Search Results (2)

The dynamics of a stochastic system that exhibits large fluctuations to a given state are almost deterministic due to weak random perturbations. Such large fluctuations occur with overwhelming probability in the vicinity of the so-called optimal path, which is a vital concept in physics, chemistry, and biology, as it uncovers the way in which a physical process escapes from the attractive domain of a metastable state and transitions between different metastable states. In this paper, we examine the prehistorical description of the optimal fluctuation with the unifying framework of Langevin dynamics by means of a quantity called prehistory probability density. We show that the optimal fluctuation has a strong connection with the time reversal of the associated diffusion process. Specifically, in the stationary or quasi-stationary cases, it is found that the prehistory probability density actually acts as the transition probability density of the reversed process. As noise intensity approaches zero, it focuses on the average dynamics of the reversed process due to the law of large numbers, which is then shown to coincide with the time reversal of the optimal path. The local dispersion of the prehistory probability density can thus be reformulated as a Gaussian distribution corresponding to the linearized part of the reversed process. In addition, as an analogue of the original definition in the stationary states, it is proven that the concept of prehistory probability density can also be extended to nonstationary cases where similar properties are still valid. Based on these theoretical results, an algorithm is designed and then successfully applied to a one-dimensional example at the end, showing its accuracy for pinpointing the location of the optimal path and its efficacy in cases where multiple optimal paths coexist. Full article

The prehistory of the Lithuanian population and genetic relationship to other populations are poorly studied. Thus, the Lithuanian population, as an object of study, is interesting due to its partial isolation with genetic distinctiveness within the European context and with preserved ancient genetic composition. The main objects of this study was to infer demographic parameters, effective population size (Ne), and divergence time using high-density single nucleotide polymorphism (SNP) genotyping data generated with the Illumina HumanOmmiExpress-12v1.1 array in 295 individuals from the Lithuanian population and to compare our data with other populations from the Human Genome Cell Line Diversity Panel (HGDP-CEPH). We also aimed to reconstruct past events between the main ethnolinguistic regions—Aukštaitija and Žemaitija of Lithuania. Historically, these regions probably developed as two independent Baltic tribes. Our results of Ne in the Lithuanian population through time demonstrated a substantial reduction of Ne over the 150,000–25,000 years before present (YBP). The estimated long-term Ne of the Lithuanian population is quite low—it equals 5404, which likely is a consequence of the bottlenecks associated with the last glacial period of 25,000–12,000 YBP in Europe. The obtained divergence time estimates between the study populations are in agreement with recent studies. The reconstructed past events in Aukštaitija and Žemaitija showed significant differences between these two regions of Lithuania. Full article