type of n ary aggregation operations depending on a univariate function this family is used in the construction of a special aggregation operation that satisfies a lipschitz condition several examples are provided and some statistical properties are studied