Arbitrary Collection Research Articles

Semi-classical gravitational effects around global monopoles in Lyra geometry

W.A. Hiscock (1990, Class. Quantum Gravitation 7, L235) obtained the vacuum expectation value of the stress-energy tensor of an arbitrary collection of conformal massless free quantum fields (scalar, spinor and vectors) in the space-time of a static global monopole. With this stress-energy tensor, the semi-classical Einstein equations are solved retaining terms up to first order in ħ in Lyra geometry.

Eddy-current losses in a conducting plate due to a collection of bus bars carrying currents of different magnitudes and phases

Losses in bus bars carrying AC current and passing near the tank wall in transformers can contribute significantly to stray losses and can produce high temperatures on the tank wall. Usually these losses are mitigated by moving the bus bars farther away from the wall or by placing a shield of high conductivity and low permeability on the tank wall near the bus bars. Although these losses in the wall or shield can be calculated by modern finite-element codes, an analytical method would obtain these losses quickly during the design phase. We present such a method here. The method works for an arbitrary collection of bus bars carrying currents from different phases. Applications to other situations where long cables or bus bars carrying AC currents and running parallel to a conducting plate are also possible.

A note on the one-deviation property in extensive form games

In an extensive form game, an assessment is said to satisfy the one-deviation property if for all possible payoffs at the terminal nodes the following holds: if a player at each of his information sets cannot improve upon his expected payoff by deviating unilaterally at this information set only, he cannot do so by deviating at any arbitrary collection of information sets. Hendon et al. (1996. Games Econom. Behav. 12, 274–282) have shown that pre-consistency of assessments implies the one-deviation property. In this note, it is shown that an appropriate weakening of pre-consistency, termed updating consistency, is both a sufficient and necessary condition for the one-deviation property. The result is extended to the context of rationalizability.

PRESENT KNOWLEDGE ON THE DISTRIBUTION OF THE LYNX (LYNX LYNX) IN AUSTRIA

To assess the present status and distribution of the lynx in the Austrian Alps we analysed documented reports on lynx presence for the period 1995 to 1999. Records on lynx presence in Austria were collected by the hunter's associations of Carinthia, Styria, Salzburg and Upper Austria, regional NGO's and wildlife biologists. For this five-year period, I06 records of lynx presence were documented for the Austrian Alps. Of these we classified 100 as Quality 3 data (unconfirmed prey remains, tracks and observations) and 5 as Quality 2 data (confirmed prey remains). The only hard fact (Quality 1 data) in the Austrian Alps was a male lynx killed on a highway in southern Salzburg in 1995. From these reported signs of lynx presence we concluded that 20 years after the first reintroductions there still is no estab- lished lynx population in the Austrian Alps. The reports rather indicate a few individuals scattered over a wide area. As the monitoring of the Austrian lynx population is more a passive and arbitrary collection of reports than a systematic monitoring, we believe that the distribution reported here is likely underes- timating the actual distribution of the lynx in the Austrian Alps. Therefore we emphasise the need to es- tablish a new systematic monitoring system covering the entire potential lynx habitat in Austria.

A construction of containing spaces

In this paper we give a set-theoretical construction of containing spaces for an arbitrary collection of spaces. This construction gives a satisfactory, in our opinion, answer to Problem 7 given in Section 3 of Arhangel'skiı̆ and Fedorchuk (Encyclopaedia of Math. Sci., Vol. 17, 1990, p. 1). Using this construction we also introduce the notion of a saturated class of spaces and prove that the class of all T 0 -spaces, the class of all regular spaces, and the class of all completely regular spaces are saturated classes.

Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games

The epistemic analysis of solution concepts for dynamic games involves statements about the players' beliefs conditional upon different histories of play, their conditional beliefs about each other's conditional beliefs, etc. To represent such statements, we construct a space of infinite (coherent) hierarchies of conditional probability systems, defined with respect to a fixed collection of relevant hypotheses concerning an external state (e.g., the strategy profile being played.) As an application, we derive results about common certainty of the opponent's rationality conditonal on an arbitrary collection of histories in multistage games with observed actions and (possibly) incomplete information. Journal of Economic Literature Classification Numbers: C72, D82.

Spheres, molecules, and hidden surface removal

We devise techniques to manipulate a collection of loosely interpenetrating spheres in three-dimensional space. Our study is motivated by the representation and manipulation of molecular configurations, modeled by a collection of spheres. We analyze the sphere model and point to properties that make it more easy to manipulate than an arbitrary collection of spheres. For this special sphere model we present efficient algorithms for computing its union boundary and for hidden surface removal. The efficiency and practicality of our approach are demonstrated by experiments on actual molecule data.

