Nontrivial One-loop Recursive Reduction Relation

In arXiv:2204.03190, we propose a universal method to reduce one-loop integrals with both tensor structure and higher-power propagators. However, the whole reduction is a little redundant since we don't use the results of lower rank cases when addressing a certain tensor integral. Recently, we found a remarkable recursion relation arXiv:2203.16881,2205.03000, where a tensor integral is reduced to lower-rank integrals and a "lower term" corresponding to integrals with one or more propagators being canceled. However, the expression of the lower term is unknown. In this paper, we derive this non-trivial recursion relation for non-degenerate and degenerate cases and give the explicit expression for the lower term. The non-trivial recursion relation makes the reduction process extremely simple. Moreover, results given in this paper can be used in the reduction of two-loop integrals along the line presented in arXiv:2203.16881.Comment: 19 pages,1 figur

Universal Treatment of Reduction for One-Loop Integrals in Projective Space

Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with the reduction problem of one-loop integrals with general tensor structures as well as propagators with arbitrary higher powers. In this paper, we show that how to combine Feynman parametrization and embedding formalism to give a universal treatment of reductions for general one-loop integrals, even including the degenerated cases, such as the vanishing Gram determinant. Results from this method can be written in a compact and symmetric form.Comment: 32 pages, 1 figur

Purification, Characterization and in vitro Anti-Tumor Activity of Proteins from Arca subcrenata Lischke

Two purified proteins G-6 and G-4-2 were obtained from Arca subcrenata Lischke using the homogenization, salting-out with ammonium sulfate, ion-exchange chromatography and gel filtration chromatography techniques. The purity of G-6 and G-4-2 was over 96%, as measured by RP-HPLC. G-6 and G-4-2 were measured by SDS-PAGE and IEF-PAGE to have molecular weights of 8.2 kDa and 16.0 kDa, and isoelectric points of 6.6 and 6.1, respectively. The amino acid constituents of G-6 and G-4-2 were also determined. The existence of saccharides in G-6 was demonstrated by the phenol-sulfuric acid method. G-6 and G-4-2 inhibited the proliferation of human tumor cells in vitro. By MTT assay, the IC50 values of G-4-2 were 22.9 μg/mL, 46.1 μg/mL and 57.7 μg/mL against Hela, HL-60 and KB cell lines, respectively, and the IC50 value of G-6 against HL-60 cell line was measured to be 123.2 μg/mL

Case Report: Massive emphysematous pyelonephritis with short-term relapse

BackgroundEmphysematous pyelonephritis (EPN) is a rare but aggressive infectious disease that lacks specificity in its early stages and tends to progress to life-threatening septic shock in a short period of time. Its diagnosis is based on imaging tests, and treatment requires a combination of staging and risk factors.Case presentationWe report a case of emphysematous pyelonephritis in a patient with massive emphysema of the left kidney (the longest diameter up to 51 mm) on CT. After multidisciplinary consultation, the patient underwent CT-guided percutaneous drainage combined with targeted antibiotic therapy, and was discharged from the hospital with improvement of the condition. However, relapse of symptoms occurred after 1 day of discharge from the hospital, prompting readmission. After an additional 7-day course of antibiotic therapy, the patient recovered completely with no recurrence during 1-month follow-up.ConclusionStaged diagnosis and individualized therapeutic measures are key to the prognosis of this disease. Despite advances in therapeutic techniques, the risk of relapse is still high, and a comprehensive assessment of infection control is recommended for discharge from the hospital, with intensive follow-up to improve the prognosis

Effects of Fermented Milk with Live Bifidobacterium lactis Y6 on Intestinal Health in People with Digestive Dysfunction

To investigate the effects of administering fermented milk with live Bifidobacterium lactis Y6 on intestinal health in people with digestive dysfunction, a dietary intervention experiment was conducted. Volunteers with digestive problems were selected to consume 200 mL Y6 fermented milk daily for 4 weeks. Clinical scores were performed before and after the intervention, the Illumina PE300 sequencing platform was used to perform high-throughput sequencing of 16S rDNA PCR product fragments of fecal microorganisms in volunteers, the content of short-chain fatty acids (SCFAs) in feces was determined using gas chromatography. The results showed that drinking Y6 fermented milk had a significant improvement on clinical symptoms caused by digestive dysfunction (P<0.01). High-throughput sequencing results showed that drinking Y6 fermented milk had significant effect on the composition of gut microbiota rather than the diversity and richness. The relative abundance of beneficial bacteria Akkermansia, Collinse and Erysipelotrichaceae_UCG_003 genera increased while the harmful bacteria Lachnoclostridium genera reduced. The contents of intestinal SCFAs (acetic acid, propionic acid and butyric acid) increased significantly (P<0.05). The intervention of fermented milk with live Bifidobacterium lactis Y6 can significantly improve the intestinal health of people with digestive dysfunction, providing a theoretical basis for the application of Y6 strains

