matematikai modellalkotási szeminárium

ME mathematics

BME applied mathematics, BME data science, Molontay Roland

BME Mathematical Modeling Seminar

Course information

The Mathematical Modeling Seminar was initiated by Professor Domokos Szász in the autumn of 2001 and has been held every autumn semester since then. For the past 20 years, Gábor Molnár-Sáska and Gergely Mádi-Nagy have also been involved in organizing the seminar. Starting from 2023, Roland Molontay has taken over the organization of the seminar. You can find more information about the seminar's history here.

The aim of the seminar is to provide a regular platform for presenting applied mathematical results, models, and problems. It serves to promote the dissemination of applied mathematical knowledge and culture within the BME Institute of Mathematics and beyond. The seminar also aims to foster productive collaborations with other institutions, including other BME departments and institutes, as well as companies and enterprises interested in mathematical modeling. This seminar series encompasses all aspects of mathematical modeling, such as the development, analysis, refinement, and validation of mathematical models in diverse applications.
Roland Molontay

Organizer: Dr Roland Molontay

Attendance at the seminar is mandatory for third-year Mathematics BSc students and all (Applied) Mathematics MSc students. However, the seminar is also frequently attended by PhD students and faculty members from our institute, and occasionally by individuals external to the institute. The seminar takes place in the Fall semester on a weekly basis, from 4:15 pm to 5:30 pm on Tuesdays. It is an open event, welcoming anyone interested to attend and participate.
Every Tuesday at 4:15 PM

BME Q Building: QB404

Speakers

Bioinformatics aspects of aging and rejuvenation

Dr Csaba Kerepesi

HUN-REN Institute for Computer Science and Control

Week 1, September 3rd

Bioinformatics aspects of aging and rejuvenation

Aging has a major impact on human health, economy and society in general, but its molecular basis remains poorly understood. Until recently, it was not possible to quantify progression through aging accurately enough to be useful for practical purposes. However, recent research suggests that omics technologies together with advanced bioinformatics and machine learning are capable of measuring the aging process by developing mathematical models („aging clocks”) that can estimate the chronological- and biological age of an individual. Aging clocks can predict the progression of age-related diseases, evaluate longevity intervention and recently emerged rejuvenation therapies.
Presentation slides
Introduction to the Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

Dr Illés Farkas

Citibank

Week 2, September 10th

Introduction to the Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

The Efficient Markets Hypothesis (EMH) assumes that on the financial markets all information is instantaneously available to everyone, and that based on identical information everyone makes the same decisions. Two classical theories (from the 1960s-70s) subsequently built on the EMH are the Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM). The MPT first maximizes the yearly return of a portfolio of risky assets (for example, stocks) at fixed variance of the portfolio's value. Next, the MPT changes the variable from portfolio variance to standard deviation (also called volatility), and adds a risk-free asset (for example, a high-quality bond) to the analyzed portfolio. On the return vs volatility plane the risk-free asset is then connected with the market portfolio to obtain the line showing the highest return at fixed volatility of the combined (risk-free plus risky) portfolio. The CAPM continues by replacing full risk (volatility) with non-diversifiable risk (measured by a quantity called beta). Even in the 2020s, the concepts of the CAPM are frequently applied to the estimation of expected portfolio return and thereby pricing.
Presentation slides

Week 3, September 17th

No lectures - Sport Day

Architecting customer churn prediction with probability models and behavioral data

Anna Takács

BEHive Consulting

Week 4, September 24th

Architecting customer churn prediction with probability models and behavioral data

This seminar delves into the core principles of probability models and their critical role in machine learning and deep learning. We will explore both classical probability theory and Bayesian approaches, understanding how these concepts underlie predictive algorithms that are foundational to AI. Emphasis will be placed on modeling uncertainty, building probabilistic models, and how these frameworks allow us to make informed predictions based on data. The second part of the seminar shifts to practical applications in the industry, such as cross-sell and churn modeling, where probability models are utilized to predict customer behavior and improve decision-making processes. By examining real-world examples, we will uncover how behavioral science insights enhance these models, highlighting the importance of understanding human behavior in constructing more accurate predictive systems. The seminar will also cover the data requirements and methodologies for building these models, offering a comprehensive view of how probability and data science converge in practical applications.
Presentation slides
Economic Complexity: past, present, and future.

