TY - JOUR A1 - Palyulin, Vladimir V. A1 - Mantsevich, Vladimir N. A1 - Klages, Rainer A1 - Metzler, Ralf A1 - Chechkin, Aleksei V. T1 - Comparison of pure and combined search strategies for single and multiple targets JF - The European physical journal : B, Condensed matter and complex systems N2 - We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Levy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a Levy searcher. Y1 - 2017 U6 - https://doi.org/10.1140/epjb/e2017-80372-4 SN - 1434-6028 SN - 1434-6036 VL - 90 SP - 20 EP - 37 PB - Springer CY - New York ER - TY - JOUR A1 - Palyulin, Vladimir V. A1 - Blackburn, George A1 - Lomholt, Michael A. A1 - Watkins, Nicholas W. A1 - Metzler, Ralf A1 - Klages, Rainer A1 - Chechkin, Aleksei V. T1 - First passage and first hitting times of Levy flights and Levy walks JF - New journal of physics : the open-access journal for physics N2 - For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms. KW - Levy flights KW - Levy walks KW - first-passage time KW - first-hitting time Y1 - 2019 U6 - https://doi.org/10.1088/1367-2630/ab41bb SN - 1367-2630 VL - 21 IS - 10 PB - IOP Publ. Ltd. CY - Bristol ER - TY - GEN A1 - Palyulin, Vladimir V A1 - Blackburn, George A1 - Lomholt, Michael A A1 - Watkins, Nicholas W A1 - Metzler, Ralf A1 - Klages, Rainer A1 - Chechkin, Aleksei V. T1 - First passage and first hitting times of Lévy flights and Lévy walks T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 785 KW - Lévy flights KW - Lévy walks KW - first-passage time KW - first-hitting time Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-439832 SN - 1866-8372 IS - 785 ER - TY - JOUR A1 - Chechkin, Aleksei V. A1 - Lenz, F. A1 - Klages, Rainer T1 - Normal and anomalous fluctuation relations for gaussian stochastic dynamics JF - Journal of statistical mechanics: theory and experiment N2 - We study transient work fluctuation relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the fluctuation dissipation relation of the second kind (FDR II) holds, and (ii) external noise without FDR II. For internal noise we demonstrate that the existence of FDR II implies the existence of the fluctuation dissipation relation of the first kind (FDR I), which in turn leads to conventional (normal) forms of transient work FRs. For systems driven by external noise we obtain violations of normal FRs, which we call anomalous FRs. We derive them in the long-time limit and demonstrate the existence of logarithmic factors in FRs for intermediate times. We also outline possible experimental verifications. KW - stochastic particle dynamics (theory) KW - fluctuations (theory) KW - stochastic processes (theory) KW - diffusion Y1 - 2012 U6 - https://doi.org/10.1088/1742-5468/2012/11/L11001 SN - 1742-5468 IS - 4 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Dieterich, Peter A1 - Klages, Rainer A1 - Chechkin, Aleksei V. T1 - Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations JF - New journal of physics : the open-access journal for physics N2 - Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations (FRs). As prototypes we study three variants of a generic time-fractional Fokker-Planck equation with constant force. Type A generates superdiffusion, type B subdiffusion and type C both super-and subdiffusion depending on parameter variation. Furthermore type C obeys a fluctuation-dissipation relation whereas A and B do not. We calculate analytically the position PDFs for all three cases and explore numerically their strongly non-Gaussian shapes. While for type C we obtain the conventional transient work FR, type A and type B both yield deviations by featuring a coefficient that depends on time and by a nonlinear dependence on the work. We discuss possible applications of these types of dynamics and FRs to experiments. KW - fluctuation relations KW - anomalous diffusion KW - stochastic processes KW - stochastic thermodynamics KW - Fokker-Planck equations Y1 - 2015 U6 - https://doi.org/10.1088/1367-2630/17/7/075004 SN - 1367-2630 VL - 17 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Palyulin, Vladimir V A1 - Blackburn, George A1 - Lomholt, Michael A A1 - Watkins, Nicholas W A1 - Metzler, Ralf A1 - Klages, Rainer A1 - Chechkin, Aleksei V. T1 - First passage and first hitting times of Lévy flights and Lévy walks JF - New Journal of Physics N2 - For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms. KW - Lévy flights KW - Lévy walks KW - first-passage time KW - first-hitting time Y1 - 2019 U6 - https://doi.org/10.1088/1367-2630/ab41bb SN - 1367-2630 VL - 21 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - JOUR A1 - Palyulin, Vladimir V. A1 - Chechkin, Aleksei V. A1 - Klages, Rainer A1 - Metzler, Ralf T1 - Search reliability and search efficiency of combined Levy-Brownian motion: long relocations mingled with thorough local exploration JF - Journal of physics : A, Mathematical and theoretical N2 - A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Levy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Levy flights with stable exponent alpha < 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent a of the Levy flight component. KW - random search process KW - first passage KW - first arrival KW - Levy flights KW - Brownian motion Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/39/394002 SN - 1751-8113 SN - 1751-8121 VL - 49 SP - 2189 EP - 2193 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Dieterich, Peter A1 - Lindemann, Otto A1 - Moskopp, Mats Leif A1 - Tauzin, Sebastien A1 - Huttenlocher, Anna A1 - Klages, Rainer A1 - Chechkin, Aleksei V. A1 - Schwab, Albrecht T1 - Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis JF - PLoS Computational Biology : a new community journal N2 - Neutrophil granulocytes are essential for the first host defense. After leaving the blood circulation they migrate efficiently towards sites of inflammation. They are guided by chemoattractants released from cells within the inflammatory foci. On a cellular level, directional migration is a consequence of cellular front-rear asymmetry which is induced by the concentration gradient of the chemoattractants. The generation and maintenance of this asymmetry, however, is not yet fully understood. Here we analyzed the paths of chemotacting neutrophils with different stochastic models to gain further insight into the underlying mechanisms. Wildtype chemotacting neutrophils show an anomalous superdiffusive behavior. CXCR2 blockade and TRPC6-knockout cause the tempering of temporal correlations and a reduction of chemotaxis. Importantly, such tempering is found both in vitro and in vivo. These findings indicate that the maintenance of anomalous dynamics is crucial for chemotactic behavior and the search efficiency of neutrophils. The motility of neutrophils and their ability to sense and to react to chemoattractants in their environment are of central importance for the innate immunity. Neutrophils are guided towards sites of inflammation following the activation of G-protein coupled chemoattractant receptors such as CXCR2 whose signaling strongly depends on the activity of Ca2+ permeable TRPC6 channels. It is the aim of this study to analyze data sets obtained in vitro (murine neutrophils) and in vivo (zebrafish neutrophils) with a stochastic mathematical model to gain deeper insight into the underlying mechanisms. The model is based on the analysis of trajectories of individual neutrophils. Bayesian data analysis, including the covariances of positions for fractional Brownian motion as well as for exponentially and power-law tempered model variants, allows the estimation of parameters and model selection. Our model-based analysis reveals that wildtype neutrophils show pure superdiffusive fractional Brownian motion. This so-called anomalous dynamics is characterized by temporal long-range correlations for the movement into the direction of the chemotactic CXCL1 gradient. Pure superdiffusion is absent vertically to this gradient. This points to an asymmetric 'memory' of the migratory machinery, which is found both in vitro and in vivo. CXCR2 blockade and TRPC6-knockout cause tempering of temporal correlations in the chemotactic gradient. This can be interpreted as a progressive loss of memory, which leads to a marked reduction of chemotaxis and search efficiency of neutrophils. In summary, our findings indicate that spatially differential regulation of anomalous dynamics appears to play a central role in guiding efficient chemotactic behavior. KW - neutrophils KW - chemotaxis KW - autocorrelation KW - zebrafish KW - cell migration KW - covariance KW - brownian motion KW - stochastic processes Y1 - 2022 U6 - https://doi.org/10.1371/journal.pcbi.1010089 SN - 1553-734X SN - 1553-7358 VL - 18 IS - 5 PB - PLoS CY - San Fransisco ER -