Related papers: Non-Archimedean analysis, T-functions, and cryptog…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
In distributed function computation, each node has an initial value and the goal is to compute a function of these values in a distributed manner. In this paper, we propose a novel token-based approach to compute a wide class of target…
Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type…
We identify fragments of the arithmetic $S_1$ that enjoy nice closure properties and have exact characterization of their definable multifunctions. To do this, in the language of $S_1$, $L_1$, starting from the formula classes,…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
We present a general method to convert algorithms into faster algorithms for almost-regular input instances. Informally, an almost-regular input is an input in which the maximum degree is larger than the average degree by at most a constant…
The paper develops a novel approach to stream cipher design: Both the state update function and the output function of the corresponding pseudorandom generators are compositions of arithmetic and bitwise logical operations, which are…
I would like to tell a story. A story about a beautiful mathematical relationship that elucidates the computational view on the classic subject of trigonometry. All stories need a language, and for this particular story an algorithmic…
We describe an efficient iterative algorithm for the computation of theta functions of non-archimedean Schottky groups and, more generally, of (non-archimedean) discontinuous groups.
Call graphs depict the static, caller-callee relation between "functions" in a program. With most source/target languages supporting functions as the primitive unit of composition, call graphs naturally form the fundamental control flow…
The operational semantics of a programming language is said to be small-step if each transition step is an atomic computation step in the language. A semantics with this property faithfully corresponds to the implementation of the language.…
Temporal-difference learning with gradient correction (TDC) is a two time-scale algorithm for policy evaluation in reinforcement learning. This algorithm was initially proposed with linear function approximation, and was later extended to…
This paper is about certain string-to-string functions, called the polyregular functions. These are like the regular string-to-string functions, except that they can have polynomial (and not just linear) growth. The class has four…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
Let $\mathbb{F}_q(T)$ be the field of rational functions in one variable over a finite field. We introduce the notion of a totally $T$-adic function: one that is algebraic over $\mathbb{F}_q(T)$ and whose minimal polynomial splits…
Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function. The arithmetic sum…
Text-to-image (T2I) research has grown explosively in the past year, owing to the large-scale pre-trained diffusion models and many emerging personalization and editing approaches. Yet, one pain point persists: the text prompt engineering,…
Formal grammars are extensively used in Computer Science and related fields to study the rules which govern production of a language. The use of these grammars can be extended beyond mere language production. One possibility is to view…
Text-and-Image-To-Image (TI2I), an extension of Text-To-Image (T2I), integrates image inputs with textual instructions to enhance image generation. Existing methods often partially utilize image inputs, focusing on specific elements like…
While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…