Prof Dr César Hidalgo

Toulose School of Economics / Corvinus University of Budapest / University of Manchester

Week 5, October 1st

Economic Complexity: past, present, and future.

For more than a decade, economic complexity has been a flagship application of machine learning methods to questions of sustainable growth and development. In this talk I will introduce the main methods used in the field, connect them to their related concepts in AI, and explore recent and upcoming research in economic complexity. I will conclude by discussing new research directions in the field, including the use of economic complexity methods to questions of economic history and digital trade.
Presentation slides
The fractal structure of treelines in high mountains

Dr Beáta Oborny

Department of Plant Taxonomy, Ecology and Theoretical Biology, Loránd Eötvös University

Week 6, October 8th

The fractal structure of treelines in high mountains

The occurrence of tree species in high mountains usually ends abruptly at some elevation. This is the treeline. Magnifying this region, we find a characteristic ‘mainland/island’ structure, in which the tree cover is continuous at lower elevations (‘mainland’), and gets fragmented at higher ones (‘islands’). Theoretical considerations from percolation theory suggest that the hull of the ‘mainland’ should be a fractal with dimension 7/4. I demonstrate how this hypothesis can be tested using real-world data and explore the broader application of this method for defining species boundaries, and identifying population shifts caused by climate change.
Presentation slides
Decoding politics: Harnessing AI and ML for Gaining Political Insights

Viktor Tisza

Eulytix

Week 7, October 15th

Decoding politics: Harnessing AI and ML for Gaining Political Insights

This speech will delve into the application of Artificial Intelligence (AI) and Machine Learning (ML) in political forecasting, illustrated by compelling examples. The first case study focuses on forecasting the 2022 Hungarian Elections through probabilistic programming. Additionally, the speech will examine the methodologies developed by Eulytix to model and predict outcomes in complex areas of European Union decision-making. By leveraging advanced AI techniques, such as Large Language Models (LLMs) for extracting structured data from unstructured political texts, applying network analysis to reveal hidden relationships between decision-makers, and utilizing ML algorithms to forecast voting outcomes, this approach provides a scientifically robust framework for enhancing the transparency and predictability of political processes. The insights aim to demonstrate the profound potential of AI and ML in systematically decoding and anticipating political events within the intricate governance structures like that of the European Union.
Presentation slides
The crisis of social and behavioral sciences - is there a statistical solution?

Dr Barnabás Szászi

Behavioral Science Lab, Loránd Eötvös University

Week 8, October 22nd

The crisis of social and behavioral sciences - is there a statistical solution?

There is considerable heterogeneity in the results of social and behavioral science findings and more specifically in the impact of behavioral intervention studies that aim to change human behavior for good. While their average effectiveness in changing behavior is modest. Although they can be highly effective in some conditions, they may be ineffective in others and counter-productive in yet others. The heterogeneity within these studies can come from different sources including population heterogeneity, design heterogeneity, and analytical heterogeneity. In this talk, I will focus on two big-team science projects where we aim to discover the robustness and generalizability of prior behavioral science findings to alternative justifiable analyses. Altogether, in these two studies, we have been leading over 1500 researchers from all over the world. Our exploration suggests that many currently applied analysis approaches in social and behavioral research cannot be held anymore and the general practices of conducting, reporting, and reviewing empirical analyses require critical reforms.
How can a person exist in cyberspace?

Ferenc Vágujhelyi

National Tax and Customs Administration

Week 9, October 29th

How can a person exist in cyberspace?

In this lecture, we will explore the fundamental requirements of digital identity (or digital citizenship) and draw parallels with its analog counterpart, where the primary challenge lies in creating an unforgeable physical document, such as a banknote. In the digital realm, where zeros and ones can be effortlessly duplicated, a different approach is necessary to confer legal authority upon an electronic document. We will discuss how only a single individual can possess the capability to sign a document, while anyone can verify the validity of the signature and the immutability of the document's content. The lecture will delve into the application of cryptographic methods for authentication, emphasizing the importance of asymmetric key schemes. Through practical examples involving hash functions and the RSA method, we will demonstrate how to link a public key to a natural person using both decentralized (web-of-trust) and centralized (Certificate Authority) systems. As the lecture progresses, we will examine the growing significance of zero-knowledge proof schemes. If time permits, we will also address the representation of decentralized digital money (blockchain) and the emerging challenges posed by quantum computing.
Differential equations in the service of chemical process engineers: focus on pharmaceutical manufacturing

