BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Justyna Signerska-Rynkowska (Politechnika Gdańska / Dioscuri Cent re in Topological Data Analysis) DTSTART:20251006T103000Z DTEND:20251006T123000Z DTSTAMP:20260422T212725Z UID:BNAT/1 DESCRIPTION:Title: Dyn amical and geometrical mechanism shaping response precision in neuron mode ls\nby Justyna Signerska-Rynkowska (Politechnika Gdańska / Dioscuri C entre in Topological Data Analysis) as part of Basic Notions and Applied T opology Seminar\n\nLecture held in Room 1 at the Institute of Mathematics PAS.\n\nAbstract\nExperimental studies of neuronal dynamics involve record ing of both spontaneous activity patterns and the responses to sustained a nd short-term inputs. In the first part of the talk\, I will describe unde rlying dynamical structures governing phenomena such as post inhibitory fa cilitation (PIF) and slope detection in a response to transient inputs in a class of nonlinear adaptive hybrid neuron models. In PIF an otherwise su bthreshold excitatory input can induce a spike if it is applied with prope r timing after an inhibitory pulse\, while neurons displaying slope-detect ion property spike to a transient input only when the input’s rate of ch ange is in a specific\, bounded range. A key concept in this analysis is a firing threshold curve which allows us to explain these phenomena in the non-autonomous systems\, building upon our understanding of corresponding systems with constant stimulus.\nOn the other hand\, studying phenomena su ch as phase locking requires the time depending sustained stimulus and the use of our knowledge on the underlying autonomous system is very limited in this case. Nevertheless\, phase-locking of ongoing oscillations to a pe riodic signal can be explored with a variety of analytical approaches. How ever\, much less is known about what factors determine the response precis ion of excitable cells that are intrinsically at rest but are activated by periodic forcing and noise. We shed light on this coding precision by int roducing a new tool\, the dynamic threshold curve (DTC)\, which we apply t o the study of well-established auditory neuron model.\nThe talk is based on joint works with Jonathan Rubin (University of Pittsburgh) and Jonathan Touboul (Brandeis University).\n LOCATION:https://researchseminars.org/talk/BNAT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Iason Papadopoulos (University of Bremen) DTSTART:20251027T113000Z DTEND:20251027T133000Z DTSTAMP:20260422T212725Z UID:BNAT/2 DESCRIPTION:Title: Mul tiparameter Persistence\nby Iason Papadopoulos (University of Bremen) as part of Basic Notions and Applied Topology Seminar\n\nLecture held in R oom 1 at the Institute of Mathematics PAS.\n\nAbstract\nThis talk is the f irst in a series of two talks (the second one will be in the Dioscuri TDA seminar)\, outlining a new vectorization method for multiparameter persist ence modules with an arbitrary number of parameters. Multiparameter persis tence extends the foundational ideas of persistent homology. Importantly\, it can capture topological information of a point clouds with several fun ctions. This talk introduces the definition and motivation behind multipar ameter persistence. We will compare the structure and interpretability of multiparameter persistence modules with their one-parameter counterparts\, highlighting the challenges that arise when working with multiple paramet ers. To address these issues\, we will explore several approaches that ext ract meaningful topological information without requiring full classificat ion of the modules. In particular\, we will take a closer look at the Gene ralized Rank Invariant Landscape (GRIL)\, a recent vectorization method th at provides a computable and interpretable invariant.\n LOCATION:https://researchseminars.org/talk/BNAT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Clemens Bannwart DTSTART:20251117T113000Z DTEND:20251117T133000Z DTSTAMP:20260422T212725Z UID:BNAT/3 DESCRIPTION:Title: Mor se-Smale vector fields: definition\, properties and induced structures \nby Clemens Bannwart as part of Basic Notions and Applied Topology Semina r\n\nLecture held in Room 1 at the Institute of Mathematics PAS.