arXiv subjects

Holger Kantz

Publications and source records attributed to Holger Kantz.

At least 55 records · Page 3Linked to original sources

arXiv2017

Stochastic dynamics and the predictability of big hits in online videos

The competition for the attention of users is a central element of the Internet. Crucial issues are the origin and predictability of big hits, the few items that capture a big portion of the total attention. We address these issues analyzing 10 million time series of videos' views from YouTube. We find that the average gain of views is linearly proportional to the number of views a video already has, in agreement with usual rich-get-richer mechanisms and Gibrat's law, but this fails to explain the prevalence of big hits. The reason is that the fluctuations around the average views are themselves heavy tailed. Based on these empirical observations, we propose a stochastic differential equation with Lévy noise as a model of the dynamics of videos. We show how this model is substantially better in estimating the probability of an ordinary item becoming a big hit, which is considerably underestimated in the traditional proportional-growth models.

physics.soc-ph↗

arXiv2016

Anomalous diffusion on a fractal mesh

An exact analytical analysis of anomalous diffusion on a fractal mesh is presented. The fractal mesh structure is a direct product of two fractal sets which belong to a main branch of backbones and side branch of fingers. The fractal sets of both backbones and fingers are constructed on the entire (infinite) $y$ and $x$ axises. To this end we suggested a special algorithm of this special construction. The transport properties of the fractal mesh is studied, in particular, subdiffusion along the backbones is obtained with the dispersion relation $\langle x^2(t)\rangle\sim t^β$, where the transport exponent $β<1$ is determined by the fractal dimensions of both backbone and fingers. Superdiffusion with $β>1$ has been observed as well when the environment is controlled by means of a memory kernel.

cond-mat.stat-mech↗

arXiv2016

Comb model with slow and ultraslow diffusion

We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in $x$ and $y$ directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both $x$ and $y$ directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We give the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process.

cond-mat.stat-mech↗

arXiv2015

Data-driven prediction and prevention of extreme events in a spatially extended excitable system

Extreme events occur in many spatially extended dynamical systems, often devastatingly affecting human life which makes their reliable prediction and efficient prevention highly desirable. We study the prediction and prevention of extreme events in a spatially extended system, a system of coupled FitzHugh-Nagumo units, in which extreme events occur in a spatially and temporally irregular way. Mimicking typical constraints faced in field studies, we assume not to know the governing equations of motion and to be able to observe only a subset of all phase-space variables for a limited period of time. Based on reconstructing the local dynamics from data and despite being challenged by the rareness of events, we are able to predict extreme events remarkably well. With small, rare, and spatiotemporally localized perturbations which are guided by our predictions, we are able to completely suppress extreme events in this system.

physics.data-an↗

arXiv2015

Fluctuation theorem between non-equilibrium states in an RC circuit

Fluctuation theorems impose constraints on the probability of observing negative entropy production in small systems driven out of equilibrium. The range of validity of fluctuation theorems has been extensively tested for transitions between equilibrium and non equilibrium stationary states, but not between general non equilibrium states. Here we report an experimental verification of the detailed fluctuation theorem for the total amount of entropy produced in the isothermal transition between two non-equilibrium states. The experimental setup is a parallel $RC$ circuit driven by an alternating current. We investigate the statistics of the heat released, of the variation of the entropy of the system, and of the entropy produced for processes of different durations. We show that the fluctuation theorem is satisfied with high accuracy for current drivings at different frequencies and different amplitudes.

cond-mat.stat-mech↗

arXiv2015

Nonlinear time-series analysis revisited

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems.

nlin.CD↗

arXiv2015

Fractional diffusion on a fractal grid comb

A grid comb model is a generalization of the well known comb model, and it consists of $N$ backbones. For $N=1$ the system reduces to the comb model where subdiffusion takes place with the transport exponent $1/2$. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite number of backbones the transport exponent does not change. Contrary to that, for an infinite number of backbones, the transport exponent depends on the fractal dimension of the backbone structure.

cond-mat.stat-mech↗

arXiv2015

Extreme events due to localisation of energy

We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show very large excitations. A detailed statistical analysis of extremes in this system reveals some unexpected properties, e.g., a pronounced pattern in the inter event interval statistics. We relate these statistical properties to underlying system dynamics, and notice that often when extreme events occur the system dynamics adopts (at least locally) an oscillatory behaviour, resulting in, for example, a quick succession of such events. The model therefore might serve as a paradigmatic model for the study of the interplay of nonlinearity, energy transport, and extreme events.

nlin.CD↗

arXiv2014

Localization and universal fluctuations in ultraslow diffusion processes

We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) $\langle x^2(t)\rangle\simeq\log^γt$. Comparison of annealed continuous time random walks (CTRWs) with logarithmic waiting time distribution $ψ(τ)\simeq1/(τ\log^{1+γ}τ)$ and Sinai diffusion in quenched random landscapes shows striking similarities, despite their very different physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time and ensemble averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble and time averaged MSD.

cond-mat.stat-mech↗

arXiv2013

Skill of data based predictions versus dynamical models -- case study on extreme temperature anomalies

