Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams

The Gauss hypergeometric functions 2F1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers. It is shown that in the case of integer and/or half-integer values of parameters there are only three types of algebraically independent Gauss hypergeometric functions. The epsilon-expansion of functions of one of this type (type F in our classification) demands the introduction of new functions related to generalizations of elliptic functions. For the five other types of functions the higher-order epsilon-expansion up to functions of weight 4 are constructed. The result of the expansion is expressible in terms of Nielsen polylogarithms only. The reductions and epsilon-expansion of q-loop off-shell propagator diagrams with one massive line and q massless lines and q-loop bubble with two-massive lines and q-1 massless lines are considered. The code (Mathematica/FORM) is available via the www at this URL http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 19 pages, LaTeX, 1-eps figure; v5: The code (Mathematica/FORM) is available via the www http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htm

Toward verification of the Riemann hypothesis: Application of the Li criterion

We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence \{\lambda_k\}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we determine new bounds for relevant Riemann zeta function sums and the sequence itself. We find that the Riemann hypothesis holds if certain conjectured properties of a sequence \eta_j are valid. The constants \eta_j enter the Laurent expansion of the logarithmic derivative of the zeta function about s=1 and appear to have remarkable characteristics. {\em On our conjecture}, not only does the Riemann hypothesis follow, but an inequality governing the values \lambda_n and inequalities for the sums of reciprocal powers of the nontrivial zeros of the zeta function.Comment: to appear in Math. Physics, Analysis and Geometry; 1 figur

Serum MicroRNAs as Biomarkers for Hepatocellular Carcinoma in Chinese Patients with Chronic Hepatitis B Virus Infection

BACKGROUND: MicroRNAs (miRNAs) have been shown to anticipate great cancer diagnostic potential. Recently, circulating miRNAs have been reported as promising biomarkers for various pathologic conditions. The objective of this study was to investigate the potential of serum miRNAs as novel biomarkers for hepatocellular carcinoma (HCC). METHODOLOGY/PRINCIPAL FINDINGS: This study was divided into four phases: (I) Ten candidate serum miRNAs were detected by using real-time RT-PCR, corresponding 10 HCC patients with chronic hepatitis B virus (HBV) infection and 10 age- and sex-matched healthy subjects. (II) Marker validation by real-time RT-PCR on HBV patients with (n = 48) or without HCC (n = 48), and healthy subjects (n = 24). (III) Marker detection by real-time RT-PCR in sera from another 14 HCC patients before and 1 month after surgical resection. (IV) We examined the correlation between the expressions of candidate serum miRNAs with clinical parameters of HCC patients. Although miR-222, miR-223 or miR-21 were significantly up- or down-regulated between HCC patients and healthy controls, no significant difference was observed in the levels of these miRNAs between HBV patients without and with HCC. MiR-122 in serum was significantly higher in HCC patients than healthy controls (p<0.001). More importantly, it was found that the levels of miR-122 were significantly reduced in the post-operative serum samples when compared to the pre-operative samples. Although serum miR-122 was also elevated in HBV patients with HCC comparing with those without HCC, the difference was at the border line (p = 0.043). CONCLUSIONS/SIGNIFICANCE: Our results suggest that serum miR-122 might serve as a novel and potential noninvasive biomarker for detection of HCC in healthy subjects, moreover, it might serve as a novel biomarker for liver injury but not specifically for detection of HCC in chronic HBV infection patients

DPHL: A DIA Pan-human Protein Mass Spectrometry Library for Robust Biomarker Discovery

To address the increasing need for detecting and validating protein biomarkers in clinical specimens, mass spectrometry (MS)-based targeted proteomic techniques, including the selected reaction monitoring (SRM), parallel reaction monitoring (PRM), and massively parallel data-independent acquisition (DIA), have been developed. For optimal performance, they require the fragment ion spectra of targeted peptides as prior knowledge. In this report, we describe a MS pipeline and spectral resource to support targeted proteomics studies for human tissue samples. To build the spectral resource, we integrated common open-source MS computational tools to assemble a freely accessible computational workflow based on Docker. We then applied the workflow to generate DPHL, a comprehensive DIA pan-human library, from 1096 data-dependent acquisition (DDA) MS raw files for 16 types of cancer samples. This extensive spectral resource was then applied to a proteomic study of 17 prostate cancer (PCa) patients. Thereafter, PRM validation was applied to a larger study of 57 PCa patients and the differential expression of three proteins in prostate tumor was validated. As a second application, the DPHL spectral resource was applied to a study consisting of plasma samples from 19 diffuse large B cell lymphoma (DLBCL) patients and 18 healthy control subjects. Differentially expressed proteins between DLBCL patients and healthy control subjects were detected by DIA-MS and confirmed by PRM. These data demonstrate that the DPHL supports DIA and PRM MS pipelines for robust protein biomarker discovery. DPHL is freely accessible at https://www.iprox.org/page/project.html?id=IPX0001400000

Does or did the supernova remnant Cassiopeia A operate as a PeVatron?

