## About

70

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Introduction

I am interested mainly in the following topics: statistical mechanics, econophysics and complex systems.

Additional affiliations

September 2017 - present

October 2016 - August 2017

October 2013 - July 2014

Education

July 2012 - May 2016

## Publications

Publications (70)

We use a comprehensive longitudinal dataset on criminal acts over five years in a European country to study specialization in criminal careers. We cluster crime categories by their relative co-occurrence within criminal careers, deriving a natural, data-based taxonomy of criminal specialization. Defining specialists as active criminals who stay wit...

The recent link discovered between generalized Legendre transforms and curved (i.e. non-Euclidean) statistical manifolds suggests a fundamental reason behind the ubiquity of R\'enyi's divergence and entropy in a wide range of physical phenomena. However, these early findings still provide little intuition on the nature of this relationship and its...

The remarkable robustness of many social systems has been associated with a peculiar triangular structure in the underlying social networks. Triples of people that have three positive relations (e.g., friendship) between each other are strongly overrepresented. Triples with two negative relations (e.g., enmity) and one positive relation are also ov...

We review and discuss the properties of various models that are used to describe the behavior of stock returns and are related in a way or another to fractional pseudo-differential operators in the space variable; we compare their main features and discuss what behaviors they are able to capture. Then, we extend the discussion by showing how the pr...

During the last few decades, the notion of entropy has become omnipresent in many scientific disciplines, ranging from traditional applications in statistical physics and chemistry, information theory, and statistical estimation to more recent applications in biology, astrophysics, geology, financial markets, or social networks[...]

Recent attempts to understand the origin of social fragmentation on the basis of spin models include terms accounting for two social phenomena: homophily—the tendency for people with similar opinions to establish positive relations—and social balance—the tendency for people to establish balanced triadic relations. Spins represent attribute vectors...

Dear colleagues,
it is a pleasure to invite you to the special session S4 at the SigmaPhi2021 conference. Main topic will be entropies and correlations in Complex Systems. You can submit your abstract here: https://lnkd.in/gCFjGND . Do not forget to choose the special section 4.

Recent attempts to understand the origin of social fragmentation on the basis of spin models include terms accounting for two social phenomena: homophily—the tendency for people with similar opinions to establish positive relations—and social balance—the tendency for people to establish balanced triadic relations. Spins represent attribute vectors...

Invitation to the WOST II virtual conference

In the real world, one almost never knows the parameters of a thermodynamic process to infinite precision. Reflecting this, here we investigate how to extend stochastic thermodynamics to systems with uncertain parameters, including uncertain number of heat baths / particle reservoirs, uncertainty in the precise values of temperatures / chemical pot...

We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when those assumptions are relaxed, then it cannot be formulated in terms of Shannon entropy. However, thermodynamic...

The aim of this focus letter is to present a comprehensive classification of the main entropic forms introduced in the last fifty years in the framework of statistical physics and information theory. Most of them can be grouped into three families, characterized by two-deformation parameters, introduced respectively by Sharma, Taneja, and Mittal (e...

Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. Here, we derive the entropy for structure-forming systems that differs from Boltzmann-Gibbs entropy by a term t...

The maximum entropy principle consists of two steps: The first step is to find the distribution which maximizes entropy under given constraints. The second step is to calculate the corresponding thermodynamic quantities. The second part is determined by Lagrange multipliers’ relation to the measurable physical quantities as temperature or Helmholtz...

Recent attempts to understand the origin of social fragmentation are based on spin models which include terms accounting for two social phenomena: homophily -- the tendency for people with similar opinions to establish positive relations -- and social balance -- the tendency for people to establish balanced triadic relations. Spins represent attrib...

We consider several market models, where time is subordinated to a stochastic process. These models are based on various time changes in the Lévy processes driving asset returns, or on fractional extensions of the diffusion equation; they were introduced to capture complex phenomena such as volatility clustering or long memory. After recalling rece...

We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when those assumptions are relaxed, then it cannot be formulated in terms of Shannon entropy. However, thermodynamic...

In this paper, we focus on option pricing models based on time-fractional diffusion with generalized Hilfer-Prabhakar derivative. It is demonstrated how the option is priced for fractional cases of European vanilla option pricing models. Series representations of the pricing formulas and the risk-neutral parameter under the time-fractional diffusio...

