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

The Vacuum Einstein Equations via Holonomy around Closed Loops on Characteristic Surfaces

We reformulate the standard local equations of general relativity for asymptotically flat spacetimes in terms of two non-local quantities, the holonomy $H$ around certain closed null loops on characteristic surfaces and the light cone cut function $Z$, which describes the intersection of the future null cones from arbitrary spacetime points, with future null infinity. We obtain a set of differential equations for $H$ and $Z$ equivalent to the vacuum Einstein equations. By finding an algebraic relation between $H$ and $Z$ this set of equations is reduced to just two coupled equations: an integro-differential equation for $Z$ which yields the conformal structure of the underlying spacetime and a linear differential equation for the ``vacuum'' conformal factor. These equations, which apply to all vacuum asymptotically flat spacetimes, are however lengthy and complicated and we do not yet know of any solution generating technique. They nevertheless are amenable to an attractive perturbative scheme which has Minkowski space as a zeroth order solution.Comment: 28 pages, RevTeX, 3 PostScript figure

The Frenet Serret Description of Gyroscopic Precession

The phenomenon of gyroscopic precession is studied within the framework of Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to the congruence vorticity is highlighted with particular reference to the irrotational congruence admitted by the stationary, axisymmetric spacetime. General precession formulae are obtained for circular orbits with arbitrary constant angular speeds. By successive reduction, different types of precessions are derived for the Kerr - Schwarzschild - Minkowski spacetime family. The phenomenon is studied in the case of other interesting spacetimes, such as the De Sitter and G\"{o}del universes as well as the general stationary, cylindrical, vacuum spacetimes.Comment: 37 pages, Paper in Late

A stochastic-Lagrangian particle system for the Navier-Stokes equations

This paper is based on a formulation of the Navier-Stokes equations developed by P. Constantin and the first author (\texttt{arxiv:math.PR/0511067}, to appear), where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. In this paper, we take $N$ copies of the above process (each based on independent Wiener processes), and replace the expected value with $\frac{1}{N}$ times the sum over these $N$ copies. (We remark that our formulation requires one to keep track of $N$ stochastic flows of diffeomorphisms, and not just the motion of $N$ particles.) We prove that in two dimensions, this system of interacting diffeomorphisms has (time) global solutions with initial data in the space \holderspace{1}{\alpha} which consists of differentiable functions whose first derivative is $\alpha$ H\"older continuous (see Section \ref{sGexist} for the precise definition). Further, we show that as $N \to \infty$ the system converges to the solution of Navier-Stokes equations on any finite interval $[0,T]$. However for fixed $N$, we prove that this system retains roughly $O(\frac{1}{N})$ times its original energy as $t \to \infty$. Hence the limit $N \to \infty$ and $T\to \infty$ do not commute. For general flows, we only provide a lower bound to this effect. In the special case of shear flows, we compute the behaviour as $t \to \infty$ explicitly.Comment: v3: Typo fixes, and a few stylistic changes. 17 pages, 2 figure

Laser isotope separation of <SUP>13</SUP>C: a comparative study

IR laser chemistry of (CF3Br/Cl2) mixture and neat CF2HCl are examined in the context of 13C enrichment. Decomposition extent, enrichment factor and energy absorbed are measured for both systems at their respective optimum conditions. A direct comparison is obtained by keeping extraneous factors such as laser, its pulse duration, cell, irradiation geometry etc. the same. The halogen scavenged CF3Br MPD requires lower fluence compared to neat CF2HCl irradiation. Overall throughput for a product with 60-65% 13C content in a single stage is the same for both systems requiring a similar amount of energy. However, at lower enrichment levels, CF2HCl MPD is better than (CF3Br/Cl2) photolysis in terms of both product yield and energy absorption

The Dirac Equation Is Separable On The Dyon Black Hole Metric

Using the tetrad formalism, we carry out the separation of variables for the massive complex Dirac equation in the gravitational and electromagnetic field of a four-parameter (mass, angular momentum, electric and magnetic charges) black hole.Comment: 13 page

A detailed study of quasinormal frequencies of the Kerr black hole

We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.Comment: REVTEX, 15 pages, 7 eps figure

The herpes simplex virus type 1 UL20 protein and the amino terminus of Glycoprotein K (gK) physically interact with gB

Herpes simplex virus type 1 (HSV-1) glycoprotein K (gK) and the UL20 protein (UL20p) are strictly required for virus-induced cell fusion, and mutations within either the gK or UL20 gene cause extensive cell fusion (syncytium formation). We have shown that gK forms a functional protein complex with UL20p, which is required for all gK and UL20p-associated functions in the HSV-1 life cycle. Recently, we showed that the amino-terminal 82 amino acids (aa) of gK (gKa) were required for the expression of the syncytial phenotype of the mutant virus gBΔ28 lacking the carboxyl-terminal 28 amino acids of gB (V. N. Chouljenko, A. V. Iyer, S. Chowdhury, D. V. Chouljenko, and K. G. Kousoulas, J. Virol. 83:12301-12313, 2009). This work suggested that the amino terminus of gK may directly or indirectly interact with gB and/or other viral glycoproteins. Two-way coimmunoprecipitation experiments revealed that UL20p interacted with gB in infected cells. Furthermore, the gKa peptide was coimmunoprecipitated with gB but not gD. Three recombinant baculoviruses were constructed, expressing the amino-terminal 82 aa of gKa together with either the extracellular portion of gB (30 to 748 aa), gD (1 to 340 aa), or gH (1 to 792 aa), respectively. Coimmunoprecipitation experiments revealed that gKa physically interacted with the extracellular portions of gB and gH but not gD. Three additional recombinant baculoviruses expressing gKa and truncated gBs encompassing aa 30 to 154, 30 to 364, and 30 to 500 were constructed. Coimmunoprecipitation experiments showed that gKa physically interacted with all three truncated gBs. Computer-assisted prediction of possible gKa binding sites on gB suggested that gKa may interact predominantly with gB domain I (E. E. Heldwein, H. Lou, F. C. Bender, G. H. Cohen, R. J. Eisenberg, and S. C. Harrison, Science 313:217-220, 2006). These results imply that the gK/UL20p protein complex modulates the fusogenic properties of gB and gH via direct physical interactions. Copyright © 2010, American Society for Microbiology. All Rights Reserved

Magnetic behavior of nanocrystalline ErCo2

We have investigated the magnetic behavior of the nanocrystalline form of a well-known Laves phase compound, ErCo2 - the bulk form of which has been known to undergo an interesting first-order ferrimagnetic ordering near 32 K - synthesized by high-energy ball-milling. It is found that, in these nanocrystallites, Co exhibits ferromagnetic order at room temperature as inferred from the magnetization data. However, the magnetic transition temperature for Er sublattice remains essentially unaffected as though the (Er)4f-Co(3d) coupling is weak on Er magnetism. The net magnetic moment as measured at high fields, sat at 120 kOe, is significantly reduced with respect to that for the bulk in the ferrimagnetically ordered state and possible reasons are outlined. We have also compared the magnetocaloric behavior for the bulk and the nano particles.Comment: JPCM, in pres