1
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Feng SF, Wang S, Zarnescu S, Wilson RC. The dynamics of explore-exploit decisions reveal a signal-to-noise mechanism for random exploration. Sci Rep 2021; 11:3077. [PMID: 33542333 PMCID: PMC7862437 DOI: 10.1038/s41598-021-82530-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 12/16/2020] [Indexed: 12/29/2022] Open
Abstract
Growing evidence suggests that behavioral variability plays a critical role in how humans manage the tradeoff between exploration and exploitation. In these decisions a little variability can help us to overcome the desire to exploit known rewards by encouraging us to randomly explore something else. Here we investigate how such 'random exploration' could be controlled using a drift-diffusion model of the explore-exploit choice. In this model, variability is controlled by either the signal-to-noise ratio with which reward is encoded (the 'drift rate'), or the amount of information required before a decision is made (the 'threshold'). By fitting this model to behavior, we find that while, statistically, both drift and threshold change when people randomly explore, numerically, the change in drift rate has by far the largest effect. This suggests that random exploration is primarily driven by changes in the signal-to-noise ratio with which reward information is represented in the brain.
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Affiliation(s)
- Samuel F Feng
- Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi, UAE
- Khalifa University Centre for Biotechnology, Khalifa University of Science and Technology, Abu Dhabi, UAE
| | - Siyu Wang
- Department of Psychology, University of Arizona, Tucson, AZ, USA
| | - Sylvia Zarnescu
- Department of Psychology, University of Arizona, Tucson, AZ, USA
| | - Robert C Wilson
- Department of Psychology, University of Arizona, Tucson, AZ, USA.
- Cognitive Science Program, University of Arizona, Tucson, AZ, USA.
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2
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Aguilar EJ, Barbosa VC, Donangelo R, Souza SR. Interspecies evolutionary dynamics mediated by public goods in bacterial quorum sensing. Phys Rev E 2021; 103:012403. [PMID: 33601496 DOI: 10.1103/physreve.103.012403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2020] [Accepted: 12/15/2020] [Indexed: 11/07/2022]
Abstract
Bacterial quorum sensing is the communication that takes place between bacteria as they secrete certain molecules into the intercellular medium that later get absorbed by the secreting cells themselves and by others. Depending on cell density, this uptake has the potential to alter gene expression and thereby affect global properties of the community. We consider the case of multiple bacterial species coexisting, referring to each one of them as a genotype and adopting the usual denomination of the molecules they collectively secrete as public goods. A crucial problem in this setting is characterizing the coevolution of genotypes as some of them secrete public goods (and pay the associated metabolic costs) while others do not but may nevertheless benefit from the available public goods. We introduce a network model to describe genotype interaction and evolution when genotype fitness depends on the production and uptake of public goods. The model comprises a random graph to summarize the possible evolutionary pathways the genotypes may take as they interact genetically with one another, and a system of coupled differential equations to characterize the behavior of genotype abundance in time. We study some simple variations of the model analytically and more complex variations computationally. Our results point to a simple trade-off affecting the long-term survival of those genotypes that do produce public goods. This trade-off involves, on the producer side, the impact of producing and that of absorbing the public good. On the nonproducer side, it involves the impact of absorbing the public good as well, now compounded by the molecular compatibility between the producer and the nonproducer. Depending on how these factors turn out, producers may or may not survive.
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Affiliation(s)
- Eduardo J Aguilar
- Instituto de Ciência e Tecnologia, Universidade Federal de Alfenas, Rodovia José Aurélio Vilela, 11999, 37715-400 Poços de Caldas, Minais Gerais, Brazil
| | - Valmir C Barbosa
- Programa de Engenharia de Sistemas e Computação, COPPE, Universidade Federal do Rio de Janeiro, Centro de Tecnologia, Sala H-319, 21941-914 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Raul Donangelo
- Instituto de Física, Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, 11300 Montevideo, Uruguay
- Instituto de Física, Universidade Federal do Rio de Janeiro, Centro de Tecnologia, Bloco A, 21941-909 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Sergio R Souza
- Instituto de Física, Universidade Federal do Rio de Janeiro, Centro de Tecnologia, Bloco A, 21941-909 Rio de Janeiro, Rio de Janeiro, Brazil
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Avenida Antônio Carlos, 6627, 31270-901 Belo Horizonte, Minais Gerais, Brazil
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3
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Dubkov AA, Dybiec B, Spagnolo B, Kharcheva A, Guarcello C, Valenti D. Statistics of residence time for Lévy flights in unstable parabolic potentials. Phys Rev E 2020; 102:042142. [PMID: 33212570 DOI: 10.1103/physreve.102.042142] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 09/22/2020] [Indexed: 11/07/2022]
Abstract
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
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Affiliation(s)
- Alexander A Dubkov
