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A motion of a mechanism is a curve in its configuration space (c-space). Singularities of the c-space are kinematic singularities of the mechanism. Any mobility analysis of a particular mechanism amounts to investigating the c-space…

We provide a complete set of linearizability conditions for nonlinear partial difference equations de- fined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to…

The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…

We study supersolvable line arrangements in ${\mathbb P}^2$ over the reals and over the complex numbers, as the first step toward a combinatorial classification. Our main results show that a nontrivial (i.e., not a pencil or near pencil)…

In this paper we indicate one method of construction of linear representations of groups and algebras with translation invariant (except, maybe , finite number) defining relationships. As an illustration of this method, we give one approach…

Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…

For the planar four-vortex problem, we show that there are finitely many stationary configurations consisting of equilibria, rigidly translating configurations, relative equilibria (uniformly rotating configurations) and collapse…

We use planar 4-valent graphs and a graphical calculus involving such graphs to construct an invariant for balanced-oriented, knotted 4-valent graphs. Our invariant is an extension of the $sl(n)$ polynomial for classical knots and links. We…

We develop a calculus of surgery data, called bridged links, which involves besides links also pairs of balls that describe one-handle attachements. As opposed to the usual link calculi of Kirby and others this description uses only…

Moduli spaces of planar polygonal linkages admit a cell structure which can be realized as a surgery on the permutohedron. We present a 3D visualization of the result of the surgery for all types of non-degenerate pentagonal linkages.

We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…

We provide a geometric approach to two combinatorically symmmetric overconstrained spatial linkages. Both contain eight bodies and twelve revolute joints and collapse in aligned poses. The first one is spherical and the union of six…

In the context of higher gauge theory, we construct a flat and fake flat 2-connection, in the configuration space of $n$ particles in the complex plane, categorifying the Knizhnik-Zamolodchikov connection. To this end, we define the…

We study relaxations for linear programs with complementarity constraints, especially instances whose complementary pairs of variables are not independent. Our formulation is based on identifying vertex covers of the conflict graph of the…

Recent entity and relation extraction works focus on investigating how to obtain a better span representation from the pre-trained encoder. However, a major limitation of existing works is that they ignore the interrelation between spans…

In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators…

Two distinct systems of commutative complex numbers in 6 dimensions of the polar and planar types of the form u=x_0+h_1x_1+h_2x_2+h_3x_3+h_4x_4+h_5x_5 are described in this work, where the variables x_0, x_1, x_2, x_3, x_4, x_5 are real…

For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the…

We study a particular class of states of a bipartite system consisting of two 4-level parties. By means of an adapted extended reduction criterion we associate their entanglement properties to the geometric patterns of a planar lattice…

This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…