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:20260404T094503Z UID:BNAT/1 DESCRIPTION:Title: Dynamical and geometrical mechanism shaping response precision in neur on models\nby Justyna Signerska-Rynkowska (Politechnika Gdańska / 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 Institute of Mathe matics PAS.\n\nAbstract\nExperimental studies of neuronal dynamics involve recording of both spontaneous activity patterns and the responses to sust ained and short-term inputs. In the first part of the talk\, I will descri be underlying dynamical structures governing phenomena such as post inhibi tory facilitation (PIF) and slope detection in a response to transient inp uts in a class of nonlinear adaptive hybrid neuron models. In PIF an other wise subthreshold excitatory input can induce a spike if it is applied wit h proper timing after an inhibitory pulse\, while neurons displaying slope -detection property spike to a transient input only when the input’s rat e of change is in a specific\, bounded range. A key concept in this analys is is a firing threshold curve which allows us to explain these phenomena in the non-autonomous systems\, building upon our understanding of corresp onding systems with constant stimulus.\nOn the other hand\, studying pheno mena such as phase locking requires the time depending sustained stimulus and the use of our knowledge on the underlying autonomous system is very l imited in this case. Nevertheless\, phase-locking of ongoing oscillations to a periodic signal can be explored with a variety of analytical approach es. However\, much less is known about what factors determine the response precision of excitable cells that are intrinsically at rest but are activ ated by periodic forcing and noise. We shed light on this coding precision by introducing a new tool\, the dynamic threshold curve (DTC)\, which we apply to the study of well-established auditory neuron model.\nThe talk is based on joint works with Jonathan Rubin (University of Pittsburgh) and J onathan Touboul (Brandeis University).\n LOCATION:https://stable.researchseminars.org/talk/BNAT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Iason Papadopoulos (University of Bremen) DTSTART:20251027T113000Z DTEND:20251027T133000Z DTSTAMP:20260404T094503Z UID:BNAT/2 DESCRIPTION:Title: Multiparameter Persistence\nby Iason Papadopoulos (University of B remen) as part of Basic Notions and Applied Topology Seminar\n\nLecture he ld in Room 1 at the Institute of Mathematics PAS.\n\nAbstract\nThis talk i s the first in a series of two talks (the second one will be in the Dioscu ri TDA seminar)\, outlining a new vectorization method for multiparameter persistence modules with an arbitrary number of parameters. Multiparameter persistence extends the foundational ideas of persistent homology. Import antly\, it can capture topological information of a point clouds with seve ral functions. This talk introduces the definition and motivation behind m ultiparameter persistence. We will compare the structure and interpretabil ity of multiparameter persistence modules with their one-parameter counter parts\, highlighting the challenges that arise when working with multiple parameters. To address these issues\, we will explore several approaches t hat extract meaningful topological information without requiring full clas sification of the modules. In particular\, we will take a closer look at t he Generalized Rank Invariant Landscape (GRIL)\, a recent vectorization me thod that provides a computable and interpretable invariant.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Clemens Bannwart DTSTART:20251117T113000Z DTEND:20251117T133000Z DTSTAMP:20260404T094503Z UID:BNAT/3 DESCRIPTION:Title: Morse-Smale vector fields: definition\, properties and induced structu res\nby Clemens Bannwart as part of Basic Notions and Applied Topology Seminar\n\nLecture held in Room 1 at the Institute of Mathematics PAS.\n\ nAbstract\nIn this talk we introduce some topics which are important for m y second talk (which will be given in the TDA Seminar on the following day ). We unpack the definition of Morse-Smale vector fields and discuss some of their properties\, such as structural stability and genericity. We devo te 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-permitting\, we discuss the relation between Morse theory and persis tent homology.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Julian Brüggemann (Dioscuri Centre in Topological Data Analysis) DTSTART:20251013T103000Z DTEND:20251013T123000Z DTSTAMP:20260404T094503Z UID:BNAT/4 DESCRIPTION:Title: Introduction to Statistical Learning\nby Julian Brüggemann (Diosc uri Centre in Topological Data Analysis) as part of Basic Notions and Appl ied Topology Seminar\n\nLecture held in Room 1 at IMPAN\, Room 1.14 at the Institute 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 statistical learning with applications in Python". In this talk\, I wi ll provide an overview over the series of talks to come and will capture s ome of the topics from chapter 1 and 2.