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia
| | - Bartłomiej Dybiec
- Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland
| | - Bernardo Spagnolo
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia.,Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123 Catania, Italy
| | - Anna Kharcheva
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia.,Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy
| | - Claudio Guarcello
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy.,INFN, Sezione di Napoli Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
| | - Davide Valenti
- Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.,CNR-IRIB, Consiglio Nazionale delle Ricerche-Istituto per la Ricerca e l'Innovazione Biomedica, Via Ugo La Malfa 153, 90146 Palermo, Italy
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4
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Sun Y, Bozdogan H. Segmentation of High Dimensional Time-Series Data Using Mixture of Sparse Principal Component Regression Model with Information Complexity. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1170. [PMID: 33286939 PMCID: PMC7597341 DOI: 10.3390/e22101170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Revised: 09/16/2020] [Accepted: 10/13/2020] [Indexed: 06/12/2023]
Abstract
This paper presents a new and novel hybrid modeling method for the segmentation of high dimensional time-series data using the mixture of the sparse principal components regression (MIX-SPCR) model with information complexity (ICOMP) criterion as the fitness function. Our approach encompasses dimension reduction in high dimensional time-series data and, at the same time, determines the number of component clusters (i.e., number of segments across time-series data) and selects the best subset of predictors. A large-scale Monte Carlo simulation is performed to show the capability of the MIX-SPCR model to identify the correct structure of the time-series data successfully. MIX-SPCR model is also applied to a high dimensional Standard & Poor's 500 (S&P 500) index data to uncover the time-series's hidden structure and identify the structure change points. The approach presented in this paper determines both the relationships among the predictor variables and how various predictor variables contribute to the explanatory power of the response variable through the sparsity settings cluster wise.
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Affiliation(s)
| | - Hamparsum Bozdogan
- Department of Business Analytics and Statistics, University of Tennessee, Knoxville, TN 37996, USA;
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5
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6
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Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems. ENTROPY 2020; 22:e22080839. [PMID: 33286610 PMCID: PMC7517439 DOI: 10.3390/e22080839] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Revised: 07/15/2020] [Accepted: 07/15/2020] [Indexed: 01/07/2023]
Abstract
We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated from a harmonic oscillator bath (environment) of Debye type with cut-off frequency wd, ergodicity breakdown is found because the velocity autocorrelation function oscillates in cosine function for asymptotic time. The steady escape rate of such a self-oscillated system from a metastable potential exhibits nonmonotonic dependence on wd, which denotes that there is an optimal cut-off frequency makes it maximal. Comparing results in classical and quantum regimes, the steady escape rate of a quantum open system reduces to a classical one with wd decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators N on the escape dynamics of a classical open system is also discussed.
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7
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Luo Y, Zeng C. Negative friction and mobilities induced by friction fluctuation. CHAOS (WOODBURY, N.Y.) 2020; 30:053115. [PMID: 32491875 DOI: 10.1063/1.5144556] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Accepted: 04/20/2020] [Indexed: 06/11/2023]
Abstract
We study the transport phenomena of an inertial Brownian particle in a symmetric potential with periodicity, which is driven by an external time-periodic force and an external constant bias for both cases of the deterministic dynamics and the existence of friction coefficient fluctuations. For the deterministic case, it is shown that for suitable parameters, the existence of certain appropriate friction coefficients can enhance the transport of the particle, which may be interpreted as the negative friction coefficient; additionally, there coexist absolute, differential negative, and giant positive mobilities with increasing friction coefficients in the system. We analyze physical mechanisms hinted behind these findings via basins of attraction. For the existence of friction coefficient fluctuations, it is shown that the fluctuation can enhance or weaken, even eliminate these phenomena. We present the probability distribution of the particle's velocity to interpret these mobilities and the suitable parameters' regimes of these phenomena. In order to further understand the physical mechanism, we also study diffusions corresponding to these mobilities and find that for the small fluctuation, the negative friction appears, and there coexists absolute negative mobility, superdiffusion, and ballistic diffusion, whereas all of them vanish for the large fluctuation. Our findings may extensively exist in materials, including different defects, strains, the number of interfacial hydrogen bonds, the arrangements of ions, or graphite concentrations, which hints at the existence of different friction coefficients.
