Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation

Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero. We study both the transient and steady-state probability laws of the stochastic process that describes the state of the system. We then derive a heavy-traffic approximation to the model that yields a jump-diffusion process. The latter is equivalent to a Wiener process subject to randomly occurring jumps, whose probability law is obtained. The goodness of the approximation is finally discussed.Comment: 18 pages, 5 figures, paper accepted by "Methodology and Computing in Applied Probability", the final publication is available at http://www.springerlink.co

Enhancer of Zeste Homolog 2 Induces Pulmonary Artery Smooth Muscle Cell Proliferation

Pulmonary Arterial Hypertension (PAH) is a progressively devastating disease characterized by excessive proliferation of the Pulmonary Arterial Smooth Muscle Cells (PASMCs). Studies suggest that PAH and cancers share an apoptosis-resistant state featuring excessive cell proliferation. The proliferation of cancer cells is mediated by increased expression of Enhancer of Zeste Homolog 2 (EZH2), a mammalian histone methyltransferase that contributes to the epigenetic silencing of target genes. However, the role of EZH2 in PAH has not been studied. In this study, it is hypothesized that EZH2 could play a role in the proliferation of PASMCs.In the present study, the expression patterns of EZH2 were investigated in normal and hypertensive mouse PASMCs. The effects of EZH2 overexpression on the proliferation of human PASMCs were tested. PASMCs were transfected with EZH2 or GFP using nucleofector system. After transfection, the cells were incubated for 48 hours at 37°C. Proliferation and cell cycle analysis were performed using flow cytometry. Apoptosis of PASMCs was determined using annexin V staining and cell migration was tested by wound healing assay.EZH2 protein expression in mouse PASMCs were correlated with an increase in right ventricular systolic pressure and Right Ventricular Hypertrophy (RVH). The overexpression of EZH2 in human PASMCs enhances proliferation, migration, and decrease in the rate of apoptosis when compared to GFP-transfected cells. In the G2/M phase of the EZH2 transfected cells, there was a 3.5 fold increase in proliferation, while there was a significant decrease in the rate of apoptosis of PASMCs, when compared to control.These findings suggest that EZH2 plays a role in the migration and proliferation of PASMCs, which is a major hallmark in PAH. It also suggests that EZH2 could play a role in the development of PAH and can serve as a potential target for new therapies for PAH

The NANOGrav 15 yr Data Set: Chromatic Gaussian Process Noise Models for Six Pulsars

\ua9 2024. The Author(s). Published by the American Astronomical Society.Pulsar timing arrays (PTAs) are designed to detect low-frequency gravitational waves (GWs). GWs induce achromatic signals in PTA data, meaning that the timing delays do not depend on radio frequency. However, pulse arrival times are also affected by radio-frequency-dependent “chromatic” noise from sources such as dispersion measure (DM) and scattering delay variations. Furthermore, the characterization of GW signals may be influenced by the choice of chromatic noise model for each pulsar. To better understand this effect, we assess if and how different chromatic noise models affect the achromatic noise properties in each pulsar. The models we compare include existing DM models used by the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and noise models used for the European PTA Data Release 2 (EPTA DR2). We perform this comparison using a subsample of six pulsars from the NANOGrav 15 yr data set, selecting the same six pulsars as from the EPTA DR2 six-pulsar data set. We find that the choice of chromatic noise model noticeably affects the achromatic noise properties of several pulsars. This is most dramatic for PSR J1713+0747, where the amplitude of its achromatic red noise lowers from log 10 A RN = − 14.1 − 0.1 + 0.1 to − 14.7 − 0.5 + 0.3 , and the spectral index broadens from γ RN = 2.6 − 0.4 + 0.5 to γ RN = 3.5 − 0.9 + 1.2 . We also compare each pulsar\u27s noise properties with those inferred from the EPTA DR2, using the same models. From the discrepancies, we identify potential areas where the noise models could be improved. These results highlight the potential for custom chromatic noise models to improve PTA sensitivity to GWs

Positive Evolutionary Selection of an HD Motif on Alzheimer Precursor Protein Orthologues Suggests a Functional Role

HD amino acid duplex has been found in the active center of many different enzymes. The dyad plays remarkably different roles in their catalytic processes that usually involve metal coordination. An HD motif is positioned directly on the amyloid beta fragment (Aβ) and on the carboxy-terminal region of the extracellular domain (CAED) of the human amyloid precursor protein (APP) and a taxonomically well defined group of APP orthologues (APPOs). In human Aβ HD is part of a presumed, RGD-like integrin-binding motif RHD; however, neither RHD nor RXD demonstrates reasonable conservation in APPOs. The sequences of CAEDs and the position of the HD are not particularly conserved either, yet we show with a novel statistical method using evolutionary modeling that the presence of HD on CAEDs cannot be the result of neutral evolutionary forces (p<0.0001). The motif is positively selected along the evolutionary process in the majority of APPOs, despite the fact that HD motif is underrepresented in the proteomes of all species of the animal kingdom. Position migration can be explained by high probability occurrence of multiple copies of HD on intermediate sequences, from which only one is kept by selective evolutionary forces, in a similar way as in the case of the “transcription binding site turnover.” CAED of all APP orthologues and homologues are predicted to bind metal ions including Amyloid-like protein 1 (APLP1) and Amyloid-like protein 2 (APLP2). Our results suggest that HDs on the CAEDs are most probably key components of metal-binding domains, which facilitate and/or regulate inter- or intra-molecular interactions in a metal ion-dependent or metal ion concentration-dependent manner. The involvement of naturally occurring mutations of HD (Tottori (D7N) and English (H6R) mutations) in early onset Alzheimer's disease gives additional support to our finding that HD has an evolutionary preserved function on APPOs

On the typology and the worship status of sacred trees with a special reference to the Middle East

This article contains the reasons for the establishment of sacred trees in Israel based on a field study. It includes 97 interviews with Muslim and Druze informants. While Muslims (Arabs and Bedouins) consider sacred trees especially as an abode of righteous figures' (Wellis') souls or as having a connection to their graves, the Druze relate sacred trees especially to the events or deeds in the lives of prophets and religious leaders. A literary review shows the existence of 24 known reasons for the establishment of sacred trees worldwide, 11 of which are known in Israel one of these is reported here for the first time. We found different trends in monotheistic and polytheistic religions concerning their current worship of sacred trees