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

Stability of Hill Slopes and Foundation Condition at Radio Astronomy Centre Ootacamand

Stability aspects of hill slopes and foundation considerations of Radio Astronomy Centre at Ootacamand are described. The analysis of slopes indicated that if joints are not covered, the material in joints may lose strength and the slopes may enter a state of instability. Footings with inclined legs were found to resist the horizontal forces, pull and overturning movements. Lime piles adopted for strengthening soft material at one of the tower locations were found to be effective

Eigenvalues of Structural Matrices Via Gerschgorin Theorem

Summary In this paper, we have presented a simple approach for determining eigenvalues for some class of structural matrices. It is based on Gerschgorin theorem. The main advantage of the proposed method is that there is no need to use time-consuming iterative numerical techniques for determining eigenvalues. The proposed approach is expected to be applicable in various computer science and control system applications

Agarose-stabilized gold nanoparticles for surface-enhanced Raman spectroscopic detection of DNA nucleosides

doi:10.1063/1.2192573 http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=APPLAB000088000015153114000001&idtype=cvips&prog=normal&doi=10.1063/1.2192573We present surface-enhanced Raman scattering (SERS) studies of DNA nucleosides using biologically benign agarose-stabilized gold nanoparticles (AAuNP). We compare the SERS activity of nucleosides with AAuNP to that of commercially obtained citrate-stabilized gold nanoparticles and find the SERS activity to be an order of magnitude higher with AAuNP. The higher SERS activity is explained in terms of the agarose matrix, which provides pathways for the gold nanoparticles to have distinct arrangements that result in stronger internal plasmon resonances.This work was supported through the University of Missouri Research Board grants URB04-023 (S.G.) and URB03-080 (M.C. and K.V.K.), NSF under Grant No. DMR-0413601and the NCI under Grant No. IR0ICA119412-01. The gold nanoparticles were produced and supplied by the University of Missouri Nanoparticle Production Core Facility