\n\nAbstra ct\nIn this talk we introduce some topics which are important for my secon d talk (which will be given in the TDA Seminar on the following day). We u npack the definition of Morse-Smale vector fields and discuss some of thei r properties\, such as structural stability and genericity. We devote some time to the gradient-like case\, which is closely linked to Morse theory. We see how in this case we can obtain a chain complex\, called the Morse complex\, as well as a CW decomposition of the underlying manifold. Time-p ermitting\, we discuss the relation between Morse theory and persistent ho mology.\n LOCATION:https://researchseminars.org/talk/BNAT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Julian Brüggemann (Dioscuri Centre in Topological Data Analysis) DTSTART:20251013T103000Z DTEND:20251013T123000Z DTSTAMP:20260422T212725Z UID:BNAT/4 DESCRIPTION:Title: Int roduction to Statistical Learning\nby Julian Brüggemann (Dioscuri Cen tre in Topological Data Analysis) as part of Basic Notions and Applied Top ology Seminar\n\nLecture held in Room 1 at IMPAN\, Room 1.14 at the Instit ute of Informatics - University of Gdańsk.\n\nAbstract\nThis talk is the first of a series of talks on the topics of statistical learning\, machine learning\, and similar topics. We follow the book "An introduction to sta tistical learning with applications in Python". In this talk\, I will prov ide an overview over the series of talks to come and will capture some of the topics from chapter 1 and 2.\n LOCATION:https://researchseminars.org/talk/BNAT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Michał Bogdan (Dioscuri Centre in Topological Data Analysis) DTSTART:20251020T103000Z DTEND:20251020T123000Z DTSTAMP:20260422T212725Z UID:BNAT/5 DESCRIPTION:Title: Int roduction to the Theory of Linear Regression\nby Michał Bogdan (Diosc uri Centre in Topological Data Analysis) as part of Basic Notions and Appl ied Topology Seminar\n\nLecture held in Room 1 at the Institute of Mathema tics PAS.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BNAT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Michał Bogdan (Dioscuri Centre in Topological Data Analysis) DTSTART:20251103T113000Z DTEND:20251103T133000Z DTSTAMP:20260422T212725Z UID:BNAT/6 DESCRIPTION:Title: Lin ear Regression in Practice\nby Michał Bogdan (Dioscuri Centre in Topo logical Data Analysis) as part of Basic Notions and Applied Topology Semin ar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nThis will be a tutorial rather than a talk\, and consider the second part of chapter 3 of "An Intr oduction to Statistical Learning with Applications in Python". We will dis cuss how to use linear regression in python and consider a couple of examp les.\n LOCATION:https://researchseminars.org/talk/BNAT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:John Rick Manzanares (Dioscuri Centre in Topological Data Analysis / University of Silesia in Katowice) DTSTART:20251201T113000Z DTEND:20251201T133000Z DTSTAMP:20260422T212725Z UID:BNAT/7 DESCRIPTION:Title: Int roduction to Classification in Machine Learning\nby John Rick Manzanar es (Dioscuri Centre in Topological Data Analysis / University of Silesia i n Katowice) as part of Basic Notions and Applied Topology Seminar\n\nLectu re held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nThis talk\, based on Chapter 4 of A n Introduction to Statistical Learning with Applications in Python\, explo res key methods for classification\, including logistic regression\, discr iminant analysis\, and $k$-nearest neighbors. We’ll discuss how these ap proaches model categorical outcomes\, evaluate their performance using met rics like accuracy and receiver-operating characteristic curve curves\, an d demonstrate their implementation through practical Python examples.\n LOCATION:https://researchseminars.org/talk/BNAT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Senge (Dioscuri Centre in Topological Data Analysis) DTSTART:20251215T113000Z DTEND:20251215T133000Z DTSTAMP:20260422T212725Z UID:BNAT/8 DESCRIPTION:Title: Int roduction to Resampling Methods in Machine Learning\nby Jan Senge (Dio scuri Centre in Topological Data Analysis) as part of Basic Notions and Ap plied Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nThis talk\, based on Chapter 5 of An Introduction to Statistical Learning with Applications in Python\, introduces Resampling Methods such as cross-vali dation and the bootstrap. We’ll discuss how these techniques improve mod el assessment and selection by providing more accurate estimates of predic tion error and model variability\, illustrated through practical Python ap plications.