Estimation of average particle size from vertical projections.

A new stereological relationship is derived for the estimation of average size (average width) of a collection of convex particles in a 3D microstructure. The average size is estimated from measurements performed on projected images of the microstructure generated by total vertical projections. The stereological relationship is as follows: D = IC/(2N0beta). D is the average width, ;IC is the average absolute number of intersections between the specifically oriented and regularly spaced cycloid shape test lines and particle boundaries observed in the total vertical projections, N0 is the total number of particles observed in the total vertical projection and the parameter beta is a characteristic of the measurement grid; it has units of reciprocal of length. The result is applicable to any arbitrary collection of convex particles; the particle orientations need not be isotropic. Only 'intersection counts' are required; it is not necessary to measure sizes of the particles in the projected images.

Estimation of integral mixed surface curvature from vertical metallographic sections

The integral mixed curvature Q V of a population of surfaces in a microstructure is defined as follows. Q v = ∫ ∫ [3(K 1) 2+2K 1K 2+3(K 2) 2] ds/4. The integration is over all surface elements of interest in a unit volume of microstructure. K 1 and K 2 are the principal normal curvatures of a surface element of area d s. A new stereological relationship is derived for the estimation of integral mixed curvature, Q V, of population of smooth surfaces from the measurements on the vertical metallographic sections. On the vertical sections, sample the boundary elements by using vertical straight test lines, and measure curvature k of only those boundary elements that intersect these test lines. From these data, compute the sum of the square of the curvatures, and divide it by the total test line length. Let [ k 2 ] L be the average value of this parameter in the vertical sections. It is shown that, Q v =2[ k 2 ] L . The stereological relationship is geometrically general and it is applicable to any arbitrary collection of smooth surfaces.

Discrete Radon transform and its approximate inversion via the EM algorithm

The problem of reconstructing a binary function f, defined on a finite subset of a lattice ℤ, from an arbitrary collection of its partial-sums is considered. The approach we present is based on (a) relaxing the binary constraints f(z) = 0 or 1 to interval constraints 0 ≤ f(z) ≤ 1, z ∈ ℤ, and (b) applying a minimum distance method (using Kullback-Leibler's information divergence index as our distance function) to find such an f—say, fˆ—for which the distance between the observed and the theoretical partial sums is as small as possible. (Turning this fˆ into a binary function can be done as a separate postprocessing step: for instance, through thresholding, or through some additional Bayesian modeling.) To derive this minimum-distance solution, we develope a new EM algorithm. This algorithm is different from the often-studied EM/maximum likelihood algorithm in emission tomography and other linear-inverse positively constrained problems because of the additional upper-bound constraint (f ≤ 1) on the signal f. Properties of the algorithm, as well as similarities with and differences from some other methods, such as the linear-programming approach or the algebraic reconstruction technique, are discussed. The methodology is demonstrated on three recently studied phantoms, and the simulation results are very promising, suggesting that the method could also work well under field conditions which may include a small or moderate level of measurement noise in the observed partial sums. The methodology has important applications in high-resolution electron microscopy for the reconstruction of the atomic structure of crystals from their projections. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 155–173, 1998

Discrete Radon transform and its approximate inversion via the EM algorithm

The problem of reconstructing a binary function f, defined on a finite subset of a lattice ℤ, from an arbitrary collection of its partial-sums is considered. The approach we present is based on (a) relaxing the binary constraints f(z) = 0 or 1 to interval constraints 0 ≤ f(z) ≤ 1, z ∈ ℤ, and (b) applying a minimum distance method (using Kullback-Leibler's information divergence index as our distance function) to find such an f—say, fˆ—for which the distance between the observed and the theoretical partial sums is as small as possible. (Turning this fˆ into a binary function can be done as a separate postprocessing step: for instance, through thresholding, or through some additional Bayesian modeling.) To derive this minimum-distance solution, we develope a new EM algorithm. This algorithm is different from the often-studied EM/maximum likelihood algorithm in emission tomography and other linear-inverse positively constrained problems because of the additional upper-bound constraint (f ≤ 1) on the signal f. Properties of the algorithm, as well as similarities with and differences from some other methods, such as the linear-programming approach or the algebraic reconstruction technique, are discussed. The methodology is demonstrated on three recently studied phantoms, and the simulation results are very promising, suggesting that the method could also work well under field conditions which may include a small or moderate level of measurement noise in the observed partial sums. The methodology has important applications in high-resolution electron microscopy for the reconstruction of the atomic structure of crystals from their projections. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 155–173, 1998

