Papers by Janusz Szwabiński
arXiv (Cornell University), May 10, 2023
Systemic risk is a rapidly developing area of research. Classical financial models often do not a... more Systemic risk is a rapidly developing area of research. Classical financial models often do not adequately reflect the phenomena of bubbles, crises, and transitions between them during credit cycles. To study very improbable events, systemic risk methodologies utilise advanced mathematical and computational tools, such as complex systems, chaos theory, and Monte Carlo simulations. In this paper, a relatively simple mathematical formalism is applied to provide a unified framework for modeling credit cycles and systemic risk assessment. The proposed model is analyzed in detail to assess whether it can reflect very different states of the economy. Basing on those results, measures of systemic risk are constructed to provide information regarding the stability of the system. The formalism is then applied to describe the full credit cycle with the explanation of causal relationships between the phases expressed in terms of parameters derived from real-world quantities. The framework can be naturally interpreted and understood with respect to different economic situations and easily incorporated into the analysis and decision-making process based on classical models, significantly enhancing their quality and flexibility.
Physica D: Nonlinear Phenomena, Feb 1, 2013
We present and discuss a Monte Carlo model describing the dynamics of three types of annual plant... more We present and discuss a Monte Carlo model describing the dynamics of three types of annual plants which have different tolerances to shade and drought. External conditions (water and light) fluctuate around some values which are our control parameters and which decide how many resources the system receives. The plants compete with their nearest neighbours for the resources, however not in the same way. We show that for certain ranges of the control parameters a coexistence of the three species is observed. We discuss how the characteristics of the the plants-their number, germination, biomass or the number of nearest neighbours, depend on the two control parameters characterising external conditions. We show that elimination is done at the level of adult plants, not seedlings. We find also cooperative behaviour of plants in difficult conditions, as observed in field studies and we propose an explanation for this fact. Apart from plants tolerating shade but requiring more water and those tolerating drought but needing more light, which are common in nature, we introduce a third species with intermediary demands. We investigate under what conditions this new species could dominate and whether the total number of plants, regardless of their type, is larger with or without the intermediate plant. We show that in our model, like in nature, systems with two kinds of plants with opposite characteristics are, in general, as effective as a system with an additional third type of plants. We show that two contradictory hypotheses made by biologists, concerning the demands of plants in drought and shade, could be both true, however in different regimes.
Physical Review E, Mar 20, 2008
We investigate in detail the model of a trophic web proposed by Amaral and Meyer [Phys. Rev. Lett... more We investigate in detail the model of a trophic web proposed by Amaral and Meyer [Phys. Rev. Lett. 82, 652 (1999)]. We focused on small-size systems that are relevant for real biological food webs and for which the fluctuations are playing an important role. We show, using Monte Carlo simulations, that such webs can be non-viable, leading to extinction of all species in small and/or weakly coupled systems. Estimations of the extinction times and survival chances are also given. We show that before the extinction the fraction of highly-connected species ("omnivores") is increasing. Viable food webs exhibit a pyramidal structure, where the density of occupied niches is higher at lower trophic levels, and moreover the occupations of adjacent levels are closely correlated. We also demonstrate that the distribution of the lengths of food chains has an exponential character and changes weakly with the parameters of the model. On the contrary, the distribution of avalanche sizes of the extinct species depends strongly on the connectedness of the web. For rather loosely connected systems we recover the power-law type of behavior with the same exponent as found in earlier studies, while for densely-connected webs the distribution is not of a power-law type.
Physica D: Nonlinear Phenomena, Jul 1, 2010
We present and study a lattice (Monte Carlo) model of a food web consisting of three levels. Agen... more We present and study a lattice (Monte Carlo) model of a food web consisting of three levels. Agents on the lowest level produce food from dead agents (detritus) of the upper levels and are themselves eaten by the first level species, which in turn are prey for the top level species. Agents which do not find food in a given time, die with a given probability, while eating enables them to produce offspring in their neighborhood. This rule applies to species on all levels, including the lowest one. The dynamics is therefore nutrient limited. We are considering two pathways-grazers and detritus (using dead organic matter). We show that the emerging dynamics is more complex than the ordinary predator-prey systems in which bottom species are indestructible. We investigate the viability of our model and we construct appropriate (extinct-alive) phase diagrams. We demonstrate how the temporal fluctuations in the densities of the three populations are correlated. We show also that the density of the middle level agents plays the key role in the viability of the investigated food web.