In response to the COVID-19 pandemic, governments have implemented a wide range of non-pharmaceutical interventions (NPIs). Monitoring and documenting government strategies during the COVID-19 crisis is crucial to understand the progression of the epidemic. Following a content analysis strategy of existing public information sources, we developed a...

In response to the COVID-19 pandemic, governments have implemented a wide range of nonpharmaceutical interventions (NPIs). Monitoring and documenting government strategies during the COVID-19 crisis is crucial to understand the progression of the epidemic. Following a content analysis strategy of existing public information sources, we developed a...

We propose a unified framework for both Shannon-Khinchin and Shore-Johnson axiomatic systems. We do it by rephrasing Shannon-Khinchine axioms in terms of generalized arithmetics of Kolmogorov and Nagumo. We prove that the two axiomatic schemes yield identical classes of entropic functionals—the Uffink class of entropies. This allows to re-establish...

We derive the entropy for a closed system of particles that can form structures, molecules in the simplest case. The entropy differs from the Boltzmann-Gibbs entropy by a term that captures the molecule states. For large systems the approach is equivalent to the grand canonical ensemble. For small systems large molecules start to play a dominant ro...

Many stochastic complex systems are characterized by the fact that their configuration space doesn’t grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth of the configuration space volume in terms of the scaling exponents of the system. These scaling exponents ca...

The collapse of ecosystems, the extinction of species, and the breakdown of economic and financial networks usually hinges on topological properties of the underlying networks, such as the existence of self-sustaining (or autocatalytic) feedback cycles. Such collapses can be understood as a massive change of network topology, usually accompanied by...

Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth of the configuration space volume in terms of the scaling exponents of the system. These scaling exponents ca...

In this paper, we analyze information flows between communities of financial markets, represented as complex networks. Each community, typically corresponding to a business sector, represents a significant part of the financial market and the detection of interactions between communities is crucial in the analysis of risk spreading in the financial...

We propose a unified framework for both Shannon--Khinchin and Shore--Johnson axiomatic systems. We do it by rephrasing Shannon--Khinchine axioms in terms of generalized arithmetics of Kolmogorov and Nagumo. We prove that the two axiomatic schemes yield identical classes of entropic functionals --- Uffink class of entropies. This allows to re-establ...

In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this...

In their recent paper [Phys. Rev. E 99, 032134 (2019)], Oikonomou and Bagci have argued that Rényi entropy is ill suited for inference purposes because it is not consistent with the Shore-Johnson axioms of statistical estimation theory. In this Comment we seek to clarify the latter statement by showing that there are several issues in Oikonomou's a...

In their recent paper [Phys. Rev. E 99 (2019) 032134], T. Oikinomou and B. Bagci have argued that R\'enyi entropy is ill-suited for inference purposes because it is not consistent with the Shore{ Johnson axioms of statistical estimation theory. In this Comment we seek to clarify the latter statement by showing that there are several issues in Oikin...

We provide ready-to-use formulas for European options prices, risk sensitivities, and P&L calculations under Lévy-stable models with maximal negative asymmetry. Particular cases, efficiency testing, and some qualitative features of the model are also discussed.

In this Letter, we show that the Shore-Johnson axioms for the maximum entropy principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought. Apart from a formal side of the proof where a one-parameter class of admissible entropies is identified, we substantiate our point by analyzin...

In this Letter, we show that the Shore-Johnson axioms for the maximum entropy principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought. Apart from a formal side of the proof where a one-parameter class of admissible entropies is identified, we substantiate our point by analyzin...

In the world of generalized entropies—which, for example, play a role in physical systems with sub- and super-exponential phase space growth per degree of freedom—there are two ways for implementing constraints in the maximum entropy principle: linear and escort constraints. Both appear naturally in different contexts. Linear constraints appear, e....

In the world of generalized entropies---which, for example, play a role in physical systems with sub- and super-exponential phasespace growth per degree of freedom---there are two ways for implementing constraints in the maximum entropy principle: linear- and escort constraints. Both appear naturally in different contexts. Linear constraints appear...

We use the maximum q-log-likelihood estimation for Least informative distributions (LIDs) in order to estimate the parameters in probability density functions (PDFs) efficiently and robustly when data include outlier(s). LIDs are derived by using convex combinations of two PDFs. A convex combination of two PDFs is composed of an underlying distribu...

In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. The series formula can be obtained from the Mellin-Barnes representation of the option price with help of residue summation in $\mathbb{C}^2$....

