Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number of dimensions, making the use of classic iterative solvers infeasible. During the last few years, low-rank tensor approaches have been developed that allow to mitigate this curse of dimensionality by exploiting the underlying structure of the linear operator. In this work, we focus on tensors represented in the Tucker and tensor train formats. We propose two preconditioned gradient methods on the corresponding low-rank tensor manifolds: A Riemannian version of the preconditioned Richardson method as well as an approximate Newton scheme based on the Riemannian Hessian. For the latter, considerable attention is given to the efficient solution of the resulting Newton equation. In numerical experiments, we compare the efficiency of our Riemannian algorithms with other established tensor-based approaches such as a truncated preconditioned Richardson method and the alternating linear scheme. The results show that our approximate Riemannian Newton scheme is significantly faster in cases when the application of the linear operator is expensive.Comment: 24 pages, 8 figure

M31* and its circumnuclear environment

We present a multiwavelength investigation of the circumnuclear environment of M31. Based on Chandra/ACIS data, we tightly constrain the X-ray luminosity of M31*, the central supermassive black hole of the galaxy, to be L (0.3-7 keV)<= 1.2x10^{36}erg/s, approximately 10^{-10} of the Eddington luminosity. From the diffuse X-ray emission, we characterize the circumnuclear hot gas with a temperature of ~0.3 keV and a density of ~0.1 cm^{-3}. In the absence of an active SMBH and recent star formation, the most likely heating source for the hot gas is Type Ia SNe. The presence of cooler, dusty gas residing in a nuclear spiral has long been known in terms of optical line emission and extinction. We further reveal the infrared emission of the nuclear spiral and evaluate the relative importance of various possible ionizing sources. We show evidence for interaction between the nuclear spiral and the hot gas, probably via thermal evaporation. This mechanism lends natural understandings to 1) the inactivity of M31*, in spite of a probably continuous supply of gas from outer disk regions, and 2) the launch of a bulge outflow of hot gas, primarily mass-loaded from the circumnuclear regions. One particular prediction of such a scenario is the presence of gas with intermediate temperatures arising from the conductive interfaces. The FUSE observations do show strong OVI$\lambda$1032 and 1038 absorption lines against the bulge starlight, but the effective OVI column density (~4x10^{14} cm^{-2}), may be attributed to foreground gas located in the bulge and/or the highly inclined disk of M31. Our study strongly argues that stellar feedback, particularly in the form of energy release from SNe Ia, may play an important role in regulating the evolution of SMBHs and the interstellar medium in galactic bulges.Comment: Submitted to MNRAS, 33 pages, 9 figures. Comments welcom

Le développement professionnel des enseignants-chercheurs de Sciences de l'Education

L'objet de cet article est d'exposer une recherche qui s'intéresse aux pratiques de valorisation des travaux dans une discipline universitaire : les Sciences de l'Education. Cette démarche vise tout d'abord à décrire et à analyser l'articulation des différentes pratiques de valorisation de la recherche menées par les enseignants-chercheurs de cette discipline. Dans unevisée plus explicative, nous mettrons ensuite en relation ces pratiques de valorisation avec l'évaluation que ces enseignants-chercheurs font de la valeur de ces différents modes de reconnaissance, ainsi qu'avec leur développement professionnel. Le développement professionnel sera d'abord analysé sous l'angle des compétences mobilisées par les enseignants-chercheurs pour mettre en œuvre leurs pratiques de valorisation. Cette notion sera ensuite considérée sous l'angle des interactions entre les différents modes de valorisation et les parcours et perspectives professionnels des enseignants-chercheurs

Why formal objections to the error theory fail

Many philosophers argue that the error theory should be rejected because it is incompatible with standard deontic logic and semantics. We argue that such formal objections to the theory fail. Our discussion has two upshots. First, it increases the dialectical weight that must be borne by objections to the error theory that target its content rather than its form. Second, it shows that standard deontic logic and semantics should be revised

Thickness-Dependent Crystallization of Ultrathin Antimony Thin Films for Monatomic Multilevel Reflectance and Phase Change Memory Designs

[Image: see text] Phase change materials, with more than one reflectance and resistance states, have been a subject of interest in the fields of phase change memories and nanophotonics. Although most current research focuses on rather complex phase change alloys, e.g., Ge2Sb2Te5, recently, monatomic antimony thin films have aroused a lot of interest. One prominent attractive feature is its simplicity, giving fewer reliability issues like segregation and phase separation. However, phase transformation and crystallization properties of ultrathin Sb thin films must be understood to fully incorporate them into future memory and nanophotonics devices. Here, we studied the thickness-dependent crystallization behavior of pulsed laser-deposited ultrathin Sb thin films by employing dynamic ellipsometry. We show that the crystallization temperature and phase transformation speed of as-deposited amorphous Sb thin films are thickness-dependent and can be precisely tuned by controlling the film thickness. Thus, crystallization temperature tuning by thickness can be applied to future memory and nanophotonic devices. As a proof of principle, we designed a heterostructure device with three Sb layers of varying thicknesses with distinct crystallization temperatures. Measurements and simulation results show that it is possible to address these layers individually and produce distinct and multiple reflectance profiles in a single device. In addition, we show that the immiscible nature of Sb and GaSb could open up possible heterostructure device designs with high stability after melt-quench and increased crystallization temperature. Our results demonstrate that the thickness-dependent phase transformation and crystallization dynamics of ultrathin Sb thin films have attractive features for future memory and nanophotonic devices

