As we know, histogram matching is a commonly-adopted technique in the applications of pattern recognition. The matching of two patterns can be accomplished by matching their corresponding histograms. In general, the number of features and the resolution of each feature will determine the size of histogram. The more the number of features and the higher the resolution of each feature, the strong...

Since it was firstly introduced by Torra and Narukawa (The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, pp. 1378–1382), the hesitant fuzzy set has attracted more and more attention due to its powerfulness and efficiency in representing uncertainty and vagueness. This paper extends the classical VIKOR (vlsekriterijumska optimizacija i kompromisno resenje in serb...

Sparsity-inducing norm has been a powerful tool for learning robust models with limited data in high dimensional space. By imposing such norms as constraints or regularizers in an optimization setting, one could bias the model towards learning sparse solutions, which in many case have been proven to be more statistically efficient [Don06]. Typical sparsityinducing norms include `1 norm [Tib96] ...

This note discusses some geometrically defined seminorms on the group Ham(M, ω) of Hamilto-nian diffeomorphisms of a closed symplectic manifold (M, ω), giving conditions under which they are nondegenerate and explaining their relation to the Hofer norm. As a consequence we show that if an element in Ham(M, ω) is sufficiently close to the identity in the C 2-topology then it may be joined to the...

In this paper we study a facility location problem in the plane in which a single point (median) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time of the clients to the facility, using the L1 or Manhattan metric. The highway is an alternative transportation system that can be used by the clients to reduce their travel time to the facility. ...

Let V be a set of n points in R, which we call voters, where d is a fixed constant. A point p ∈ R is preferred over another point p′ ∈ R by a voter v ∈ V if dist(v, p) < dist(v, p′). A point p is called a plurality point if it is preferred by at least as many voters as any other point p′. We present an algorithm that decides in O(n logn) time whether V admits a plurality point in the L2 norm an...

We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online L1norm minimization of the residual. It is shown why this is a natural framework for hyperbolic problems and tested on nonlinear problems such as Burgers’ equati...

First exit times from regions and their dependence on variations of boundaries are discussed for diffusion processes. The paper presents an estimate of L1-distance between exit times from two regions via expectations of exit times. Abbreviated title: On L1-distance between first exit times It is known that first exit times from a region for smooth solutions of ordinary equations does not depend...

We give an explicit bound for the L1-distance between two additive processes of local characteristics (fj(·), σ(·), νj), j = 1, 2. The cases σ = 0 and σ(·) > 0 are both treated. We allow ν1 and ν2 to be time-homogeneous Lévy measures, possibly with infinite variation. Some examples of possible applications are discussed.

We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of distributions both for a drifting PAC scenario and a tracking scenario. Our bounds are always tighter and in some cases substantially improve upon previous o...