For decades, supernova remnants (SNRs) have been considered the prime sources of Galactic Cosmic rays (CRs). But whether SNRs can accelerate CR protons to PeV energies and thus dominate CR flux up to the knee is currently under intensive theoretical and phenomenological debate. The direct test of the ability of SNRs to operate as CR PeVatrons can be provided by ultrahigh-energy (UHE; $E_\gamma \geq 100$~TeV) $\gamma$-rays. In this context, the historical SNR Cassiopeia A (Cas A) is considered one of the most promising target for UHE observations. This paper presents the observation of Cas A and its vicinity by the LHAASO KM2A detector. The exceptional sensitivity of LHAASO KM2A in the UHE band, combined with the young age of Cas A, enabled us to derive stringent model-independent limits on the energy budget of UHE protons and nuclei accelerated by Cas A at any epoch after the explosion. The results challenge the prevailing paradigm that Cas A-type SNRs are major suppliers of PeV CRs in the Milky Way.Comment: 11 pages, 3 figures, Accepted by the APJ

Measurement of ultra-high-energy diffuse gamma-ray emission of the Galactic plane from 10 TeV to 1 PeV with LHAASO-KM2A

The diffuse Galactic $\gamma$-ray emission, mainly produced via interactions between cosmic rays and the interstellar medium and/or radiation field, is a very important probe of the distribution, propagation, and interaction of cosmic rays in the Milky Way. In this work we report the measurements of diffuse $\gamma$-rays from the Galactic plane between 10 TeV and 1 PeV energies, with the square kilometer array of the Large High Altitude Air Shower Observatory (LHAASO). Diffuse emissions from the inner ($15^{\circ}<l<125^{\circ}$, $|b|<5^{\circ}$) and outer ($125^{\circ}<l<235^{\circ}$, $|b|<5^{\circ}$) Galactic plane are detected with $29.1\sigma$ and $12.7\sigma$ significance, respectively. The outer Galactic plane diffuse emission is detected for the first time in the very- to ultra-high-energy domain ($E>10$~TeV). The energy spectrum in the inner Galaxy regions can be described by a power-law function with an index of $-2.99\pm0.04$, which is different from the curved spectrum as expected from hadronic interactions between locally measured cosmic rays and the line-of-sight integrated gas content. Furthermore, the measured flux is higher by a factor of $\sim3$ than the prediction. A similar spectrum with an index of $-2.99\pm0.07$ is found in the outer Galaxy region, and the absolute flux for $10\lesssim E\lesssim60$ TeV is again higher than the prediction for hadronic cosmic ray interactions. The latitude distributions of the diffuse emission are consistent with the gas distribution, while the longitude distributions show clear deviation from the gas distribution. The LHAASO measurements imply that either additional emission sources exist or cosmic ray intensities have spatial variations.Comment: 12 pages, 8 figures, 5 tables; accepted for publication in Physical Review Letters; source mask file provided as ancillary fil

Spontaneous doping of the basal plane of MoS2 single layers through oxygen substitution under ambient conditions

The chemical inertness of the defect-free basal plane confers environmental stability to MoS2 single-layers, but it also limits their chemical versatility and catalytic activity. The stability of the pristine MoS2 basal plane against oxidation under ambient conditions is a widely accepted assumption in the interpretation of various studies and applications. However, single-atom level structural investigations reported here reveal that oxygen atoms spontaneously incorporate into the basal plane of MoS2 single layers during ambient exposure. Our scanning tunneling microscopy investigations reveal a slow oxygen substitution reaction, upon which individual sulfur atoms are one by one replaced by oxygen, giving rise to solid solution type 2D MoS2-xOx crystals. O substitution sites present all over the basal plane act as single-atomic active reaction centers, substantially increasing the catalytic activity of the entire MoS2 basal plane for the electrochemical H2 evolution reaction.Comment: 6 pages, 5 figure