Related papers: On the d-complexity of strings
We introduce a method to estimate the complexity function of symbolic dynamical systems from a finite sequence of symbols. We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly.…
The past year has seen enormous progress in string theory. It has become clear that all of the different string theories are different limits of a single theory. Moreover, in certain limits, one obtains a new, eleven-dimensional structure…
We argue that string theory should have a formulation for which stability and causality are evident. Rather than regard strings as fundamental objects, we suggest they should be regarded as composite systems of more fundamental point-like…
I review work developing the idea that string is a composite of point-like entities called string bits. Old and new insights this picture brings into the nature of string theory are discussed. This paper summarizes my talk presented to the…
We give a lightning introduction to critical string theory, including the 26-dimensional bosonic string, the 10-dimensional superstrings and heterotic strings with and without spacetime supersymmetry. We also discuss open strings and…
A two-dimensional configuration is a coloring of the infinite grid Z^2 with finitely many colors. For a finite subset D of Z^2, the D-patterns of a configuration are the colored patterns of shape D that appear in the configuration. The…
Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
String theory in d dimensions has n+1=11-d parameters that may be thought of as being inherited from the geometry of an n+1 torus which may be used to construct the theory using dimensional reduction from eleven dimensions. We give the…
In this paper, which is a revised version of the author's PhD thesis, we analyze two different applications of string theory. In the first part, we focus on four dimensional compactifications of Type II string theories preserving N=1…
This is an introduction to the non-perturbative excitations of string theory known as D-branes. Topics covered include their definition and main properties, their role in dualities and their dynamics. Based on lectures given at LACES 2019,…
The subword complexity of a word $w$ over a finite alphabet $\mathcal{A}$ is a function that assigns for each positive integer $n$, the number of distinct subwords of length $n$ in $w$. The subword complexity of a word is a good measure of…
Using the theory of Kolmogorov complexity the notion of facticity {\phi}(x) of a string is defined as the amount of self-descriptive information it contains. It is proved that (under reasonable assumptions: the existence of an empty machine…
A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…
The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…