Related papers: An Experimental Mathematics Approach to Several Co…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past…
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…
We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
Combinatorial problems such as combinatorial optimization and constraint satisfaction problems arise in decision-making across various fields of science and technology. In real-world applications, when multiple optimal or…