The Number of Optimal Matchings for Euclidean Assignment on the Line

We consider the Random Euclidean Assignment Problem in dimension $$d=1$$ d = 1 , with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings (say, $$\sim \exp (S_N)$$ ∼ exp ( S N ) at size N). We characterize all possible optimal matchings of a given instance of the problem, and we give a simple product formula for their number. Then, we study the probability distribution of $$S_N$$ S N (the zero-temperature entropy of the model), in the uniform random ensemble. We find that, for large N, $$S_N \sim \frac{1}{2} N \log N + N s + {\mathcal {O}}\left( \log N \right) $$ S N ∼ 1 2 N log N + N s + O log N , where s is a random variable whose distribution p(s) does not depend on N. We give expressions for the moments of p(s), both from a formulation as a Brownian process, and via singularity analysis of the generating functions associated to $$S_N$$ S N . The latter approach provides a combinatorial framework that allows to compute an asymptotic expansion to arbitrary order in 1/N for the mean and the variance of $$S_N$$ S N .

Dynamics of the COVID-19 epidemic in Ireland under mitigation

Background: In Ireland and across the European Union, cases of COVID-19 continue to rise with recent increases in reported cases following a period of stability. Public health interventions continue in their attempts to control the epidemic in spite of a lack of information on the scale of silent transmission. Methods: To tackle this challenge and the non-stationary aspect of the epidemic we used a modified SEIR stochastic model with time-varying parameters, following Brownian process. This model is coupled with Bayesian inference (PMCMC) for parameter estimation and used mainly confirmed reported hospitalized cases. Results: Mitigation measures provided an 80% reduction in transmission between March and May 2020. By end of October our estimated seroprevalence rate was 1.1% (95% CI: 0.5%–2.8%) far from herd immunity. We estimated that the proportion of asymptomatic transmission was approximately 40% but with large uncertainty (95% CI: 14%–73%). Finally we demonstrate that the available observed confirmed cases are not reliable for any analysis owing to the fact that their reporting rate has greatly evolved. Conclusion: We provide the first estimations of the dynamics of the COVID-19 epidemic in Ireland and its key parameters. We also quantify the effects of mitigation measures on the virus transmission before, during and after mitigation. Our results demonstrate that Ireland has significantly reduced transmission by employing mitigation measures, physical distancing and lockdown. This has to date avoided the saturation of healthcare infrastructures, flattened the epidemic curve and likely reduced mortality. However, as mitigation measures change silent transmission remain an ongoing challenge.

Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints

In this work, we study an optimization problem arising in the management of a natural resource over an infinite time horizon. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager is allowed to harvest the resource and sell it at a stochastic market price modeled by a geometric Brownian process. We assume that there are delay constraints imposed on the decisions of the manager. More precisely, starting harvesting order and selling order are executed after a delay. By using the dynamic programming approach, we characterize the value function as the unique solution to an original partial differential equation. We complete our study with some numerical illustrations.

Long-term statistics of pulsar glitches triggered by a Brownian stress accumulation process

ABSTRACT A microphysics-agnostic meta-model of rotational glitches in rotation-powered pulsars is developed, wherein the globally averaged internal stress accumulates as a Brownian process between glitches, and a glitch is triggered once a critical threshold is surmounted. Precise, falsifiable predictions are made regarding long-term event statistics in individual pulsars. For example, the Spearman cross-correlation coefficient between the size of a glitch and the waiting time until the next glitch should exceed 0.25 in all pulsars. Among the six pulsars with the most recorded glitches, PSR J0537−6910 and PSR J0835−4510 are consistent with the predictions of the meta-model, while PSR J1740−3015 and PSR J0631+1036 are not. PSR J0534+2200 and PSR J1341−6220 are only consistent with the meta-model, if there exists an undetected population of small glitches with small waiting times, which we do not resolve. The results are compared with a state-dependent Poisson process, another microphysics-agnostic meta-model in the literature. The results are also applied briefly to recent pulse-to-pulse observations of PSRJ0835−4510, which appear to reveal evidence for a negative fluctuation in rotation frequency just prior to the 2016 glitch.

