Bulk Connectedness and Boundary Entanglement

We prove, for any state in a conformal field theory defined on a set of boundary manifolds with corresponding classical holographic bulk geometry, that for any bipartition of the boundary into two non-clopen sets, the density matrix cannot be a tensor product of the reduced density matrices on each region of the bipartition. In particular, there must be entanglement across the bipartition surface. We extend this no-go theorem to general, arbitrary partitions of the boundary manifolds into non-clopen parts, proving that the density matrix cannot be a tensor product. This result gives a necessary condition for states to potentially correspond to holographic duals.Comment: 12 pages, 2 figure

Rain or Shine: Where is the Weather Effect?

Saunders (1993) and Hirshleifer and Shumway (2001) document the effect of weather on stock returns. The proposed explanation in both papers is that investor mood affects cognitive processes and trading decisions. In this paper, we use a database of individual investor accounts to examine the weather effects on traders. Our analysis of the trading activity in five major U.S. cities over a six-year period finds vistually no difference in individuals propensity to buy or sell equities on cloudy days as opposed to sunny days. If the association between cloud cover and stock returns documented for New York and other world cities is indeed caused by investor mood swings, our findings suggest that researchers should focus on the attitudes of market-makers, news providers or other agents physically located in the city hosting the exchange. NYSE spreads widen on cloudy days. When we control for this, the significance of the weather effect is dramatically reduced. We interpret this as evidence that the behavior of market-makers, rather than individual investors, may be responsible for the relation between returns and weather.

Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for Wormholes

We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throat separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. This theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.Comment: 16 pages, 2 figure

Splitting Spacetime and Cloning Qubits: Linking No-Go Theorems across the ER=EPR Duality

We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement.Comment: 6 pages, 2 figure

Entanglement of Purification and Multiboundary Wormhole Geometries

We posit a geometrical description of the entanglement of purification for subregions in a holographic CFT. The bulk description naturally generalizes the two-party case and leads to interesting inequalities among multi-party entanglements of purification that can be geometrically proven from the conjecture. Further, we study the relationship between holographic entanglements of purification in locally-AdS3 spacetimes and entanglement entropies in multi-throated wormhole geometries constructed via quotienting by isometries. In particular, we derive new holographic inequalities for geometries that are locally AdS3 relating entanglements of purification for subregions and entanglement entropies in the wormhole geometries.Comment: 23 pages, 12 figures; v2 added references; v3 fixed inequality direction in Eq.(2), expanded discussion - reflects published versio

Efficiency and the Bear: Short Sales and Markets around the World

We analyze cross-sectional and time series information from forty-seven equity markets around the world, to consider whether short-sales restrictions affect the efficiency of the market, and the distributional characteristics of returns to individual stocks and market indices. Using the approach developed in Morck et.al. (2000) we find significantly more cross-sectional variation in equity returns in markets where short selling is feasible and practiced, controlling for a host of other factors. This evidence is consistent with more efficient price discovery at the individual security level. A common conjecture by regulators is that short-selling restrictions can reduce the relative severity of a market panic. We test this conjecture by examining the skewness of market returns. We find that in markets where short selling is either prohibited or not practiced, returns display significantly less negative skewness, and the frequency of extreme negative returns is lower. On the other hand, the overall volatility of individual returns and market returns is higher.

Gear optimization

The use of formal numerical optimization methods for the design of gears is investigated. To achieve this, computer codes were developed for the analysis of spur gears and spiral bevel gears. These codes calculate the life, dynamic load, bending strength, surface durability, gear weight and size, and various geometric parameters. It is necessary to calculate all such important responses because they all represent competing requirements in the design process. The codes developed here were written in subroutine form and coupled to the COPES/ADS general purpose optimization program. This code allows the user to define the optimization problem at the time of program execution. Typical design variables include face width, number of teeth and diametral pitch. The user is free to choose any calculated response as the design objective to minimize or maximize and may impose lower and upper bounds on any calculated responses. Typical examples include life maximization with limits on dynamic load, stress, weight, etc. or minimization of weight subject to limits on life, dynamic load, etc. The research codes were written in modular form for easy expansion and so that they could be combined to create a multiple reduction optimization capability in future

Power-Law Distributions in Circulating Money: Effect of Preferential Behavior

We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mechanism to ensure the robustness of power-law distributions.Comment: 4 pages, 2 figure

Using natural language processing to improve biomedical concept normalization and relation mining

This thesis concerns the use of natural language processing for improving biomedical concept normalization and relation mining. We begin with introducing the background of biomedical text mining, and subsequently we will continue by describing a typical text mining pipeline, some key issues and problems in mining biomedical texts, and the possibility of using natural language procesing to solve the problems. Finally we end an outline of the work done in this thesis