Counting statistics based on the analytic solutions of the differential-difference equation for birth-death processes

Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on the system size (corresponding to the number of products or customers undergoing the birth-death process) and thus vary every time birth or death occurs, which makes fluctuations in the rates inevitable. The differential-difference equation governing the time evolution of such a birth-death process is well established, but it resists solving for a non-asymptotic solution. In this work, we present the analytic solution of the differential-difference equation for birth-death processes without approximation. The time-dependent solution we obtain leads to an analytical expression for counting statistics of products (or customers). We further examine the relationship between the system size fluctuations and the birth and death rates, and find that statistical properties (variance subtracted by mean) of the system size are determined by the mean death rate as well as the covariance of the system size and the net growth rate (i.e., the birth rate minus the death rate). This work suggests a promising new direction for quantitative investigations into birth-death processes

Warm needle acupuncture for osteoarthritis: A systematic review and meta-analysis.

Warm needle acupuncture (WA) is considered a potential intervention in the treatment of osteoarthritis (OA). To systematically evaluate the clinical efficacy and safety of WA in the treatment of OA. Systematic review and meta-analysis METHODS: Fourteen databases were searched from their inception until May 2022. Randomized controlled trials (RCTs) of WA for treating OA were identified. Study selection and data extraction were performed by two independent reviewers. The Cochrane risk of bias tool and the Grading of Recommendations Assessment, Development and Evaluation program were used to assess all included RCTs. A total of 66 RCTs met the inclusion criteria for this review. Most of the included studies had an unclear risk of bias, and the certainty of the evidence was very low. Twenty-four RCTs compared the effects of WA with those of oral drug therapies. Meta-analysis showed superior effects of WA for the total effective rate (risk ratio (RR): 1.22, 95% confidence interval (CI): 1.17 to 1.27, I  = 26%, p < 0.001, 24 studies, n = 2278), pain, and function. Eight RCTs compared the effects of WA+drug therapy, and meta-analysis showed favorable effects for the total effective rate (RR: 1.27, 95% CI: 1.18 to 1.35, I =0%, p < 0.001, 8 studies, n = 646). Eight RCTs compared the effects of WA and intra-articular sodium hyaluronate (IASH) injection on OA and found equivalent effects of WA on the symptoms of OA. Twenty-eight RCTs compared the effects of WA+IASH injection with those of IASH injection, and meta-analysis showed superior effects of WA+IASH in terms of the total effective rate (RR: 1.15, 95% CI: 1.11 to 1.19, I =27.3%, p < 0.001, 25 studies, n = 2208), pain, and function. None of the RCTs reported serious adverse events. WA may have some distinct advantages in the treatment of OA. However, well-designed RCTs with larger sample sizes are needed. [Abstract copyright: Copyright © 2022 The Author(s). Published by Elsevier GmbH.. All rights reserved.

A key to room-temperature ferromagnetism in Fe-doped ZnO: Cu

Successful synthesis of room-temperature ferromagnetic semiconductors, Zn$_{1-x}$Fe$_{x}$O, is reported. The essential ingredient in achieving room-temperature ferromagnetism in bulk Zn$_{1-x}$Fe$_{x}$O was found to be additional Cu doping. A transition temperature as high as 550 K was obtained in Zn$_{0.94}$Fe$_{0.05}$Cu$_{0.01}$O; the saturation magnetization at room temperature reached a value of $0.75 \mu_{\rm B}$ per Fe. Large magnetoresistance was also observed below $100$K.Comment: 11 pages, 4 figures; to appear in Appl. Phys. Let

Ideals of pseudo MV-algebras based on vague set theory,

Abstract. The notion of vague ideals in pseudo MV-algebras is introduced, and several properties are investigated. Conditions for a vague set to be a vague ideal are provided. Conditions for a vague ideal to be implicative are given. Characterizations of (implicative, prime) vague ideals are discussed. The smallest vague ideal containing a given vague set is established. Prime and implicative extension property for a vague ideal is discussed

Entropic sampling dynamics of the globally-coupled kinetic Ising model

The entropic sampling dynamics based on the reversible information transfer to and from the environment is applied to the globally coupled Ising model in the presence of an oscillating magnetic field. When the driving frequency is low enough, coherence between the magnetization and the external magnetic field is observed; such behavior tends to weaken with the system size. The time-scale matching between the intrinsic time scale, defined in the absence of the external magnetic field, and the extrinsic time scale, given by the inverse of the driving frequency, is used to explain the observed coherence behavior.Comment: 8 page