Recent works on quantum resource theories of non-Gaussianity, which are based upon the type tools available in contemporary experimental settings, put Gaussian states and their convex combinations equal footing. Motivated by this, this article, we derive a new model dissipative time evolution unitary Lindblad operators which, while does not preserve set states, preserves combinations, i.e. so-c...

The consistency of classification algorithm plays a central role in statistical learning theory. A consistent algorithm guarantees us that taking more samples essentially suffices to roughly reconstruct the unknown distribution. We consider the consistency of ERM scheme over classes of combinations of very simple rules (base classifiers) in multiclass classification. Our approach is, under some...

Determining the minimum distance between two convex objects is a problem that has been solved using many di¤erent approaches. Some methods rely on computational geometry techniques, while others rely on optimization techniques to ...nd the solution. Some fast algorithms sacri...ce precision for speed while others are limited in the types of objects that they can handle (e.g. linearly bound obje...

In this paper, we present a novel method for the robust control problem of uncertain nonlinear discrete-time linear systems with sector and slope restrictions. The nonlinear function considered in this paper is expressed as convex combinations of sector and slope bounds. Then the equality constraint is derived by using convex properties of the nonlinear function. A stabilization criterion for t...

We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly nonexpansive mappings is nearly equal to the average of the ranges of the mappings. A striking application of this result yields that the average of asymptotically r...

We propose Deep Optimistic Linear Support Learning (DOL) to solve highdimensional multi-objective decision problems where the relative importances of the objectives are not known a priori. Using features from the high-dimensional inputs, DOL computes the convex coverage set containing all potential optimal solutions of the convex combinations of the objectives. To our knowledge, this is the fir...

Abstract. The aim of this paper is to obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-toconvexity, starlikeness and convexity for functions belonging to the subclass TSγ(f, g; α, β) of uniformly starlike and convex functions, we consider integral operators associated with functions in this class. Furthermore partial sums fn(z) of functions f(z) i...

The use of interpolants in verification is gaining more and more importance. Sincetheories used in applications are usually obtained as (disjoint) combinations of simplertheories, it is important to modularly re-use interpolation algorithms for the componenttheories. We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the compon...

In convex nonnegative matrix factorization, the feature vectors are modeled by convex combinations of observation vectors. In the paper, we propose to express the factorization model in terms of the sum of rank-1 matrices. Then the sparse factors can be easily estimated by applying the concept of the Hierarchical Alternating Least Squares (HALS) algorithm which is still regarded as one of the m...