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A fast algorithm for counting intersections of two normal curves on a triangulated surface is proposed. It yields a convenient way for treating mapping class groups of punctured surfaces by presenting mapping classes by matrices, and the…
We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.
Goldbach partitions can be used in creation of ellipses and circles on the number line. We extend this work and determine the count and other properties of concentric Goldbach circles for different values of n. The autocorrelation function…
We show that the cycle relation between Dehn twists about curves in a circuit detects whether the circuit bounds an embedded disc. This is done by determining the isomorphism type of the group generated by said Dehn twists for various…
Understanding the structure of relationships between objects in a given database is one of the most important problems in the field of data mining. The structure can be defined for a set of single objects (clustering) or a set of groups of…
We present a method for the calculation of electronic structure of systems that contain tens of thousands of atoms. The method is based on the division of the system into mutually overlapping fragments and the representation of the…
This paper presents a decomposition method for solving elliptic boundary value problems in one-dimension. The method is an improvement to an existing technique for approximating elliptic systems. It is demonstrated to be computationally…
We show that one can define through the symmetry approach a procedure to check the linearizability of a difference equation via a point or a discrete Cole-Hopf transformation. If the equation is linearizable the symmetry provides the…
We outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete…
We describe a simple, but effective, method for deriving families of elliptic curves, with high rank, all of whose members have the same torsion subgroup structure.
A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…
Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise…
The problem of large-scale correlations of particles produced in high-energy collisions is discussed. Among them are, e.g., those correlations which lead to ring-like and elliptic flow shapes of individual high-multiplicity events in the…
In this short note we prove a formula for local heights on elliptic curves over number fields in terms of intersection theory on a regular model over the ring of integers.
A sufficient condition for entanglement in two-mode continuous systems is constructed based on interference visibility and the uncertainty of the total particle number. The observables to be measured (particle numbers and particle number…
We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of $p$ elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first $N$…
Classical entanglement refers to non-separable correlations between the polarization direction and the polarization amplitude of a light field. The degree of entanglement is quantified by the Schmidt number, taking the value of unity for a…
Networks (or graphs) are used to model the dyadic relations between entities in a complex system. In cases where there exists multiple relations between the entities, the complex system can be represented as a multilayer network, where the…
We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…
We consider diagrams of links in $S^2$ obtained by projection from $S^3$ with the Hopf map and the minimal crossing number for such diagrams. Knots admitting diagrams with at most one crossing are classified. Some properties of these knots…