SPMS 2021

24 Jun 2021, 12:00 → 28 Jun 2021, 13:00 Europe/Prague

Jana Vacková (Department of Mathematics, FNSPE Czech Technical University in Prague), Jiří Franc (The Czech Technical University in Prague), Václav Kůs (Department of Mathematics, FNSPE Czech Technical University in Prague)

The Stochastic and Physical Monitoring Systems (SPMS) has been an annual international conference since 2010 with the aim to bring together students and researchers with areas of interest related to the following topics:

• Traffic and pedestrian modeling, microscopic structure of vehicular streams.
• Elasticity and classification in material defectoscopy;
• Small area estimation and Generalized mixed linear model;
• Data analysis in particle and experimental physics.
• Stochastic models, Bayesian analysis, competitive games.

The meeting is organized by the Group of Applied Mathematics and Stochastics (GAMS), Department of Mathematics, Czech Technical University in Prague.

The SPMS 2021 conference will be held at Hotel Kavka, Malá Skála, Czech Republic from 24th to 28th of June, 2021.

SPMS2021_instructions.pdf

SPMS2021_paper_template.zip

SPMS2021_poster.pdf

SPMS_proceedings20_21.pdf

Thursday, 24 June

12:00 → 13:30 Registration

13:30 → 14:30 Lunch

14:30 → 15:00 Welcome Session

Convener: Jiří Franc (Czech Technical University (CZ))

15:00 → 16:00 Stochastic Monitoring Systems

Convener: Jiří Franc (Czech Technical University (CZ))

15:00 Performance Analysis of Fast Independent Component Extraction

A novel extension of Independent Component Analysis for blind extraction/separation of one or several sources from time-varying mixtures is proposed. The Signals of Interest in mixtures are assumed to be dynamic, i.e., they are moving, while the other sources are static. The extension version of popular FastICA algorithm is analysed. The algorithms are derived within a unified framework so that they are applicable in the real-valued as well as complex-valued domains, and jointly to several mixtures, similarly to Independent Vector Analysis. Performance analysis of the one-unit algorithm is provided; it shows its asymptotic efficiency under the given mixing and statistical models. Numerical simulations confirm the validity of the analysis, and show the usefulness of the algorithms in separation of moving sources.

Speaker: Václav Kautský (Department of Mathematics, FNSPE, Czech Technical University in Prague)

spms2021_vk.pptx

15:20 Variational Inference for Blind Image Deconvolution

Blind image deconvolution aims on recovering sharp image from a blurred one while the blur is unknown. It is a highly ill-posed problem requiring suitable regularization. One of the commonly used approaches for solving this problem is variational Bayesian inference. Hierarchical Bayesian models allow for a good representation of both sharp image and blur kernel and Variational Bayes can be used to find posterior distributions. While Variational Bayes offers easy optimization, it is very restrictive when it comes to the choices of prior distributions. For example, if the blur is spatially variant, finding solution under this framework would be very complicated. Higher flexibility could be achieved via numerical optimization of evidence lower bound, which does not require the distributions to be from conjugate system. These two methods - Variational Bayes and ELBO optimization - will be compared in this presentation.

Speaker: Antonie Brožová (Department of Mathematics, FNSPE, Czech Technical University in Prague)

prezentace_spms2021.pdf

15:40 The Role of a priori Distributions for Sparse Parametrization of Models

In the modern world of lots of data, there is a large number of powerful and effective tools for estimating the parameters of models, on the basis of which it is then possible to predict new values. To save valuable computational time, various types of regularizations can be added to the models to force sparse parameterization. Thanks to such parameterization, it can be aimed at better explanability and less complexity of the model. This contribution deals with the introduction of the concept of sparse parameterizations and their corresponding a priori distributions, such as Automatic Relevance Determination. It will be shown how it is possible to remove excess parameters from the model and still keep the main information in the data. In other words, we want as many parameters as possible to be zero, provided that they are insignificant to the model.