Dr Botond Szilágyi

Department of Chemical and Environmental Process Engineering, BME

Week 10, November 5th

Differential equations in the service of chemical process engineers: focus on pharmaceutical manufacturing

Many of us may have heard the famous phrase of Antoine Lavoisier that "nothing is lost, nothing is created, everything is transformed". For the chemical engineer, this is the foundation of the so-alled balance equation, which is a nothing more but the mathematical description of the above phrase applied to various levels (micro or macro), equipment (reactors, separators, heat exchangers etc.), chemical or biomolecular reactions, etc. Like many models in different fields of science and technology, these balance equations translate to ordinary or partial (integral) differential equations whose solution can mimic the real chemical system's behavior. In other words, they enable us to simulate the real system, which is invaluable for a chemical engineer as it can replace costly and/or dangerous experiments and, moreover, allow an unprecedented understanding of complex systems and processes. The lecture will explain how these balance equations are born and translated into the language of mathematics, how are we solving them, what are the cutting-edge applications in general, and how we use them to support pharmaceutical manufacturing for cleaner and more competitive production of drug products, with the overarching aim of making the life-saving medicines accessible for broader population worldwide.
FX Swaps and Forwards

Viktor Binzberger

Morgan Stanley

Week 11, November 12nd

FX Swaps and Forwards

The presentation gives a high-level overview of FX derivative markets, the common financial products and the typical use cases why institutional clients use and trade such products. We will cover the pricing of FX derivatives with particular focus on FX Forwards and FX Swaps.
Fractional calculus, functional calculus, and anomalous transport

Prof Dr Mihály Kovács

Department of Analyis and Operations Research, BME, Pázmány Péter Catholic University

Week 12, November 19th

Fractional calculus, functional calculus, and anomalous transport

Non-integer (also known a fractional) order derivatives are almost as old as their integer order counterparts. Until the 20th century they did not receive the same attention as integer order derivatives due to their apparent lack of practical applications. However, after P. Lévy announced his famous generalized central limit theorem in 1934 it became apparent that fractional derivatives are deeply linked to anomalous diffusion/dispersion observed in many fields of sciences. It this talk I will give a short introduction to fractional order derivatives and advection-diffusion/dispersion equations and discuss their relevance in modelling contaminant transport in subsurface groundwater flow. The talk will even go beyond fractional order derivatives and will introduce the abstract notion of functional calculus, in particular fractional powers of linear operators, which is then used for practical modelling purposes.
Road traffic modeling and control

Prof Dr Tamás Tettamanti

Traffic Lab, BME

Week 13, November 26th

Road traffic modeling and control

Road traffic control starts with proper mathematical modeling, i.e., describing and understanding the complex nature of vehicular traffic dynamics is the first step of traffic control solutions. The macroscopic traffic variables and related concept of the fundamental diagram are introduced. The main elements and tools for traffic management are discussed. Finally, a case study of a freeway control problem is presented with simulations.
A beginner’s guide to machine learning with graphs: Theory and Applications

Szabolcs Nováczki

NOKIA Bell Labs

Week 14, December 3rd

A beginner’s guide to machine learning with graphs: Theory and Applications

This introductory lecture will explore the field of machine learning with graphs, focusing on how graph structures can be used to uncover patterns and relationships in data. We begin by explaining the basic concept of graphs and their relevance in representing real-world data, such as communication networks. We will then introduce key machine learning techniques tailored for graphs, including Graph Neural Networks (GNNs) and Graph Convolutional Networks (GCNs), breaking down how these models learn from graph data to make predictions. The lecture will also highlight practical applications in communication networks. Finally, we will discuss challenges in working with graph data, such as handling large-scale graphs and ensuring model fairness. By the end of the lecture, students will gain a foundational understanding of graph-based machine learning and its diverse applications.

Requirements

Attendance Requirements

Successful completion of this course is contingent upon attending a minimum of 70% of scheduled lectures. Vigilant attendance tracking will be maintained throughout the duration of the course to ensure adherence to this guideline.

Limited exceptions to this attendance policy can be considered, exclusively through application for a reduced study timetable. Further details regarding this option can be found in Chapter IV, Section 37 of the BME Study and Examination Regulations.

