Time-domain response of nabla discrete fractional order systems

This paper investigates the time--domain response of nabla discrete fractional order systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag--Leffler function. In particular, we establish two fundamental properties of a nabla discrete fractional order system with nonzero initial instant: i) the existence and uniqueness of the system time--domain response; and ii) the dynamic behavior of the zero input response. Finally, one numerical example is provided to show the validity of the theoretical results.Comment: 13 pages, 6 figure

The global geometrical property of jet events in high-energy nuclear collisions

We present the first theoretical study of medium modifications of the global geometrical pattern, i.e., transverse sphericity ($S_{\perp}$) distribution of jet events with parton energy loss in relativistic heavy-ion collisions. In our investigation, POWHEG+PYTHIA is employed to make an accurate description of transverse sphericity in the p+p baseline, which combines the next-to-leading order (NLO) pQCD calculations with the matched parton shower (PS). The Linear Boltzmann Transport (LBT) model of the parton energy loss is implemented to simulate the in-medium evolution of jets. We calculate the event normalized transverse sphericity distribution in central Pb+Pb collisions at the LHC, and give its medium modifications. An enhancement of transverse sphericity distribution at small $S_{\perp}$ region but a suppression at large $S_{\perp}$ region are observed in A+A collisions as compared to their p+p references, which indicates that in overall the geometry of jet events in Pb+Pb becomes more pencil-like. We demonstrate that for events with 2 jets in the final-state of heavy-ion collisions, the jet quenching makes the geometry more sphere-like with medium-induced gluon radiation. However, for events with $\ge 3$~jets, parton energy loss in the QCD medium leads to the events more pencil-like due to jet number reduction, where less energetic jets may lose their energies and then fall off the jet selection kinematic cut. These two effects offset each other and in the end result in more jetty events in heavy-ion collisions relative to that in p+p.Comment: 9 pages, 9 figure

Four-state rock-paper-scissors games on constrained Newman-Watts networks

We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{max}$ in Newman-Watts networks with the long-rang connection probability $p$, we depict more realistically the stochastic interactions among species within ecosystems. When we fix mobility and vary the value of $p$ or $R_{max}$, the Monte Carlo simulations show that the spiral waves grow in size, and the system becomes unstable and biodiversity is lost with increasing $p$ or $R_{max}$. These results are similar to recent results of Reichenbach \textit{et al.} [Nature (London) \textbf{448}, 1046 (2007)], in which they increase the mobility only without including long-range interactions. We compared extinctions with or without long-range connections and computed spatial correlation functions and correlation length. We conclude that long-range connections could improve the mobility of species, drastically changing their crossover to extinction and making the system more unstable.Comment: 6 pages, 7 figure

Effect of Achyranthes bidentata Blume extract on carrageenan-induced chronic prostatitis in rats

Purpose: To investigate the effect of Achyranthes bidentata Blume. Extract (ABBE) on carrageenaninduced chronic prostatitis in rats.Methods: Experimental chronic non-bacterial prostatitis (CNP) was induced in rats by 1 % carrageenan (0.1 mL). Prostate index (PI) and prostate specific antigen (PSA) were determined after 3 weeks of adiministration. Relative inflammatory factors, viz, tumor necrosis factor-α (TNF-α), interleukin1β (IL-1β), cyclooxygenase-2 (COX-2), prostaglandin E2 (PEG2), transforming growth factor-β1 (TGF-β1) and connective tissue growth factor (CTGF) in the prostate tissues of all group rats were measured.Results: In CNP model, ABBE decreased PI and PSA compared with untreated control group (p < 0.01). Morphometric analysis showed a significant reduction in chronic inflammatory cell infiltrates and interstitial fibrosis compared to control group. Reduced values of TNF-α, IL-1β, COX-2, PEG2 were observed in ABBE-treated groups compared with model group respectively (p < 0.01). Moreover, the levels of TGF-β1 and CTGF in ABBE-treated groups were significantly lower, and in addition, there was alleviation of the inflammatory state of the prostate gland (p < 0.01).Conclusion: ABBE showed antichronic non-bacterial prostatitis effect by multiple ways in rats, thus indicating its potential suitability for the treatment of chronic prostatitis.Keywords: Achyranthes bidentata Blume., Chronic prostatitis, Inflammatory cel

Infinite series representation of fractional calculus: theory and applications

This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the current time. The framework takes into account of the Riemann-Liouville definition, the Caputo definition, the constant order and the variable order. On this basis, some properties of fractional calculus are confirmed conveniently. An intuitive numerical approximation scheme via truncation is proposed subsequently. Finally, several illustrative examples are presented to validate the effectiveness and practicability of the obtained results

Genome-wide in silico identification and analysis of cis natural antisense transcripts (cis-NATs) in ten species

We developed a fast, integrative pipeline to identify cis natural antisense transcripts (cis-NATs) at genome scale. The pipeline mapped mRNAs and ESTs in UniGene to genome sequences in GoldenPath to find overlapping transcripts and combining information from coding sequence, poly(A) signal, poly(A) tail and splicing sites to deduce transcription orientation. We identified cis-NATs in 10 eukaryotic species, including 7830 candidate sense–antisense (SA) genes in 3915 SA pairs in human. The abundance of SA genes is remarkably low in worm and does not seem to be caused by the prevalence of operons. Hundreds of SA pairs are conserved across different species, even maintaining the same overlapping patterns. The convergent SA class is prevalent in fly, worm and sea squirt, but not in human or mouse as reported previously. The percentage of SA genes among imprinted genes in human and mouse is 24–47%, a range between the two previous reports. There is significant shortage of SA genes on Chromosome X in human and mouse but not in fly or worm, supporting X-inactivation in mammals as a possible cause. SA genes are over-represented in the catalytic activities and basic metabolism functions. All candidate cis-NATs can be downloaded from