Vascular Dementia: Current Concepts

Vascular Dementia: Current Concepts edited by I. Prohovnik, J. Wade, S. Knezevic, T. Tatemichi, and T. Erkinjuntti , 362 pp., West Sussex, England, John Wiley & Sons, 1996, $79.95. The editors of Vascular Dementia: Current Concepts pose the central theme of the book in their introduction: Is there a dementia syndrome caused by cerebral vascular disease, rather than an arbitrary collection of cognitive deficits? In other words, is vascular dementia a disease, a syndrome, or a random set of symptoms? By the end of the book, many aspects of the question remain unanswered, and the comment by Marler …

Phase noise in externally injection-locked oscillator arrays

Previous investigations of noise in mutually synchronized coupled-oscillator systems are extended to include the effects of phase noise introduced by externally injected signals. The analysis is developed for arbitrarily coupled arrays and an arbitrary collection of coherent injected signals, and is illustrated with the specific case of linear chains of nearest neighbor coupled oscillators either globally locked (locking signal applied to each array element) or with the locking signal applied to a single-array element. It is shown that the general behavior is qualitatively similar to a single injection-locked oscillator, with the output noise tracking the injected noise near the carrier, and returning to the free-running array noise far from the carrier, with intermediate behavior significantly influenced by the number of array elements and injection strength. The theory is validated using a five-element GaAs MESFET oscillator array operating at S-band.

Scattering of polarized radiation by an arbitrary collection of closely spaced parallel nonhomogeneous tilted cylinders

A theory of scattering of polarized light by an arbitrary configuration of closely spaced, parallel nonhomogeneous infinite circular cylinders at oblique incidence is presented in this paper. The polarization of the incident wave can be linear, circular, or elliptic. The diameter of the cylinders, the spacing between the cylinders, and the incident wavelength are comparable with each other. Each cylinder can have an arbitrary number of concentric layers of stratification, and the complex index of refraction in each layer can be different. An exact solution of Maxwell’s equations that accounts for near-field multiple scattering and far-field wave interference is developed. Formulas are developed for the extinction and scattering cross sections and the scattering amplitude. The corresponding expressions for an isolated cylinder are also obtained as a special case. The light-scattering characteristics of a collection of cylinders are examined by numerical data for various incidence angles and polarizations.

Bayes Linear Sufficiency and Systems of Expert Posterior Assessments

SUMMARY Data arising in the form of expert assessments are received by a decision maker. The decision maker is required to estimate a set of unknown quantities, and receives expert assessments at varying levels of accuracy, on samples of the quantities of interest. We present a Bayes linear analysis of this problem. In the absence of other assessments, the decision maker will accept as his or her current estimate of any single quantity the most accurate received assessment of that quantity. This leads to a sufficiency property which allows a simple decomposition of the error structure of assessments. Bayes linear estimation is then used by the decision maker to estimate each quantity of interest given an arbitrary collection of received assessments. The analysis is motivated throughout by a practical context in which a large company needs to estimate costs for renovation of assets. The methodology is illustrated with a numerical example.

The Wijsman and Attouch-Wets topologies on hyperspaces revisited

In this paper we will prove that, for an arbitrary metric space X and a fairly arbitrary collection Σ of subsets of X, it is possible to endow the hyperspace CL( X) of all nonempty closed subsets of X (to be identified with their distance functionals) with a canonical distance function having the topology of uniform convergence on members of Σ as topological coreflection and the Hausdorff metric as metric coreflection. For particular choices of Σ, we obtain canonical distance functions overlying the Wijsman and Attouch-Wets topologies. Consequently we apply the general theory of spaces endowed with a distance function and compare the results with those obtained for the classical hyperspace topologies. In all cases we are able to prove results which are both stronger and more general than the classical ones.