Speaker: Lukáš Kulička (Department of Mathematics, FNSPE, Czech Technical University in Prague)

Kulička_prezentace_SPMS.pdf

16:00 → 16:20 Coffee Break

16:30 → 18:30 Outdoor Session

Convener: Jiří Franc (Czech Technical University (CZ))

19:00 → 20:00 Dinner

Friday, 25 June

09:00 → 10:20 Traffic and Agent Monitoring Systems

Convener: Pavel Hrabák (FIT CTU)

09:00 10 years of pedestrian research on FNSPE

The presented contribution aims to illustrate the pedestrian research history on our faculty. Initial aim was to improve the microscopic properties of cellular models of pedestrian movement, focusing mainly on (experimentally) observed behavior.
A custom variant of the Floor Field model was implemented with incorporated original elements that brought the model closer to the reality. In order to calibrate the model and describe the standard behavior of pedestrians, author designed and performed four evacuation experiments; analysis of data extracted from cameras and other detectors pointed to several undescribed phenomena - their detailed study become rather independent research matter.
To be more specific, the observed heterogeneity in speed, aggressiveness and path selection was projected into the custom model resulting in a better fit of the observed quantities distribution, especially the evacuation time. In the mathematical description of experimental observations, the author dealt with the creation of a general concept of density covering various calculation methods. The properties of these methods has been further investigated by team members in detail and illustrated on experimental data.
In addition to evaluating calibration experiments, team members also participated in the organization and evaluation of two train unit egress experiments and he organized two merging pedestrian streams experiments focusing on more complex infrastructure. Using such complex geometry, the custom model was validated on in-house measured data as well as the data measured by a foreign research group.

Speaker: Marek Bukáček (Department of Mathematics, FNSPE, Czech Technical University in Prague)

prezentaceSPMS21_MB.pdf

09:20 Pedestrian Density Estimates and Their Real Applications

Density is one of the fundamental quantities for a description of pedestrian dynamics. In the last decade, there is an increasing need to define density better than "the count of pedestrians divided by the size of the detector". Hence this contribution deals with the very promising approach defining pedestrian density using the assumption that every pedestrian is a source of the density distribution. This kind of (kernel) density estimate opens up a lot of new possibilities in real applications.

Speaker: Jana Vacková (Department of Mathematics, FNSPE, Czech Technical University in Prague)

prezentace_SPMS_2021.pdf

09:40 Heterogeneous agents in cellular models of pedestrian flow

Despite their simplicity, cellular models are able to capture important phenomena of collective behaviour. In order to obtain higher level of realism, indistinguishable particles in cellular models are replaced by agents having various properties or following different strategies.
Several approaches how to introduce heterogenity into multi-agent cellular systems have been investigated in last decades. Contrary to continuous models, where heterogeneity is usually achieved by variations in agents parameters, the space and time discrete nature of cellular models implied to introduce the heterogeneity in agents rules or preferences defining its strategy.
A review of various concepts of heterogenity in cellular models is provided together with the discussion of the impact on system realism and advantages over the simple system with homogeneous agents-particles.

Speaker: Pavel Hrabák (FIT, Czech Technical University in Prague)

SPMS_21_prezentation.pdf

10:00 Conflict solution in cellular evacuation model

Agent-based cellular models can be used to simulate the process of evacuation of people from a room. The actions and interactions of heterogeneous agents create collective motion and capture complex phenomena of pedestrian dynamics. This thesis presents a multi-agent cellular model based on floor-field model and is extended by a new strategy for solving conflicts when two or more agents attempt to enter the same cell. The agents and the model have various parameters that influence the conflict solution. A sensitivity analysis on these parameters is performed that reveals the individual contribution of variance in the results.

Speaker: Matej Šutý (FIT, Czech Technical University in Prague)

SPMS_SUTY_MATEJ.pdf

10:20 → 10:50 Coffee Break

10:50 → 12:10 Traffic and Agent Monitoring Systems

Convener: Jana Vacková (Department of Mathematics, FNSPE Czech Technical University in Prague)

10:50 Superrandom states of thermodynamical traffic gas and their mathematical properties

This paper deals with a thermodynamical traffic gas model, variance of clearances in traffic data and super random states in traffic theory.
The first part offers an introduction to vehicular headway modelling and its history. Furthermore, it is focused on the aforementioned thermodynamical traffic gas model and its mathematical properties. Relevant functions for clearance distributions are from the GIG class of functions, which is exceptionally suitable for traffic flow description. This paper also contains improved proofs from particle systems mathematics and recurrent equation for GIG functions moments. The last part includes an algorithmic simulation of a traffic system that has a super random stationary state.

