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Nonograms are a popular type of puzzle, where an arrangement of curves in the plane (in the classic version, a rectangular grid) is given together with a series of hints, indicating which cells of the subdivision are to be colored. The…
Many complex chemical problems encoded in terms of physics-based models become computationally intractable for traditional numerical approaches due to their unfavourable scaling with increasing molecular size. Tensor decomposition…
Transformer-decoder language models are a core innovation in text based generative artificial intelligence. These models are being deployed as general-purpose intelligence systems in many applications. Central to their utility is the…
We discuss well known geometric constructions via paper-folding. The note is written primary for school students.
Malleable Glyph is a new visualization problem and a public challenge. It originated from UX research (namely from research on card sorting UX), but its applications can be diverse (UI, gaming, information presentation, maps, and others).…
We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…
The success of Large Language Models (LLMs) in human-AI collaborative decision-making hinges on their ability to provide trustworthy, gradual, and tailored explanations. Solving complex puzzles, such as Sudoku, offers a canonical example of…
Jigsaw puzzle solving is an intriguing problem which has been explored in computer vision for decades. This paper focuses on a specific variant of the problem - solving puzzles with eroded boundaries. Such erosion makes the problem…
Solving Sudoku puzzles is one of the most popular pastimes in the world. Puzzles range in difficulty from easy to very challenging; the hardest puzzles tend to have the most empty cells. The current paper explains and compares three…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are…
Can outreach inspire and lead to research and vice versa? In this work, we introduce our approach to the gamification of research in mathematics and computer science through three illustrative examples. We discuss our primary motivations…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Novel user interfaces based on artificial intelligence, such as natural-language agents, present new categories of engineering challenges. These systems need to cope with uncertainty and ambiguity, interface with machine learning…
We discuss fun problems, vaguely related to notions and theorems of a course in differential geometry. This paper can be regarded as a weekend "treasure chest" supplementing the course weekday lecture notes. The problems and solutions are…