Low Cost Swarm Based Diligent Cargo Transit System

The goal of this paper is to present the design and development of a low cost cargo transit system which can be adapted in developing countries like India where there is abundant and cheap human labour which makes the process of automation in any industry a challenge to innovators. The need of the hour is an automation system that can diligently transfer cargo from one place to another and minimize human intervention in the cargo transit industry. Therefore, a solution is being proposed which could effectively bring down human labour and the resources needed to implement them. The reduction in human labour and resources is achieved by the use of low cost components and very limited modification of the surroundings and the existing vehicles themselves. The operation of the cargo transit system has been verified and the relevant results are presented. An economical and robust cargo transit system is designed and implemented.Comment: 6 pages, 9 figures, 1 block diagra

Safety and efficacy of antibiotics compared with appendicectomy for treatment of uncomplicated acute appendicitis: meta-analysis of randomised controlled trials

Objective To compare the safety and efficacy of antibiotic treatment versus appendicectomy for the primary treatment of uncomplicated acute appendicitis. Design Meta-analysis of randomised controlled trials. Population Randomised controlled trials of adult patients presenting with uncomplicated acute appendicitis, diagnosed by haematological and radiological investigations. Interventions Antibiotic treatment versus appendicectomy. Outcome measures The primary outcome measure was complications. The secondary outcome measures were efficacy of treatment, length of stay, and incidence of complicated appendicitis and readmissions. Results Four randomised controlled trials with a total of 900 patients (470 antibiotic treatment, 430 appendicectomy) met the inclusion criteria. Antibiotic treatment was associated with a 63% (277/438) success rate at one year. Meta-analysis of complications showed a relative risk reduction of 31% for antibiotic treatment compared with appendicectomy (risk ratio (Mantel-Haenszel, fixed) 0.69 (95% confidence interval 0.54 to 0.89); I2=0%; P=0.004). A secondary analysis, excluding the study with crossover of patients between the two interventions after randomisation, showed a significant relative risk reduction of 39% for antibiotic therapy (risk ratio 0.61 (0.40 to 0.92); I2=0%; P=0.02). Of the 65 (20%) patients who had appendicectomy after readmission, nine had perforated appendicitis and four had gangrenous appendicitis. No significant differences were seen for treatment efficacy, length of stay, or risk of developing complicated appendicitis. Conclusion Antibiotics are both effective and safe as primary treatment for patients with uncomplicated acute appendicitis. Initial antibiotic treatment merits consideration as a primary treatment option for early uncomplicated appendicitis

Work probability distribution and tossing a biased coin

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modelling other physical phenomena where rare events play an important role.Comment: 6 pages, 4 figures

Sub-Gaussian short time asymptotics for measure metric Dirichlet spaces

This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on particular fractals and further less regular cases as well. The proof is based on a new chaining argument and it is free of volume growth assumptions

Transfer matrices for the totally asymmetric exclusion process

We consider the totally asymmetric simple exclusion process (TASEP) on a finite lattice with open boundaries. We show, using the recursive structure of the Markov matrix that encodes the dynamics, that there exist two transfer matrices $T_{L-1,L}$ and $\tilde{T}_{L-1,L}$ that intertwine the Markov matrices of consecutive system sizes: $\tilde{T}_{L-1,L}M_{L-1}=M_{L}T_{L-1,L}$. This semi-conjugation property of the dynamics provides an algebraic counterpart for the matrix-product representation of the steady state of the process.Comment: 7 page

Brownian bridges to submanifolds

We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower bounds, an asymptotic relation and derivative estimates. We also see a connection to hypersurface local time. This work is motivated by the desire to extend the analysis of path and loop spaces to measures on paths which terminate on a submanifold

Detailed balance has a counterpart in non-equilibrium steady states

When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is theoretically well founded. Hypothesising ergodicity constrains the transition rates in driven steady states to respect relations analogous to, but different from the equilibrium principle of detailed balance. The constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables. This prevents over-description of the non-equilibrium reservoir, and implies that not all stochastic equations of motion are equally valid. The resulting recipe for transition rates has many features in common with equilibrium statistical mechanics.Comment: Replaced with minor revisions to introduction and conclusions. Accepted for publication in Journal of Physics

Bismut-Elworthy-Li formulae for Bessel processes

In this article we are interested in the differentiability property of the Markovian semi-group corresponding to the Bessel processes of nonnegative dimension. More precisely, for all δ ≥ 0 and T > 0, we compute the derivative of the function x↦PδTF(x), where (Pδt)t≥0 is the transition semi-group associated to the δ-dimensional Bessel process, and F is any bounded Borel function on R+. The obtained expression shows a nice interplay between the transition semi-groups of the δ—and the (δ + 2)-dimensional Bessel processes. As a consequence, we deduce that the Bessel processes satisfy the strong Feller property, with a continuity modulus which is independent of the dimension. Moreover, we provide a probabilistic interpretation of this expression as a Bismut-Elworthy-Li formula

Systemic Risk and Default Clustering for Large Financial Systems

As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and computational tools for the quantification of such phenomena. Limiting analysis such as law of large numbers and central limit theorems allow to approximate the distribution in large systems and study quantities such as the loss distribution in large portfolios. Large deviations analysis allow us to study the tail of the loss distribution and to identify pathways to default clustering. Sensitivity analysis allows to understand the most likely ways in which different effects, such as contagion and systematic risks, combine to lead to large default rates. Such results could give useful insights into how to optimally safeguard against such events.Comment: in Large Deviations and Asymptotic Methods in Finance, (Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer Proceedings in Mathematics and Statistics, Vol. 110 2015

Linear Statistics of Point Processes via Orthogonal Polynomials

For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these statistics then prove a joint central limit theorem. In the circular case, similar statements have been proved using different methods by a number of authors. In the Jacobi case these results are new.Comment: Added references, corrected typos. To appear, J. Stat. Phy