Absent alternatives and insider interests in postcrisis financial reform

The credit crisis that began in the summer of 2007 has fundamentally challenged much financial regulation and the political institutions that produced it. Measured against the criticisms that have been brought forth against previous financial governance, the extent of governments’ overall reform ambitions has been disappointing, generating little hope that the threat of future crises is being tackled seriously. Starting from this observation, this article asks: what explains governments’ reform choices, and thus also their limited ambitions? To explore this question, this article focuses on the positions that four governments central to global financial regulation (the USA, the UK, Germany and France) have taken in advance of the G20 meetings in 2009 across four key issue areas in financial regulation: accounting standards, derivatives trading, credit ratings agencies and banking rules. It evaluates both the overlap between positions across domains and governments as well as the differences between them. Such variation, we argue, provides key clues to the overall drivers behind reforms – as well as their limits. The overall picture that emerges can be summarized as follows: governments have been staunch defenders of their national firms’ competitive interests in regulatory reforms. That has not necessarily meant that they followed industry preferences across the board – new rules that might dent profits were imposed in several cases. It has been the relative impact, compared to foreign competitors, that counted in reform positions, not the absolute impact. As this article also shows, these differences of opinion have played out within the context and the limits of the overall debates about thinkable policy alternatives. In spite of fundamental criticisms of pre-crisis regulatory orthodoxy, convincing and coherent alternatives have been forthcoming slowly at best. This has made reform proposals less radical than criticisms, seen on their own, might suggest.Die Kreditkrise, ausgebrochen im Sommer 2007, hat gängige Regulierungsmodelle und die ihnen zugrunde liegenden politischen Institutionen grundsätzlich in Frage gestellt. Gemessen an der fundamentalen Kritik die seitdem an bestehenden Strukturen geäußert worden ist, sind die Reformambitionen westlicher Regierungen in diesem Bereich allerdings enttäuschend und geben kaum Hoffnung, dass der Bedrohung durch zukünftige Krisen ernsthaft begegnet wird. Diese Beobachtung generiert die zentrale Frage dieses Beitrags: wie lassen sich die Reformschritte verschiedener Regierungen, und insbesondere deren begrenzter Umfang, erklären? Unsere Analyse konzentriert sich auf die Reformpositionen die vier Regierungen mit Schlüsselpositionen in globalen Finanzfragen (USA, Großbritannien, Frankreich, Deutschland) im Vorfeld der G20-Treffen 2009 eingenommen haben. Vier Regulierungsfeldern stehen dabei zentral: Rechnungslegungsstandards, Derivathandel, Bankenregulierung und Ratingagenturen. Der Beitrag nimmt dabei sowohl bemerkenswerte Überlappungen der Regierungspositionen sowie Unterschiede zwischen ihnen in den Blick. Vor allem letztere erlauben Rückschlüsse auf die treibenden Kräfte hinter Reformbemühungen. Die Analyseergebnisse lassen sich wie folgt zusammenfassen: Regierungen haben in internationalen Verhandlungen die Wettbewerbsinteressen ihrer nationalen Finanzdienstleister verteidigt. Das heißt nicht, dass Industrieinteressen durchgängig in politische Positionen übernommen worden sind - nicht selten haben neue Regeln Bankprofite eher geschmälert. Vielmehr ist es der relative Einfluss der neuen Regeln auf Wettbewerbsfähigkeit gewesen, verglichen mit ausländischen Firmen, der entscheidend war. Gleichzeitig zeigt dieser Beitrag, dass die verschiedenen Regierungspositionen sich alle innerhalb eines Rahmens bewegen, der auf ‚denkbare‘ Regulierungsalternativen begrenzt ist. Ungeachtet der Fundamentalkritik gegenüber dem seinerzeit gängigen Regulierungsparadigma, die nach der Krise laut geworden ist, mangelt es nach wie vor an überzeugenden, grundlegenden Alternativansätzen. Darum sind viele Reformvorschläge weniger radikal ausgefallen als die Kritik, isoliert betrachtet, nahegelegt hätte

Generalized Geologic Map for Land-Use Planning: Trimble County, Kentucky

This map is not intended to be used for selecting individual sites. Its purpose is to inform land-use planners, government officials, and the public in a general way about geologic bedrock conditions that affect the selection of sites for various purposes. The properties of thick soils may supercede those of the underlying bedrock and should be considered on a site-to-site basis. At any site, it is important to understand the characteristics of both the soils and the underlying rock

Generalized Geologic Map for Land-Use Planning: Madison County, Kentucky

This map is not intended to be used for selecting individual sites. Its purpose is to inform land-use planners, government officials, and the public in a general way about geologic bedrock conditions that affect the selection of sites for various purposes. The properties of thick soils may supercede those of the underlying bedrock and should be considered on a site-to-site basis. At any site, it is important to understand the characteristics of both the soils and the underlying rock