Speaker: Vít Pánek (Department of Mathematics, FNSPE, Czech Technical University in Prague)

spms_prezentace_engss.pdf

11:10 Scaling of the Generalized Inverse Gaussian Distribution with negative parameter

The Generalized Inverse Gaussian distribution (GIG) is frequently used in the traffic modeling fields. Its properties for non-negative value of parameter $\alpha$ were presented in previous research [1]. The objective of this paper is to follow up discovered relations and further explore properties of GIG with the negative value of parameter $\alpha$, such as normalization constant and the approximation of scaling constant. Because of the symmetric properties of Macdonalds funcition, many procedures from previous research can be adjusted and re-applied for GIG with negative value of $\alpha$. The main idea is to highlight these similarities and capture the differences, which come in the form of scaling condition.

Speaker: Anežka Lhotáková (Department of Mathematics, FNSPE, Czech Technical University in Prague)

Lhotakova_SPMS.pdf

11:30 Innovative Approach to Capacity Calculation Methodology for Unsignalized T-intersection

This work challenges one section of the gap acceptance theory related to the analysis of unsignalized intersections. The focus is on the methodology for capacity calculations put forward by Siegloch in 1973 which is still widely used today. Analyzing data from a given intersection in Dresden, it is shown that one of Siegloch’s assumptions– exponential distribution of time clearances on the main road, presented in his capacity calculation– does not correspond with our data. For this reason, other time clearance distributions are considered and used. Lastly, it is shown that the interpretation and use of linear approximation for Siegloch’s function–mean number of vehicles that accept a given gap, in the capacity calculation– is often used incorrectly and its correction further improves resulting capacities.

Speaker: Nikola Groverová (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_Capacities_Groverová.pdf

12:30 → 13:30 Lunch

13:30 → 14:00 Traffic and Agent Monitoring Systems

Convener: Jana Vacková (Department of Mathematics, FNSPE Czech Technical University in Prague)

13:30 Pedestrian modeling in Julia

Julia is a relatively new programming language whose popularity among people is growing significantly every year. One of the reasons for that is Julia's type system and multiple-dispatch. These two concepts allow building very complex frameworks for solving different tasks (differential equations, neural networks, ... ) that are easily customizable for non-standard problems. An example is the Agents.jl framework for agent-based modeling. This talk aims to show how to use Agents.jl to create a model of pedestrian movement.

Speaker: Václav Mácha (Department of Mathematics, FNSPE, Czech Technical University in Prague)

14:00 → 14:40 Machine Learning in Acoustic Emission

Convener: Václav Kůs (Department of Mathematics, FNSPE Czech Technical University in Prague)

14:00 Deep Learning Methods for Acoustic Emission Evaluation

The goal of this paper is to summarize deep learning methods and apply some of these architectures to real data from tensile tests of metallic materials. Here many existing neural networks are applied to a signal gained from acoustic emission to determine the beginning of plasticity in the material. Plastic deformation is accompanied by microscopic events such as a slip of atomic plane dislocations which is hardly detectable by other methods. The potential of machine learning is demonstrated on two tensile tests where the material is strained until it collapses. The examined networks proved well to reliably predict the risk of collapse together with changes in the ultrasound signal emission.

Speaker: Martin Kovanda (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_Kovanda_Presentation.pdf

14:20 Classification of acoustic emission signals in material defectoscopy based on statistics and machine learning

Reliable classification of acoustic emission signals is crucial for practical use of this nondestructive testing technique. During classification, signals are represented by a convenient, low-dimensional set of attributes. This presentation adresses the problem of selecting appropriate atributes and consequently describes and compares several classification methods, specifically Division methods, Model Based method, KDE method and classification using Supervised Divergence Decision Tree. The paper proposes new attribute and classification method. The methods were tested and compared on a set of laboratory measured data. The most reliable method seems to be the supervised KDE classification method.

