From chemical Langevin equations to Fokker-Planck equation: application of Hodge decomposition and Klein-Kramers equation

The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful. However, what are the sufficient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reflect complex chemical reaction systems. We analysis the conditions for the existence of potential landscape of the systems. By mapping the stochastic differential equations to a Hamiltonian mechanical system, we obtain the Fokker-Planck equation of the chemical reaction systems. The obtained Fokker-Planck equation can be used in further studies of other steady properties of complex chemical reaction systems, such as their steady state entropies.Comment: 6 pages, 0 figure, submitted to J. Phys. A: Math. Theo

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

In this paper we define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph obtain by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determine probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product cayley graphs (complete cycle, complete $K_n$, charter and $n$-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as $t\longrightarrow \infty$ but for quantum state is not always satisfy.Comment: 21, page. Accepted for publication on CT

On the exact solubility in momentum space of the trigonometric Rosen-Morse potential

The Schrodinger equation with the trigonometric Rosen-Morse potential in flat three dimensional Euclidean space, E3, and its exact solutions are shown to be also exactly transformable to momentum space, though the resulting equation is purely algebraic and can not be cast into the canonical form of an integral Lippmann-Schwinger equation. This is because the cotangent function does not allow for an exact Fourier transform in E3. In addition we recall, that the above potential can be also viewed as an angular function of the second polar angle parametrizing the three dimensional spherical surface, S3, of a constant radius, in which case the cotangent function would allow for an exact integral transform to momentum space. On that basis, we obtain a momentum space Lippmann-Schwinger-type equation, though the corresponding wavefunctions have to be obtained numerically.Comment: 10 pages, 5 figure

Ammonium regeneration: Its contribution to phytoplankton nitrogen requirements in a eutrophic environment

Ammonium regeneration, nutrient uptake, bacterial activity and primary production were measured from March to August 1980 in Bedford Basin, Nova Scotia, Canada, a eutrophic environment. Rates of regeneration and nutrient uptake were determined using 15N isotope dilution and tracer methodology. Although primary production, nutrient uptake and ammonium regeneration were significantly intercorrelated, no relationship was detected between these parameters and heterotrophic activity. The average contribution of ammonium to total nitrogen (ammonium+nitrate) uptake was similar in the spring and in the summer (approximately 60%). On a seasonal average basis, 36% of the phytoplankton ammonium uptake could be supplied by rapid remineralization processes. In spite of the high average contribution of NH4 regeneration to phytoplankton ammonia uptake, there is indirect evidence suggesting that other NH4 sources may occasionally be important

Predicting Quantitative Genetic Interactions by Means of Sequential Matrix Approximation

Despite the emerging experimental techniques for perturbing multiple genes and measuring their quantitative phenotypic effects, genetic interactions have remained extremely difficult to predict on a large scale. Using a recent high-resolution screen of genetic interactions in yeast as a case study, we investigated whether the extraction of pertinent information encoded in the quantitative phenotypic measurements could be improved by computational means. By taking advantage of the observation that most gene pairs in the genetic interaction screens have no significant interactions with each other, we developed a sequential approximation procedure which ranks the mutation pairs in order of evidence for a genetic interaction. The sequential approximations can efficiently remove background variation in the double-mutation screens and give increasingly accurate estimates of the single-mutant fitness measurements. Interestingly, these estimates not only provide predictions for genetic interactions which are consistent with those obtained using the measured fitness, but they can even significantly improve the accuracy with which one can distinguish functionally-related gene pairs from the non-interacting pairs. The computational approach, in general, enables an efficient exploration and classification of genetic interactions in other studies and systems as well

Duality and distance formulas in spaces defined by means of oscillation

For the classical space of functions with bounded mean oscillation, it is well known that VMO∗∗=BMOVMO∗∗=BMO and there are many characterizations of the distance from a function f in BMOBMO to VMOVMO. When considering the Bloch space, results in the same vein are available with respect to the little Bloch space. In this paper such duality results and distance formulas are obtained by pure functional analysis. Applications include general Möbius invariant spaces such as QK-spaces, weighted spaces, Lipschitz–Hölder spaces and rectangular BMOBMO of several variables

Impact of primary kidney disease on the effects of empagliflozin in patients with chronic kidney disease: secondary analyses of the EMPA-KIDNEY trial

Background: The EMPA KIDNEY trial showed that empagliflozin reduced the risk of the primary composite outcome of kidney disease progression or cardiovascular death in patients with chronic kidney disease mainly through slowing progression. We aimed to assess how effects of empagliflozin might differ by primary kidney disease across its broad population. Methods: EMPA-KIDNEY, a randomised, controlled, phase 3 trial, was conducted at 241 centres in eight countries (Canada, China, Germany, Italy, Japan, Malaysia, the UK, and the USA). Patients were eligible if their estimated glomerular filtration rate (eGFR) was 20 to less than 45 mL/min per 1·73 m2, or 45 to less than 90 mL/min per 1·73 m2 with a urinary albumin-to-creatinine ratio (uACR) of 200 mg/g or higher at screening. They were randomly assigned (1:1) to 10 mg oral empagliflozin once daily or matching placebo. Effects on kidney disease progression (defined as a sustained ≥40% eGFR decline from randomisation, end-stage kidney disease, a sustained eGFR below 10 mL/min per 1·73 m2, or death from kidney failure) were assessed using prespecified Cox models, and eGFR slope analyses used shared parameter models. Subgroup comparisons were performed by including relevant interaction terms in models. EMPA-KIDNEY is registered with ClinicalTrials.gov, NCT03594110. Findings: Between May 15, 2019, and April 16, 2021, 6609 participants were randomly assigned and followed up for a median of 2·0 years (IQR 1·5–2·4). Prespecified subgroupings by primary kidney disease included 2057 (31·1%) participants with diabetic kidney disease, 1669 (25·3%) with glomerular disease, 1445 (21·9%) with hypertensive or renovascular disease, and 1438 (21·8%) with other or unknown causes. Kidney disease progression occurred in 384 (11·6%) of 3304 patients in the empagliflozin group and 504 (15·2%) of 3305 patients in the placebo group (hazard ratio 0·71 [95% CI 0·62–0·81]), with no evidence that the relative effect size varied significantly by primary kidney disease (pheterogeneity=0·62). The between-group difference in chronic eGFR slopes (ie, from 2 months to final follow-up) was 1·37 mL/min per 1·73 m2 per year (95% CI 1·16–1·59), representing a 50% (42–58) reduction in the rate of chronic eGFR decline. This relative effect of empagliflozin on chronic eGFR slope was similar in analyses by different primary kidney diseases, including in explorations by type of glomerular disease and diabetes (p values for heterogeneity all >0·1). Interpretation: In a broad range of patients with chronic kidney disease at risk of progression, including a wide range of non-diabetic causes of chronic kidney disease, empagliflozin reduced risk of kidney disease progression. Relative effect sizes were broadly similar irrespective of the cause of primary kidney disease, suggesting that SGLT2 inhibitors should be part of a standard of care to minimise risk of kidney failure in chronic kidney disease. Funding: Boehringer Ingelheim, Eli Lilly, and UK Medical Research Council