The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states W(N) depends on the size N of the system. Here we propose a scaling expansion of the phasespace volume W(N) of a stochastic system. The corresponding expansion coefficients (exponents) define th...

The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states W(N) depends on the size N of the system. Here we propose a scaling expansion of the phasespace volume W(N) of a stochastic system. The corresponding expansion coefficients (exponents) define th...

In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results to the data from real markets. We focus on estimation of model parameters from the market data and es...

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show that a multi-scale generalization...

We introduce novel information-entropic variables -- a Point Divergence Gain (PDG), a Point Divergence Gain Entropy (PDGE) and a Point Divergence Gain Entropy Density (PDGED) -- which are derived from the R\'enyi entropy and describe spatio-temporal changes between two consecutive discrete multidimensional distributions. The behavior of PDG is simu...

Dynamics of complex systems described by large networks, as e.g. financial markets, includes many non-trivial phenomena, as e.g., non-linear interactions, emergence and collective behavior. The interactions between the nodes can be measured by several measures, e.g., by cross-correlations. Cross-correlation is a popular measure with simple formula....

We discuss the idea that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can be determined uniquely only when one fixes the prescription for handling conditional entropies. Our point is s...

The paper introduces nonadditivity parameter transformation group induced by Tsallis entropy. We discuss a simple physical application of a system in the contact with finite heat bath. The transformation describes rescaling the number of particles in the bath. With help of the transformation, it is possible to introduce generalized distributive rul...

With the help of transfer entropy, we analyze information flows between communities of complex networks. We show that the transfer entropy provides a coherent description of interactions between communities, including non-linear interactions. To put some flesh on the bare bones, we analyze transfer entropies between communities of five largest fina...

Jizba-Arimitsu entropy (also called hybrid entropy) combines axiomatics of R\'enyi and Tsallis entropy. It has many common properties with them, on the other hand, some aspects as e.g., MaxEnt distributions, are completely different from the former two entropies. In this paper, we demonstrate the statistical properties of hybrid entropy, including...

Recently in [Physica A 411 (2014) 138] Ili\'{c} and Stankovi\'{c} have suggested that there may be problem for the class of hybrid entropies introduced in [P.~Jizba and T.~Arimitsu, Physica A 340 (2004) 110]. In this Comment we point out that the problem can be traced down to the $q$-additive entropic chain rule and to a peculiar behavior of the De...

In this paper we point out that the generalized statistics of Tsallis-Havrda-Charvát can be conveniently used as a conceptual framework for statistical treatment of random chains. In particular, we use the path-integral approach to show that the ensuing partition function can be identified with the partition function of a fluctuating oriented rando...

In this paper, a new model for financial processes in form of a space-time
fractional diffusion equation of varying order is introduced, analyzed,
and applied for some financial data. While the orders of the spatial and
temporal derivatives of this equation can very on different time intervals,
their ratio remains constant and thus the global scali...

We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $\alpha$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the L\'evy propagator. Using distributional and $\mathbb{C}^n$ tools, we derive an analytic closed formula for the...

We discuss several aspects of Mellin transform, including distributional Mellin transform and inversion of multiple Mellin-Barnes integrals in $\mathbb{C}^n$ and its connection to residue expansion or evaluation of Laplace integrals. These mathematical concepts are demonstrated on several option-pricing models. This includes European option models...

We generalize the Point information gain (PIG) and derived quantities, i.e.
Point information entropy (PIE) and Point information entropy density (PIED),
for the case of R\'enyi entropy and simulate the behavior of PIG for typical
distributions. We also use these methods for the analysis of multidimensional
datasets. We demonstrate the main propert...

We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the...

Our paper is currently under review. If you want to quote it, please write:
Tozzi A, Peters JF, Çankaya MN, Korbel J, Zare M, Papo D. 2016. Energetic Link Between Spike Frequencies and Brain Fractal Dimensions. viXra:1609.0105.
Oscillations in brain activity exhibit a power law distribution which appears as a straight line when plotted on logari...

We establish an explicit pricing formula for a class of non-Gaussian models (the Levy-stable, or Log-Levy model with finite moments and stability parameter between 1 and 2) allowing a straightforward evaluation of an European option, without numerical simulations and with as much accuracy as one wishes. The formula can be used by any practitioner,...

