this paper uses the weighted l$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. when all variables are integer it finds the whole set of efficient solutions. in each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...

This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional space, 2-Sinkhorn divergence strictly weaker than exact 2-Wasserstein distance. Specifically, a sequence centered converges if corresponding covariance operators converge Hilbert–...

We analyze and compare different measures for the degree of non-Markovianity in dynamics open quantum systems. These are based on distinguishability states, which is quantified, one hand, by trace distance or, more generally, norm Helstrom matrix and, other entropic quantifiers: Jensen-Shannon divergence Holevo or skew divergence. explicitly construct a qubit trace-norm-based measure nonzero, w...

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition. In this paper we introduce a pseudo-distance dT that represents a possible solution to this problem. Indeed, dT is a pseudo-distance between multidimensional persistent homology groups with coeffic...

The chemical distance D(x, y) is the length of the shortest open path between two points x and y in an infinite Bernoulli percolation cluster. In this work, we study the asymptotic behaviour of this random metric, and we prove that, for an appropriate norm μ depending on the dimension and the percolation parameter, the probability of the event

Abstract. The present paper discusses the question of formulating and solving minimal-distance problems over the group-manifold of real symplectic matrices. In order to tackle the related optimization problem, the real symplectic group is regarded as a pseudo-Riemannian manifold and a metric is chosen that affords the computation of geodesic arcs in closed forms. Then, the considered minimal-di...

In this work, we revisit the curse of dimensionality, especially the concentration of the norm phenomenon which is the inability of distance functions to separate points well in high dimensions. We study the influence of the different properties of a distance measure, viz., triangle inequality, boundedness and translation invariance and on this phenomenon. Our studies indicate that unbounded di...

In air traffic management, the aircraft separation requirement is defined by a minimum horizontal distance and a minimum vertical distance that the aircraft have to maintain. Since this requirement defines a cylinder around each aircraft rather than a sphere, the three-dimensional Euclidean distance does not provide an appropriate basis for the definition of time of closest approach. For instan...

We present some related families of orthogonal polynomials of a discrete variable and survey some of their applications in the study of (distance-regular) graphs and (completely regular) codes. One of the main peculiarities of such orthogonal systems is their non-standard normalization condition, requiring that the square norm of each polynomial must equal its value at a given point of the mesh...