Cauchy Problem for Fractional Ricatti‎ Differential Equations ‎Type with Alpha Order Caputo Fractional Derivatives

In this paper, we investigate solution of the fractional Ricatti differential equations (FRDEs) with alpha order Caputo fractional derivatives. In fact, FRDEs are analogous of the Ricatti‎ ordinary differential equations. The multi power series method is used to obtain a useful formula that is implemented to find an explicit solution of Cauchy problem for FRDEs without solving any integral. This formula is explicit and easy to compute by using Maple software to get explicit solution. Also, it is shown that the proposed formula can be used to solve the Cauchy problem for Ricatti‎ ordinary differential equations

Ice-lens formation and geometrical supercooling in soils and other colloidal materials

We present a new, physically-intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a freezing soil. At low temperatures, ice in the crack exerts large pressures on the crack walls that will eventually cause the crack to split open. We show that the crack will then propagate across the soil to form a new lens. The process is controlled by two factors: the cohesion of the soil, and the geometrical supercooling of the water in the soil; a new concept introduced to measure the energy available to form a new ice lens. When the supercooling exceeds a critical amount (proportional to the cohesive strength of the soil) a new ice lens forms. This condition for ice-lens formation and growth does not appeal to any ad hoc, empirical assumptions, and explains how periodic ice lenses can form with or without the presence of a frozen fringe. The proposed mechanism is in good agreement with experiments, in particular explaining ice-lens pattern formation, and surges in heave rate associated with the growth of new lenses. Importantly for systems with no frozen fringe, ice-lens formation and frost heave can be predicted given only the unfrozen properties of the soil. We use our theory to estimate ice-lens growth temperatures obtaining quantitative agreement with the limited experimental data that is currently available. Finally we suggest experiments that might be performed in order to verify this theory in more detail. The theory is generalizable to complex natural-soil scenarios, and should therefore be useful in the prediction of macroscopic frost heave rates.Comment: Submitted to PR

Evaluation of Galanin Expression in Colorectal Cancer: An Immunohistochemical and Transcriptomic Study

Colorectal cancer (CRC) represents around 10% of all cancers, with an increasing incidence in the younger age group. The gut is considered a unique organ with its distinctive neuronal supply. The neuropeptide, human galanin, is widely distributed in the colon and expressed in many cancers, including the CRC. The current study aimed to explore the role of galanin at different stages of CRC. Eighty-one CRC cases (TNM stages I – IV) were recruited, and formalin-fixed paraffin-embedded samples were analyzed for the expression of galanin and galanin receptor 1 (GALR1) by immunohistochemistry (IHC). Galanin intensity was significantly lower in stage IV (n= 6) in comparison to other stages (p= 0.037 using the Mann-Whitney U test). Whole transcriptomics analysis using NGS was performed for selected samples based on the galanin expression by IHC [early (n=5) with high galanin expression and late (n=6) with low galanin expression]. Five differentially regulated pathways (using Absolute GSEA) were identified as drivers for tumor progression and associated with higher galanin expression, namely, cell cycle, cell division, autophagy, transcriptional regulation of TP53, and immune system process. The top shared genes among the upregulated pathways are AURKA, BIRC5, CCNA1, CCNA2, CDC25C, CDK2, CDK6, EREG, LIG3, PIN1, TGFB1, TPX2. The results were validated using real-time PCR carried out on four cell lines [two primaries (HCT116 and HT29) and two metastatic (LoVo and SK-Co-1)]. The current study shows galanin as a potential negative biomarker. Galanin downregulation is correlated with advanced CRC staging and linked to cell cycle and division, autophagy, transcriptional regulation of TP53 and immune system response

Changes in Clinical Context for Kaposi's Sarcoma and Non-Hodgkin Lymphoma Among People With HIV Infection in the United States

The biology of HIV-associated cancers may differ depending on immunologic and virologic context during development. Therefore, an understanding of the burden of Kaposi's sarcoma (KS) and non-Hodgkin lymphoma (NHL) relative to antiretroviral therapy (ART), virologic suppression, and CD4 count is important

Identifying Immunological and Clinical Predictors of COVID-19 Severity and Sequelae by Mathematical Modeling