We combine an axiomatics of R\'enyi with the $q$--deformed version of
Khinchin axioms to obtain a measure of information (i.e., entropy) which
account both for systems with embedded self-similarity and non-extensivity. We
show that the entropy thus obtained is uniquely solved in terms of a
one-parameter family of information measures. The ensuing m...

A slightly different version of this manuscript has been published. Please quote as: Tozzi A, Peters JF, Cankaya MN. 2018. The informational entropy endowed in cortical oscillations. Cognitive Neurodynamics, 12(5), 501-507. DOI: 10.1007/s11571-018-9491-3. ------------------------- The brain electric activity exhibits a power law distribution which...

We show that a multifractal analysis offers a new and potentially promising avenue for quantifying the com-plexity of various time series. In particular, we compare the most common techniques used for multifractal scaling exponents estimation. This is done from both a theoretical and phenomenological point of view. In our discussion we specifically...

Tozzi A, Korbel J. The probabilistic virtues of the temperature in the bayesian brain (electronic response to: Lee E, Seo M, Dal Monte O, Averbeck BB. Injection of a dopamine type 2 receptor antagonist into the dorsal striatum disrupts choices driven by previous outcomes, but not perceptual inference).
The exciting paper from Lee et al. highlights...

We show how the prices of options can be determined with the help of
double-fractional differential equation in such a way that their admixture to a
portfolio of stocks provides a more reliable hedge against dramatic price drops
than the use of options whose prices were fixed by the Black-Scholes formula.

Scaling properties and fractal structure are one of the most important aspects of real systems that point to their complexity. These properties are closely related to the theory of multifractal systems and theory of entropy. Estimation of scaling (or multifractal) exponents belongs to the essential techniques that can reveal complexity and inner st...

Measuring information transfer between time series is a challenging task. Classical statistical approaches based on correlations do not provide complete image about sources of the information flow. On the other hand, there have been introduced many sophisticated approaches that enable us to reveal the complex nature of many processes. One of these...

We show that a number of realistic financial time series can be well mimicked by multiplicative multifractal cascade processes. The key observation is that the multi-scale behavior in financial progressions fits well the multifractal cascade scaling paradigm. Connections with Kolmogorov’s idea of multiplicative cascade of eddies in the well develop...

In the framework of Multifractal Diffusion Entropy Analysis we propose a
method for choosing an optimal bin-width in histograms generated from
underlying probability distributions of interest. This presented method uses
techniques of Renyi's entropy and the mean square error analysis to discuss the
conditions under which the error in Renyi's entrop...

In this paper, we compare two key approaches used in time series analysis, namely the Multifractal Detrended Fluctuation Analysis and Multifractal Diffusion Entropy Analysis. The comparison is done from both the theoretical and numerical point of view. To put some flesh on bare bones, we illustrate our analysis by applying both methods to three mod...

## Questions

Questions (7)

Hi everyone,

I would like to ask the RG community for the favorite journals. Where do you like to publish your research? Can you describe your experience about the review process (lenght, objectivity, proffesionality)? I am primarily interested in physics journals, but you can add favorite journals from any field:-)

Best

Jan

I would like to ask for your opinion on hottest problem of econophysics... please feel free to add your suggestions

I am curious about your opinion on future perspectives of non-equilibrium thermodynamics? Is it in connection with quantum systems? In financial applications? what about new possible applications (sociology, ...)?

Feel free to express your opinion!

This is more a survey than a question: I am interested in your opinions of what are possible future hot topics in statistics and what new applications will be found.

Feel free to write your opinion

Jan

I am interested in generlized means, particularly in escort means and Kolmogorov-Nagumo means, which are closely related to several physical problems. Do you know any overview litereture on the topic?

Hello,

I would like to ask, whether you know some overview of properties and conditions of Schur convexity/concavity. I know the rule

(x-y)(dF/dx - dF/dy) >= 0 (resp <= 0)

are there any other tests? And what about other interesting properties?

Thank you for your comments

## Projects

Projects (5)

We want to clarify the main driving forces behind social fragmentation within the framework of physics-inspired opinion formation models. We propose a model of a toy society that incorporates two fundamentals of social dynamics, opinion formation based on homophily, and structural social balance. By combining these we expect that the resulting model will have a phase structure where a fragmented phase is clearly present and depends on a number of critical parameters that can so be identified. A key question is to find out if an increased density of social contacts leads to fragmentation.