We study, in type A, the algebraic cycles (MV-cycles) discovered by I. Mirkovi´c and K. Vilonen [MV]. In particular, we partition the loop Grassmannian into smooth pieces such that the MV-cycles are their closures. We explicitly describe the points in each piece using the lattice model of the loop Grassmannian in type A. The partition is invariant under the action of the coweights and, up to th...

In this paper a video coding scheme with Layered Block Matching Super-resolution (LBM-SR) is presented. At the encoder side, it divides the video frames into key and non-key frames, which are encoded at original resolution and reduced resolution respectively. During the resolution reduction process, most of the high frequency information in non-key frames is dropped to save the bit-rate. At the...

The standard notion of NS-NS 3-form flux is lifted to Hitchin’s generalized geometry. This generalized flux is given in terms of an integral of a modified Nijenhuis operator over a generalized 3-cycle. Explicitly evaluating the generalized flux in a number of familiar examples, we show that it can compute three-form flux, geometric flux and non-geometric Q-flux. Finally, a generalized connectio...

We prove that for an arbitrarily small constant ε > 0, assuming NP 6⊆DTIME(2log n), the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than 2log 1−ε n. This improves upon the previous hardness factor of (log n)δ for some δ > 0 due to [AKKV05].

This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property of the network together with minimum length routing. More specifically, it is shown that, in a large n-dimensional hyperbolic ball B of radius R viewed as a ...

An important problem in applications of formal concept analysis is a possibly large number of clusters extracted from data. Factorization is one of the methods being used to cope with the number of clusters. We present an algorithm for computing a factor lattice of a concept lattice from the data and a user-specified similarity threshold a. The elements of the factor lattice are collections of ...

More and more data are being published in the form of machine readable RDF graphs over Linked Open Data (LOD) Cloud accessible through SPARQL queries. This study provides interactive navigation of RDF graphs obtained by SPARQL queries using Formal Concept Analysis. With the help of this View By clause a concept lattice is created as an answer to the SPARQL query which can then be visualized and...

We consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $X$, $(X, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $X$. We also show that, for a strong residuated lattice $X$, $bigcap {P_{lambda} ,|,P_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

Concept lattice is an effective tool for data analysis. Constrained concept lattice, with the characteristics of higher constructing efficiency, practicability and pertinence, is a new concept lattice structure. For classification rule acquisition, a classification rule acquisition algorithm based on the constrained concept lattice is presented by using the concept of partition support accordin...