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Michał Bogdan (Dioscuri Centre in Topological Data Analysis) DTSTART:20251020T103000Z DTEND:20251020T123000Z DTSTAMP:20260404T094503Z UID:BNAT/5 DESCRIPTION:Title: Introduction to the Theory of Linear Regression\nby Michał Bogdan (Dioscuri Centre in Topological Data Analysis) as part of Basic Notions a nd Applied Topology Seminar\n\nLecture held in Room 1 at the Institute of Mathematics PAS.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BNAT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Michał Bogdan (Dioscuri Centre in Topological Data Analysis) DTSTART:20251103T113000Z DTEND:20251103T133000Z DTSTAMP:20260404T094503Z UID:BNAT/6 DESCRIPTION:Title: Linear Regression in Practice\nby Michał Bogdan (Dioscuri Centre in Topological Data Analysis) as part of Basic Notions and Applied Topolog y Seminar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Instit ute of Informatics (University of Gdańsk).\n\nAbstract\nThis will be a tu torial rather than a talk\, and consider the second part of chapter 3 of " An Introduction to Statistical Learning with Applications in Python". We w ill discuss how to use linear regression in python and consider a couple o f examples.\n LOCATION:https://stable.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:20260404T094503Z UID:BNAT/7 DESCRIPTION:Title: Introduction to Classification in Machine Learning\nby John Rick M anzanares (Dioscuri Centre in Topological Data Analysis / University of Si lesia in Katowice) 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 talk\, based on Chapter 4 of An Introduction to Statistical Learning with Applications in Python\ , explores key methods for classification\, including logistic regression\ , discriminant analysis\, and $k$-nearest neighbors. We’ll discuss how t hese approaches model categorical outcomes\, evaluate their performance us ing metrics like accuracy and receiver-operating characteristic curve curv es\, and demonstrate their implementation through practical Python example s.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Senge (Dioscuri Centre in Topological Data Analysis) DTSTART:20251215T113000Z DTEND:20251215T133000Z DTSTAMP:20260404T094503Z UID:BNAT/8 DESCRIPTION:Title: Introduction to Resampling Methods in Machine Learning\nby Jan Sen ge (Dioscuri Centre in Topological Data Analysis) as part of Basic Notions and Applied Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, Roo m 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstrac t\nThis talk\, based on Chapter 5 of An Introduction to Statistical Learni ng with Applications in Python\, introduces Resampling Methods such as cro ss-validation and the bootstrap. We’ll discuss how these techniques impr ove model assessment and selection by providing more accurate estimates of prediction error and model variability\, illustrated through practical Py thon applications.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Mateusz Masłowski (Dioscuri Centre in Topological Data Analysis) DTSTART:20260112T113000Z DTEND:20260112T133000Z DTSTAMP:20260404T094503Z UID:BNAT/10 DESCRIPTION:Title: Linear Model Selection and Regularization (Part 1)\nby Mateusz Ma słowski (Dioscuri Centre in Topological Data Analysis) as part of Basic N otions 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\nA bstract\nThis session\, based on the first half of Chapter 6 of An Introdu ction to Statistical Learning with Applications in Python\, explores Linea r Model Selection techniques for improving model interpretability and perf ormance. We’ll cover best subset\, forward\, and backward stepwise selec tion\, discussing how these approaches identify the most informative predi ctors and balance complexity with predictive power.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacek Gulgowski DTSTART:20260119T113000Z DTEND:20260119T133000Z DTSTAMP:20260404T094503Z UID:BNAT/11 DESCRIPTION:Title: Linear Model Selection and Regularization (Part 2)\nby Jacek Gulg owski as part of Basic Notions and Applied Topology Seminar\n\nLecture hel d in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (Univ ersity of Gdańsk).\n\nAbstract\nIn the second session\, we turn to Regula rization Methods\, focusing on ridge regression and the lasso. We'll exami ne how these techniques use penalty terms to control model flexibility\, r educe overfitting\, and enhance prediction accuracy\, with hands-on Python examples illustrating their practical differences and applications.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Marszewska (Dioscuri Centre in Topological Data Analysis) DTSTART:20260209T113000Z DTEND:20260209T133000Z DTSTAMP:20260404T094503Z UID:BNAT/13 DESCRIPTION:Title: Tree-Based Methods\nby Marta Marszewska (Dioscuri Centre in Topol ogical Data Analysis) as part of Basic Notions and Applied Topology Semina r\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of I nformatics (University of Gdańsk).