Reply to Comments of P. W. Smith, Jr.

In his comments on this subject, Smith has put emphasis on the special nature of the plane-wave solution in acoustic problems. It is perhaps unnecessary to defend the importance of the plane-wave solution in a linear theory

Materials Design - Towards a Functionally Graded Electrical Conductor

In this study, we discuss functionally graded (FG) materials as pulsed electrical conductors. These conductors can be designed to be more efficient and longer lasting by applying numerical modeling tools. One focus is on limiting the thermal fatigue damage in conductors caused by very high temperatures that develop during pulse heating. We have quantified the effect of various grading functions on the pulsed Joule heating generated and the peak temperature experienced in the conductors of an electromagnetic launcher by using a 1D numerical code and a state of the art 3D coupled finite element code, EMAP3D. Because FG materials incorporate applications-tailored compositions, structures, and dimensions, smoothly graded properties in lateral and longitudinal cross sections are obtainable. The Solid Freeform Fabrication (SFF) processing approach allows for architectures with a series of important features. These features include the selective use of high efficiency conducting materials in the core, preconditioned conductor/structure interfaces, and built-in features for enhanced cooling where necessary.Mechanical Engineerin

A Divide-and-Conquer Solver for Kernel Support Vector Machines

The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the division step, we partition the kernel SVM problem into smaller subproblems by clustering the data, so that each subproblem can be solved independently and efficiently. We show theoretically that the support vectors identified by the subproblem solution are likely to be support vectors of the entire kernel SVM problem, provided that the problem is partitioned appropriately by kernel clustering. In the conquer step, the local solutions from the subproblems are used to initialize a global coordinate descent solver, which converges quickly as suggested by our analysis. By extending this idea, we develop a multilevel Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction strategy, which outperforms state-of-the-art methods in terms of training speed, testing accuracy, and memory usage. As an example, on the covtype dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in obtaining the exact SVM solution (to within $10^{-6}$ relative error) which achieves 96.15% prediction accuracy. Moreover, with our proposed early prediction strategy, DC-SVM achieves about 96% accuracy in only 12 minutes, which is more than 100 times faster than LIBSVM

Evaluation of aerothermal modeling computer programs

Various computer programs based upon the SIMPLE or SIMPLER algorithm were studied and compared for numerical accuracy, efficiency, and grid dependency. Four two-dimensional and one three-dimensional code originally developed by a number of research groups were considered. In general, the accuracy and computational efficieny of these TEACH type programs were improved by modifying the differencing schemes and their solvers. A brief description of each program is given. Error reduction, spline flux and second upwind differencing programs are covered

Applications of Geographic Information Systems for the Analysis of Apartment Rents

This study is the first to incorporate comprehensive regional factors into the analysis of the variations of apartment rent in a particular metropolitan area. A Geographic Information Systems (GIS) procedure is developed to generate regional variables for the analysis. Results show that not only the individual apartment's characteristics, but also the regional factors are important in determining apartment rents.

Anomeric O-Functionalization of Carbohydrates for Chemical Conjugation to Vaccine Constructs.

Carbohydrates mediate a wide range of biological interactions, and understanding these processes benefits the development of new therapeutics. Isolating sufficient quantities of glycoconjugates from biological samples remains a significant challenge. With advances in chemical and enzymatic carbohydrate synthesis, the availability of complex carbohydrates is increasing and developing methods for stereoselective conjugation these polar head groups to proteins and lipids is critically important for pharmaceutical applications. The aim of this review is to provide an overview of commonly employed strategies for installing a functionalized linker at the anomeric position as well as examples of further transformations that have successfully led to glycoconjugation to vaccine constructs for biological evaluation as carbohydrate-based therapeutics

Dimensional crossover in a layered ferromagnet detected by spin correlation driven distortions

Magneto-elastic distortions are commonly detected across magnetic long-range ordering (LRO) transitions. In principle, they are also induced by the magnetic short-range ordering (SRO) that precedes a LRO transition, which contains information about short-range correlations and energetics that are essential for understanding how LRO is established. However these distortions are difficult to resolve because the associated atomic displacements are exceedingly small and do not break symmetry. Here we demonstrate high-multipole nonlinear optical polarimetry as a sensitive and mode selective probe of SRO induced distortions using CrSiTe$_3$ as a testbed. This compound is composed of weakly bonded sheets of nearly isotropic ferromagnetically interacting spins that, in the Heisenberg limit, would individually be impeded from LRO by the Mermin-Wagner theorem. Our results show that CrSiTe$_3$ evades this law via a two-step crossover from two- to three-dimensional magnetic SRO, manifested through two successive and previously undetected totally symmetric distortions above its Curie temperature.Comment: 17 pages main text, 4 figures, 12 pages supplementary informatio

A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels

We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum hypothesis testing in terms of the smooth max-relative entropy of the two states representing the two hypotheses. Using then a relative entropy version of the Quantum Asymptotic Equipartition Property (QAEP), we can recover the strong converse rate of the i.i.d. hypothesis testing problem in the asymptotics. On the other hand, combining Stein's lemma with our bounds, we obtain a stronger (\ep-independent) version of the relative entropy-QAEP. Similarly, we provide bounds on the one-shot \ep-error classical capacity of a quantum channel in terms of a smooth max-relative entropy variant of its Holevo capacity. Using these bounds and the \ep-independent version of the relative entropy-QAEP, we can recover both the Holevo-Schumacher-Westmoreland theorem about the optimal direct rate of a memoryless quantum channel with product state encoding, as well as its strong converse counterpart.Comment: v4: Title changed, improved bounds, both direct and strong converse rates are covered, a new Discussion section added. 20 page