It is becoming increasingly common to issue forecasts that are probabilistic, in the form of probability distributions over all possible outcomes. To generate good probabilistic forecasts, we must first be able to evaluate how good a forecast is. The evaluation of probabilistic forecasts focuses on two aspects of forecast performance: forecast accuracy and forecast calibration. Forecast accuracy refers to how 'close' the forecast is to the corresponding observation, which can be quantified using proper scoring rules. Forecast calibration considers whether probabilistic forecasts are trustworthy. While most scoring rules and calibration checks treat all possible outcomes equally, some outcomes are often of more interest than others when evaluating forecasts, and one could argue that these outcomes should therefore be emphasised during forecast evaluation. For example, extreme outcomes typically lead to the largest impacts on forecast users, making accurate and calibrated forecasts for these outcomes particularly valuable. In this talk, we discuss methods to focus on particular outcomes when evaluating probabilistic forecasts. We review weighted scoring rules, which allow practitioners to incorporate a weight function into conventional scoring rules when calculating forecast accuracy, and we demonstrate that the theory underlying weighted scoring rules can readily be extended to forecast calibration. Using this, we introduce methods to evaluate the calibration of probabilistic forecasts for extreme events.
\r\n
We investigate an anisotropic vanishing viscosity limit of the 3D stochastic Navier-Stokes equations posed between two horizontal plates, with Dirichlet no-slip boundary condition. The turbulent viscosity is split into horizontal and vertical directions, each of which approaches zero at a different rate. The underlying Cylindrical Brownian Motion driving our transport-stretching noise is decomposed into horizontal and vertical components, which are scaled by the square root of the respective directional viscosities. We prove that if the ratio of the vertical to horizontal viscosities approaches zero, then there exists a sequence of weak martingale solutions convergent to the strong solution of the deterministic Euler equation on its lifetime of existence. A particular challenge is that the anisotropic scaling ruins the divergence-free property for the spatial correlation functions of the noise.
","image_description":"","creation_date":"2026-02-18T12:59:24","last_modification_date":"2026-03-22T19:58:56","link_label":"Working-Reading Seminar","link_url":"https://www.epfl.ch/labs/stoan/reading-working-seminar/","canceled":"True","cancel_reason":"","place_and_room":"MA B2 485","url_place_and_room":"","url_online_room":"","spoken_languages":["https://memento.epfl.ch/api/v1/spoken_languages/2/?format=json"],"speaker":"Dr Daniel Goodair (EPFL)","organizer":"Xue-Mei Li","contact":"Xue-Mei Li","is_internal":"False","theme":"","vulgarization":{"id":3,"fr_label":"Expert","en_label":"Expert"},"registration":{"id":3,"fr_label":"Entrée libre","en_label":"Free"},"keywords":"Working-Reading seminar, Probability, stochastic analysis","file":null,"icalendar_url":"https://memento.epfl.ch/event/export/119781/","category":{"id":1,"code":"CONF","fr_label":"Conférences - Séminaires","en_label":"Conferences - Seminars","activated":true},"academic_calendar_category":null,"domains":[],"mementos":["https://memento.epfl.ch/api/v1/mementos/7/?format=json"]},{"id":71457,"title":"lunch&LEARN: Bridging the gap between the math taught in first-year courses and the math used in life sciences research","slug":"lunchlearn-bridging-the-gap-between-the-math-taugh","event_url":"https://memento.epfl.ch/event/lunchlearn-bridging-the-gap-between-the-math-taugh","visual_url":"https://memento.epfl.ch/image/32806/200x112.jpg","visual_large_url":"https://memento.epfl.ch/image/32806/720x405.jpg","visual_maxsize_url":"https://memento.epfl.ch/image/32806/max-size.jpg","lang":"en","start_date":"2026-04-21","end_date":"2026-04-21","start_time":"12:15:00","end_time":"13:00:00","description":"For more than two decades leading professional organizations have called for a reform of the mathematics education of biology and life sciences students. Reflecting the growing importance of mathematics in life sciences research, such reform should bridge the gap between the mathematics students learn and the mathematics used in research.
\r\n
\r\nIn this talk, Steve Bennoun, UCLA, will present how the study of modeling and dynamical systems can be used to create a first-year course that introduces mathematical concepts used in life sciences research in a contextualized way.
\r\n
\r\nStudents first learn to write models for important biological systems such as hormone levels, epidemiological models, and predator-prey models.
\r\n
\r\nTaking a geometrical approach, students learn how to determine the long-term behaviors of models by studying phase plane trajectories and the stability of equilibrium points.
\r\n
\r\nThis enables the study of the concept of “biological switch” or how a cell can start or stop the production of a protein. This is followed by the important notion of qualitative change in a biological systems, or bifurcation.
