A Model of Two Dimensional Turbulence Using Random Matrix Theory

We derive a formula for the entropy of two dimensional incompressible inviscid flow, by determining the volume of the space of vorticity distributions with fixed values for the moments Q_k= \int_w(x)^k d^2 x. This space is approximated by a sequence of spaces of finite volume, by using a regularization of the system that is geometrically natural and connected with the theory of random matrices. In taking the limit we get a simple formula for the entropy of a vortex field. We predict vorticity distributions of maximum entropy with given mean vorticity and enstrophy; also we predict the cylindrically symmetric vortex field with maximum entropy. This could be an approximate description of a hurricane.Comment: latex, 12 pages, 2 figures, acknowledgement adde

First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories

The first law of black hole mechanics is derived from the Einstein-Maxwell (EM) Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills (EYM) theory is also derived.Comment: Modified version, major changes made in the introduction. 14 pages, no figur

An Efficient Bandit Algorithm for Realtime Multivariate Optimization

Optimization is commonly employed to determine the content of web pages, such as to maximize conversions on landing pages or click-through rates on search engine result pages. Often the layout of these pages can be decoupled into several separate decisions. For example, the composition of a landing page may involve deciding which image to show, which wording to use, what color background to display, etc. Such optimization is a combinatorial problem over an exponentially large decision space. Randomized experiments do not scale well to this setting, and therefore, in practice, one is typically limited to optimizing a single aspect of a web page at a time. This represents a missed opportunity in both the speed of experimentation and the exploitation of possible interactions between layout decisions. Here we focus on multivariate optimization of interactive web pages. We formulate an approach where the possible interactions between different components of the page are modeled explicitly. We apply bandit methodology to explore the layout space efficiently and use hill-climbing to select optimal content in realtime. Our algorithm also extends to contextualization and personalization of layout selection. Simulation results show the suitability of our approach to large decision spaces with strong interactions between content. We further apply our algorithm to optimize a message that promotes adoption of an Amazon service. After only a single week of online optimization, we saw a 21% conversion increase compared to the median layout. Our technique is currently being deployed to optimize content across several locations at Amazon.com.Comment: KDD'17 Audience Appreciation Awar

A nucleosome-free dG-dC-rich sequence element promotes constitutive transcription of the essential yeast RIO1 gene

RIO1 is an essential gene that encodes a protein serine kinase and is transcribed constitutively at a very low level. Transcriptional activation of RIO1 dispenses with a canonical TATA box as well as with classical transactivators or specific DNAbinding factors. Instead, a dGdCrich sequence element, that is located 40 to 48 bp upstream the single site of mRNA initiation, is essential and presumably constitutes the basal promoter. In addition, we demonstrate here that this promoter element comprises a nucleosomefree gap which is centered at the dGdC tract and flanked by two positioned nucleosomes. This element is both, necessary and sufficient, for basal transcription initiation at the RIO1 promoter and, thus, constitutes a novel type of core promoter element

On the Noether charge form of the first law of black hole mechanics

The first law of black hole mechanics was derived by Wald in a general covariant theory of gravity for stationary variations around a stationary black hole. It is formulated in terms of Noether charges, and has many advantages. In this paper several issues are discussed to strengthen the validity of the Noether charge form of the first law. In particular, a gauge condition used in the derivation is justified. After that, we justify the generalization to non-stationary variations done by Iyer-Wald.Comment: Latex, 16 pages, arguments on gauge conditions and near-stationary entropy are added, accepted for publication in Physical Review

Magnetic anomalies in Gd6Co1.67Si3 and Tb6Co1.67Si3

The compounds, Gd6Co1.67Si3 and Tb6Co1.67Si3, recently reported to form in a Ce6Ni2Si3-derived hexagonal structure (space group: P6_3 / m) and to order magnetically below 295 and 190 K respectively, have been investigated by detailed magnetization (M) studies in the temperature interval 1.8-330 K as a function of magnetic field (H). The points of emphasis are: We observe multiple steps in the M(H) curve for the Tb compound at 1.8 K while increasing H, but these steps do not appear in the reverse cycle of H. At higher temperatures, such steps are absent. However, this 'staircase' behavior of M(H) is not observed for the Gd compound at any temperature and the isothermal magnetization is not hysteretic unlike in Tb compound. From the M(H) data measured at close intervals of temperature, we have derived isothermal entropy change (Delta S) and it is found that Delta S follows a theoretically predicted H^2/3-dependence