\n LOCATION:https://researchseminars.org/talk/BNAT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Mateusz Masłowski (Dioscuri Centre in Topological Data Analysis) DTSTART:20260112T113000Z DTEND:20260112T133000Z DTSTAMP:20260422T212725Z UID:BNAT/10 DESCRIPTION:Title: Li near Model Selection and Regularization (Part 1)\nby Mateusz Masłowsk i (Dioscuri Centre in Topological Data Analysis) as part of Basic Notions and Applied Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract \nThis session\, based on the first half of Chapter 6 of An Introduction t o Statistical Learning with Applications in Python\, explores Linear Model Selection techniques for improving model interpretability and performance . We’ll cover best subset\, forward\, and backward stepwise selection\, discussing how these approaches identify the most informative predictors a nd balance complexity with predictive power.\n LOCATION:https://researchseminars.org/talk/BNAT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacek Gulgowski DTSTART:20260119T113000Z DTEND:20260119T133000Z DTSTAMP:20260422T212725Z UID:BNAT/11 DESCRIPTION:Title: Li near Model Selection and Regularization (Part 2)\nby Jacek Gulgowski a s part of Basic Notions and Applied Topology Seminar\n\nLecture held in Ro om 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nIn the second session\, we turn to Regularizatio n Methods\, focusing on ridge regression and the lasso. We'll examine how these techniques use penalty terms to control model flexibility\, reduce o verfitting\, and enhance prediction accuracy\, with hands-on Python exampl es illustrating their practical differences and applications.\n LOCATION:https://researchseminars.org/talk/BNAT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Marszewska (Dioscuri Centre in Topological Data Analysis) DTSTART:20260209T113000Z DTEND:20260209T133000Z DTSTAMP:20260422T212725Z UID:BNAT/13 DESCRIPTION:Title: Tr ee-Based Methods\nby Marta Marszewska (Dioscuri Centre in Topological Data Analysis) as part of Basic Notions and Applied Topology Seminar\n\nLe cture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informat ics (University of Gdańsk).\n\nAbstract\nThis talk provides an accessible overview of tree-based methods for regression and classification. We will explore the fundamental concepts behind decision trees\, including recurs ive partitioning\, tree construction\, and pruning for improved generaliza tion. Building on these foundations\, we will introduce ensemble methods - bagging\, random forests\, and boosting - which substantially enhance pre dictive accuracy by aggregating many weak learners.\n LOCATION:https://researchseminars.org/talk/BNAT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Scoville DTSTART:20260216T113000Z DTEND:20260216T133000Z DTSTAMP:20260422T212725Z UID:BNAT/14 DESCRIPTION:Title: A McCord theorem for (Čech) closure spaces\nby Nick Scoville as part of Basic Notions and Applied Topology Seminar\n\nLecture held in Room 1 at t he IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańs k).\n\nAbstract\nIn this talk\, we verify analogues of classical results f or higher homotopy groups and singular homology groups of (\\v{C}ech) clos ure spaces. Closure spaces are a generalization of topological spaces that also include graphs and directed graphs and are thus a bridge that connec ts classical algebraic topology with the more applied side of topology\, s uch as digital topology. Our main result is the construction of a weak hom otopy equivalence between the geometric realizations of (directed) Vietori s-Rips complexes and their underlying (directed) graphs. This implies that singular homology groups of finite graphs can be efficiently calculated f rom finite combinatorial structures\, despite their associated chain group s being infinite dimensional. This work is similar to the work McCord did for finite topological spaces\, but in the context of closure spaces. This is joint work with Nikolai Milicevic.\n LOCATION:https://researchseminars.org/talk/BNAT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacek Gulgowski DTSTART:20260223T113000Z DTEND:20260223T133000Z DTSTAMP:20260422T212725Z UID:BNAT/15 DESCRIPTION:Title: Mo ving Beyond Linearity\nby Jacek Gulgowski as part of Basic Notions and Applied Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, Room 1. 