Desert Storm Syndrome and Immunization

The latest report¹about the search for causes of the "Desert Storm syndrome" must be very disappointing, not only for the 20 000 victims, but also for medical scientists. Four years after the end of the Gulf War, information still derives from the arbitrary collection of very restricted data from small cohorts of veterans. Is this a question of medical concepts? Are the symptoms of the Desert Storm syndrome or "Gulf War disease" indeed so unique and unpredictable^1,2that it is not possible to develop reasonable concepts for investigation? Together with the predominant chronic fatigue syndrome, joint pain, and rash, there have been reports of increased polyspecific antibody concentrations against viruses such as Epstein-Barr virus, cytomegalovirus, and arbovirus, as well as symptoms that resemble those of immunologic disorders. What can be a consistent explanation of these disseminated symptoms of obviously chronic disease other than changes in immune responses?

Evaluation of atomic level mean force potentials via inverse folding and inverse refinement of protein structures: atomic burial position and pairwise non-bonded interactions.

Two atomic level knowledge-based mean force interaction potentials (KBPs), a centrosymmetric burial position term and a long-range pairwise term, were developed. These were tested by comparing multiple configurations of three structurally unrelated proteins and were found successfully to (i) discriminate native state proteins from grossly misfolded structures in inverse folding tests, (ii) rank identify, using the KBP energy/r.m.s.d. correlation, native from progressively less native-like (compact and dilated) structures generated via molecular dynamics sampling, providing an energy gradient sloping from partially unfolded structures towards near-native states in inverse refinement tests (iii) smooth the overall potential energy surface in the region of dilated non-native structures by countering local minima of the in vacuo molecular mechanical potential and (iv) serve as a local minimum detector during simulated temperature quenching studies. These atomic KBPs discriminated native from non-native structures with greater overall sensitivity than did either a residue-based pairwise interaction potential or an effective solvation potential based on atomic contact volume occupancy. The KBPs presented here are immediately useful as a tool for selecting "good refinement candidates' from an arbitrary collection of protein configurations and may play a role in dynamic computational protein refinement.

Book review: Challenges in Natural Language Processing Madeleine Bates & Ralph M. Weischedel (Eds.) (Cambridge University Press 1993)

A recurrent event in almost every branch of science is the attempt of renowned experts from the field to look into its future. For the area of computational linguistics (CL) David Waltz, in 1982, has made the last assessment of the current state and future perspectives of natural language processing (NLP) research that I am aware of [1]. The book under review shares that predictive concern, ten years after. The intention behind- Challenges in Natural Language Processing 1 is to explore the future shape of CL and to outline the most significant problems and challenges this field will face in the current decade. The papers it contains reflect the discussions from a symposium on Future Directions in Natural Language Processing which was held at Bolt Beranek and Newman, Inc. (BBN), in Cambridge, Massachusetts, from November 29, 1989 to December 1, 1989 2 . Access to this symposium was restricted to invited participants (people from government, industry, and academia, altogether thirty-six symposium attendees). Speakers were encouraged to present both recently completed and speculative work, and to focus on topics that they considered to have the most impact on the field in the coming (now, the current) decade. Their perception of unsolved problems of long standing and presentation of new possibilities was intended as a contribution to long-range planning by funding agencies, research groups, academic institutions, and others interested in CL. Except for the two contributions by the editors, which directly meet the intentions laid out above, the book contains an almost arbitrary collection of papers which could have been written on any other occasion, too. They cover highly specialized research topics but are uncommitted to in-depth deliberations concerning the future of CL. Therefore, I doubt that the targeted audience - even the domain specialists - will be focused on the field's perspectives after having read the published symposium contributions. In the strict sense, this book fails to accomplish its advisory goals. As a thematically entirely open collection of CL papers, it has its merits, nevertheless.

Statistical Mechanics of a Multipolar Gas: A Lattice Field Theory Approach

A recently proposed lattice field theory approach to the statistical mechanics of a classical Coulomb gas (J. Chem. Phys. 1992, 97, 5653) is generalized to treat particles with arbitrary electric multipole moments. Explicit development of the mean-field approximation is given for the case of mobile dipoles and monopoles (ions) surrounding an arbitrary collection of fixed charges embedded in macroions. In particular, a modified Poisson−Boltzmann (PB) equation is derived in which the mobile dipoles provide an effective spatially dependent dielectric constant. This equation implies a self-consistent iteration procedure by which the monopole and dipole densities are simultaneously determined in terms of single scalar (PB) field. Moreover, this equation can be derived from a minimum principle; an annealing strategy for computing the PB field is thereby suggested. In addition, explicit mean-field expressions for thermodynamic free energies are obtained as simple functionals of the PB field. Connection to the well-known Langevin dipole model is made. A numerical application to a system consisting of two parallel plates is presented in order to illustrate the utility of the formulation.