arXiv subjects

Kristoffer Rypdal

Publications and source records attributed to Kristoffer Rypdal.

16 recordsLinked to original sources

arXiv2021

The tipping effect of delayed interventions on the evolution of COVID-19 incidence

We combine infectious disease transmission and the non-pharmaceutical intervention (NPI) response to disease incidence into one closed model consisting of two coupled delay differential equations for the incidence rate and the time-dependent reproduction number. The model contains three free parameters, the initial reproduction number, the intervention strength, and the response delay relative to the time of infection. The NPI response is modeled by assuming that the rate of change of the reproduction number is proportional to the negative deviation of the incidence rate from an intervention threshold. This delay dynamical system exhibits damped oscillations in one part of the parameter space, and growing oscillations in another, and these are separated by a surface where the solution is a strictly periodic nonlinear oscillation. For parameters relevant for the COVID-19 pandemic, the tipping transition from damped to growing oscillations occurs for response delays of the order of one week, and suggests that effective control and mitigation of successive epidemic waves cannot be achieved unless NPIs are implemented in a precautionary manner, rather than merely as a response to the present incidence rate.

q-bio.QM↗

arXiv2020

Intervention fatigue is the primary cause of strong secondary waves in the COVID-19 pandemic

As of November 2020, the number of COVID-19 cases is increasing rapidly in many countries. In Europe, the virus spread slowed considerably in the late spring due to strict lockdown, but a second wave of the pandemic grew throughout the fall. In this study, we first reconstruct the time evolution of the effective reproduction numbers ${\cal R}(t)$ for each country by integrating the equations of the classic SIR model. We cluster countries based on the estimated ${\cal R}(t)$ through a suitable time series dissimilarity. The result suggests that simple dynamical mechanisms determine how countries respond to changes in COVID-19 case counts. Inspired by these results, we extend the SIR model to include a social response to explain the number $X(t)$ of new confirmed daily cases. As a first-order model, we assume that the social response is on the form $d_t{\cal R}=-ν(X-X^*)$, where $X^*$ is a threshold for response. The response rate $ν$ depends on whether $X^*$ is below or above this threshold, on three parameters $ν_1,\;ν_2,\,ν_3,$, and on $t$. When $X X^*$, $ν=ν_2\exp{(-ν_3t)}$, models the impact of interventions when incidence rate is high. The parameter $ν_3$ represents the fatigue, i.e., the reduced effect of intervention as time passes. The proposed model reproduces typical evolving patterns of COVID-19 epidemic waves observed in many countries. Estimating the parameters $ν_1,\,ν_2,\,ν_3$ and initial conditions, such as ${\cal R}_0$, for different countries helps to identify important dynamics in their social responses. One conclusion is that the leading cause of the strong second wave in Europe in the fall of 2020 was not the relaxation of interventions during the summer, but rather the general fatigue to interventions developing in the fall.

q-bio.QM↗

arXiv2020

A parsimonious description and cross-country analysis of COVID-19 epidemic curve

In a given country, the cumulative death toll of the first wave of the COVID-19 epidemic follows a sigmoid curve as a function of time. In most cases, the curve is well described by the Gompertz function, which is characterized by two essential parameters, the initial growth rate and the decay rate as the first epidemic wave subsides. These parameters are determined by socioeconomic factors and the countermeasures to halt the epidemic. The Gompertz model implies that the total death toll depends exponentially, and hence very sensitively, on the ratio between these rates. The remarkably different epidemic curves for the first epidemic wave in Sweden and Norway and many other countries are classified and discussed in this framework, and their usefulness for the planning of mitigation strategies is discussed.

q-bio.PE↗

arXiv2013

Statistical significance of rising and oscillatory trends in global ocean and land temperature in the past 160 years

Various interpretations of the notion of a trend in the context of global warming are discussed, contrasting the difference between viewing a trend as the deterministic response to an external forcing and viewing it as a slow variation which can be separated from the background spectral continuum of long-range persistent climate noise. The emphasis in this paper is on the latter notion, and a general scheme is presented for testing a multi-parameter trend model against a null hypothesis which models the observed climate record as an autocorrelated noise. The scheme is employed to the instrumental global sea-surface temperature record and the global land-temperature record. A trend model comprising a linear plus an oscillatory trend with period of approximately 60 yr, and the statistical significance of the trends, are tested against three different null models: first-order autoregressive process, fractional Gaussian noise, and fractional Brownian motion. The linear trend is significant in all cases, but the oscillatory trend is insignificant for ocean data and barely significant for land data. By means of a Bayesian iteration, however, using the significance of the linear trend to formulate a sharper null hypothesis, the oscillatory trend in the land record appears to be statistically significant. The results suggest that the global land record may be better suited for detection of the global warming signal than the ocean record.

