Juridifcation of the Concept of “Artifcial intelligence” and the Limits of the Use of Artifcial Intelligence Technology in the Judicial Process

The active development of artificial intelligence (AI) technology poses the question of how to integrate this phenomenon into legal reality, about the limits of using this technology in social practices regulated by law, and ultimately about developing an optimal model of legal regulation of AI. The paper focuses on the problem of developing the legal content of the concept of AI, including some methodological and ontological foundations of such work. The author brings to the scientific discussion certain constant characteristics of AI that are significant for legal regulation, which, if adopted by the legal scientific community, could be used as a scientifically sound basis for constructing specific variants of legal regulation that meet the needs of a particular sphere of social practice. The author believes that the scientifically based legal concept of AI is largely able to determine the direction and scope of applied legal research on the multidimensional problems of using AI technology in social interaction practices, including in the administration of justice, to distinguish the legal issues and problems related to this from ethical, philosophical, technological and other issues.According to the author, the task of forming the legal concept of AI is not limited to the formulation of specific legal definitions and cannot be solved at this level. The result of the juridification of the concept of AI should be a set of unchangeable (constant) legal characteristics, while specific definitions of this term in regulations may differ depending on the needs of legal regulation practice. In the work on the formation of a legally significant concept of AI, it is proposed to abandon the descriptive essentialist approach aimed at identifying the essence of AI in favor of an ascriptive constructivist approach, which involves attributing to the content of the concept of AI those legal properties that, on the one hand, are significant for the purposes of legal regulation, and on the other hand, limit the limits of legal regulation.

Constrained nonsmooth problems of the calculus of variations

The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric constraints. To derive optimality conditions, we study generalised concepts of differentiability of nonsmooth functions called codifferentiability and quasidifferentiability. Under some natural and easily verifiable assumptions we prove that a nonsmooth integral functional defined on the Sobolev space is continuously codifferentiable and compute its codifferential and quasidifferential. Then we apply general optimality conditions for nonsmooth optimisation problems in Banach spaces to obtain optimality conditions for nonsmooth problems of the calculus of variations. Through a series of simple examples we demonstrate that our optimality conditions are sometimes better than existing ones in terms of various subdifferentials, in the sense that our optimality conditions can detect the non-optimality of a given point, when subdifferential-based optimality conditions fail to disqualify this point as non-optimal.

The Need To Visualize Sudoku

<div>Sudoku puzzles are easily solved using backtracking algorithms. Yet, literature is scattered with various shy and often opaque attempts at using evolutionary algorithms and hybridizing them with known strategies of solving the puzzle. Evolutionary methods are serendipitous in nature, and this paper demonstrates the behaviour of such serendipity under constraints, using visuals that depict the sheer magnitude of the problem space and the nature in which intertwined constraints affect the scope for locating a solution, with the hope that it could inspire a new way of looking at the problem. We propose a method of visualizing the sudoku fitness landscape, the vastness and complexity of even partially brute forcing the puzzle, and a unique method of mutating puzzle states using circular swaps. These insights could potentially serve as a link to comprehend the problem space when designing solutions for vast, multidimensional problems. Additionally, finding the optimal solution for some puzzles was notably harder, compared to puzzles in the same category of given clues. A short investigation was conducted into this phenomenon, which revealed hints that compel us to propose that the direction of research that should be taken, is in discovering more about puzzle states and definitive mathematical properties of the puzzle, rather than merely designing brute-force, stochastic or hybrid approaches of finding solutions.</div>

The Need To Visualize Sudoku

<div>Sudoku puzzles are easily solved using backtracking algorithms. Yet, literature is scattered with various shy and often opaque attempts at using evolutionary algorithms and hybridizing them with known strategies of solving the puzzle. Evolutionary methods are serendipitous in nature, and this paper demonstrates the behaviour of such serendipity under constraints, using visuals that depict the sheer magnitude of the problem space and the nature in which intertwined constraints affect the scope for locating a solution, with the hope that it could inspire a new way of looking at the problem. We propose a method of visualizing the sudoku fitness landscape, the vastness and complexity of even partially brute forcing the puzzle, and a unique method of mutating puzzle states using circular swaps. These insights could potentially serve as a link to comprehend the problem space when designing solutions for vast, multidimensional problems. Additionally, finding the optimal solution for some puzzles was notably harder, compared to puzzles in the same category of given clues. A short investigation was conducted into this phenomenon, which revealed hints that compel us to propose that the direction of research that should be taken, is in discovering more about puzzle states and definitive mathematical properties of the puzzle, rather than merely designing brute-force, stochastic or hybrid approaches of finding solutions.</div>

The Need to Visualize Sudoku

Sudoku puzzles are easily solved using backtracking algorithms. Yet, literature is scattered with various shy and often opaque attempts at using evolutionary algorithms and hybridizing them with known strategies of solving the puzzle. Evolutionary methods are serendipitous in nature, and this paper demonstrates the behaviour of such serendipity under constraints, using visuals that depict the sheer magnitude of the problem space and the nature in which intertwined constraints affect the scope for locating a solution, with the hope that it could inspire a new way of looking at the problem. We propose a method of visualizing the sudoku fitness landscape, the vastness and complexity of even partially brute forcing the puzzle, and a unique method of mutating puzzle states using circular swaps. These insights could potentially serve as a link to comprehend the problem space when designing solutions for vast, multidimensional problems. Additionally, finding the optimal solution for some puzzles was notably harder, compared to puzzles in the same category of given clues. A short investigation was conducted into this phenomenon, which revealed hints that compel us to propose that the direction of research that should be taken, is in discovering more about puzzle states and definitive mathematical properties of the puzzle, rather than merely designing brute-force, stochastic or hybrid approaches of finding solutions.

Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

In this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problems.

Crank-Nicholson difference scheme for the system of nonlinear parabolic equations observing epidemic models with general nonlinear incidence rate

<abstract><p>In this work, we study second order Crank-Nicholson difference scheme (DS) for the approximate solution of problem (1). The existence and uniqueness of the theorem on a bounded solution of Crank-Nicholson DS uniformly with respect to time step $ \tau $ is proved. In practice, theoretical results are presented on four systems of nonlinear parabolic equations to explain how it works on one and multidimensional problems. Numerical results are provided.</p></abstract>

Pandemic effect on the elderly and their caregivers

COVID-19 pandemic forced governments to enact mobility restrictions to contain the spread of infection. Elderly, especially those with co-morbidities, are highly susceptible to infections. Hence, reverse quarantine measures have been enacted to protect the elderly. The barriers in social connectedness have an impact on the mental and physical well-being of the elderly. Stress, anxiety, anger, confusion, depression, and suicidal tendencies are reported among the elderly kept in social isolation. Apart from the elderly, their family caregivers also go through similar physical and psycho-social stress. Many times, the caregivers are also having additional responsibilities of childcare and homeschooling during the pandemic time. The authors outline the various intricate issues and dimensions of the pandemic's effect on the elderly and their caregivers. Various feasible strategies to address these multidimensional problems faced by the elderly and their caregivers during the pandemic time, like mobile-based mindfulness meditation training, spiritual support, telephone-based psychotherapy, telehealth services, physical exercise promotion, and social support measures, are recommended.