Related papers: On inversion formulas and Fibonomial coefficients
An inverse problem for the wave equation outside an obstacle with a {\it dissipative boundary condition} is considered. The observed data are given by a single solution of the wave equation generated by an initial data supported on an open…
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in…
A lot of recent machine learning research papers have ``open-ended learning'' in their title. But very few of them attempt to define what they mean when using the term. Even worse, when looking more closely there seems to be no consensus on…
This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor…
The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) There exists a bi-orderable, two-generated recursively presented solvable group…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…
The design of any technical Computer Science course must involve its context within the institution's CS program, but also incorporate any new material that is relevant and appropriately accessible to students. In many institutions, theory…
Causal discovery studies the problem of mining causal relationships between variables from data, which is of primary interest in science. During the past decades, significant amount of progresses have been made toward this fundamental data…
The split covariance intersection filter (split CIF) is a useful tool for general data fusion and has the potential to be applied in a variety of engineering tasks. An indispensable optimization step (referred to as w-optimization) involved…
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…
Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any…
In this paper we introduce the convex fragment of {\L}ukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
There is a cognitive limit in Human Mind. This cognitive limit has played a decisive role in almost all fields including computer sciences. The cognitive limit replicated in computer sciences is responsible for inherent Computational…
In its most general form, a `secret objective' is any inconsistency between the experimental reality and the information provided to students prior to starting work on an experiment. Students are challenged to identify the secret objectives…
The declared goal of this paper is to fill this gap: "... cognitive systems research needs questions or challenges that define progress. The challenges are not (yet more) predictions of the future, but a guideline to what are the aims and…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…