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We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…

In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…

We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification…

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.

We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature $(2,n-2)$.…

In this paper, which is a complement of \cite{BG}, we study a few elementary invariants for configurations of skew lines, as introduced and analyzed first by Viro and his collaborators. We slightly simplify the exposition of some known…

The construction of lagrangians describing the various representations of the Poincare group is given in terms of the BRST approach.

Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…

This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On a characterization of critical points of the scalar curvature functional (Russian), Tr. Rubtsovsk. Ind. Inst., 7, 211-217 (2000), Zbl.…

This article contributes to the search for a notion of postural style, focusing on the issue of classifying subjects in terms of how they maintain posture. Longer term, the hope is to make it possible to determine on a case by case basis…

We study the spectrum of transfer operators associated to various dynamical systems. Our aim is to obtain precise information on the discrete spectrum. To this end we propose a unitary approach. We consider various settings where new…

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…

The simulations of the light scalar mesons on the lattice are presented at the introductory level. The methods for determining the scalar meson masses are described. The problems related to some of these methods are presented and their…

Accurate and efficient lumbar spine disease identification is crucial for clinical diagnosis. However, existing deep learning models with millions of parameters often fail to learn with only hundreds or dozens of medical images. These…

This work proposes a framework for the patient-specific characterization of the spine, which integrates information on the tissues with geometric information on the spine morphology. Key elements are the extraction of 3D patient-specific…

By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…

In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders.

We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.

The paper is devoted to the study of the lattice of subgroups of the Lamplighter type groups and to the relative gradient rank.

This paper presents a large publicly available multi-center lumbar spine magnetic resonance imaging (MRI) dataset with reference segmentations of vertebrae, intervertebral discs (IVDs), and spinal canal. The dataset includes 447 sagittal T1…