The list of q-Painlevé equations we are going to investigate is given in section 3 below. We remark that these q-Painlevé equations were discovered through various approaches to discrete Painlevé equations, including singularity confinement analysis, compatibility conditions of linear difference equations, affine Weyl group symmetries and τ-functions on the lattices. Also, in Sakai’s framework ...

We develop a probabilistic framework for feature based multi-image matching that explicitly models the joint distribution of corresponding feature positions across several images. Conditioning this distribution on feature positions in some of the images gives welllocalized distributions for their correspondents in the others, which directly guide the correspondence search. This general framewor...

In this paper, we propose a controllable embedding method for highand low-dimensional geometry processing through sparse matrix eigenanalysis. Our approach is equally suitable to perform non-linear dimensionality reduction on big data, or to offer non-linear shape editing of 3D meshes and pointsets. At the core of our approach is the construction of a multi-Laplacian quadratic form that is asse...

Motivated by questions in property testing, we search for linear error-correcting codes that have the “single local orbit” property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every “sparse” binary code whose coordinates are indexed by elements of F2n for prime n, and whose symmetry group includes the...

The paper is devoted to the local classification of generic control-affine systems on an n-dimensional manifold with scalar input for any n ≥ 4 or with two inputs for n = 4 and n = 5, up to state-feedback transformations, preserving the affine structure (in C∞ category for n = 4 and Cω category for n ≥ 5). First using the Poincare series of moduli numbers we introduce the intrinsic numbers of f...

ـ ـــ Finding multiplicative inverse (Modular Inversion) operation is the most time-consuming operation in Elliptic Curve Crypto-system (ECC) operations which affects the performance of ECC. Moreover, several factors that affect the design of ECC have not been intensively investigated in the majority of researches related to ECC, Such as system utilization, area, resources-consuming and area*ti...

In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP 3. Namely, we show i) that the tangent developable of any convex curve in RP 3 has degree 4 and ii) construct an example of 4 tangent lines to a convex curve in RP 3 such that no real line intersects all four of them...

Multiple-point multiplication on elliptic curves is the highest computational complex operation in the elliptic curve cyptographic based digital signature schemes. We describe three algorithms for multiple-point multiplication on elliptic curves over prime and binary fields, based on the representations of two scalars, as sums of mixed powers of 2 and 3. Our approaches include sliding window me...

A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based upon the eigenvalue-eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant coordinate system for the multivariate data. Consequently, we view this met...