arXiv subjects

Jarosław Klamut

Publications and source records attributed to Jarosław Klamut.

6 recordsLinked to original sources

arXiv2023

Vulnerability of democratic electoral systems

The two most common types of electoral systems (ES) used in electing national legislatures are proportional representation and plurality voting. When they are evaluated, most often the arguments come from social choice theory and political sciences. The former overall uses an axiomatic approach including a list of mathematical criteria a system should fulfill. The latter predominantly focuses on the trade-off between proportionality of apportionment and governability. However, there is no consensus on the best ES, nor on the set of indexes and measures that would be the most important in such assessment. Moreover, the ongoing debate about the fairness of national elections neglects the study of their vulnerabilities. Here we address this research gap with a framework that can measure electoral systems' vulnerability to different means of influence. Using in silico analysis we show that plurality voting systems are less stable than proportional representation. They are also more susceptible to political agitators and media propaganda. A review of real-world ES reveals possible improvements in their design leading to lower susceptibility. Additionally, our simulation framework allows computation of popular indexes, as the Gallagher index or the effective number of parties, in different scenarios. Our work provides a new tool for dealing with modern threats to democracy that could destabilize voting processes. Furthermore, our results add an important argument in a long-standing discussion on evaluation of ES.

physics.soc-ph↗

arXiv2020

Towards a Universal Measure of Complexity

Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and propose a universal measure of complexity based on the Gell-Mann's view of complexity. Our universal measure of complexity bases on a non-linear transformation of time-dependent entropy, where the system state with the highest complexity is the most distant from all the states of the system of lesser or no complexity. We have shown that the most complex is optimally mixed states consisting of pure states i.e., of the most regular and most disordered which the space of states of a given system allows. A parsimonious paradigmatic example of the simplest system with a small and a large number of degrees of freedom, is shown to support this methodology. Several important features of this universal measure are pointed out, especially its flexibility (i.e., its openness to extensions), ability to the analysis of a system critical behavior, and ability to study the dynamic complexity.

cond-mat.stat-mech↗

arXiv2020

The new face of multifractality: Multi-branchedness and the phase transitions in time series of mean inter-event times

Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent $h(q)$ -- the fundamental exponent in the study of multifractals. The consequence of this behavior is the non-monotonic behavior of the coarse Hölder exponent $α(q)$ leading to multi-branchedness of the spectrum of dimensions. The Legendre-Fenchel transform is used instead of the routinely used canonical Legendre (single-branched) contact transform. Thermodynamic consequences of the multi-branched multifractality are revealed. These are directly expressed in the language of phase transitions between thermally stable, metastable, and unstable phases. These phase transitions are of the first and second orders according to Mandelbrot's modified Ehrenfest classification. The discovery of multi-branchedness is tantamount in significance to extending multifractal analysis.

q-fin.ST↗

arXiv2020

Continuous Time Random Walk with correlated waiting times. The crucial role of inter-trade times in volatility clustering

In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the Continuous Time Random Walk (CTRW). Despite the popularity of this type of stochastic processes and strong empirical motivation, models with a long-term memory within the sequence of time intervals between observations are missing. Here, we fill this gap by introducing a new family of CTRWs. The memory is introduced to the model by the assumption that many consecutive time intervals can be the same. Surprisingly, in this process we can observe a slowly decaying nonlinear autocorrelation function without a fat-tailed distribution of time intervals. Our model applied to high-frequency stock market data can successfully describe the slope of decay of nonlinear autocorrelation function of stock market returns. The model achieves this result with no dependence between consecutive price changes. It proves the crucial role of inter-event times in the volatility clustering phenomenon observed in all stock markets.

q-fin.ST↗

arXiv2019

Multi-phase long-term autocorrelated diffusion: Stationary continuous-time Weierstrass walk vs. flight

In this paper we are examining diffusion properties of stationary continuous-time Weierstrass walk (CTWW). We are showing it is a multi-phase representation of the Lévy walk. The hierarchical spatial-temporal coupling, combined with coupling between dynamic variables define the CTWW process. The walker moves here with a piecewise constant velocity between trajectory turning points. We have found the diffusion phase diagram of the CTWW consisting not only of anomalous non-Gaussian or non-fBm phases but also Brownian yet non-Gaussian ones. We compare the diffusion phase diagram of the stationary CTWW with the corresponding hierarchical continuous-time Weierstress flight (CTWF). The instantaneous jumps between trajectory turning points preceded by waiting define the CTWF process. It is a hierarchical representation of the Lévy flight. We have found the diffusion phase diagram of the CTWF to be a small part of the corresponding CTWW one.

cond-mat.stat-mech↗

arXiv2018

Directed Continuous-Time Random Walk with memory

We propose a new Directed Continuous-Time Random Walk (CTRW) model with memory. As CTRW trajectory consists of spatial jumps preceded by waiting times, in Directed CTRW, we consider the case with only positive spatial jumps. Moreover, we consider the memory in the model as each spatial jump depends on the previous one. Our model is motivated by the financial application of the CTRW presented in [Phys. Rev. E 82:046119][Eur. Phys. J. B 90:50]. As CTRW can successfully describe the short term negative autocorrelation of returns in high-frequency financial data (caused by the bid-ask bounce phenomena), we asked ourselves to what extent the observed long-term autocorrelation of absolute values of returns can be explained by the same phenomena. It turned out that the bid-ask bounce can be responsible only for the small fraction of the memory observed in the high-frequency financial data.

q-fin.ST↗