Since its emergence as a pandemic in March 2020, coronavirus disease (COVID-19) outcome has been explored via several predictive models, using specific clinical or biochemical parameters. In the current study, we developed an integrative non-linear predictive model of COVID-19 outcome, using clinical, biochemical, immunological, and radiological data of patients with different disease severities. Initially, the immunological signature of the disease was investigated through transcriptomics analysis of nasopharyngeal swab samples of patients with different COVID-19 severity versus control subjects (exploratory cohort, n=61), identifying significant differential expression of several cytokines. Accordingly, 24 cytokines were validated using a multiplex assay in the serum of COVID-19 patients and control subjects (validation cohort, n=77). Predictors of severity were Interleukin (IL)-10, Programmed Death-Ligand-1 (PDL-1), Tumor necrosis factors-α, absolute neutrophil count, C-reactive protein, lactate dehydrogenase, blood urea nitrogen, and ferritin; with high predictive efficacy (AUC=0.93 and 0.98 using ROC analysis of the predictive capacity of cytokines and biochemical markers, respectively). Increased IL-6 and granzyme B were found to predict liver injury in COVID-19 patients, whereas interferon-gamma (IFN-γ), IL-1 receptor-a (IL-1Ra) and PD-L1 were predictors of remarkable radiological findings. The model revealed consistent elevation of IL-15 and IL-10 in severe cases. Combining basic biochemical and radiological investigations with a limited number of curated cytokines will likely attain accurate predictive value in COVID-19. The model-derived cytokines highlight critical pathways in the pathophysiology of the COVID-19 with insight towards potential therapeutic targets. Our modeling methodology can be implemented using new datasets to identify key players and predict outcomes in new variants of COVID-19

Update of the Search for the Neutrinoless Decay τ→μγ\tau\to \mu\gamma

We present an update of the search for the lepton family number violating decay $\tau \to \mu\gamma$ using a complete CLEO II data sample of 12.6 million $\tau^+\tau^-$ pairs. No evidence of a signal has been found and the corresponding upper limit is \BR(\tau \to \mu\gamma) < 1.0 \times 10^{-6} at 90% CL, significantly smaller than previous limits. All quoted results are preliminary.Comment: 9 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Neutral strange particle production in deep inelastic scattering at HERA

This paper presents measurements of K0 and Λ production in neutral current, deep inelastic scattering of 26.7 GeV electrons and 820 GeV protons in the kinematic range 100.04. Average multiplicities for K0 and Λ production are determined for transverse momenta pT\u3e0.5 GeV and pseudorapidities |η|\u3c1.3. The multiplicities favour a stronger strange to light quark suppression in the fragmentation chain than found in e+e- experiments. The production properties of K0\u27 s in events with and without a large rapidity gap with respect to the proton direction are compared. The ratio of neutral K0\u27 s to charged particles per event in the measured kinematic range is, within the present statistics, the same in both samples. © 1995 Springer-Verlag

Measurement of αsfrom jet rates in deep inelastic scattering at HERA

Jet production in deep inelastic scattering for 120 \u3c Q2\u3c 3600 GeV2has been studied using data from an integrated luminosity of 3.2 pb-1collected with the ZEUS detector at HERA. Jets are identified with the JADE algorithm. A cut on the angular distribution of parton emission in the γ*-parton centre-of-mass system minimises the experimental and theoretical uncertainties in the determination of the jet rates. The jet rates, when compared to O(αs2) perturbative QCD calculations, allow a precise determination of αs(Q) in three Q2-intervals. The values are consistent with a running of ifαs(Q), as expected from QCD. Extrapolating to Q = MZ0αs(MZ0) = 0.117 ± 0.005 (stat)-0.005+0.004(systexp) ± 0.007 (systtheory). © 1995

Dijet cross sections in photoproduction at HERA

Dijet production by almost real photons has been studied at HERA with the ZEUS detector. Jets have been identified using the cone algorithm. A cut on xγOBS, the fraction of the photon energy participating in the production of the two jets of highest transverse energy, is used to define cross sections sensitive to the parton distributions in the proton and in the photon. The dependence of the dijet cross sections on pseudorapidity has been measured for xγOBS ≥ 0.75 and xγOBS \u3c 0.75. The former is sensitive to the gluon momentum density in the proton. The latter is sensitive to the ginon in the photon. The cross sections are corrected for detector acceptance and compared to leading order QCD calculations. © 1995