In the event that a student participates in the ERASMUS program during the autumn semester, with a desire to avoid a gap in progress, specific actions need to be taken. The student is required to formally notify the responsible instructor about the impending absence. Subsequently, the responsible instructor will outline alternative pathways for course completion within the academic year. This could involve selecting a relevant subject for study during the international program or engaging in an independent project. Notably, the course will not be offered during the spring semester

Course Requirements for students on the 2-credit version of the course:

In addition to fulfilling attendance criteria, active participation in lectures and engagement with lecture materials through independent study are expected. The following activities can earn points:

  1. Attending lectures beyond the minimum attendance requirement: 10 points per lecture.
  2. Formulating relevant professional questions or observations to the lecturer after the lectures: 15 points per question (a maximum of 15 points can be earned per lecture, even if multiple questions are posed by the student).
  3. Undertaking supplementary independent research related to the lecture, resulting in a 2-3 page study. This study could involve:
      4. - Critical analysis, extension, or discussion of topics covered in the lecture.
      - Overview, summary, and analysis of articles presented during the lecture or related to its subject.
      - Performing simulations or programming tasks motivated by the lecture's topic.
      - Any other research inspired by the lecture.
    The task can be completed in groups of 2-3 students (in which case, the study should be proportionally longer).
    Earns 40-50 points per study. The paper can be written in Hungarian or English according to the student's preference.

Point Thresholds:

0 - 591

60 - 89 2

90- 119 3

120 - 149 4

150 - 5

Course Requirements for students on the 1-credit version of the course:

In addition to fulfilling attendance criteria, active participation in lectures and engagement with lecture materials through independent study are expected. The following activities can earn points:

  1. Attending lectures beyond the minimum attendance requirement: 10 points per lecture.
  2. Formulating relevant professional questions or observations to the lecturer after the lectures: 10 points per question (a maximum of 10 points can be earned per lecture, even if multiple questions are posed by the student).
  3. Undertaking supplementary independent research related to the lecture, resulting in a 2-3 page study. This study could involve:
      4. - Critical analysis, extension, or discussion of topics covered in the lecture.
      - Overview, summary, and analysis of articles presented during the lecture or related to its subject.
      - Performing simulations or programming tasks motivated by the lecture's topic.
      - Any other research inspired by the lecture.
    The task can be completed in groups of 2-3 students (in which case, the study should be proportionally longer).
    Earns 20-30 points per study. The paper can be written in Hungarian or English according to the student's preference.

Point Thresholds:

0 - 29 1

30 - 49 2

50- 69 3

70 - 89 4

90 - 5

History

The BME Mathematical Modelling Seminar is almost the same age as the mathematics program of the BME. The seminar was initiated by Professor Domokos Szász in 2001. Around the millennium and since then, the range of applications of mathematics has grown by leaps and bounds, just think of its role in artificial intelligence research or financial mathematics. Professor Tamás Szántai helped to launch the seminar, and Gábor Molnár-Sáska was its secretary between 2001 and 2006. In 2006, Gergely Mádi-Nagy took over the role of the seminar secretary, and he held this position until 2022. The seminar proved to be a great success, and to this day it is part of the curriculum not only of the mathematics students of the Budapest University of Technology and Economics, but it also plays an important role in the whole Hungarian applied mathematics scene.

Professor 2

Prof Dr Domokos Szász

Professor 1

Dr Gergely Mádi-Nagy

Professor Domokos Szász said that he had conceived the seminar to provide a regular forum for the presentation of applied mathematics results, models, and problems. The aim of the seminar from the very beginning has been to promote the dissemination of applied mathematics knowledge and culture both within the BME Mathematics Institute and more widely. Another fundamental objective is to give the students a plastic picture of the perspective areas of applied mathematics as a profession. Gergely Mádi-Nagy added that during the more than two decades of the seminar, it has been possible to invite a number of high-quality speakers, often highly recognized experts in their fields. As examples, he mentioned a few names that are more widely known, such as Gábor Bojár (founder of Graphisoft), Albert-László Barabási (one of the leading researchers in network science), Botond Kőszegi (one of the pioneers of behavioral economics), the Abel Prize (equivalent to Nobel Prize in Mathematics) mathematicians Péter Lax and László Lovász, or Alfio Quarteroni (designer of America's Cup winning sailing boat Alinghí).

Past seminars

2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001