Algorithms for Spectral Analysis of Irregularly Sampled Time Series

In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications

Fundamental Interfaciology : Indistinguishability and Time's arrow

It is argued that the notion of indistinguishability provides a link between epistemological and fundamentally ontological reasoning, i.e., for the interface problem or endophysics. In Newtonian molecular dynamics simulations of autocatalytic chemical reactions as a basic step to describe life one encounters with the problem of reversible computation which has been compared with Newtonian physics by Fredkin and many others. The introduction of chemical identities in such simulations raise questions concerning the link of information to ontic qualities and in turn to the experience of Time’s arrow. In reactions like A + B → 2A, the production of indistinguishability on a molecular level strikingly leads to an apory. In the backward path after a reversal of momenta in a traditional computation it is impossible to assign the correct identities, A or B, to the two indistinguishable molecules of species A. If the logical operation were reversible then this information is available but contradicts a “true” indistinguishability of molecules. Both, treating it as an objective or as an obsever dependent, i.e. subjective entity lead to inconsistencies of a kind that have been summarized by Heidegger as “self-missing”(Selbstverfehlung) of Being (Dasein). According to Heidegger’ view, being has no difference, thus our exploration of Being by necessarily drawing difference fails. To speak of indistinguishability is the result of an epistemological distinction of subject and object that is avoided Heidegger’s approach, however, somehow on the cost of losing grip to nature. Related problem are the complementarity of discreteness and continuity and many others. Even quantum mechanics that address problems at the micro level, although inherently endowed with complementarity, not really supplies and explanatory basis for the aforementioned problem because concepts like indistinguishability are here introduce by fiat, too. 8zSà . This paper is dedicated to Otto E. Rossler on the occasion of his 65th birthday in May 2005. Keywords: indistinguishability; molecular dynamics simulations; micro-macro-interface; endo-physics; time reversibility; fundamental ontolog

Performativität und Heideggers Hermeneutik der Faktizität

For a compatibility of Heideggers Contributions with today's questions of meaning and performative processes of self-interpretation, Rüdiger Rimpler recently suggested to draw on studies from the field of performativity research. From the viewpoint of a phenomenology of temporality and performance (living out) a promising opening of Heidegger's work appears, which transcends Heidegger in line with him as well as against him to be preserved for the present age. It is shown in this article, in retrospect from the perspective of performativity research, that with „hermeneutics of facticity“ Heidegger laid the fundament for an ontologically construed performativity already before his „Contributions“. Therefore, in contrast to Rimpler's view, Heidegger's work has the potential to be preserved for the present age much more with than against him. Performativity research hardly referred to Heidegger so far but can enormously benefit from Heidegger's foundation. In addition, this article is intended to contribute to a necessary differentiation of the concept of performativity

Application of Chaos Theory to Engine Systems

We focus on the control issue for engine systems from the perspective of chaos theory, which is based on the fact that engine systems have a low-dimensional chaotic dynamics. Two approaches are discussed: controlling chaos and harnessing chaos, respectively. We apply Pyragas' chaos control method to an actual engine system. The experimental results show that the chaotic motion of an engine system may be stabilized to a periodic motion. Alternatively, harnessing chaos for engine systems is addressed, which regards chaos as an essential dynamic mode for the engine.2008-32-0010 (SAE) / 20084710 (JSAE

Exploring COVID-19 daily records of diagnosed cases and fatalities based on simple nonparametric methods

Containment strategies to combat epidemics such as SARS-CoV-2/COVID-19 require the availability of epidemiological parameters, e.g., the effective reproduction number. Parametric models such as the commonly used susceptible-infected-removed (SIR) compartment models fitted to observed incidence time series have limitations due to the time-dependency of the parameters. Furthermore, fatalities are delayed with respect to the counts of new cases, and the reproduction cycle leads to periodic patterns in incidence time series. Therefore, based on comprehensible nonparametric methods including time-delay correlation analyses, estimates of crucial parameters that characterise the COVID-19 pandemic with a focus on the German epidemic are presented using publicly available time-series data on prevalence and fatalities. The estimates for Germany are compared with the results for seven other countries (France, Italy, the United States of America, the United Kingdom, Spain, Switzerland, and Brazil). The duration from diagnosis to death resulting from delay-time correlations turns out to be 13 days with high accuracy for Germany and Switzerland. For the other countries, the time-to-death durations have wider confidence intervals. With respect to the German data, the two time series of new cases and fatalities exhibit a strong coherence. Based on the time lag between diagnoses and deaths, properly delayed asymptotic as well as instantaneous fatality–case ratios are calculated. The temporal median of the instantaneous fatality–case ratio with time lag of 13 days between cases and deaths for Germany turns out to be $\bf 0.02$. Time courses of asymptotic fatality–case ratios are presented for other countries, which substantially differ during the first half of the pandemic but converge to a narrow range with standard deviation $\bf 0.0057$ and mean $\bf 0.024.$ Similar results are obtained from comparing time courses of instantaneous fatality–case ratios with optimal delay for the 8 exemplarily chosen countries. The basic reproduction number, $R_0$, for Germany is estimated to be between $\bf 2.4$ and $\bf 3.4$ depending on the generation time, which is estimated based on a delay autocorrelation analysis. Resonances at about 4 days and 7 days are observed, partially attributable to weekly periodicity of sampling. The instantaneous (time-dependent) reproduction number is estimated from the incident (counts of new) cases, thus allowing us to infer the temporal behaviour of the reproduction number during the epidemic course. The time course of the reproduction number turns out to be consistent with the time-dependent per capita growth