physics.ao-ph↗

arXiv2013

Long-memory effects in linear-response models of Earth's temperature and implications for future global warming

A linearized energy-balance model for global temperature is formulated, featuring a scale-free long-range memory (LRM) response and stochastic forcing representing the influence on the ocean heat reservoir from atmospheric weather systems. The model is parametrized by an effective response strength, the stochastic forcing strength, and the memory exponent. The instrumental global surface temperature record and the deterministic component of the forcing are used to estimate these parameters by means of the maximum-likelihood method. The residual obtained by subtracting the deterministic solution from the observed record is analyzed as a noise process and shown to be consistent with a long-memory time-series model and inconsistent with a short-memory model. By decomposing the forcing record in contributions from solar, volcanic, and anthropogenic activity one can estimate the contribution of each to 20'th century global warming. The LRM model is applied with a reconstruction of the forcing for the last millennium to predict the large-scale features of northern hemisphere temperature reconstructions, and the analysis of the residual also clearly favors the LRM model on millennium time scale. The decomposition of the forcing shows that volcanic aerosols give a considerably greater contribution to the cooling during the Little Ice Age than the reduction in solar irradiance associated with the Maunder minimum in solar activity. The LRM model implies a transient climate response in agreement with IPCC AR4 projections, but the stronger response on longer time scales suggests to replace the notion of equilibrium climate sensitivity by a time-scale dependent sensitivity.

physics.ao-ph↗

arXiv2012

ENSO dynamics: low-dimensional-chaotic or stochastic?

We apply a test for low-dimensional, deterministic dynamics to the Nino 3 time series for the El Nino Southern Oscillation (ENSO). The test is negative, indicating that the dynamics is high-dimensional/stochastic. However, application of stochastic forcing to a time-delay equation for equatorial-wave dynamics can reproduce this stochastic dynamics and other important aspects of ENSO. Without such stochastic forcing this model yields low-dimensional, deterministic dynamics, hence these results emphasize the importance of the stochastic nature of the atmosphere-ocean interaction in low-dimensional models of ENSO.

physics.ao-ph↗

arXiv2012

Assessing market uncertainty by means of a time-varying intermittency parameter for asset price fluctuations

Maximum likelihood estimation applied to high-frequency data allows us to quantify intermittency in the fluctu- ations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency parameter λ characterising the degree of volatility clustering of asset prices. We can therefore study the time evolution of volatility clustering and test the statistical significance of this variability. By analysing data from the Oslo Stock Exchange, and comparing the results with the investment grade spread, we find that the estimates of λ are lower at times of high market uncertainty.

q-fin.ST↗

arXiv2011

Is there long-range memory in solar activity on time scales shorter than the sunspot period?

The sunspot number (SSN), the total solar irradiance (TSI), a TSI reconstruction, and the solar flare index (SFI), are analyzed for long-range persistence (LRP). Standard Hurst analysis yields $H \approx 0.9$, which suggests strong LRP. However, solar activity time series are non-stationary due to the almost periodic 11 year smooth component, and the analysis does not give the correct $H$ for the stochastic component. Better estimates are obtained by detrended fluctuations analysis (DFA), but estimates are biased and errors are large due to the short time records. These time series can be modeled as a stochastic process of the form $x(t)=y(t)+σ\sqrt{y(t)}\, w_H(t)$, where $y(t)$ is the smooth component, and $w_H(t) $ is a stationary fractional noise with Hurst exponent $H$. From ensembles of numerical solutions to the stochastic model, and application of Bayes' theorem, we can obtain bias and error bars on $H$ and also a test of the hypothesis that a process is uncorrelated ($H=1/2$). The conclusions from the present data sets are that SSN, TSI and TSI reconstruction almost certainly are long-range persistent, but with most probable value $H\approx 0.7$. The SFI process, however, is either very weakly persistent ($H<0.6$) or completely uncorrelated. Some differences between stochastic properties of the TSI and its reconstruction indicate some error in the reconstruction scheme.

physics.space-ph↗

arXiv2011

Organization of the magnetosphere during substorms

The change in degree of organization of the magnetosphere during substorms is investigated by analyzing various geomagnetic indices, as well as interplanetary magnetic field z-component and solar wind flow speed. We conclude that the magnetosphere self-organizes globally during substorms, but neither the magnetosphere nor the solar wind become more predictable in the course of a substorm. This conclusion is based on analysis of five hundred substorms in the period from 2000 to 2002. A minimal dynamic-stochastic model of the driven magnetosphere that reproduces many statistical features of substorm indices is discussed.

physics.space-ph↗

arXiv2011

Low-dimensionality and predictability of solar wind and global magnetosphere during magnetic storms

