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.

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

Staircase baker's map generates flaring-type time series

The baker’s map, invented by Eberhard Hopf in 1937, is an intuitively accesible, two-dimensional chaos-generating discrete dynamical system. This map, which describes the transformation of an idealized two-dimensional dough by stretching, cutting and piling, is non-dissipative. Nevertheless the “x” variable is identical with the dissipative, one-dimensional Bernoulli-shift-generating map. The generalization proposed here takes up ideas of Yaacov Sinai in a modified form. It has a staircase-like shape, with every next step half as high as the preceding one. Each pair of neighboring elements exchanges an equal volume (area) during every iteration step in a scaled manner. Since the density of iterated points is constant, the thin tail (to the right, say) is visited only exponentially rarely. This observation already explains the map's main qualitative behavior: The “x” variable shows “flares”. The time series of this variable is closely analogous to that of a flaring-type dissipative dynamical system – like those recently described in an abstract economic model. An initial point starting its journey in the tale (or “antenna”, if we tilt the map upwards by 90 degrees) is predictably attracted by the broad left hand (bottom) part, in order to only very rarely venture out again to the tip. Yet whenever it does so, it thereby creates, with the top of a flare, a new “far-from-equilibrium” initial condition, in this reversible system. The system therefore qualifies as a discrete analogue to a far-from-equilibrium multiparticle Hamiltonian system. The height of the flare hereby corresponds to the momentary height of the H function of a gas. An observable which is even more closely related to the momentary negative entropy was recently described. Dependent on the numerical accuracy chosen, “Poincaré cycles” of two different types (periodic and nonperiodic) can be observed for the first time

Mathematical Modeling of Malaria Infection with Innate and Adaptive Immunity in Individuals and Agent-Based Communities

Background: Agent-based modeling of Plasmodium falciparum infection offers an attractive alternative to the conventional Ross-Macdonald methodology, as it allows simulation of heterogeneous communities subjected to realistic transmission (inoculation patterns). Methodology/Principal Findings: We developed a new, agent based model that accounts for the essential in-host processes: parasite replication and its regulation by innate and adaptive immunity. The model also incorporates a simplified version of antigenic variation by Plasmodium falciparum. We calibrated the model using data from malaria-therapy (MT) studies, and developed a novel calibration procedure that accounts for a deterministic and a pseudo-random component in the observed parasite density patterns. Using the parasite density patterns of 122 MT patients, we generated a large number of calibrated parameters. The resulting data set served as a basis for constructing and simulating heterogeneous agent-based (AB) communities of MT-like hosts. We conducted several numerical experiments subjecting AB communities to realistic inoculation patterns reported from previous field studies, and compared the model output to the observed malaria prevalence in the field. There was overall consistency, supporting the potential of this agent-based methodology to represent transmission in realistic communities. Conclusions/Significance: Our approach represents a novel, convenient and versatile method to model Plasmodiu

Optimally timing primaquine treatment to reduce Plasmodium falciparum transmission in low endemicity Thai-Myanmar border populations

<p>Abstract</p> <p>Background</p> <p>Effective malaria control has successfully reduced the malaria burden in many countries, but to eliminate malaria, these countries will need to further improve their control efforts. Here, a malaria control programme was critically evaluated in a very low-endemicity Thai-Myanmar border population, where early detection and prompt treatment have substantially reduced, though not ended, <it>Plasmodium falciparum </it>transmission, in part due to carriage of late-maturing gametocytes that remain post-treatment. To counter this effect, the WHO recommends the use of a single oral dose of primaquine along with an effective blood schizonticide. However, while the effectiveness of primaquine as a gametocidal agent is widely documented, the mismatch between primaquine's short half-life, the long-delay for gametocyte maturation and the proper timing of primaquine administration have not been studied.</p> <p>Methods</p> <p>Mathematical models were constructed to simulate 8-year surveillance data, between 1999 and 2006, of seven villages along the Thai-Myanmar border. A simple model was developed to consider primaquine pharmacokinetics and pharmacodynamics, gametocyte carriage, and infectivity.</p> <p>Results</p> <p>In these populations, transmission intensity is very low, so the <it>P. falciparum </it>parasite rate is strongly linked to imported malaria and to the fraction of cases not treated. Given a 3.6-day half-life of gametocyte, the estimated duration of infectiousness would be reduced by 10 days for every 10-fold reduction in initial gametocyte densities. Infectiousness from mature gametocytes would last two to four weeks and sustain some transmission, depending on the initial parasite densities, but the residual mature gametocytes could be eliminated by primaquine. Because of the short half-life of primaquine (approximately eight hours), it was immediately obvious that with early administration (within three days after an acute attack), primaquine would not be present when mature gametocytes emerged eight days after the appearance of asexual blood-stage parasites. A model of optimal timing suggests that primaquine follow-up approximately eight days after a clinical episode could further reduce the duration of infectiousness from two to four weeks down to a few days. The prospects of malaria elimination would be substantially improved by changing the timing of primaquine administration and combining this with effective detection and management of imported malaria cases. The value of using primaquine to reduce residual gametocyte densities and to reduce malaria transmission was considered in the context of a malaria transmission model; the added benefit of the primaquine follow-up treatment would be relatively large only if a high fraction of patients (>95%) are initially treated with schizonticidal agents.</p> <p>Conclusion</p> <p>Mathematical models have previously identified the long duration of <it>P. falciparum </it>asexual blood-stage infections as a critical point in maintaining malaria transmission, but infectiousness can persist for two to four weeks because of residual populations of mature gametocytes. Simulations from new models suggest that, in areas where a large fraction of malaria cases are treated, curing the asexual parasitaemia in a primary infection, and curing mature gametocyte infections with an eight-day follow-up treatment with primaquine have approximately the same proportional effects on reducing the infectious period. Changing the timing of primaquine administration would, in all likelihood, interrupt transmission in this area with very good health systems and with very low endemicity.</p

