The early historical roots of Lee-Yang theorem

A deep and detailed historiographical analysis of a particular case study concerning the so-called Lee-Yang theorem of theoretical statistical mechanics of phase transitions, has emphasized what real historical roots underlie such a case study. To be precise, it turned out that some well-determined aspects of entire function theory have been at the primeval origins of this important formal result of statistical physics.Comment: History of Physics case study. arXiv admin note: substantial text overlap with arXiv:1106.4348, arXiv:math/0601653, arXiv:0809.3087, arXiv:1311.0596 by other author

Comparisons of Heterogeneous Distributions and Dominance Criteria

We are interested in the comparisons of standard-of-living across societies when observations of both income and household structure are available. We generalise the approach of Atkinson and Bourguignon (1987) to the case where the marginal distributions of needs can vary across the household populations under comparison. We assume that a sympathetic observer uses a utilitarian social welfare function in order to rank heterogeneous income distributions. Insofar as any individual can play the role of the observer, we take the unanimity point of view according to which the planner’s judgements have to comply with a certain number of basic normative principles. We impose increasingly restrictive conditions on the household’s utility function and we investigate their effects on the resulting rankings of the distributions. This leads us to propose four dominance criteria that can be used for providing an unambiguous ranking of income distributions for heterogeneous populations.Normative Analysis, Utilitarianism, Welfarism, Multidimensional Inequality and Welfare, Bidimensional Stochastic Dominance, Inequality Reducing Transformations.

Boosting AND/OR-Based Computational Protein Design: Dynamic Heuristics and Generalizable UFO

Scientific computing has experienced a surge empowered by advancements in technologies such as neural networks. However, certain important tasks are less amenable to these technologies, benefiting from innovations to traditional inference schemes. One such task is protein re-design. Recently a new re-design algorithm, AOBB-K*, was introduced and was competitive with state-of-the-art BBK* on small protein re-design problems. However, AOBB-K* did not scale well. In this work we focus on scaling up AOBB-K* and introduce three new versions: AOBB-K*-b (boosted), AOBB-K*-DH (with dynamic heuristics), and AOBB-K*-UFO (with underflow optimization) that significantly enhance scalability.Comment: In proceedings of the 39th Conference on Uncertainty in Artificial Intelligence (UAI 2023) and published in Proceedings of Machine Learning Research (PMLR

Parameter recovery vs. parameter prediction for the Weibull distribution validated for Scots pine stands in Finland

201

A Contribution to Metric Diophantine Approximation : the Lebesgue and Hausdorff Theories

This thesis is concerned with the theory of Diophantine approximation from the point of view of measure theory. After the prolegomena which conclude with a number of conjectures set to understand better the distribution of rational points on algebraic planar curves, Chapter 1 provides an extension of the celebrated Theorem of Duffin and Schaeffer. This enables one to set a generalized version of the Duffin–Schaeffer conjecture. Chapter 2 deals with the topic of simultaneous approximation on manifolds, more precisely on polynomial curves. The aim is to develop a theory of approximation in the so far unstudied case when such curves are not defined by integer polynomials. A new concept of so–called “liminf sets” is then introduced in Chapters 3 and 4 in the framework of simultaneous approximation of independent quantities. In short, in this type of problem, one prescribes the set of integers which the denominators of all the possible rational approximants of a given vector have to belong to. Finally, a reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in chapter 5. This provides the first example of a Khintchine type result in the context of so–called uniform approximation

Modular forms and lattice point counting problems

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 14-12-201