Superficies mínimas: Introducción a la teoría estructural de Colding y Minicozzi.
Gamma processes are a special case of subordinators (increasing Lévy processes). Their increasing nature makes them particularly well-suited for modeling risk insurance problems of cumulative claims (see, for example, Risk Theory with the Gamma Process (177–192)), monotonic degradation (see, for example, Survival in Dynamic Environments (86–103)), and so on. In the latter reference, the authors use the gamma process to model cumulative claims in risk processes. They also tabulated the probabilities of ruin for the standardized gamma process.
This presentation follows on from article Diffusion Approximation of Gamma Processes in Semi-Markov Random Media. We consider gamma processes in random media (environment) represented by semi-Markovian processes. We approximate these gamma processes using diffusion processes. We first obtain an average result, which will serve as an equilibrium, and then the diffusion approximation. This is a diffusion approximation with equilibrium or normal deviation of the gamma process in semi-Markovian random media. The tools used here differ from those employed in the case of Markov (see a previous article by the first author [Normal Deviation of Gamma Processes in Random Environment With Applications]) because we do not have semigroups. Applications are also discussed.
In this talk, we study elliptic helicoidal translating solitons of the mean curvature flow in three-dimensional Minkowski space, that is, helicoidal translators whose axis is timelike. By expressing the generating curve in terms of its Frenet frame, we reformulate the translator equation in terms of curvature and support functions, obtaining a planar system of ordinary differential equations. We then employ techniques from the qualitative theory of dynamical systems, together with an inversion that transforms the dynamics at infinity into a bounded region, to investigate the equilibrium points and the global behavior of the phase portrait. A bifurcation occurs at the critical pitch value $h=2$, where the number of equilibrium points increases from two to six. This analysis leads to a complete classification of the corresponding translating solitons and a description of their causal characters. Our results illustrate how dynamical systems techniques provide an effective framework for understanding the geometry and global structure of helicoidal translators in Lorentzian settings.
This talk presents a novel latent Markov model with Plackett-Luce emission distributions for the analysis of longitudinal ranking data. The proposed framework models preference dynamics through a finite number of latent preference regimes, allowing for abrupt changes in individual ranking behavior rather than assuming smooth temporal evolution. Individuals transition between latent states over time according to a first-order Markov process, capturing unobserved heterogeneity in preference trajectories. Model parameters are estimated by maximum likelihood via an Expectation-Maximization (EM) algorithm. An application to experimental task scheduling data illustrates the ability of the proposed model to identify distinct behavioral profiles, characterize temporal heterogeneity, and detect individual transitions between latent preference regimes.
This talk presents the Fairness Uncertainty-Aware Classification Tree (FUNACT), a novel in-processing framework that extends the classical CART algorithm to jointly optimize predictive accuracy and algorithmic fairness. The proposed approach explicitly accounts for the statistical uncertainty associated with fairness estimation by constructing confidence intervals for group fairness metrics, such as statistical parity, at each candidate split. Splits exhibiting statistically significant fairness violations, identified when the corresponding confidence interval excludes zero, are penalized through a graduated adjustment of the Information Gain criterion. A tunable regularization parameter allows us to flexibly balance predictive performance and fairness according to the application context. Experimental results on both synthetic and benchmark datasets show that FUNACT effectively mitigates algorithmic bias while preserving the transparency, interpretability, and computational efficiency of decision trees.
A logical model of the intracellular signaling network in CD8+ T cells was developed, formalized as a Boolean dynamical system, to investigate the influence of interleukin-2 (IL-2) and its engineered muteins on cell fate decisions. The model was implemented via continuous-time stochastic simulation using a Markov chain framework, explicitly representing the three IL-2 receptor subunits and antigen-presenting cell (APC) signaling inputs. Systematic attractor analysis identified eleven stable steady states — null, memory, and effector phenotypes — and differentiation probabilities were computed across distinct input configurations. The system exhibits multistability: bistability under IL-2+APC stimulation, monostability toward the effector attractor under NASB+APC, and monostability toward the memory attractor under NA+APC. Sensitivity analysis over the network topology identified CD28, FOXO, AMPK, and SATB1 as critical nodes governing attractor selection and cell fate determination.
Abstract: The geometric formulation of thermodynamics has a long history, from Gibbs to Carathéodory to the more recent developments in contact and information geometry. In this talk I will give a panoramic view of the latter, focusing on how differential geometry provides a natural language for understanding equilibrium and non‑equilibrium phenomena. I will begin by introducing the structures underlying information geometry, presenting several recent results along the way. The talk will be self‑contained and aims to show how geometry offers a unified framework to study thermodynamics, stochastic dynamics, and information theory.