Related papers: A newly-generalized problem from a problem for the…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
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…
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…
We present a method for the solution of polynomial equations. We do not intend to present one more method among several others, because today there are many excellent methods. Our main aim is educational. Here we attempt to present a method…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
In this short paper we present an algorithm for finding a solution to a generalized Sudoku.
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…
A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…
An Ito formula is developed in a context consistent with the development of abstract existence and unique- ness theorems for nonlinear stochastic partial differential equations, which are singular or degenerate. This is a generalization of…
We survey the concept of multiplicativity from its initial appearance in the theory of Poisson-Lie groups to the far-reaching generalizations, for multivectors and differential forms in the geometry and the generalized geometry of Lie…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in…
Game semantics and winning strategies offer a potential conceptual bridge between semantics and proof systems of logics. We illustrate this link for hybrid logic -- an extension of modal logic that allows for explicit reference to worlds…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
Motivated by the recent 10 million dollar AIMO challenge, this paper targets the problem of finding all functions conforming to a given specification. This is a popular problem at mathematical competitions and it brings about a number of…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…