Effects and formula optimization of Rosa roxbunghii pomace substrate on the yield and volatile flavor compounds of Lentinulaedodes

IntroductionRosa roxbunghii pomace (RRP), a by-product of R. roxbunghii processing, remains largely underutilized. Given the increasing demand for sustainable and resource-efficient mushroom cultivation methods, exploring RRP as a mushroom cultivation medium could not only address waste management issues but also potentially enhance the quality of cultivated mushrooms. This study aimed to investigate the effects of RRP at different proportions on the yield and volatile flavor compounds of Lentinula edodes, and to optimize the formula of the cultivation substrate.MethodsDifferent proportions of RRP were incorporated into the cultivation substrate of Lentinula edodes to form various test formulas. The mushroom yield of each formula was measured by counting the harvested weight per cultivation bag. Advanced gas chromatography-mass spectrometry (GC-MS) was employed to analyze the volatile flavor profiles of the mushrooms cultivated under different formulas. Principal component analysis (PCA) was conducted to explore the differences in volatile flavor substances among formulas and compared with the control group.ResultsAmong the tested formulas, a mixture containing 30% RRP (Formula 2) showed the highest yield, reaching 0.85 kg per cultivation bag, significantly outperforming other formulas. GC-MS analysis revealed distinct volatile flavor profiles for each formula. Formula 2 was characterized by its unique flavor attributes, with 1-octen-3-ol accounting for 29.16% of the relative content, a key compound contributing to the umami flavor of mushrooms. PCA results further confirmed that the volatile flavor substances of Formula 2 were significantly different from those of the control group.DiscussionThese findings demonstrate that incorporating RRP into mushroom cultivation substrates can enhance both yield and flavor characteristics of L. edodes. The optimal formulation (30% RRP) not only supported maximum productivity but also contributed to a more desirable aroma profile. This study presents an innovative and sustainable approach to repurposing agricultural waste, adding value to both mushroom production and resource utilization

Antioxidant Activities of Hydrolysates of Arca Subcrenata Prepared with Three Proteases

In order to get products with antioxidant activity from Arca subcrenata Lischke, the optimal hydrolase and hydrolysis conditions were investigated in the paper. Three proteases (neutrase, alcalase and papain) were applied to hydrolyze the homogenate of A. subcrenata. An orthogonal design was used to optimize hydrolysis conditions, and the pH-stat methods was used to determine the degree of hydrolysis. Viewed from the angle of reducing power, such as scavenging activities against α,α-diphenyl-β-picrylhydrazyl (DPPH) radical and hydrogen peroxide, the antioxidant activities of the alcalase hydrolysate (AH) were superior to neutrase hydrolysate (NH) and papain hydrolysate (PH), and its EC50 values in DPPH radical and hydrogen peroxide scavenging effect were 6.23 mg/ml and 19.09 mg/ml, respectively. Moreover, compared with products hydrolyzed by neutrase and papain, the molecular mass of AH was lower and its content of amino acid of peptides was higher. Therefore, alcalase was selected as the optimal enzyme to produce active ingredients since its hydrolysate exhibited the best antioxidant activity among them and possessed large amount of potential active peptides

PV-reduction of sunset topology with auxiliary vector

Abstract The Passarino–Veltman (PV) reduction method has proven to be very useful for the computation of general one-loop integrals. However, not much progress has been made when it is applied to higher loops. Recently, we have improved the PV-reduction method by introducing an auxiliary vector. In this paper, we apply our new method to the simplest two-loop integrals, i.e., the sunset topology. We show how to use differential operators to establish algebraic recursion relations for reduction coefficients. Our algorithm can be easily applied to the reduction of integrals with arbitrary high-rank tensor structures. We demonstrate the efficiency of our algorithm by computing the reduction with the total tensor rank up to four.</jats:p

Analytic tadpole coefficients of one-loop integrals

Abstract One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators over an auxiliary vector R. Using differential operators, we establish the corresponding differential equations for tadpole coefficients at the first step. Then using the tensor structure of tadpole coefficients, we transform the differential equations to the recurrence relations for undetermined tensor coefficients. These recurrence relations can be solved easily by iteration and we can obtain analytic expressions of tadpole coefficients for arbitrary one-loop integrals.</jats:p