The quantum probability ranking principle for information retrieval

While the Probability Ranking Principle for Information Retrieval provides the basis for formal models, it makes a very strong assumption regarding the dependence between documents. However, it has been observed that in real situations this assumption does not always hold. In this paper we propose a reformulation of the Probability Ranking Principle based on quantum theory. Quantum probability theory naturally includes interference effects between events. We posit that this interference captures the dependency between the judgement of document relevance. The outcome is a more sophisticated principle, the Quantum Probability Ranking Principle, that provides a more sensitive ranking which caters for interference/dependence between documents’ relevanc

Generalized Korn's inequality and conformal Killing vectors

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its trace free part. That is, we obtain a stronger inequality in which the kernel of the relevant operator are the conformal Killing vectors. The new inequality has applications in General Relativity.Comment: 8 page

Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the {\em universal} character of the Casimir force in systems with short-ranged interactions. The effects due to dispersion forces are discussed for systems with periodic or realistic boundary conditions. In contrast to systems with short-ranged interactions, for $L/\xi \gg 1$ one observes leading finite-size contributions governed by power laws in $L$ due to the subleading long-ranged character of the interaction, where $L$ is the finite system size and $\xi$ is the correlation length.Comment: 11 pages, revtex, to appear in Phys. Rev. E 68 (2003

Duality between quantum symmetric algebras

Using certain pairings of couples, we obtain a large class of two-sided non-degenerated graded Hopf pairings for quantum symmetric algebras.Comment: 15 pages. Letters in Math. Phy., to appear soo

Foreign Ownership and Firm Performance: Emerging-Market Acquisitions in the United States

This paper examines the recent upsurge in foreign acquisitions of U.S. firms, specifically focusing on acquisitions made by firms located in emerging markets. Neoclassical theory predicts that, on net, capital should flow from countries that are capital-abundant to countries that are capital-scarce. Yet increasingly emerging market firms are acquiring assets in developed countries. Using transaction-specific acquisition data and firm-level accounting data we evaluate the post-acquisition performance of publicly traded U.S. firms that have been acquired by firms from emerging markets over the period 1980-2007. Our empirical methodology uses a difference-in-differences approach combined with propensity score matching to create an appropriate control group of non-acquired firms. The results suggest that emerging country acquirers tend to choose U.S. targets that are larger in size (measured as sales, total assets and employment), relative to matched non-acquired U.S. firms before the acquisition year. In the years following the acquisition, sales and employment decline while profitability rises, suggesting significant restructuring of the target firms.

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining $\gamma=1.2373(2)$, $\nu=0.63012(16)$, $\alpha=0.1096(5)$, $\eta=0.03639(15)$, $\beta=0.32653(10)$, $\delta=4.7893(8)$. Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate $\Delta=0.52(3)$ for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.Comment: 40 pages, 15 figure

Test of renormalization predictions for universal finite-size scaling functions

We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular epsilon-expansion, where epsilon is the distance to the upper critical dimension. Subsequently, we check the results by numerical simulations of spin models in the same universality class. Our systems offer the essential advantage that epsilon can be varied continuously, allowing an accurate examination of the region where epsilon is small. The numerical calculations turn out to be in striking disagreement with the predicted singularity.Comment: 6 pages, including 3 EPS figures. To appear in Phys. Rev. E. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

General relations of heavy quark-antiquark potentials induced by reparameterization invariance

A set of general relations between the spin-independent and spin-dependent potentials of heavy quark and anti-quark interactions are derived from reparameterization invariance in the Heavy Quark Effective Theory. It covers the Gromes relation and includes some new interesting relations which are useful in understanding the spin-independent and spin-dependent relativistic corrections to the leading order nonrelativistic potential.Comment: 11 pages, TUIMP-TH-93/54, CCAST-93-3

Projective and Coarse Projective Integration for Problems with Continuous Symmetries

Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a ``co-evolving'' frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in the new spatial frame. The slower time behavior permits the use of {\it projective} and {\it coarse projective} integration with longer projective steps in the computation of the time evolution of partial differential equations and multiscale systems, respectively. These methods are also demonstrated to be effective for systems which only approximately or asymptotically possess continuous symmetries. The ideas of projective integration in a co-evolving frame are illustrated on the one-dimensional, translationally invariant Nagumo partial differential equation (PDE). A corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is used to illustrate the coarse-grained method. A simple, one-dimensional diffusion problem is used to illustrate the scale invariant case. The efficiency of projective integration in the co-evolving frame for both the macroscopic diffusion PDE and for a random-walker particle based model is again demonstrated

A New Concept to Numerically Evaluate the Performance of Yielding Support under Impulsive Loading

The dynamic capacity of a support system is dependent on the connectivity and compatibility of its reinforcement and surface support elements. Connectivity refers to the capacity of a system to transfer the dynamic load from an element to another, for example, from the reinforcement to the surface support through plates and terminating arrangements (split set rings, nuts, etc.), or from a reinforcement/holding element to others via the surface support. Compatibility is related to the difference in stiffness amongst support elements. Load transfer may not take place appropriately when there are strong stiffness contrasts within a ground support system. Case studies revealed premature failures of stiffer elements prior to utilising the full capacity of more deformable elements within the same system. From a design perspective, it is important to understand that the dynamic-load capacity of a ground support system depends not only on the capacity of its reinforcement elements but also, and perhaps most importantly, on their compatibility with other elements of the system and on the strength of the connections. The failure of one component of the support system usually leads to the failure of the system