Test to distinguish a Brownian motion from a Brownian bridge using Polya tree process

The problem of distinguishing a Brownian bridge from a Brownian motion, both with possible drift, on the closed unit interval, is investigated via a pair of hypothesis tests. The first, tests for observations obtained at n discrete time points to be arising from a Brownian bridge with drift by embedding the Brownian bridge into a mixture of Polya trees which represents the non-parametric alternative. The second test, tests in an identical manner, for the observations to be coming from a Brownian motion with drift. The Bayes factors for the two tests are derived and then combined to obtain the Bayes factor for the test to distinguish between the two Gaussian processes. The Tierney-Kadane approximation of the Bayes factor is derived with an error approximation of order O(n⁻⁴).     

Highly Concise and Stereoselective Total Synthesis of (5R,7S)‐Kurzilactone

A highly concise and stereoselective total synthesis of (5R,7S)‐kurzilactone ( 1 ) was performed by a convergent approach by means of a Jacobsen's hydrolytic kinetic resolution, a Horner? Wadsworth? Emmons reaction for the construction of the α,β‐unsaturated δ‐lactone ring system, and a highly diastereoselective Mukaiyama aldol reaction for the introduction of the formal anti‐1,3‐diol unit (Schemes 2 and 3).     

Distributionally robust mixed integer linear programs: Persistency models with applications

In this paper, we review recent advances in the distributional analysis of mixed integer linear programs with random objective coefficients. Suppose that the probability distribution of the objective coefficients is incompletely specified and characterized through partial moment information. Conic programming methods have been recently used to find distributionally robust bounds for the expected optimal value of mixed integer linear programs over the set of all distributions with the given moment information. These methods also provide additional information on the probability that a binary variable attains a value of 1 in the optimal solution for 0–1 integer linear programs. This probability is defined as the persistency of a binary variable. In this paper, we provide an overview of the complexity results for these models, conic programming formulations that are readily implementable with standard solvers and important applications of persistency models. The main message that we hope to convey through this review is that tools of conic programming provide important insights in the probabilistic analysis of discrete optimization problems. These tools lead to distributionally robust bounds with applications in activity networks, vertex packing, discrete choice models, random walks and sequencing problems, and newsvendor problems.     

Asymptotics of the Empirical Cross-over Function

We consider a combination of heavily trimmed sums and sample quantiles which arises when examining properties of clustering criteria and prove limit theorems. The object of interest, which we call the Empirical Cross-over Function, is an L-statistic whose weights do not comply with the requisite regularity conditions for usage of existing limit results. The law of large numbers, CLT and a functional CLT are proven.     

Real-coded genetic algorithm for system identification and controller tuning

This paper presents an application of real-coded genetic algorithm (RGA) for system identification and controller tuning in process plants. The genetic algorithm is applied sequentially for system identification and controller tuning. First GA is applied to identify the changes in system parameters. Once the process parameters are identified, the optimal controller parameters are identified using GA. In the proposed genetic algorithm, the optimization variables are represented as floating point numbers. Also, cross over and mutation operators that can directly deal with the floating point numbers are used. The proposed approach has been applied for system identification and controller tuning in nonlinear pH process. The simulation results show that the GA based approach is effective in identifying the parameters of the system and the nonlinearity at various operating points in the nonlinear system.     

Jet forking driven by pipe tone

The present work deals with an experimental investigation of flow of air through a square-edged circular orifice at the downstream end of a circular duct. Self-excited acoustic oscillations at the natural duct modes are observed for certain flow velocities when the orifice is sufficiently thick. For a specific Reynolds number based on the orifice diameter and the mean jet velocity (9150 < Re < 9850), the jet forks into two trains, with the alternating vortices falling into the same branch of the forked train. Whereas this phenomenon has been reported earlier to have occurred when the density ratio of the jet is less than 0.72, the present results show that it is possible for a jet having the same density as the ambient atmosphere. The jet forking is coincident with jump in the acoustic frequency from one natural acoustic mode to another with comparable amplitudes of both the modes.