On Explicit Probability Densities Associated with Fuss-Catalan Numbers

In this note we give explicitly a family of probability densities, the moments of which are Fuss-Catalan numbers. The densities appear naturally in random matrices, free probability and other contexts.Comment: 4 page

q -Analogs of Identities Involving Harmonic Numbers and Binomial Coefficients

Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic numbers, one of which generalizes an identity used to prove the Apéry number supercongruence. In 2008, Prodinger provided human proofs of identities initially obtained by Osburn and Schneider using the computer program Sigma. In this paper, we establish q -analogs of a fair number of the identities appearing in McCarthy (Integers 11 (2011): A37) and Prodinger (Integers 8 (2008): A10) by making use of q -partial fractions

The and -Analogs of Zagreb Indices and Coindices of Graphs

The first and second Zagreb indices were first introduced by Gutman and Trinajstić (1972). It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical instances, and in elsewhere. Recently, the first and second Zagreb coindices, a new pair of invariants, were introduced in Došlić (2008). In this paper we introduce the and ()-analogs of the above Zagreb indices and coindices and investigate the relationship between the enhanced versions to get a unified theory.</jats:p

A mobile assisted coverage hole patching scheme based on particle swarm optimization for WSNs

Wireless sensor networks (WSNs) have drawn much research attention in recent years due to the superior performance in multiple applications, such as military and industrial monitoring, smart home, disaster restoration etc. In such applications, massive sensor nodes are randomly deployed and they remain static after the deployment, to fully cover the target sensing area. This will usually cause coverage redundancy or coverage hole problem. In order to effectively deploy sensors to cover whole area, we present a novel node deployment algorithm based on mobile sensors. First, sensor nodes are randomly deployed in target area, and they remain static or switch to the sleep mode after deployment. Second, we partition the network into grids and calculate the coverage rate of each grid. We select grids with lower coverage rate as candidate grids. Finally, we awake mobile sensors from sleep mode to fix coverage hole, particle swarm optimization (PSO) algorithm is used to calculate moving position of mobile sensors. Simulation results show that our algorithm can effectively improve the coverage rate of WSNs

Contrastive Learning for Enhancing Robust Scene Transfer in Vision-based Agile Flight

Scene transfer for vision-based mobile robotics applications is a highly relevant and challenging problem. The utility of a robot greatly depends on its ability to perform a task in the real world, outside of a well-controlled lab environment. Existing scene transfer end-to-end policy learning approaches often suffer from poor sample efficiency or limited generalization capabilities, making them unsuitable for mobile robotics applications. This work proposes an adaptive multi-pair contrastive learning strategy for visual representation learning that enables zero-shot scene transfer and real-world deployment. Control policies relying on the embedding are able to operate in unseen environments without the need for finetuning in the deployment environment. We demonstrate the performance of our approach on the task of agile, vision-based quadrotor flight. Extensive simulation and real-world experiments demonstrate that our approach successfully generalizes beyond the training domain and outperforms all baselines

The microbiota continuum along the female reproductive tract and its relation to uterine-related diseases

Reports on bacteria detected in maternal fluids during pregnancy are typically associated with adverse consequences, and whether the female reproductive tract harbours distinct microbial communities beyond the vagina has been a matter of debate. Here we systematically sample the microbiota within the female reproductive tract in 110 women of reproductive age, and examine the nature of colonisation by 16S rRNA gene amplicon sequencing and cultivation. We find distinct microbial communities in cervical canal, uterus, fallopian tubes and peritoneal fluid, differing from that of the vagina. The results reflect a microbiota continuum along the female reproductive tract, indicative of a non-sterile environment. We also identify microbial taxa and potential functions that correlate with the menstrual cycle or are over-represented in subjects with adenomyosis or infertility due to endometriosis. The study provides insight into the nature of the vagino-uterine microbiome, and suggests that surveying the vaginal or cervical microbiota might be useful for detection of common diseases in the upper reproductive tract.Shenzhen Municipal Government of China [JCYJ20160229172757249, JCYJ20150601090833370]; Danish Strategic Research Council [2106-07-0021]; Ole Romer grant from Danish Natural Science Research Council; Solexa project [272-07-0196]SCI(E)ARTICLE