Related papers: On tabulating virtual strings
This paper gives a polynomial invariant for flat virtual links. In the case of one component, the polynomial specializes to Turaev's virtual string polynomial. We show that Turaev's polynomial has the property that it is non-zero precisely…
While there exist many methods in machine learning for comparison of letter string data, most are better equipped to handle strings that represent natural language, and their performance will not hold up when presented with strings that…
By adding or removing appropriate structures to Gauss diagram, one can create useful objects related to virtual links. In this paper few objects of this kind are studied: twisted virtual links generalizing virtual links; signed chord…
I study a relativistic open string coupling through its endpoints to a plane wave with arbitrary temporal profile. The string's transverse oscillations respond linearly to the external field. This makes it possible to solve the classical…
An important concept in digital geometry for computer imagery is that of tunnel. In this paper we obtain a formula for the number of tunnels as a function of the number of the object vertices, pixels, holes, connected components, and 2x2…
A simple graph is called triangular if every edge of it belongs to a triangle. We conjecture that any graphical degree sequence all terms of which are greater than or equal to 4 has a triangular realisation, and establish this conjecture…
Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection…
The Turaev-Viro invariant is defined as a certain state sum calculated on an arbitrary simple spine of a 3-manifold. We specify each term of the sum as 0-term, 1-term or 2-term such that each sum of the terms having the same type is an…
Virtual racks and virtual quandles are nonassociative algebraic structures based on the Reidemeister moves of virtual knots. In this note, we enumerate virtual dihedral quandles and several families of virtual permutation racks and virtual…
The phenomenon of six degrees of separation is an old but interesting problem. The considerations of the clustering coefficient reflecting triangular structures and its extension to square one to six degrees of separation have been…
In this talk, based on work done in collaboration with G. Landi and R.J Szabo, I will review how string theory can be considered as a noncommutative geometry based on an algebra of vertex operators. The spectral triple of strings is…
In this letter we present an operator formalism for Closed String Field Theory based on closed half-strings. Our results indicate that the restricted polyhedra of the classical non-polynomial string field theory, can be represented as…
String theory in two-dimensional spacetime illuminates two main threads of recent development in string theory: (1) Open/closed string duality, and (2) Tachyon condensation. In two dimensions, many aspects of these phenomena can be explored…
We show that the Casson knot invariant, linking number and Milnor's triple linking number, together with a certain 2-string link invariant $V_2$, are necessary and sufficient to express any string link Vassiliev invariant of order two.…
We define the cohomogeneity one string, string with continuous symmetries, as its world surface is tangent to a Killing vector field of a target space. We classify the Killing vector fields by an equivalence relation using isometries of the…
We propose new topological vertex formalism for Type IIB $(p,q)$ 5-brane web with an O5-plane. We apply our proposal to 5d $\mathcal{N}=1$ Sp(1) gauge theory with $N_f=0,1,8$ flavors to compute the topological string partition functions and…
We investigate the variation of the string field action under changes of the string field vertices giving rise to different decompositions of the moduli spaces of Riemann surfaces. We establish that any such change in the string action…
We consider the group of unrestricted virtual braids, describe its structure and explore its relations with fused links. Also, we define the groups of flat virtual braids and virtual Gauss braids and study some of their properties, in…
We start from a quantum computational principle suggested for string theory in a previous paper and discuss how it might lead to a dynamical principle implying the correct classical gravitational limit. Besides this, we briefly look at some…
We present a new representation of the string vertices of the cubic open string field theory. By using this three-string vertex, we attempt to identify open string fields as huge-sized matrices by following Witten's idea. By using these…