\n\nAbstract\nThis talk provides an acc essible overview of tree-based methods for regression and classification. We will explore the fundamental concepts behind decision trees\, including recursive partitioning\, tree construction\, and pruning for improved gen eralization. Building on these foundations\, we will introduce ensemble me thods - bagging\, random forests\, and boosting - which substantially enha nce predictive accuracy by aggregating many weak learners.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Scoville DTSTART:20260216T113000Z DTEND:20260216T133000Z DTSTAMP:20260404T094503Z 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 the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nIn this talk\, we verify analogues of classical re sults for higher homotopy groups and singular homology groups of (\\v{C}ec h) closure spaces. Closure spaces are a generalization of topological spac es that also include graphs and directed graphs and are thus a bridge that connects classical algebraic topology with the more applied side of topol ogy\, such as digital topology. Our main result is the construction of a w eak homotopy equivalence between the geometric realizations of (directed) Vietoris-Rips complexes and their underlying (directed) graphs. This impli es that singular homology groups of finite graphs can be efficiently calcu lated from finite combinatorial structures\, despite their associated chai n groups being infinite dimensional. This work is similar to the work McCo rd did for finite topological spaces\, but in the context of closure space s. This is joint work with Nikolai Milicevic.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacek Gulgowski DTSTART:20260223T113000Z DTEND:20260223T133000Z DTSTAMP:20260404T094503Z UID:BNAT/15 DESCRIPTION:Title: Moving Beyond Linearity\nby Jacek Gulgowski as part of Basic Noti ons 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\nAbst ract\nThis talk introduces key techniques for modeling nonlinear relations hips in supervised learning. We begin by examining polynomial regression a nd step functions\, then develop more flexible approaches using basis func tions and splines\, including cubic splines and smoothing splines\, to cap ture complex structure in data. The seminar also covers Generalized Additi ve Models (GAMs)\, which extend linear models by allowing nonlinear functi ons of predictors while retaining interpretability.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Senge DTSTART:20260302T113000Z DTEND:20260302T133000Z DTSTAMP:20260404T094503Z UID:BNAT/16 DESCRIPTION:Title: Support Vector Machines\nby Jan Senge as part of Basic Notions an d 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\n This seminar provides an intuitive introduction to Support Vector Machines (SVMs). We begin with the maximal margin classifier and support vector cl assifier\, building geometric intuition for how SVMs separate classes with optimal margins. We then extend these ideas to the kernel trick\, enablin g highly flexible nonlinear decision boundaries through polynomial and rad ial basis function kernels. The talk also highlights key tuning parameters \, practical considerations for model fitting\, and strategies for avoidin g overfitting.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Jakub Malinowski (Dioscuri Centre in Topological Data Analysis) DTSTART:20260309T113000Z DTEND:20260309T133000Z DTSTAMP:20260404T094503Z UID:BNAT/17 DESCRIPTION:Title: Deep Learning (Part 1)\nby Jakub Malinowski (Dioscuri Centre in T opological Data Analysis) as part of Basic Notions and Applied Topology Se minar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nThis first session in troduces the fundamental concepts and motivations behind deep learning. We begin with a discussion of why and when deep learning can outperform trad itional statistical methods - especially for large\, high-dimensional data . Next\, we explore the architecture of neural networks: from simple singl e-layer networks to multilayer (deep) networks. Key learning mechanisms - including backpropagation\, regularization\, and stochastic gradient desce nt (SGD) - will be explained intuitively and with math as appropriate. We will also review practical considerations (e.g.\, network tuning\, overfit ting\, capacity control)\, providing Python code examples to illustrate ho w deep networks are defined and trained in a real-world context.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Omer Eryilmaz (University of Birmingham) DTSTART:20260316T113000Z DTEND:20260316T133000Z DTSTAMP:20260404T094503Z UID:BNAT/18 DESCRIPTION:Title: Flow-Aware Ellipsoidal Filtration for Persistent Homology of Recurren t Signals\nby Omer Eryilmaz (University of Birmingham) as part of Basi c Notions and Applied Topology Seminar\n\nLecture held in Room 1 at the IM PAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n \nAbstract\nRecurrent signals give rise to trajectories that repeatedly re turn close to earlier states in state space. Analysing such data therefore requires a principled notion of similarity between states. In practice\, this depends on how local neighbourhoods are defined and scaled. These nei ghbourhoods are also important for topology-preserving denoising in state space\, where the aim is to reduce noise