Related papers: String-to-String Interpretations with Polynomial-S…
Self-attention is an attention mechanism that learns a representation by relating different positions in the sequence. The transformer, which is a sequence model solely based on self-attention, and its variants achieved state-of-the-art…
The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies…
We study the modular invariance of strings on pp-waves with RR-flux. We explicitly show that the one-loop partition functions of the maximally supersymmetric pp-waves and their orbifolds can be modular invariant in spite of the mass terms…
It is well-known that the SO(32) and $E_8\times E_8$ heterotic strings can be continuously connected to each other in nine dimensions. Since the strong-coupling duals of these theories are respectively the SO(32) Type I theory and M-theory…
In these lectures we give a brief introduction to perturbative and non-perturbative string theory. The outline is the following: 1. Introduction to perturbative string theory 1.1 From point particle to extended objects 1.2 Free closed and…
We extend the structure of string topology from mapping spaces to embedding spaces $Emb(S^n,M)$. This extension comes from an action of the cleavage operad, a coloured $E_{n+1}$-operad. For all values of $n \in \mathbb{N}$, this gives an…
There are at present two known string theories in $(2,2)$ dimensions. One of them is the well known $N=2$ string, and the other one is a more recently constructed $N=1$ spacetime supersymmetric string. They are both based on certain…
An exponent-string is an extension of traditional strings that can incorporate real-numbered exponents, indicating the quantity of characters. This novel representation overcomes the limitations of traditional discrete string by enabling…
N=2 heterotic strings may provide a window into the physics of M-theory radically different than that found via the other supersymmetric string theories. In addition to their supersymmetric structure, these strings carry a four-dimensional…
We analyse the dipole solution of heterotic string theory in four dimensions. It has the structure of monopole and anti-monopole connected by flux line (string). Due to growing coupling near the poles, the length of the string diverges.…
Sequentiable structures are a subclass of monoids that generalise the free monoids and the monoid of non-negative real numbers with addition. In this paper we consider functions $f:\Sigma^*\rightarrow {\cal M}$ and define the Myhill-Nerode…
We review the status of solitons in superstring theory, with a view to understanding the strong coupling regime. These {\it solitonic} solutions are non-singular field configurations which solve the empty-space low-energy field equations…
A new approach to the computation of correlation functions involving two determinant operators as well as one non-protected single trace operator has recently been developed by Jiang, Komatsu and Vescovi. This correlation function provides…
We study the expressive power and succinctness of order-invariant sentences of first-order (FO) and monadic second-order (MSO) logic on structures of bounded tree-depth. Order- invariance is undecidable in general and, thus, one strives for…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…
Laminar set systems consist of non-crossing subsets of a universe with set inclusion essentially corresponding to the descendant relationship of a tree, the so-called laminar tree. Laminar set systems lie at the core of many graph…
We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers,…
We show that the equivalence of deterministic linear top-down tree-to-word transducers is decidable in polynomial time. Linear tree-to-word transducers are non-copying but not necessarily order-preserving and can be used to express XML and…
A simple sparse coding mechanism appears in the sensory systems of several organisms: to a coarse approximation, an input $x \in \R^d$ is mapped to much higher dimension $m \gg d$ by a random linear transformation, and is then sparsified by…
We find nonlocal particle theories with two dimensional conformal symmetry, including examples equivalent to the bosonic open string and closed string. This work provides a new approach to construct solvable consistent backgrounds in string…