Speaker: Jan Zavadil (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_21 Zavadil.pdf

14:40 → 15:00 Coffee Break

15:00 → 16:30 Seminar: From real data to the deployed solution

Convener: Jiří Franc (Czech Technical University (CZ))

15:00 From Provider To Client - The Journey of Data In A Fintech Firm

The talk focuses on the general steps of the data processing cycle and its implementation in a firm that operates in the fintech industry. While statisticians often discuss the actual processing of data - such as making the best possible models and thoroughly verifying that the results satisfy the necessary conditions - this work discusses the various steps that teams in companies have to complete that are essential for the data processing cycle to bear fruit, i.e. so that the client receives their desired outcome. In the first part, 4 basic steps of the cycle are outlined - data collection, preprocessing, processing and output. The second part of the talk focuses on the processing of data in terms of the continuous integration cycle - from the detailed description of the issue on a "ticket" through development and testing all the way to the successful deployment of the fix in production. Examples from firms in the industry are shown to better illustrate the discussed concepts.

Speaker: Tomáš Košlab (FinMason Europe)

Koslab_prezentaceSPMS21.pdf

15:25 Testing in software development

Testing in terms of programmatic tests has become a vital part of software development. Companies and individuals have been using it to gain confidence in their applications' correctness, avoid repeating the same mistakes over and over and test their applications with inputs that are rare and the applications need to deal with them nonetheless.
Testing, in the form of writing unit tests, integration tests, end-to-end tests or any other kind should be a skill of every programmer who takes their job seriously enough and wants to deliver an application with a certain level of robustness.
Let us have a look at examples of how to write simple tests of various kinds, the challenges it brings, the benefits and how (and if) it has an impact on the code of our applications. Let us discuss how and if is this component of software engineering used by mathematics researchers, how useful it may actually be in this field and how people actually deal with the difficulties of how to test something when we don't know exactly what it is supposed to do.

Speaker: René Kliment (Quantlane, WOOD & Company Financial Services, a.s.)

16:30 → 19:00 Outdoor Session

19:00 → 20:00 Dinner

Saturday, 26 June

09:30 → 18:00 Whole day trip joined with Student Questions and Answers Session

19:00 → 21:00 Dinner

Sunday, 27 June

09:30 → 10:50 Stochastic Monitoring Systems

Convener: Václav Kůs (Department of Mathematics, FNSPE Czech Technical University in Prague)

09:30 Stochastic Modeling of Fractal Diffusion

Stochastic models of diffusion in spatial domains of noninteger dimension are widely applicable as a basis of simulations. Obtaining data having fractal properties requires the construction of fine enough discrete latices that is computationally expensive. This contribution presents a novel way of representing graph-based finite models using a generalized coordinate system. Presented methods allow for convenient selection of random vertices and also for representing movement between vertices. Fractal properties of obtained simulation data are tested and presented and show the applicability of introduced methods in statical testing of dimension estimates.

Speaker: František Gašpar (Department of Software Engineering, FNSPE, Czech Technical University in Prague)

SPMS2021.pdf

09:50 Multisolution Approach to Classification Tasks in Biomedicine

Simultaneous search for multiple sparse solutions of a classification/regression problems differs fundamentally from common approaches to these classical machine learning problems. At the same time, it is strongly motivated by practical requirements, e.g. in applications in biomedicine. In such tasks, we face high dimensions, limited number of samples, errors in data and, most importantly, the necessity of providing a human-interpretable model. On the other hand, field-related expertise is usually available.
This contribution shall convey the concept of multisolution feature selection within a classification problem. Using a real world example, we shall introduce the core ideas. We shall also outline the individual steps leading to the problem's formal definition and its potential solution.

Speaker: Kateřina Henclová (Department of Mathematics, FNSPE, Czech Technical University in Prague)

spms2021_henclova.pdf

10:10 Real Options Valuation: A Dynamic Programming Approach

The theory of real option analysis (ROA) is considered as an advanced project valuation technique, which respects the value of future project alternations (real options).

To our best knowledge, the current state of ROA does not offer a unified valuation algorithm that would be able to cover valuations of more complex projects, such as those with multiple random variables or different types and a larger number of possible actions.

This thesis takes the problem of ROA and tries to interpret it as a problem of decision-making under uncertainty from the statistical decision theory (SDT).
We present a general valuation algorithm that builds on the knowledge of SDT, covers the solutions proposed by ROA and preserves the business-specific concepts as time value of money and risk aversion of investors.