without distorting the underlying trajectory structure. This talk introduces a flow-aware ellipsoidal filtr ation for persistent homology based on a spatio-temporal covariance constr uction that estimates local flow geometry from both temporal and spatial n eighbours. Unlike isotropic constructions based on balls\, such as the Vie toris--Rips filtration\, the proposed method assigns an ellipsoid to each point\, with orientation and axis lengths determined by local flow varianc es. When a dominant $H_1$ feature captures the main recurrent loop structu re\, its persistence interval can be used as a data-driven scale selection rule. Experiments on synthetic and real signals suggest that flow-aware e llipsoidal neighbourhoods can improve topology-preserving denoising and fi rst-recurrence-time estimation compared with the Vietoris--Rips filtration . More broadly\, the results illustrate how incorporating anisotropy into persistent homology can provide a more informative description of recurren t dynamical systems.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylwester Piątek (Dioscuri Centre in Topological Data Analysis) DTSTART:20260323T113000Z DTEND:20260323T133000Z DTSTAMP:20260404T094503Z UID:BNAT/19 DESCRIPTION:Title: Survival Analysis and Censored Data\nby Sylwester Piątek (Dioscu ri Centre in Topological Data Analysis) 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 introduces the key concepts and methods of survival analysis. We beg in by discussing the nature of survival (or time-to-event) data and the co mplications introduced by censoring - when the event of interest has not o ccurred for some subjects by study end or loss to follow-up. The talk then presents classical and modern tools for analyzing such data: we will cove r the nonparametric estimation of survival curves (via the Kaplan-Meier es timator)\, compare survival experiences with the Log-Rank test\, and intro duce regression models for survival outcomes - in particular\, the Cox pro portional hazards model (hazard-based modeling)\, including discussion of the hazard function and handling of covariates. The talk also touches on m ore advanced considerations such as shrinkage for Cox models\, time-depend ent covariates\, and diagnostic checks (e.g.\, verifying the proportional hazards assumption).\n LOCATION:https://stable.researchseminars.org/talk/BNAT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jakub Malinowski (Dioscuri Centre in Topological Data Analysis) DTSTART:20260413T103000Z DTEND:20260413T123000Z DTSTAMP:20260404T094503Z UID:BNAT/21 DESCRIPTION:Title: Deep Learning (Part 2)\nby Jakub Malinowski (Dioscuri Centre in T opological Data Analysis) as part of Basic Notions and Applied Topology Se minar\n\nLecture held in Room 1 at the IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstract\nThe second session ex pands on the foundations by covering more advanced deep-learning technique s and their applications. We will examine methods such as dropout learning \, network tuning strategies\, and architectural choices that influence mo del performance. The talk will show how deep learning can tackle complex t asks in domains like image recognition\, text classification\, or other hi gh-dimensional prediction problems.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Janusz Przewocki DTSTART:20260420T103000Z DTEND:20260420T123000Z DTSTAMP:20260404T094503Z UID:BNAT/22 DESCRIPTION:Title: Unsupervised Learning (Part 1)\nby Janusz Przewocki as part of Ba sic 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 first session introduces the motivations and foundation al methods for dimensionality reduction under unsupervised learning. We be gin by discussing why dimension reduction matters - especially in high-dim ensional data settings - and how it helps address issues like the "curse o f dimensionality\," multicollinearity\, overfitting\, and challenges in vi sualization and interpretation. Then we focus on Principal Component Analy sis (PCA): its mathematical foundations\, how it identifies dominant modes of variation\, how to interpret the principal components\, and how to cho ose the number of components.\n LOCATION:https://stable.researchseminars.org/talk/BNAT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Janusz Przewocki DTSTART:20260427T103000Z DTEND:20260427T123000Z DTSTAMP:20260404T094503Z UID:BNAT/25 DESCRIPTION:Title: Unsupervised Learning (Part 2)\nby Janusz Przewocki as part of Ba sic 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\nThe second session delves into clustering methods and other techniques for uncovering latent structure in data without relying on resp onse variables. We cover K-means clustering and Hierarchical clustering\, including how they work\, how to choose the number of clusters\, how to de cide on distance metrics\, and practical pitfalls (e.g. scaling\, sensitiv ity to initialization). We discuss how to interpret clusters\, validate cl ustering solutions\, and when unsupervised grouping might be appropriate.\ n LOCATION:https://stable.researchseminars.org/talk/BNAT/25/ END:VEVENT END:VCALENDAR