Noticias en español
Shortest Odd path on undirected graphs with conservative weights.
Abstract: We consider the Shortest Odd Path (SOP) problem, where given an undirected graph $G$, a weight function on its edges, and two vertices $s$ and $t$ in $G$, the aim is to find an $(s,t)$-path with odd length and, among all such paths, of minimum weight. For the case when the weight function is conservative, i.e., when every cycle has non-negative total weight, the complexity of the SOP problem had been open for 20 years, and was recently shown to be NP-hard. I’ll present a polynomial-time algorithm for the special case when the weight function is conservative and the set of...
Read MoreThe k-Yamabe flow and its solitons.
Abstract: The Yamabe problem is a classical question in conformal geometry that seeks for existence of metrics with constant scalar curvature within a conformal class. The problem was posed by H. Yamabe in 1960 as a possible extension of the famous uniformization theorem, which states that every simply connected Riemann surface is conformally equivalent to the open unit disk, the complex plane or the Riemann sphere. After the conjecture was already confirmed by the work of R. Schoen, an alternative approach was proposed by R.Hamilton in 1989. He suggested to use a geometric flow, which is...
Read MoreStatistical, mathematical, and computational methods for the advancement of ecology and climate change biology.
Abstract: I will delve into three key topics of my research in quantitative ecology and how the outcomes contribute to understanding and preventing biodiversity loss. In each case, I will describe the ecological context, the data at hand, and the primary modeling tools used to address the problems of interest. First, I will talk about optimal survey design, which involves techniques to efficiently estimate population density by balancing sample size, spatial distribution, and survey effort. Next, I will explain how statistical calibration techniques are applied for error correction and data...
Read MoreA stroll through monotone inclusion problems and their splitting algorithms.
Abstract: Many situations in convex optimization can be modeled as the problem of finding a zero of a monotone operator, which can be regarded as a generalization of the gradient of a differentiable convex function. In order to numerically address this monotone inclusion problem it is vital to be able to exploit the inherent structure of the monotone operator defining it. The algorithms in the family of the splitting methods are able to do this by iteratively solving simpler subtasks which are defined by separately using some parts of the original problem. In this talk, we will introduce...
Read MoreManifold Learning, Diffusion-Maps and Applications.
Summary: We introduce the nonlinear dimensionality reduction problem known as Manifold Learning and present the diffusion maps algorithm (Coiffman and Lafon, 2006). Dif- fusion maps utilize the connectivity between data points through a diffusion process on the dataset. Additionally, we show some applications of this technique to 2D tomography reconstruction when the angles are unknown
Read MoreTree Embedding Problem for Digraphs.
Abstract: The \textit{tree embedding problem} focuses on identifying the minimal conditions a graph $G$ must satisfy to ensure it contains all trees with $k$ edges. Here, a graph $G$ consists of a set $V$ of elements called vertices, and a set $E$ of (unordered) pairs of vertices, called edges. We say that a graph $G$ is a tree if, for any pair of vertices, there is exactly one path connecting them. Erd\H{o}s and Sós conjectured that any graph $G$ with $n$ vertices and more than $(k-1)n/2$ edges contains every tree with $k$ edges. This conjecture has been generalized into the Antitree...
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