A family of perfect hashing methods

Minimal perfect hash functions are used for memory efficient storage and fast retrieval of items from static sets. We present an infinite family of efficient and practical algorithms for generating order preserving minimal perfect hash functions. We show that almost all members of the family construct space and time optimal order preserving minimal perfect hash functions, and we identify the one with minimum constants. Members of the family generate a hash function in two steps. First a special kind of function into an r-graph is computed probabilistically. Then this function is refined deterministically to a minimal perfect hash function. We give strong theoretical evidence that the first step uses linear random time. The second step runs in linear deterministic time. The family not only has theoretical importance, but also offers the fastest known method for generating perfect hash functions.

Reliability of multiple frequency bioelectrical impedance analysis: An intermachine comparison

The technical reliability (i.e., interinstrument and interoperator reliability) of three SEAC-swept frequency bioimpedance monitors was assessed for both errors of measurement and associated analyses. In addition, intraoperator and intrainstrument variability was evaluated for repeat measures over a 4-hour period. The measured impedance values from a range of resistance-capacitance circuits were accurate to within 3% of theoretical values over a range of 50-800 ohms. Similarly, phase was measured over the range 1 degrees-19 degrees with a maximum deviation of 1.3 degrees from the theoretical value. The extrapolated impedance at zero frequency was equally well determined (+/-3%). However, the accuracy of the extrapolated value at infinite frequency was decreased, particularly at impedances below 50 ohms (approaching the lower limit of the measurement range of the instrument). The interinstrument/operator variation for whole body measurements were recorded on human volunteers with biases of less than +/-1% for measured impedance values and less than 3% for phase. The variation in the extrapolated values of impedance at zero and infinite frequencies included variations due to operator choice of the analysis parameters but was still less than +/-0.5%. (C) 1997 Wiley-Liss, Inc.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

A simple solution of the laminar dam break wave

The sudden release of a mass of fluid in a channel generates a highly unsteady flow motion, called dam break wave. While industrial fluids exhibit sometimes non-Newtonian behaviours, the viscous fluid flow assumption remains a useful approximation for simplified analyses. In this study, new solutions of laminar dam break wave are proposed for a semi-infinite reservoir based upon the method of characteristics. The solutions yield simple explicit expressions of the wave front location, wave front celerity and instantaneous free-surface profiles that compare favourably with experimental observations. Both horizontal and sloping channel configurations are treated. The simplicity of the equations may allow future extension to more complicated fluid flows.

Izergin-Korepin model with a boundary

The Izergin-Korepin model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the twisted quantum affine algebra U-q[((2))(2)]. We give the bosonization of the vacuum state with zero particle content. Excitation states are given by the action of the vertex operators on the vacuum state. We derive the boundary S-matrix. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. (C) 2001 Elsevier Science B.V. All rights reserved.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

Can increasing the viscosity of formulations be used to reduce the human skin penetration of the sunscreen oxybenzone?

The effect of adding thickening agents on the penetration of a sunscreen benzophenone-3 through epidermal and a high-density polyethylene membrane was studied using both very thick (infinite dose) and thin tin use) applications. Contradictory results were obtained. Thickening agents retard skin penetration, in a manner consistent with a diffusional resistance in the formulation, when applied as an infinite dose. In contrast, when applied as in thin (in use) doses, thickening agents promote penetration, most likely through greater stratum corneum diffusivity arising from an enhanced hydration by the thicker formulations. The two key implications from this work are (i) a recognition of the danger in the potential extrapolation of infinite dosing to in use situations, and (ii) to recognize that thicker formulations may sometimes enhance the penetration of other topical agents when applied in use.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

The City as Territory: Aerial Photography and the Everyday

For most of us, the modern city is somewhat unintelligible, both in terms of its structure and its significance. As an urbanised population, the city should be our natural territory, but the pace and scope of its change leads to an illegibility of its form and character. There is infinite, seemingly significant, activity - demolition, building and makeover - but there is little sense of the city as a site of meaning.

Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches.

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

An equivalent waveguide approach to designing of reflect arrays with the use of variable-size microstrip patches

An equivalent unit cell waveguide approach (WGA) is described to study the behavior of a multilayer reflect array of variable-size patches/dipoles, The approach considers normal incidence of a plane wave on an infinite periodic array of identical radiating elements and introduces an equivalent unit cell waveguide to obtain the reflection coefficient. A field matching technique and method of moments (MoM) is used to determine fields in different layers of the equivalent waveguide. Good agreements for the phase of the reflection coefficient between the proposed model and those published in selected literatures are obtained. (C) 2002 Wiley Periodicals, Inc.

Preparing encoded states in an oscillator

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.

Evaluation of various pre-treatments for the dehydration of banana and selection of suitable drying models

The thin-layer drying behaviour of bananas in a beat pump dehumidifier dryer was examined. Four pre-treatments (blanching, chilling, freezing and combined blanching and freezing) were applied to the bananas, which were dried at 50 degreesC with an air velocity of 3.1 m s(-1) and with the relative humidity of the inlet air of 10-35%. Three drying models, the simple model, the two-term exponential model and the Page model were examined. All models were evaluated using three statistical measures, correlation coefficient, root means square error, and mean absolute percent error. Moisture diffusivity was calculated based on the diffusion equation for an infinite cylindrical shape using the slope method. The rate of drying was higher for the pre-treatments involving freezing. The sample which was blanched only did not show any improvement in drying rate. In fact, a longer drying time resulted due to water absorption during blanching. There was no change in the rate for the chilled sample compared with the control. While all models closely fitted the drying data, the simple model showed greatest deviation from the experimental results. The two-term exponential model was found to be the best model for describing the drying curves of bananas because its parameters represent better the physical characteristics of the drying process. Moisture diffusivities of bananas were in the range 4.3-13.2 x 10(-10) m(2)s(-1). (C) 2002 Published by Elsevier Science Ltd.