in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

This work concerns primal-dual interior-point methods for semideenite programming (SDP) that use a search direction originally proposed by Helmberg-Rendl-Vanderbei-Wolkowicz 5] and Kojima-Shindoh-Hara 11], and recently rediscovered by Monteiro 15] in a more explicit form. In analyzing these methods, a number of basic equalities and inequalities were developed in 11] and also in 15] through diie...

Choosing a diverse subset of a large collection of points in a metric space is a fundamental problem, with applications in feature selection, recommender systems, web search, data summarization, etc. Various notions of diversity have been proposed, tailored to different applications. The general algorithmic goal is to find a subset of points that maximize diversity, while obeying a cardinality ...

Individuals genetically susceptible to hypertension may have preexisting membrane defects influencing cell sodium permeability. Fourteen Minnesotan families of Northern European descent were selected as having one or both progenitors with either high (HP) or low (LP) erythrocyte sodium permeability. We earlier found that over one-half of the (22)Na(+) influx into HP erythrocytes can be inhibite...

We introduce a notion of large-scale foliation for metric measure spaces and we prove that if X is large-scale foliated by Y , and if Y satisfies a Sobolev inequality at large-scale, then so does X. In particular the Lp-isoperimetric of Y grows faster than the one of X. A special case is when Y = H is a closed subgroup of a locally compact group X = G. The class of elementary solvable groups is...

Recent studies show that widely used deep neural networks (DNNs) are vulnerable to carefully crafted adversarial examples. Many advanced algorithms have been proposed to generate adversarial examples by leveraging the Lp distance for penalizing perturbations. Researchers have explored different defense methods to defend against such adversarial attacks. While the effectiveness of Lp distance as...

We develop an axiomatic approach to the theory of Sobolev spaces on metric measure spaces and we show that this axiomatic construction covers the main known examples (Hajtasz Sobolev spaces, weighted Sobolev spaces, Upper-gradients, etc). We then introduce the notion of variational p-capacity and discuss its relation with the geometric properties of the metric space. The notions of p-parabolic ...