Physica D: Nonlinear Phenomena, Nov 1, 2012
A food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulatio... more A food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The model consists of three trophic levels, each of which is populated by animals of one distinct species. While the species at the intermediate level feeds on the basal species, and is eaten by the predators living at the highest level, the basal species itself uses the detritus of animals from higher levels as the food resource. The individual organisms remain localized, but the species can invade new lattice areas via proliferation. The impact of different proliferation strategies on the viability of the system is investigated. From the phase diagrams generated in the simulations it follows that in general a strategy with the intermediate level species searching for food is the best for the survival of the system. The results indicate that both the intermediate and top level species play a critical role in maintaining the structure of the system.
European Physical Journal B, May 5, 2009
We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a squar... more We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategy therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.
Physical review, Oct 19, 2001
We study the dynamic structure factor S(q, ω) of superfluid 4 He at zero temperature in the roton... more We study the dynamic structure factor S(q, ω) of superfluid 4 He at zero temperature in the roton momentum region and beyond using field-theoretical Green's function techniques. We start from the Gavoret-Nozières two-particle propagator and introduce the concept of quasiparticles. We treat the residual (weak) interaction between quasiparticles as being local in coordinate space and weakly energy dependent. Our quasiparticle model explicitly incorporates the Bose-Einstein condensate. A complete formula for the dynamic susceptibility, which is related to S(q, ω), is derived. The structure factor is numerically calculated in a self-consistent way in the special case of a momentum independent interaction between quasiparticles. Results are compared with experiment and other theoretical approaches.
Entropy, May 22, 2021
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Physica D: Nonlinear Phenomena, 2006
The influence of habitat destruction on a population of predators and prey is studied. We show, v... more The influence of habitat destruction on a population of predators and prey is studied. We show, via Monte Carlo simulations of a lattice model, that with growing devastation the oscillations in the densities of both species, as well as cross-correlations between the two densities diminish. As should be expected, predators are more vulnerable and disappear before the prey. Devastation of the habitat is never beneficial and the percentage of coexisting (prey and predators) states decreases with destruction. Because of the high fragmentation of the environment in the case of large devastation, animals' populations are separated into small sub-populations living in restricted areas. Such small populations become extinct more easily. We have also shown that in the case of large habitat devastation the density of the population of prey depends on its history.
Entropy, Dec 19, 2020
The growing interest in machine learning methods has raised the need for a careful study of their... more The growing interest in machine learning methods has raised the need for a careful study of their application to the experimental single-particle tracking data. In this paper, we present the differences in the classification of the fractional anomalous diffusion trajectories that arise from the selection of the features used in random forest and gradient boosting algorithms. Comparing two recently used sets of human-engineered attributes with a new one, which was tailor-made for the problem, we show the importance of a thoughtful choice of the features and parameters. We also analyse the influence of alterations of synthetic training data set on the classification results. The trained classifiers are tested on real trajectories of G proteins and their receptors on a plasma membrane.
Physical Review E, Feb 26, 2009
International Journal of Modern Physics C, Nov 1, 2006
A model which consists of a predator and two prey species is presented. The prey compete for the ... more A model which consists of a predator and two prey species is presented. The prey compete for the same limited resource (food). The predator preys on both prey species but with different severity. We show that the coexistence of all three species is possible in a mean-field approach, whereas from Monte Carlo simulation it follows that the stochastic fluctuations drive one of the prey populations into extinction.
Entropy, Jan 26, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Physica D: Nonlinear Phenomena, Jul 1, 2021
There is a great number of factors to take into account when building and managing an investment ... more There is a great number of factors to take into account when building and managing an investment portfolio. It is widely believed that a proper setup of the portfolio combined with a good, robust management strategy is the key to successful investment. In this paper, we aim at an analysis of two aspects that may have an impact on investment performance: diversity of assets and inclusion of cash in the portfolio. We also propose two new management strategies based on the MACD and RSI factors known from technical analysis. Monte Carlo simulations within the Heston model of a market are used to perform numerical experiments.
Physica D: Nonlinear Phenomena, Sep 1, 2013
A spatial three level food web model with a closed nutrient cycle is presented and analyzed via M... more A spatial three level food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The time evolution of the model reveals two asymptotic states: an absorbing one with all species being extinct, and a coexisting one, in which concentrations of all species are non-zero. There are two possible ways for the system to reach the absorbing state. In some cases the densities increase very quickly at the beginning of a simulation and then decline slowly and almost monotonically. In others, well pronounced peaks in the R, C and D densities appear regularly before the extinction. Those peaks correspond to density outbursts (waves) traveling through the system. We investigate the mechanisms leading to the waves. In particular, we show that the percolation of the detritus (i. e. the accumulation of nutrients) is necessary for the emergence of the waves. Moreover, our results corroborate the hypothesis that top-level predators play an essential role in maintaining the stability of a food web (top-down control).