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Affiliation(s)
- Yuhui Luo
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, China
| | - Chunhua Zeng
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, China
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8
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Mikhaylov A, Pimashkin A, Pigareva Y, Gerasimova S, Gryaznov E, Shchanikov S, Zuev A, Talanov M, Lavrov I, Demin V, Erokhin V, Lobov S, Mukhina I, Kazantsev V, Wu H, Spagnolo B. Neurohybrid Memristive CMOS-Integrated Systems for Biosensors and Neuroprosthetics. Front Neurosci 2020; 14:358. [PMID: 32410943 PMCID: PMC7199501 DOI: 10.3389/fnins.2020.00358] [Citation(s) in RCA: 110] [Impact Index Per Article: 27.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Accepted: 03/24/2020] [Indexed: 11/18/2022] Open
Abstract
Here we provide a perspective concept of neurohybrid memristive chip based on the combination of living neural networks cultivated in microfluidic/microelectrode system, metal-oxide memristive devices or arrays integrated with mixed-signal CMOS layer to control the analog memristive circuits, process the decoded information, and arrange a feedback stimulation of biological culture as parts of a bidirectional neurointerface. Our main focus is on the state-of-the-art approaches for cultivation and spatial ordering of the network of dissociated hippocampal neuron cells, fabrication of a large-scale cross-bar array of memristive devices tailored using device engineering, resistive state programming, or non-linear dynamics, as well as hardware implementation of spiking neural networks (SNNs) based on the arrays of memristive devices and integrated CMOS electronics. The concept represents an example of a brain-on-chip system belonging to a more general class of memristive neurohybrid systems for a new-generation robotics, artificial intelligence, and personalized medicine, discussed in the framework of the proposed roadmap for the next decade period.
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Affiliation(s)
- Alexey Mikhaylov
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Alexey Pimashkin
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Yana Pigareva
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | | | - Evgeny Gryaznov
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Sergey Shchanikov
- Department of Information Technologies, Vladimir State University, Murom, Russia
| | - Anton Zuev
- Department of Information Technologies, Vladimir State University, Murom, Russia
| | - Max Talanov
- Neuroscience Laboratory, Kazan Federal University, Kazan, Russia
| | - Igor Lavrov
- Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, United States
- Laboratory of Motor Neurorehabilitation, Kazan Federal University, Kazan, Russia
| | | | - Victor Erokhin
- Neuroscience Laboratory, Kazan Federal University, Kazan, Russia
- Kurchatov Institute, Moscow, Russia
- CNR-Institute of Materials for Electronics and Magnetism, Italian National Research Council, Parma, Italy
| | - Sergey Lobov
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
| | - Irina Mukhina
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Cell Technology Group, Privolzhsky Research Medical University, Nizhny Novgorod, Russia
| | - Victor Kazantsev
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
| | - Huaqiang Wu
- Institute of Microelectronics, Tsinghua University, Beijing, China
| | - Bernardo Spagnolo
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Dipartimento di Fisica e Chimica-Emilio Segrè, Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Palermo, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Catania, Italy
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9
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Leonforte L, Valenti D, Spagnolo B, Carollo A. Uhlmann number in translational invariant systems. Sci Rep 2019; 9:9106. [PMID: 31235825 PMCID: PMC6591291 DOI: 10.1038/s41598-019-45546-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Accepted: 06/06/2019] [Indexed: 11/08/2022] Open
Abstract
We define the Uhlmann number as an extension of the Chern number, and we use this quantity to describe the topology of 2D translational invariant Fermionic systems at finite temperature. We consider two paradigmatic systems and we study the changes in their topology through the Uhlmann number. Through the linear response theory we link two geometrical quantities of the system, the mean Uhlmann curvature and the Uhlmann number, to directly measurable physical quantities, i.e. the dynamical susceptibility and the dynamical conductivity, respectively. In particular, we derive a non-zero temperature generalisation of the Thouless-Kohmoto-Nightingale-den Nijs formula.
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Affiliation(s)
- Luca Leonforte
- Department of Physics and Chemistry - Emilio Segrè, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.
| | - Davide Valenti
- Department of Physics and Chemistry - Emilio Segrè, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy
- Istituto di Biomedicina ed Immunologia Molecolare (IBIM) "Alberto Monroy", CNR, Via Ugo La Malfa 153, I-90146, Palermo, Italy
| | - Bernardo Spagnolo
- Department of Physics and Chemistry - Emilio Segrè, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni Novgorod, 603950, Russia
- Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-95123, Catania, Italy
| | - Angelo Carollo
- Department of Physics and Chemistry - Emilio Segrè, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni Novgorod, 603950, Russia
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10
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Šiler M, Ornigotti L, Brzobohatý O, Jákl P, Ryabov A, Holubec V, Zemánek P, Filip R. Diffusing up the Hill: Dynamics and Equipartition in Highly Unstable Systems. PHYSICAL REVIEW LETTERS 2018; 121:230601. [PMID: 30576167 DOI: 10.1103/physrevlett.121.230601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2018] [Revised: 08/20/2018] [Indexed: 06/09/2023]
Abstract
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard statistical analysis of unstable mechanical processes and their applications. A newly proposed approach takes advantage of the local characteristics of the most probable particle motion instead of the divergent averages. We experimentally verify its theoretical predictions for a Brownian particle moving near an inflection in a highly unstable cubic optical potential. The most likely position of the particle atypically shifts against the force, despite the trajectories diverging in the opposite direction. The local uncertainty around the most likely position saturates even for strong diffusion and enables well-resolved position detection. Remarkably, the measured particle distribution quickly converges to a quasistationary one with the same atypical shift for different initial particle positions. The demonstrated experimental confirmation of the theoretical predictions approves the utility of local characteristics for highly unstable systems which can be exploited in thermodynamic processes to uncover energetics of unstable systems.