14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nT his talk introduces key techniques for modeling nonlinear relationships in supervised learning. We begin by examining polynomial regression and step functions\, then develop more flexible approaches using basis functions a nd splines\, including cubic splines and smoothing splines\, to capture co mplex structure in data. The seminar also covers Generalized Additive Mode ls (GAMs)\, which extend linear models by allowing nonlinear functions of predictors while retaining interpretability.\n LOCATION:https://researchseminars.org/talk/BNAT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Senge DTSTART:20260302T113000Z DTEND:20260302T133000Z DTSTAMP:20260422T212725Z UID:BNAT/16 DESCRIPTION:Title: Su pport Vector Machines\nby Jan Senge as part of Basic Notions and Appli ed Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nThis se minar provides an intuitive introduction to Support Vector Machines (SVMs) . We begin with the maximal margin classifier and support vector classifie r\, building geometric intuition for how SVMs separate classes with optima l margins. We then extend these ideas to the kernel trick\, enabling highl y flexible nonlinear decision boundaries through polynomial and radial bas is function kernels. The talk also highlights key tuning parameters\, prac tical considerations for model fitting\, and strategies for avoiding overf itting.\n LOCATION:https://researchseminars.org/talk/BNAT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Jakub Malinowski (Dioscuri Centre in Topological Data Analysis) DTSTART:20260309T113000Z DTEND:20260309T133000Z DTSTAMP:20260422T212725Z UID:BNAT/17 DESCRIPTION:Title: De ep Learning (Part 1)\nby Jakub Malinowski (Dioscuri Centre in Topologi cal Data Analysis) as part of Basic Notions and Applied Topology Seminar\n \nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Info rmatics (University of Gdańsk).\n\nAbstract\nThis first session introduce s the fundamental concepts and motivations behind deep learning. We begin with a discussion of why and when deep learning can outperform traditional statistical methods - especially for large\, high-dimensional data. Next\ , we explore the architecture of neural networks: from simple single-layer networks to multilayer (deep) networks. Key learning mechanisms - includi ng backpropagation\, regularization\, and stochastic gradient descent (SGD ) - will be explained intuitively and with math as appropriate. We will al so review practical considerations (e.g.\, network tuning\, overfitting\, capacity control)\, providing Python code examples to illustrate how deep networks are defined and trained in a real-world context.\n LOCATION:https://researchseminars.org/talk/BNAT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Omer Eryilmaz (University of Birmingham) DTSTART:20260316T113000Z DTEND:20260316T133000Z DTSTAMP:20260422T212725Z UID:BNAT/18 DESCRIPTION:Title: Fl ow-Aware Ellipsoidal Filtration for Persistent Homology of Recurrent Signa ls\nby Omer Eryilmaz (University of Birmingham) as part of Basic Notio ns and Applied Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, R oom 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstr act\nRecurrent signals give rise to trajectories that repeatedly return cl ose to earlier states in state space. Analysing such data therefore requir es a principled notion of similarity between states. In practice\, this de pends on how local neighbourhoods are defined and scaled. These neighbourh oods are also important for topology-preserving denoising in state space\, where the aim is to reduce noise without distorting the underlying trajec tory structure. This talk introduces a flow-aware ellipsoidal filtration f or persistent homology based on a spatio-temporal covariance construction that estimates local flow geometry from both temporal and spatial neighbou rs. Unlike isotropic constructions based on balls\, such as the Vietoris-- Rips filtration\, the proposed method assigns an ellipsoid to each point\, with orientation and axis lengths determined by local flow variances. Whe n a dominant $H_1$ feature captures the main recurrent loop structure\, it s persistence interval can be used as a data-driven scale selection rule. Experiments on synthetic and real signals suggest that flow-aware ellipsoi dal neighbourhoods can improve topology-preserving denoising and first-rec urrence-time estimation compared with the Vietoris--Rips filtration. More broadly\, the results illustrate how incorporating anisotropy into persist ent homology can provide a more informative description of recurrent dynam ical systems.