Mod-phi convergence I: Normality zones and precise deviations

In this paper, we use the framework of mod-$\phi$ convergence to prove precise large or moderate deviations for quite general sequences of real valued random variables $(X_{n})_{n \in \mathbb{N}}$, which can be lattice or non-lattice distributed. We establish precise estimates of the fluctuations $P[X_{n} \in t_{n}B]$, instead of the usual estimates for the rate of exponential decay $\log( P[X_{n}\in t_{n}B])$. Our approach provides us with a systematic way to characterise the normality zone, that is the zone in which the Gaussian approximation for the tails is still valid. Besides, the residue function measures the extent to which this approximation fails to hold at the edge of the normality zone. The first sections of the article are devoted to a proof of these abstract results and comparisons with existing results. We then propose new examples covered by this theory and coming from various areas of mathematics: classical probability theory, number theory (statistics of additive arithmetic functions), combinatorics (statistics of random permutations), random matrix theory (characteristic polynomials of random matrices in compact Lie groups), graph theory (number of subgraphs in a random Erd\H{o}s-R\'enyi graph), and non-commutative probability theory (asymptotics of random character values of symmetric groups). In particular, we complete our theory of precise deviations by a concrete method of cumulants and dependency graphs, which applies to many examples of sums of "weakly dependent" random variables. The large number as well as the variety of examples hint at a universality class for second order fluctuations.Comment: 103 pages. New (final) version: multiple small improvements ; a new section on mod-Gaussian convergence coming from the factorization of the generating function ; the multi-dimensional results have been moved to a forthcoming paper ; and the introduction has been reworke

Simulation of industrial gravity separation processes using a general purpose simulator

Gravity separation processes have been used in the mineral industry to separate particles under the action of hydr-odynamic and gravitational forces. Although these equip-ments are extensively used for tonnage processing in coal industry, their use has been now extended to waste trea-tment such as separation of valuable metallic matter from slag. However, these processes never run at their best due to lack of understanding of the process and the under-lying principles of separation. For efficient operation it is desirable that trial runs and pilot tests are conducted but these are often time consuming and expensive. Against this background, this paper attempts to show the capabi-lities of numerical simulation to gain a better under-standing of the process with a view to improve its performance.Data from different coal washeries are colle-cted to simulate the behaviour of the plants. Results of simulation utilizing jigging for coal washing is found to be in good agreement with the plant data. The same coal is also treated in other gravity separation processes in order to decide upon a particular washing circuit

Reach and Operating Time Correction of Digital Distance Relay

Current and voltage signals recieved from conventional iron core Current Transformer (CT) and Voltage Transformer plays very important role for correct operation of Distance Distance Relay (DDR). Increase in secondary burden connected to CT causes it to saturate at earlier stage. The saturated CT produces distorted secondary current, causing DDR to under reach and to operate by certain time delay. Rogowski Coils (RCs) are attaining increased acceptance and use in electrical power system due to their inherent linearity, greater accuracy and wide operating current range. This paper presents use of RC as an advanced measurement device suitable for DDR. Case study for validation of use of RC is carried out on low voltage system. The simulation results of Distance protection scheme used for protection of part of 220kV AC system shows excellent performance of RC over CT under abnormal conditions

Green nanotechnology of MGF‑AuNPs for immunomodulatory intervention in prostate cancer therapy

Abstract Men with castration-resistant prostate cancer (CRPC) face poor prognosis and increased risk of treatment-incurred adverse effects resulting in one of the highest mortalities among patient population globally. Immune cells act as double-edged sword depending on the tumor microenvironment, which leads to increased infiltration of pro-tumor (M2) macrophages. Development of new immunomodulatory therapeutic agents capable of targeting the tumor microenvironment, and hence orchestrating the transformation of pro-tumor M2 macrophages to anti-tumor M1, would substantially improve treatment outcomes of CRPC patients. We report, herein, Mangiferin functionalized gold nanoparticulate agent (MGF-AuNPs) and its immunomodulatory characteristics in treating prostate cancer. We provide evidence of immunomodulatory intervention of MGF-AuNPs in prostate cancers through observations of enhanced levels of anti-tumor cytokines (IL-12 and TNF-α) with concomitant reductions in the levels of pro-tumor cytokines (IL-10 and IL-6). In the MGF-AuNPs treated groups, IL-12 was elevated to ten-fold while TNF-α was elevated to about 50-fold, while IL-10 and IL-6 were reduced by two-fold. Ability of MGF-AuNPs to target splenic macrophages is invoked via targeting of NF-kB signaling pathway. Finally, therapeutic efficacy of MGF-AuNPs, in treating prostate cancer in vivo in tumor bearing mice, is described taking into consideration various immunomodulatory interventions triggered by this green nanotechnology-based nanomedicine agent