The storm index SYM-H, the solar wind velocity v, and interplanetary magnetic field Bz show no signatures of low-dimensional dynamics in quiet periods, but tests for determinism in the time series indicate that SYM-H exhibits a significant low-dimensional component during storm time, suggesting that self-organization takes place during magnetic storms. Even though our analysis yields no discernible change in determinism during magnetic storms for the solar wind parameters, there are significant enhancement of the predictability and exponents measuring persistence. Thus, magnetic storms are typically preceded by an increase in the persistence of the solar wind dynamics, and this increase is also present in the magnetospheric response to the solar wind.

physics.space-ph↗

arXiv2008

A stochastic theory for temporal fluctuations in self-organized critical systems

A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization of the Itô stochastic differential equation with an anti-persistent fractional Gaussian noise source. An essential element of the theory is re-scaling to obtain a proper thermodynamic limit, and it captures all temporal features of the toppling process obtained by numerical simulation of the Bak-Tang-Wiesenfeld sandpile in this limit.

q-fin.ST↗

arXiv2008

Modeling temporal fluctuations in avalanching systems

We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as a generalization of Itoh's SDE. This equation contains a fractional Gaussian noise term representing the branching of an avalanche into small active clusters, and a drift term reflecting the tendency for small avalanches to grow and large avalanches to be constricted by the finite system size. If one defines avalanching to take place when the toppling activity exceeds a certain threshold the stochastic model allows us to compute the avalanche exponents in the continum limit as functions of the Hurst exponent of the noise. The results are found to agree well with numerical simulations in the Bak-Tang-Wiesenfeld and Zhang sandpile models. The stochastic model also provides a method for computing the probability density functions of the fluctuations in the toppling activity itself. We show that the sandpiles do not belong to the class of phenomena giving rise to universal non-Gaussian probability density functions for the global activity. Moreover, we demonstrate essential differences between the fluctuations of total kinetic energy in a two-dimensional turbulence simulation and the toppling activity in sandpiles.

nlin.AO↗

arXiv2008

Evidence of low-dimensional chaos in magnetized plasma turbulence

We analyze probe data obtained from a toroidal magnetized plasma configuration suitable for studies of low-frequency gradient-driven instabilities. These instabilities give rise to field-aligned convection rolls analogous to Rayleigh-Benard cells in neutral fluids, and may theoretically develop similar routes to chaos. When using mean-field dimension analysis, we observe low dimensionality, but this could originate from either low-dimensional chaos, periodicity or quasi-periodicity. Therefore, we apply recurrence plot analysis as well as estimation of the largest Lyapunov exponent. These analyses provide evidence of low-dimensional chaos, in agreement with theoretical predictions.

physics.plasm-ph↗

arXiv2008

Scale-free vortex cascade emerging from random forcing in a strongly coupled system

The notions of self-organised criticality (SOC) and turbulence are traditionally considered to be applicable to disjoint classes of phenomena. Nevertheless, scale-free burst statistics is a feature shared by turbulent as well as self-organised critical dynamics. It has also been suggested that another shared feature is universal non-gaussian probability density functions (PDFs) of global fluctuations. Here, we elucidate the unifying aspects through analysis of data from a laboratory dusty plasma monolayer. We compare analysis of experimental data with simulations of a two-dimensional (2D) many-body system, of 2D fluid turbulence, and a 2D SOC model, all subject to random forcing at small scales. The scale-free vortex cascade is apparent from structure functions as well as spatio-temporal avalanche analysis, the latter giving similar results for the experimental and all model systems studied. The experiment exhibits global fluctuation statistics consistent with a non-gaussian universal PDF, but the model systems yield this result only in a restricted range of forcing conditions.

physics.plasm-ph↗

arXiv2007

Stretched-exponential decay functions from a self-consistent model of dielectric relaxation

There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter of debate in the literature. In this paper we suggest a model of dielectric relaxation, which naturally leads to a stretched exponential decay function. Some essential characteristics of the underlying charge conduction mechanisms are considered. A kinetic description of the relaxation and charge transport processes is proposed in terms of equations with time-fractional derivatives.

cond-mat.mtrl-sci↗

arXiv2007

Stretched exponential relaxation and ac universality in disordered dielectrics

This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues are, stretched exponential character of dielectric relaxation, power-law power spectral density, and anomalous dependence of ac conduction coefficient on frequency. We propose a self-consistent model of dielectric relaxation, in which the relaxations are described by a stretched exponential decay function. Mathematically, our study refers to the expanding area of fractional calculus and we propose a systematic derivation of the fractional relaxation and fractional diffusion equations from the property of ac universality.

cond-mat.dis-nn↗