Journal of Chemical Physics, May 24, 2018
The ergodicity breaking phenomenon has already been in the area of interest of many scientists, w... more The ergodicity breaking phenomenon has already been in the area of interest of many scientists, who tried to uncover its biological and chemical origins. Unfortunately, testing ergodicity in real-life data can be challenging, as sample paths are often too short for approximating their asymptotic behaviour. In this paper, the authors analyze the minimal lengths of empirical trajectories needed for claiming the ε-ergodicity based on two commonly used variants of an autoregressive fractionally integrated moving average model. The dependence of the dynamical functional on the parameters of the process is studied. The problem of choosing proper ε for ε-ergodicity testing is discussed with respect to especially the variation of the innovation process and the data sample length, with a presentation on two real-life examples.
Physica D: Nonlinear Phenomena, Feb 1, 2020
Managing investment portfolios is an old and well know problem in multiple fields including finan... more Managing investment portfolios is an old and well know problem in multiple fields including financial mathematics and financial engineering as well as econometrics and econophysics. Multiple different concepts and theories were used so far to describe methods of handling with financial assets, including differential equations, stochastic calculus and advanced statistics. In this paper, using a set of tools from the probability theory, various strategies of building financial portfolios are analysed in different market conditions. A special attention is given to several realisations of a so called balanced portfolio, which is rooted in the natural "buy-low-sell-high" principle. Results show that there is no universal strategy, because they perform differently in different circumstances (e.g. for varying transaction costs). Moreover, the planned time of investment may also have a significant impact on the profitability of certain strategies. All methods have been tested with both simulated trajectories and real data from the Polish stock market.
Entropy, Jul 19, 2017
Understanding and quantifying polarization in social systems is important because of many reasons... more Understanding and quantifying polarization in social systems is important because of many reasons. It could for instance help to avoid segregation and conflicts in the society or to control polarized debates and predict their outcomes. In this paper, we present a version of the q-voter model of opinion dynamics with two types of responses to social influence: conformity (like in the original q-voter model) and anticonformity. We put the model on a social network with the double-clique topology in order to check how the interplay between those responses impacts the opinion dynamics in a population divided into two antagonistic segments. The model is analyzed analytically, numerically and by means of Monte Carlo simulations. Our results show that the system undergoes two bifurcations as the number of cross-links between cliques changes. Below the first critical point, consensus in the entire system is possible. Thus, two antagonistic cliques may share the same opinion only if they are loosely connected. Above that point, the system ends up in a polarized state.
Physical review, Sep 1, 2020
Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of ... more Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the cells. For this reason, one of the first steps in the analysis of SPT data is the identification of the diffusion type of the observed particles. The most popular method to identify the class of a trajectory is based on the mean square displacement (MSD). However, due to its known limitations, several other approaches have been already proposed. With the recent advances in algorithms and the developments of modern hardware, the classification attempts rooted in machine learning (ML) are of particular interest. In this work, we adopt two ML ensemble algorithms, i.e. random forest and gradient boosting, to the problem of trajectory classification. We present a new set of features used to transform the raw trajectories data into input vectors required by the classifiers. The resulting models are then applied to real data for G protein-coupled receptors and G proteins. The classification results are compared to recent statistical methods going beyond MSD.
Physical review, Sep 20, 2019
Single-particle trajectories measured in microscopy experiments contain important information abo... more Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes undergoing in a range of materials including living cells and tissues. However, extracting that information is not a trivial task due to the stochastic nature of particles' movement and the sampling noise. In this paper, we adopt a deep-learning method known as a convolutional neural network (CNN) to classify modes of diffusion from given trajectories. We compare this fully automated approach working with raw data to classical machine learning techniques that require data preprocessing and extraction of human-engineered features from the trajectories to feed classifiers like random forest or gradient boosting. All methods are tested using simulated trajectories for which the underlying physical model is known. From the results it follows that CNN is usually slightly better than the feature-based methods, but at the costs of much longer processing times. Moreover, there are still some borderline cases, in which the classical methods perform better than CNN.
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Papers by Janusz Szwabiński