This algorithm's usage is demonstrated on a problem of gas power plant's valuation, where the problem of uncountable state space is solved via the approximate dynamic programming technique of value function approximation, where we use piecewise linear models to cover the option-like structure.

Speaker: Filip Rolenec (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_2021_Rolenec.pdf

10:30 Emergence of Novelty in Evolutionary Algorithms

Evolutionary algorithms are known to converge to non-evolving populations rather quickly. Rewarding with respect to an objective does not improve overall performance. Novelty Search is one of the solutions to this problem. We explored and developed techniques which can complement the popular divergent algorithm called Novelty Search. We believe its main drawback lies in attempting to define the diversity of a population. In our case, we instead explored approaches where novelty arises from more basic principles, such as the environment itself.

Speaker: Dominika Zogatová (Department of Mathematics, FNSPE, Czech Technical University in Prague)

novelty_search_prez.pdf

10:50 → 11:10 Coffee Break

11:10 → 11:30 Stochastic Monitoring Systems

Convener: Jiří Franc (Czech Technical University (CZ))

11:10 Application of stochastic control methods for trading on power markets

This work deals with the application of stochastic control methods for trading on power markets. It acquaints readers with the basics of the functioning of the electronic exchange and with the specifics of the energy market. This is followed by the theory of stochastic differential equations and stochastic optimal control. The objective is to understand the current results in the field of optimal trading on the energy exchange, which includes the implementation of a suitable numerical scheme to solve the Hamilton–Jacobi–Bellman equation, and come up with a modification of the solution that would include current real business aspects and constraints in the energy market.

Speaker: Filip Mairinger (Department of Mathematics, FNSPE, Czech Technical University in Prague)

11:30 → 12:30 Machine Learning and Data Processing

Convener: Jiří Franc (Czech Technical University (CZ))

11:30 Introduction to Spiking Neural Networks

Artificial Neural Networks (ANNs) such as Convolutional Neural Networks (CNNs) or Recurrent Neural Networks (RNNs) have become the building stone of deep learning models for complex tasks like image recognition or speech recognition. A perceptron model, the core cell of the ANNs, has been inspired by the neural processes in the human brain. However, the biological neural dynamics are much more complicated and differ significantly after a closer look. In this session, we present the idea behind the Spiking Neural Networks (SNNs) - biologically-feasible spiking neurons with rich temporal dynamics and high-power efficiency.

Speaker: Miroslav Kubů (Department of Mathematics, FNSPE, Czech Technical University in Prague)

Introduction_to_SNNs_SPMS_2021.pdf

11:50 Homogeneity testing of weighted datasets in HEP

Simulations of elementary particles are fundamental to new discoveries in the field of high energy physics. The Monte Carlo-based simulations often take form of a weighted datasets that need to be compared with real measurements. This work explores different modifications of standard homogeneity tests to weighted datasets using numerical simulations.

Speaker: Kristina Jarůšková (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS2021_Jaruskova.pdf

12:10 Machine Learning Methods for Algorithmic Trading on Power Markets

Along with the growing share of renewable energy sources together with pan European integration of day-ahead and intraday electricity markets, volatility in all kind of energy markets has been increasing in recent years. Increased liquidity in intraday markets helps to minimize deviations and stabilize the transmission system, and in long-term markets it helps to hedge contracts. With this increasing number of trades, market participants, and huge amount of data, the possibility to use machine learning models and neural networks for trading also comes into play. This text focuses on the research of these models and their implementation in energy markets. The aim is to process available data from energy markets and weather data from Europe and to explore possible correlations. The next goal is to prepare and train a robust model and verify it on recent data. The implementation of a solution for time series on algorithmic trading is an upcoming task of this work.

Speaker: Vojtěch Obhlídal (Department of Mathematics, FNSPE, Czech Technical University in Prague)

13:00 → 14:00 Lunch

14:00 → 16:00 Questions and Answers Session

16:00 → 19:00 Outdoor Session

19:00 → 20:00 Dinner

Monday, 28 June

09:00 → 10:00 Closing Remarks & Evaluation of the Conference

10:00 → 10:20 Coffee Break

10:20 → 11:00 Departure of all participants