\r\n
\r\nStudents learn in particular about Hopf bifurcations or how a system can start or stop oscillating. The second part of the course moves somewhat away from the geometrical approach and focuses on how to determine the stability of equilibrium points using the linearization of a model, motivating the study of the necessary notions from linear algebra by studying discrete-time models.
\r\n
\r\nThis talk will end with a discussion focusing on research by Sanders et al. (2021) suggesting that such a course supports students success and can reduce equity gaps.
\r\n
\r\n- - - - - - - - - - - - -
\r\n
\r\nlunch&LEARN sessions are intended for anyone who teaches at EPFL.
\r\nThis session is hybrid and can be attended in person or followed via zoom.
\r\nMost sessions are recorded and can be found on the Center LEARN's YouTube channel.
\r\nTo get in touch with the team, to suggest a session, or to make inquiries, please send an email to lunchLEARN@groupes.epfl.ch
The classification of the symplectic fillings of a given contact 3-manifold poses an interesting problem. It is motivated by results that demonstrate that the symplectic fillings of a contact 3-manifold hold information on the contact structure. Most notably, the contact structure of any contact 3-manifold that admits a strong symplectic filling is tight. Although the symplectic fillings of certain contact manifolds have been classified, the general classification remains an open problem. Working towards this, one can consider the geography problem for symplectic fillings. In the paper Spine removal surgery and the geography of symplectic fillings, Sam Lisi and Chris Wendl prove the existence of a universal bound for the geography (Euler characteristic and signature) of possible minimal strong symplectic fillings of a closed contact 3-manifold with a supporting planar spinal open book decomposition. Following a brief introduction to symplectic and contact topology, the aim of my talk is to explain Lisi and Wendl's result. For this purpose, I will provide an overview of symplectic fillings and the related geography problem, and introduce spinal open book decompositions.
\r\n
\r\n
The classification of gait patterns is an important challenge in movement analysis, as it supports clinical assessment and decision-making by enabling diagnosis and severity stratification. In this talk, I will discuss the potential of Topological Data Analysis (TDA) for gait pattern classification. Unlike conventional approaches that rely on explicit detection of Gait Events (GEs) to compute Spatiotemporal Gait Parameters (SGPs), TDA characterises the global structure of gait signals directly, capturing relationships and patterns in the data without requiring GEs. This is particularly relevant in real-world settings, where GE detection can be diQicult due to heterogeneity in walking conditions and gait patterns, potentially biasing clinically relevant metrics and, consequently, decision-making.
\r\nWithin our department, preliminary results have shown that TDA-based features can achieve classification performance comparable to that of SGPs in fall-risk assessment. These findings suggest that topology oQers a competitive alternative for representing gait data, with the potential to better handle variability across subjects and pathological
\r\nconditions.
\r\nBuilding on these results, we plan to further extend the TDA framework in two directions. First, we aim to investigate time-aware topological methods to better capture the
\r\ntemporal structure of gait signals. Second, we will explore Topological Deep Learning (TDL) approaches to reduce reliance on handcrafted design choices and potentially
\r\nimprove classification performance. By combining the robustness of topology with datadriven representation learning, this work seeks to provide robust tools for the classification of typical and pathological gait patterns.
\r\n
Abstract:
\r\nAs anticipated by Onsager's conjecture, low-regularity solutions of the Euler equations exhibit greater flexibility than classical solutions. In the first part of this talk we focus on steady solutions, showing that in the low-regularity regime their streamlines can realize any prescribed topology, a phenomenon that cannot occur for classical solutions. The key tool is a novel implementation of convex integration that preserves the topology of the streamlines throughout the iteration. In the second part we extend these ideas to the MHD equations, constructing continuous weak solutions with constant nonzero helicity that nevertheless fail to conserve energy and cross helicity.
We present a novel necessary and sufficient principle for multiple testing methods controlling an expected loss. This principle asserts that every such multiple testing method is a special case of a general closed testing procedure based on e-values. It generalizes the Closure Principle, known to underlie all methods controlling familywise error and tail probabilities of false discovery proportions, to a large class of error rates -- in particular to the false discovery rate (FDR). By writing existing methods as special cases of this procedure, we can achieve uniform improvements, as we demonstrate for the e-Benjamini-Hochberg and the Benjamini-Yekutieli procedures, and the self-consistent method of Su (2018). We also show that methods derived using our novel e-Closure Principle generally control their error rate not just for one rejected set, but simultaneously over many, allowing post hoc flexibility for the researcher.
\r\nMoreover, we show that because all multiple testing methods for all error metrics are derived from the same procedure, researchers may even choose the error metric post hoc. Under certain conditions, this flexibility even extends to post hoc choice of the nominal error rate.
\r\n
\r\n
\r\n