Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning

We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime

Bregman Voronoi Diagrams: Properties, Algorithms and Applications

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures

Mass-Enhanced Fermi Liquid Ground State in Na1.5_{1.5}Co2_2O4_4

Magnetic, transport, and specific heat measurements have been performed on layered metallic oxide Na$_{1.5}$Co$_2$O$_4$ as a function of temperature $T$. Below a characteristic temperature $T^*$=30$-$40 K, electrical resistivity shows a metallic conductivity with a $T^2$ behavior and magnetic susceptibility deviates from the Curie-Weiss behavior showing a broad peak at $\sim$14 K. The electronic specific heat coefficient $\gamma$ is $\sim$60 mJ/molK$^2$ at 2 K. No evidence for magnetic ordering is found. These behaviors suggest the formation of mass-enhanced Fermi liquid ground state analogous to that in $d$-electron heavy fermion compound LiV$_2$O$_4$.Comment: 4 pages, 4 figures, to be published in Phys. Rev. B 69 (2004

Heat capacity studies of Ce and Rh site substitution in the heavy fermion antiferromagnet CeRhIn_5;: Short-range magnetic interactions and non-Fermi-liquid behavior

In heavy fermion materials superconductivity tends to appear when long range magnetic order is suppressed by chemical doping or applying pressure. Here we report heat capacity measurements on diluted alloyes of the heavy fermion superconductor CeRhIn_5;. Heat capacity measurements have been performed on CeRh_{1-y}Ir_{y}In_5; (y <= 0.10) and Ce_{1-x}La_{x}Rh_{1-y}Ir_{y}In_5; (x <= 0.50) in applied fields up to 90 kOe to study the affect of doping and magnetic field on the magnetic ground state. The magnetic phase diagram of CeRh_{0.9}Ir_{0.1}In_5; is consistent with the magnetic structure of CeRhIn_5; being unchanged by Ir doping. Doping of Ir in small concentrations is shown to slightly increase the antiferromagnetic transition temperature T_{N} (T_{N}=3.8 K in the undoped sample). La doping which causes disorder on the Ce sublattice is shown to lower T_{N} with no long range order observed above 0.34 K for Ce_{0.50}La_{0.50}RhIn_5;. Measurements on Ce_{0.50}La_{0.50}RhIn_5; show a coexistence of short range magnetic order and non-Fermi-liquid behavior. This dual nature of the Ce 4f-electrons is very similar to the observed results on CeRhIn_5; when long range magnetic order is suppressed at high pressure.Comment: 8 pages, 9 figure

Theory of the first-order isostructural valence phase transitions in mixed valence compounds YbIn_{x}Ag_{1-x}Cu_{4}

For describing the first-order isostructural valence phase transition in mixed valence compounds we develop a new approach based on the lattice Anderson model. We take into account the Coulomb interaction between localized f and conduction band electrons and two mechanisms of electron-lattice coupling. One is related to the volume dependence of the hybridization. The other is related to local deformations produced by f- shell size fluctuations accompanying valence fluctuations. The large f -state degeneracy allows us to use the 1/N expansion method. Within the model we develop a mean-field theory for the first-order valence phase transition in YbInCu_{4}. It is shown that the Coulomb interaction enhances the exchange interaction between f and conduction band electron spins and is the driving force of the phase transition. A comparison between the theoretical calculations and experimental measurements of the valence change, susceptibility, specific heat, entropy, elastic constants and volume change in YbInCu_{4} and YbAgCu_{4} are presented, and a good quantitative agreement is found. On the basis of the model we describe the evolution from the first-order valence phase transition to the continuous transition into the heavy-fermion ground state in the series of compounds YbIn_{1-x}Ag_{x}Cu_{4}. The effect of pressure on physical properties of YbInCu_{4} is studied and the H-T phase diagram is found.Comment: 17 pages RevTeX, 9 Postscript figures, to be submitted to Phys.Rev.

The Metronome: A Simpler Approach to Garbage Collection in Real-time Systems

With the wide-spread adoption of Java, there is significant interest in using the language for programming real-time systems. The community has generally viewed a truly real-time garbage collector as being impossible to build, and has instead focused its efforts on adding manual memory management mechanisms to Java. Unfortunately, these mechanisms are an awkward fit for the language: they introduce significant run-time overhead, introduce run-time memory access exceptions, and greatly complicate the development of library code. In recent work we have shown that it is possible to build a real-time collector for Java with highly regular CPU utilization and greatly reduced memory footprint. The system currently achieves 6 ms pause times with 50% CPU utilization (MMU) and virtually no &quot;tail&quot; in the distribution. We show how this work can be incorporated into a general real-time framework, and extended to systems with higher task frequencies. We argue that the community should focus more effort on such a simple, orthogonal solution that is true to the spirit of the Java language

Controlling Fragmentation and Space Consumption in the Metronome, a Real-time Garbage Collector for Java

Now that the use of garbage collection in languages like Java is becoming widely accepted due to the safety and software engineering benefits it provides, there is significant interest in applying garbage collection to hard real-time systems. Past approaches have generally suffered from one of two major flaws: either they were not provably real-time, or they imposed large space overheads to meet the real-time bounds