Optimal and efficient crossover designs for comparing test treatments with a control treatment

This paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t+1. Among other results it specifies sufficient conditions for a crossover design to be simultaneously A-optimal and MV-optimal in a very large and appealing class of crossover designs. It is expected that these optimal designs are highly efficient in the entire class of crossover designs. Some computationally useful tools are given and used to build assorted small optimal and efficient crossover designs. The model robustness of these newly discovered crossover designs is discussed.Comment: Published at http://dx.doi.org/10.1214/009053604000000887 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Novel Approach to Elastodynamics: II. The Three-Dimensional Case

A new approach was recently introduced by the authors for constructing analytic solutions of the linear PDEs describing elastodynamics. Here, this approach is applied to the case of a homogeneous isotropic half-space body satisfying arbitrary initial conditions and Lamb's boundary conditions. A particular case of this problem, namely the case of homogeneous initial conditions and normal point load boundary conditions, was first solved by Lamb using the Fourier-Laplace transform. The general problem solved here can also be analysed via the Fourier transform, but in this case, the solution representation involves transforms of \textit{unknown} boundary values; this necessitates the formulation and solution of a cumbersome auxiliary problem, which expresses the unknown boundary values in terms of the Laplace transform of the given boundary data. The new approach, which is applicable to arbitrary initial and boundary conditions, bypasses the above auxiliary problem and expresses the solutions directly in terms of the given initial and boundary conditions

On a Novel Class of Integrable ODEs Related to the Painlev\'e Equations

One of the authors has recently introduced the concept of conjugate Hamiltonian systems: the solution of the equation $h=H(p,q,t),$ where $H$ is a given Hamiltonian containing $t$ explicitly, yields the function $t=T(p,q,h)$, which defines a new Hamiltonian system with Hamiltonian $T$ and independent variable $h.$ By employing this construction and by using the fact that the classical Painlev\'e equations are Hamiltonian systems, it is straightforward to associate with each Painlev\'e equation two new integrable ODEs. Here, we investigate the conjugate Painlev\'e II equations. In particular, for these novel integrable ODEs, we present a Lax pair formulation, as well as a class of implicit solutions. We also construct conjugate equations associated with Painlev\'e I and Painlev\'e IV equations.Comment: This paper is dedicated to Professor T. Bountis on the occasion of his 60th birthday with appreciation of his important contributions to "Nonlinear Science

Asymmetric vortex solitons in nonlinear periodic lattices

We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices, and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice, and also describe novel coherent states where the populations of clockwise and anti-clockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in different nonlinear lattice systems including optically-induced photonic lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical lattices.Comment: 4 pages, 5 figure

Associative memory scheme for genetic algorithms in dynamic environments

Copyright @ Springer-Verlag Berlin Heidelberg 2006.In recent years dynamic optimization problems have attracted a growing interest from the community of genetic algorithms with several approaches developed to address these problems, of which the memory scheme is a major one. In this paper an associative memory scheme is proposed for genetic algorithms to enhance their performance in dynamic environments. In this memory scheme, the environmental information is also stored and associated with current best individual of the population in the memory. When the environment changes the stored environmental information that is associated with the best re-evaluated memory solution is extracted to create new individuals into the population. Based on a series of systematically constructed dynamic test environments, experiments are carried out to validate the proposed associative memory scheme. The environmental results show the efficiency of the associative memory scheme for genetic algorithms in dynamic environments

A low-power opportunistic communication protocol for wearable applications

© 2015 IEEE.Recent trends in wearable applications demand flexible architectures being able to monitor people while they move in free-living environments. Current solutions use either store-download-offline processing or simple communication schemes with real-time streaming of sensor data. This limits the applicability of wearable applications to controlled environments (e.g, clinics, homes, or laboratories), because they need to maintain connectivity with the base station throughout the monitoring process. In this paper, we present the design and implementation of an opportunistic communication framework that simplifies the general use of wearable devices in free-living environments. It relies on a low-power data collection protocol that allows the end user to opportunistically, yet seamlessly manage the transmission of sensor data. We validate the feasibility of the framework by demonstrating its use for swimming, where the normal wireless communication is constantly interfered by the environment

Estimation of causal effects using instrumental variables with nonignorable missing covariates: Application to effect of type of delivery NICU on premature infants

Understanding how effective high-level NICUs (neonatal intensive care units that have the capacity for sustained mechanical assisted ventilation and high volume) are compared to low-level NICUs is important and valuable for both individual mothers and for public policy decisions. The goal of this paper is to estimate the effect on mortality of premature babies being delivered in a high-level NICU vs. a low-level NICU through an observational study where there are unmeasured confounders as well as nonignorable missing covariates. We consider the use of excess travel time as an instrumental variable (IV) to control for unmeasured confounders. In order for an IV to be valid, we must condition on confounders of the IV---outcome relationship, for example, month prenatal care started must be conditioned on for excess travel time to be a valid IV. However, sometimes month prenatal care started is missing, and the missingness may be nonignorable because it is related to the not fully measured mother's/infant's risk of complications. We develop a method to estimate the causal effect of a treatment using an IV when there are nonignorable missing covariates as in our data, where we allow the missingness to depend on the fully observed outcome as well as the partially observed compliance class, which is a proxy for the unmeasured risk of complications. A simulation study shows that under our nonignorable missingness assumption, the commonly used estimation methods, complete-case analysis and multiple imputation by chained equations assuming missingness at random, provide biased estimates, while our method provides approximately unbiased estimates. We apply our method to the NICU study and find evidence that high-level NICUs significantly reduce deaths for babies of small gestational age, whereas for almost mature babies like 37 weeks, the level of NICUs makes little difference. A sensitivity analysis is conducted to assess the sensitivity of our conclusions to key assumptions about the missing covariates. The method we develop in this paper may be useful for many observational studies facing similar issues of unmeasured confounders and nonignorable missing data as ours.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS699 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org