We compare probabilistic predictions of extreme temperature anomalies issued by two different forecast schemes. One is a dynamical physical weather model, the other a simple data model. We recall the concept of skill scores in order to assess the performance of these two different predictors. Although the result confirms the expectation that the (computationally expensive) weather model outperforms the simple data model, the performance of the latter is surprisingly good. More specifically, for some parameter range, it is even better than the uncalibrated weather model. Since probabilistic predictions are not easily interpreted by the end user, we convert them into deterministic yes/no statements and measure the performance of these by ROC statistics. Scored in this way, conclusions about model performance partly change, which illustrates that predictive power depends on how it is quantified.

stat.AP↗

arXiv2013

Spatiotemporal clustering and separation in regional earthquakes

Spatiotemporal clustering of earthquake events is a generally-established fact, and is important for designing models and assessment techniques in seismicity. Here, we investigate how this behavior can manifest in the statistical distributions of inter-event distances and times between earthquakes from different regional catalogs. We complement the analysis of previous authors (Touati et al., PRL 102, 168501 (2009)) and observe histograms best described by a superposition of two component distributions for "short" and "long" distances and times. Our results quantify the spatiotemporal clustering of earthquakes that are possibly generated by the same triggering mechanism. Independent earthquakes, on the other hand, are found to be separated by long inter-event distances and times. The statistics presented reveal regional differences, suggesting non-universality of the distributions.

physics.geo-ph↗

arXiv2013

Differential Landauer's principle

Landauer's principle states that the erasure of information must be a dissipative process. In this paper, we carefully analyze the recording and erasure of information on a physical memory. On the one hand, we show that in order to record some information, the memory has to be driven out of equilibrium. On the other hand, we derive a differential version of Landauer's principle: We link the rate at which entropy is produced at every time of the erasure process to the rate at which information is erased.

cond-mat.stat-mech↗

arXiv2012

Fluctuations of $1/f$ noise and the low frequency cutoff paradox

Recent experiments on blinking quantum dots and weak turbulence in liquid crystals reveal the fundamental connection between $1/f$ noise and power law intermittency. The non-stationarity of the process implies that the power spectrum is random -- a manifestation of weak ergodicity breaking. Here we obtain the universal distribution of the power spectrum, which can be used to identify intermittency as the source of the noise. We solve an outstanding paradox on the non integrability of $1/f$ noise and the violation of Parseval's theorem. We explain why there is no physical low frequency cutoff and therefore cannot be found in experiments.

cond-mat.stat-mech↗

arXiv2012

Application of the modified method of simplest equation for obtaining exact traveling-wave solutions for the extended Korteweg - de Vries equation and generalized Camassa-Holm equation

The modified method of simplest equation is applied to the extended Korteweg - de Vries equation and to generalized Camassa - Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained. The equations of Bernoulli, Riccati and the extended tanh - equation are used as simplest equations. Some of the obtained solutions correspond to surface water waves.

nlin.SI↗

arXiv2011

The thermodynamic cost of measurements

The measurement of thermal fluctuations provides information about the microscopic state of a thermodynamic system and can be used in order to extract work from a single heat bath in a suitable cyclic process. We present a minimal framework for the modeling of a measurement device and we propose a protocol for the measurement of thermal fluctuations. In this framework, the measurement of thermal fluctuations naturally leads to the dissipation of work. We illustrate this framework on a simple two states system inspired by the Szilard's information engine.

cond-mat.stat-mech↗

arXiv2010

1/f^beta noise in a model for weak ergodicity breaking

In systems with weak ergodicity breaking, the equivalence of time averages and ensemble averages is known to be broken. We study here the computation of the power spectrum from realizations of a specific process exhibiting 1/f^beta noise, the Rebenshtok-Barkai model. We show that even the binned power spectrum does not converge in the limit of infinite time, but that instead the resulting value is a random variable stemming from a distribution with finite variance. However, due to the strong correlations in neighboring frequency bins of the spectrum, the exponent beta can be safely estimated by time averages of this type. Analytical calculations are illustrated by numerical simulations.

cond-mat.stat-mech↗

arXiv2010

Crooks' fluctuation theorem for the fluctuating lattice-Boltzmann model

We probe the validity of Crooks' fluctuation relation on the fluctuating lattice-Boltzmann model (FLBM), a highly simplified lattice model for a thermal ideal gas. We drive the system between two thermodynamic equilibrium states and compute the distribution of the work performed. By comparing the distributions of the work performed during the forward driving and time reversed driving, we show that the system satisfies Crooks' relation. The results of the numerical experiment suggest that the temperature and the free energy of the system are well defined.

cond-mat.stat-mech↗

arXiv2010

Prediction of extreme events in the OFC model on a small world network

We investigate the predictability of extreme events in a dissipative Olami-Feder-Christensen model on a small world topology. Due to the mechanism of self-organized criticality, it is impossible to predict the magnitude of the next event knowing previous ones, if the system has an infinite size. However, by exploiting the finite size effects, we show that probabilistic predictions of the occurrence of extreme events in the next time step are possible in a finite system. In particular, the finiteness of the system unavoidably leads to repulsive temporal correlations of extreme events. The predictability of those is higher for larger magnitudes and for larger complex network sizes. Finally, we show that our prediction analysis is also robust by remarkably reducing the accessible number of events used to construct the optimal predictor.

cond-mat.stat-mech↗