\n LOCATION:https://researchseminars.org/talk/BNAT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylwester Piątek (Dioscuri Centre in Topological Data Analysis) DTSTART:20260323T113000Z DTEND:20260323T133000Z DTSTAMP:20260422T212725Z UID:BNAT/19 DESCRIPTION:Title: Su rvival Analysis and Censored Data\nby Sylwester Piątek (Dioscuri Cent re in Topological Data Analysis) as part of Basic Notions and Applied Topo logy Seminar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Ins titute of Informatics (University of Gdańsk).\n\nAbstract\nThis seminar i ntroduces the key concepts and methods of survival analysis. We begin by d iscussing the nature of survival (or time-to-event) data and the complicat ions introduced by censoring - when the event of interest has not occurred for some subjects by study end or loss to follow-up. The talk then presen ts classical and modern tools for analyzing such data: we will cover the n onparametric estimation of survival curves (via the Kaplan-Meier estimator )\, compare survival experiences with the Log-Rank test\, and introduce re gression models for survival outcomes - in particular\, the Cox proportion al hazards model (hazard-based modeling)\, including discussion of the haz ard function and handling of covariates. The talk also touches on more adv anced considerations such as shrinkage for Cox models\, time-dependent cov ariates\, and diagnostic checks (e.g.\, verifying the proportional hazards assumption).\n LOCATION:https://researchseminars.org/talk/BNAT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jakub Malinowski (Dioscuri Centre in Topological Data Analysis) DTSTART:20260413T103000Z DTEND:20260413T123000Z DTSTAMP:20260422T212725Z UID:BNAT/21 DESCRIPTION:Title: De ep Learning (Part 2)\nby Jakub Malinowski (Dioscuri Centre in Topologi cal Data Analysis) as part of Basic Notions and Applied Topology Seminar\n \nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Info rmatics (University of Gdańsk).\n\nAbstract\nThe second session expands o n the foundations by covering more advanced deep-learning techniques and t heir applications. We will examine methods such as dropout learning\, netw ork tuning strategies\, and architectural choices that influence model per formance. The talk will show how deep learning can tackle complex tasks in domains like image recognition\, text classification\, or other high-dime nsional prediction problems.\n LOCATION:https://researchseminars.org/talk/BNAT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Janusz Przewocki DTSTART:20260420T103000Z DTEND:20260420T123000Z DTSTAMP:20260422T212725Z UID:BNAT/22 DESCRIPTION:Title: Un supervised Learning (Part 1)\nby Janusz Przewocki as part of Basic Not ions and Applied Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbs tract\nThis first session introduces the motivations and foundational meth ods for dimensionality reduction under unsupervised learning. We begin by discussing why dimension reduction matters - especially in high-dimensiona l data settings - and how it helps address issues like the "curse of dimen sionality\," multicollinearity\, overfitting\, and challenges in visualiza tion and interpretation. Then we focus on Principal Component Analysis (PC A): its mathematical foundations\, how it identifies dominant modes of var iation\, how to interpret the principal components\, and how to choose the number of components.\n LOCATION:https://researchseminars.org/talk/BNAT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Janusz Przewocki DTSTART:20260427T103000Z DTEND:20260427T123000Z DTSTAMP:20260422T212725Z UID:BNAT/25 DESCRIPTION:Title: Un supervised Learning (Part 2)\nby Janusz Przewocki as part of Basic Not ions and Applied Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbs tract\nThe second session delves into clustering methods and other techniq ues for uncovering latent structure in data without relying on response va riables. We cover K-means clustering and Hierarchical clustering\, includi ng how they work\, how to choose the number of clusters\, how to decide on distance metrics\, and practical pitfalls (e.g. scaling\, sensitivity to initialization). We discuss how to interpret clusters\, validate clusterin g solutions\, and when unsupervised grouping might be appropriate.\n LOCATION:https://researchseminars.org/talk/BNAT/25/ END:VEVENT END:VCALENDAR