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Affiliation(s)
- Martin Šiler
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - Luca Ornigotti
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - Oto Brzobohatý
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - Petr Jákl
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
| | - Viktor Holubec
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
- Universität Leipzig, Institut für Theoretische Physik, Postfach 100 920, D-04009 Leipzig, Germany
| | - Pavel Zemánek
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - Radim Filip
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
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11
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Valenti D, Fazio G, Spagnolo B. Stabilizing effect of volatility in financial markets. Phys Rev E 2018; 97:062307. [PMID: 30011541 DOI: 10.1103/physreve.97.062307] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2017] [Indexed: 11/07/2022]
Abstract
In financial markets, greater volatility is usually considered to be synonymous with greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To investigate this surprising feature, here we propose using the mean first hitting time, i.e., the average time a stock return takes to undergo for the first time a large negative (crashes) or positive variation (rallies), as an indicator of price stability, and relate this to a standard measure of volatility. In an empirical analysis of daily returns for 1071 stocks traded in the New York Stock Exchange, we find that this measure of stability displays nonmonotonic behavior, with a maximum, as a function of volatility. Also, we show that the statistical properties of the empirical data can be reproduced by a nonlinear Heston model. This analysis implies that, contrary to conventional wisdom, not only high, but also low volatility values can be associated with higher instability in financial markets. This proposed measure of stability can be extremely useful in risk control.
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Affiliation(s)
- Davide Valenti
- Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics and CNISM, Università di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.,IBIM-CNR Istituto di Biomedicina ed Immunologia Molecolare "Alberto Monroy," Via Ugo La Malfa 153, I-90146 Palermo, Italy
| | - Giorgio Fazio
- Business School, Newcastle University, 5 Barrack Road, NE1 4SE Newcastle upon Tyne, United Kingdom.,SEAS, Università di Palermo, I-90128 Palermo, Italy
| | - Bernardo Spagnolo
- Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics and CNISM, Università di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123 Catania, Italy.,Radiophysics Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia
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12
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Ornigotti L, Ryabov A, Holubec V, Filip R. Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon. Phys Rev E 2018; 97:032127. [PMID: 29776045 DOI: 10.1103/physreve.97.032127] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2017] [Indexed: 06/08/2023]
Abstract
The trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance of position grows much faster than its mean. A description of the dynamics by moments is therefore not informative. Instead, we propose and analyze local directly measurable characteristics, which overcome this limitation. We discuss the most probable particle position (position of the maximum of the probability density) and the local uncertainty in an unstable cubic potential, V(x)∼x^{3}, both in the transient regime and in the long-time limit. The maximum shifts against the acting force as a function of time and temperature. Simultaneously, the local uncertainty does not increase faster than the observable shift. In the long-time limit, the probability density naturally attains a quasistationary form. We interpret this process as a stabilization via the measurement-feedback mechanism, the Maxwell demon, which works as an entropy pump. The rules for measurement and feedback naturally arise from the basic properties of the unstable dynamics. All reported effects are inherent in any unstable system. Their detailed understanding will stimulate the development of stochastic engines and amplifiers and, later, their quantum counterparts.
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Affiliation(s)
- Luca Ornigotti
- Department of Optics, Palacký University, 17. listopadu 1192/12, CZ-771 46 Olomouc, Czech Republic
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha 8, Czech Republic
| | - Viktor Holubec
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha 8, Czech Republic
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Radim Filip
- Department of Optics, Palacký University, 17. listopadu 1192/12, CZ-771 46 Olomouc, Czech Republic
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13
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Wang H, Cheng X, Duan J, Kurths J, Li X. Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise. CHAOS (WOODBURY, N.Y.) 2018; 28:013121. [PMID: 29390613 DOI: 10.1063/1.5010026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β≈-0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.
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Affiliation(s)
- Hui Wang
- Center for Mathematical Sciences and School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Xiujun Cheng
- Center for Mathematical Sciences and School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jinqiao Duan
- Center for Mathematical Sciences and School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jürgen Kurths
- Department of Physics, Humboldt University of Berlin, Newtonstrate 15, 12489 Berlin, Germany
| | - Xiaofan Li
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
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