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We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems,…
We study the strong convergence and bounded perturbation resilience of iterative algorithms based on the Generalized Modular String-Averaging (GMSA) procedure for infinite sequences of input operators under a general admissible control.…
R2 score is the standard metric for evaluating regression tasks, offering a normalized magnitude-agnostic measure of accuracy that captures variance. However, R2 has three key limitations: it is limited to at most two dimensional inputs, it…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
Irreversible adsorption of spheres on flat collectors having dimension $d<2$ is studied. Molecules are adsorbed on Sierpinski's Triangle and Carpet like fractals ($1<d<2$), and on General Cantor Set ($d<1$). Adsorption process is modeled…
These lectures present some topics of string phenomenology and contain two parts. In the first part, I review the possibility of lowering the string scale in the TeV region, that provides a theoretical framework for solving the mass…
Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…
I discuss several aspects of strings as unified theories. After recalling the difficulties of the simplest supersymmetric grand unification schemes I emphasize the distinct features of string unification. An important role in constraining…
This article presents effective (dynamic) algorithm for solving a problem of counting the number of substrings of given string which are also substrings of second string. Presented algorithm can be used for example for quick calculation of…
We consider correlation functions in Neveu--Schwarz string theory coupled to two dimensional gravity. The action for the 2D gravity consists of the string induced Liouville action and the Jackiw--Teitelboim action describing pure 2D…
We review some examples of heterotic/type II string duality which shed light on the infrared dynamics of string compactifications with N=2 and N=1 supersymmetry in four dimensions.
In this paper we present $LCSk$++: a new metric for measuring the similarity of long strings, and provide an algorithm for its efficient computation. With ever increasing size of strings occuring in practice, e.g. large genomes of plants…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
In this dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. Part one is devoted to the study of string universality in high spacetime dimensions.…
Graphs are a powerful tool for analyzing large data sets, but many real-world phenomena involve interactions that go beyond the simple pairwise relationships captured by a graph. In this paper we introduce and study a simple combinatorial…
We review some of the recent developments in the construction of $W$-string theories. These are generalisations of ordinary strings in which the two-dimensional ``worldsheet'' theory, instead of being a gauging of the Virasoro algebra, is a…
Kolmogorov complexity measures the algorithmic complexity of a finite binary string $\sigma$ in terms of the length of the shortest description $\sigma^*$ of $\sigma$. Traditionally, the length of a string is taken to measure the amount of…
This study investigates the learnability of Recurrent Neural Networks (RNNs) in classifying structured formal languages, focusing on counter and Dyck languages. Traditionally, both first-order (LSTM) and second-order (O2RNN) RNNs have been…