Inference of population genetic structure from temporal samples of DNA

The recent years have seen a growing number of studies investigating evolutionary questions using ancient DNA techniques and temporal samples of DNA. To address these questions, one of the most frequently-used algorithm is based on principal component analysis (PCA). When PCA is applied to temporal samples, the sample dates are, however, ignored during analysis, which could lead to some misinterpretations of the results. Here we introduce a new factor analysis (FA) method for which individual scores are corrected for the effect of allele frequency drift through time. Based on a diffusion approximation, our approach approximates allele frequency drift in a random mating population by a Brownian process. Exact solutions for estimates of corrected factors are obtained, and a fast estimation algorithm is presented. We compared data representations obtained from the FA method with PCA and with PC projections in simulations of divergence and admixture scenarios. Then we applied FA with correction for temporal drift to study the evolution of hepatitis C virus in a patient infected by multiple strains, and to describe the population structure of ancient European samples.

Non-Linear Dynamics Analysis of Protein Sequences. Application to CYP450

The nature of changes involved in crossed-sequence scale and inner-sequence scale is very challenging in protein biology. This study is a new attempt to assess with a phenomenological approach the non-stationary and nonlinear fluctuation of changes encountered in protein sequence. We have computed fluctuations from an encoded amino acid index dataset using cumulative sum technique and extracted the departure from the linear trend found in each protein sequence. For inner-sequence analysis, we found that the fluctuations of changes statistically follow a −5/3 Kolmogorov power and behave like an incremental Brownian process. The pattern of the changes in the inner sequence seems to be monofractal in essence and to be bounded between Hurst exponent [1/3,1/2] range, which respectively corresponds to the Kolmogorov and Brownian monofractal process. In addition, the changes in the inner sequence exhibit moderate complexity and chaos, which seems to be coherent with the monofractal and stochastic process highlighted previously in the study. The crossed-sequence changes analysis was achieved using an external parameter, which is the activity available for each protein sequence, and some results obtained for the inner sequence, specifically the drift and Kolmogorov complexity spectrum. We found a significant linear relationship between activity changes and drift changes, and also between activity and Kolmogorov complexity. An analysis of the mean square displacement of trajectories in the bivariate space (drift, activity) and (Kolmogorov complexity spectrum, activity) seems to present a superdiffusive law with a 1.6 power law value.

MATERIALS SCIENCE AND ENERGY FRACTAL NATURE NEW FRONTIERS

The modern material science faces very important priorities of the future new frontiers which open new directions within higher and deeper structure knowledge even down to nano and due to the lack of energy, towards new and alternative energy sources. For example, in our up to date research we have recognized that BaTiO3 and other ceramics have fractal configuration nature based on three different phenomena. First, ceramic grains have fractal shape looking as a contour in cross section or as a surface. Second, there is the so-called “negative space” made of pores and inter-granular space. Being extremely complex, the pore space plays an important role in microelectronics, micro-capacity, PTC, piezoelectric and other phenomena. Third, there is a Brownian process of fractal motions inside the material during and after sintering in the form of micro-particles flow: ions, atoms and electrons. Here we met an exciting task of the Coble model, with already extended and generalized geometries. These triple factors, in combination, make the microelectronic environment of very peculiar electro-static/dynamic combination. The stress is here set on inter-granular micro-capacity and super micro-capacitors in function of higher energy harvesting and energy storage. An attention is paid to components affecting overall impedances distribution. Con­struc­tive fractal theory allows recognizing micro-capacitors with fractal electrodes. The method is based on the iterative process of interpolation which is compatible with the model of grains itself. Inter-granular permeability is taken as a function of temperature as fundamental thermodynamic parameter.

FRACTAL CHARACTERISTICS OF PHASE SPECTRUM OF EARTHQUAKE MOTION

The purpose of this research is to make clear the phase spectrum characteristic of earthquake motion. After the introduction of past researches we introduce the concept of fractional Brownian process (FBP). A simple method is proposed to determine the Hurst index and the variance of a given process characterized by the FBP. We find that the phase characteristic of earthquake motion can be expressed by this process which is a non-stationery function of the circular frequency with a constant correlation coefficient. Using several observed earthquake motion we demonstrate this fact and show the efficiency of newly founded result to simulate realistic earthquake motion phase and also compare simulated earthquake motions with those of observed ones. We also simulate design response spectrum compatible earthquake motions by simulating the earthquake motion phase using the identified Hurst index and variance of the given earthquake motion. We investigate the effect of hypocenter distance on the variance and Hurst index of earthquake motion phase, as well as on the mean gradient of earthquake motion phase with respect to the circular frequency.