Quantitative Analysis of Immune Response and Erythropoiesis during Rodent Malarial Infection

Malarial infection is associated with complex immune and erythropoietic responses in the host. A quantitative understanding of these processes is essential to help inform malaria therapy and for the design of effective vaccines. In this study, we use a statistical model-fitting approach to investigate the immune and erythropoietic responses in Plasmodium chabaudi infections of mice. Three mouse phenotypes (wildtype, T-cell-deficient nude mice, and nude mice reconstituted with T-cells taken from wildtype mice) were infected with one of two parasite clones (AS or AJ). Under a Bayesian framework, we use an adaptive population-based Markov chain Monte Carlo method and fit a set of dynamical models to observed data on parasite and red blood cell (RBC) densities. Model fits are compared using Bayes' factors and parameter estimates obtained. We consider three independent immune mechanisms: clearance of parasitised RBCs (pRBC), clearance of unparasitised RBCs (uRBC), and clearance of parasites that burst from RBCs (merozoites). Our results suggest that the immune response of wildtype mice is associated with less destruction of uRBCs, compared to the immune response of nude mice. There is a greater degree of synchronisation between pRBC and uRBC clearance than between either mechanism and merozoite clearance. In all three mouse phenotypes, control of the peak of parasite density is associated with pRBC clearance. In wildtype mice and AS-infected nude mice, control of the peak is also associated with uRBC clearance. Our results suggest that uRBC clearance, rather than RBC infection, is the major determinant of RBC dynamics from approximately day 12 post-innoculation. During the first 2–3 weeks of blood-stage infection, immune-mediated clearance of pRBCs and uRBCs appears to have a much stronger effect than immune-mediated merozoite clearance. Upregulation of erythropoiesis is dependent on mouse phenotype and is greater in wildtype and reconstitited mice. Our study highlights the informative power of statistically rigorous model-fitting techniques in elucidating biological systems

Associations between Season and Gametocyte Dynamics in Chronic Plasmodium falciparum Infections

Introduction: In a markedly seasonal malaria setting, the transition from the transmission-free dry season to the transmission season depends on the resurgence of the mosquito population following the start of annual rains. The sudden onset of malaria outbreaks at the start of the transmission season suggests that parasites persist during the dry season and respond to either the reappearance of vectors, or correlated events, by increasing the production of transmission stages. Here, we investigate whether Plasmodium falciparum gametocyte density and the correlation between gametocyte density and parasite density show seasonal variation in chronic (largely asymptomatic) carriers in eastern Sudan. Materials and Methods: We recruited and treated 123 malaria patients in the transmission season 2001. We then followed them monthly during four distinct consecutive epidemiological seasons: transmission season 1, transmission-free season, pre-clinical period, and transmission season 2. In samples collected from 25 participants who fulfilled the selection criteria of the current analysis, we used quantitative PCR (qPCR) and RT-qPCR to quantify parasite and gametocyte densities, respectively. Results and Discussion: We observed a significant increase in gametocyte density and a significantly steeper positive correlation between gametocyte density and total parasite density during the pre-clinical period compared to the preceding transmission-free season. However, there was no corresponding increase in the density or prevalence of total parasites or gametocyte prevalence. The increase in gametocyte production during the pre-clinical period supports the hypothesis that P. falciparum may respond to environmental cues, such as mosquito biting, to modulate its transmission strategy. Thus, seasonal changes may be important to ignite transmission in unstable-malaria settings

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

Spatio-temporal patterns of the SARS-CoV-2 epidemic in Germany

Results from an explorative study revealing spatio-temporal patterns of the SARS-CoV-2/ COVID-19 epidemic in Germany are presented. We dispense with contestable model assumptions and show the intrinsic spatio-temporal patterns of the epidemic dynamics. The analysis is based on COVID-19 incidence data, which are age-stratified and spatially resolved at the county level, provided by the Federal Government's Public Health Institute of Germany (RKI) for public use. Although the 400 county-related incidence time series shows enormous heterogeneity, both with respect to temporal features as well as spatial distributions, the counties' incidence curves organise into well-distinguished clusters that coincide with East and West Germany. The analysis is based on dimensionality reduction, multidimensional scaling, network analysis, and diversity measures. Dynamical changes are captured by means of difference-in-difference methods, which are related to fold changes of the effective reproduction numbers. The age-related dynamical patterns suggest a considerably stronger impact of children, adolescents and seniors on the epidemic activity than previously expected. Besides these concrete interpretations, the work mainly aims at providing an atlas for spatio-temporal patterns of the epidemic, which serves as a basis to be further explored with the expertise of different disciplines, particularly sociology and policy makers. The study should also be understood as a methodological contribution to getting a handle on the unusual complexity of the COVID-19 pandemic