Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Experimental characterization of the nonlinear optical and magneto-optical properties of interfaces

An effective ellipsometric technique to determine parameters that characterize second-harmonic optical and magneto-optical effects in centrosymmetric media within the electric-dipole approximation is proposed and outlined in detail. The parameters, which are ratios of components of the nonlinear-surface-susceptibility tensors, are obtained from experimental data related to the state of polarization of the second-harmonic-generated radiation as a function of the angle between the plane of incidence and the polarization plane of the incident, linearly polarized, fundamental radiation. Experimental details of the technique are described. A corresponding theoretical model is given as an example for a single isotropic surface assuming polycrystalline samples. The surfaces of air-Au and air-Ni (in magnetized and demagnetized states) have been investigated ex situ in ambient air, and the results are presented. A nonlinear, least-squares-minimization fitting procedure between experimental data and theoretical formulas has been shown to yield realistic, unambiguous results for the ratios corresponding to each of the above materials. Independent methods for verifying the validity of the fitting parameters are also presented. The influence of temporal variations at the surfaces on the state of polarization (due to adsorption, contamination, or oxidation) is also illustrated for the demagnetized air-Ni surface. (C) 2005 Optical Society of America

Spatially Correlated Multiple-Ananna Channel Capacity Distributions

In this paper, we investigate the capacity of multiple-input multiple-output (MIMO) wireless communication systems over spatially correlated Rayleigh distributed flat fading channels with complex Gaussian additive noise. Specifically, we derive the probability density function of the mutual information between transmitted and received complex signals of MIMO systems. Using this density we derive the closed-form ergodic capacity (mean), delay-limited capacity, capacity variance and outage capacity formulas for spatially correlated channels and then evaluate these formulas numerically. Numerical results show how the channel correlation degrades the capacity of MIMO communication systems. We also show that the density of mutual information of correlated/uncorrelated MIMO systems can be approximated by a Gaussian density with derived mean and variance, even for a finite number of inputs and outputs.

Time operators for one parameter semigroups

We develop two simple approaches to the construction of time operators for semigroups of continuous linear operators in Hilbert spaces provided that the generators of these semigroups are normal operators. The first approach enables us to give explicit formulas (in the spectral representations) both for the time operators and for their eigenfunctions. The other approach provides no explicit formula. However, it enables us to find necessary and sufficient conditions for the existence of time operators for semigroups of continuous linear operators in separable Hilbert spaces with normal generators. Time superoperators corresponding to unitary groups are also discussed.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Simple and accurate analytical model of planar grids and high-impedance surfaces, comprising metal strips or patches

Simple analytical formulas are introduced for the grid impedance of electrically dense arrays of square patches and for the surface impedance of high-impedance surfaces based on the dense arrays of metal strips or square patches over ground planes. Emphasis is on the oblique-incidence excitation. The approach is based on the known analytical models for strip grids combined with the approximate Babinet principle for planar grids located at a dielectric interface. Analytical expressions for the surface impedance and reflection coefficient resulting from our analysis are thoroughly verified by full-wave simulations and compared with available data in open literature for particular cases. The results can be used in the design of various antennas and microwave or millimeter wave devices which use artificial impedance surfaces and artificial magnetic conductors (reflect-array antennas, tunable phase shifters, etc.), as well as for the derivation of accurate higher-order impedance boundary conditions for artificial (high-) impedance surfaces. As an example, the propagation properties of surface waves along the high-impedance surfaces are studied.

Query cost estimation through remote system contention states analysis over the Internet

Query processing over the Internet involving autonomous data sources is a major task in data integration. It requires the estimated costs of possible queries in order to select the best one that has the minimum cost. In this context, the cost of a query is affected by three factors: network congestion, server contention state, and complexity of the query. In this paper, we study the effects of both the network congestion and server contention state on the cost of a query. We refer to these two factors together as system contention states. We present a new approach to determining the system contention states by clustering the costs of a sample query. For each system contention state, we construct two cost formulas for unary and join queries respectively using the multiple regression process. When a new query is submitted, its system contention state is estimated first using either the time slides method or the statistical method. The cost of the query is then calculated using the corresponding cost formulas. The estimated cost of the query is further adjusted to improve its accuracy. Our experiments show that our methods can produce quite accurate cost estimates of the submitted queries to remote data sources over the Internet.

Effect of pooling samples on the efficiency of comparative studies using microarrays

Motivation: Many biomedical experiments are carried out by pooling individual biological samples. However, pooling samples can potentially hide biological variance and give false confidence concerning the data significance. In the context of microarray experiments for detecting differentially expressed genes, recent publications have addressed the problem of the efficiency of sample pooling, and some approximate formulas were provided for the power and sample size calculations. It is desirable to have exact formulas for these calculations and have the approximate results checked against the exact ones. We show that the difference between the approximate and the exact results can be large.

Spectrally efficient cooperative diversity protocol for uplink wireless transmission

A spectrally efficient cooperative protocol for uplink wireless transmission in a centralised communication system is proposed, where each of the N users play the relaying and source roles simultaneously by using superposition (SP) modulation. The probability density function of the mutual information between SP-modulated transmitted and received signals of the cooperative uplink channels is derived. Using the high-signal-to-noise ratio (SNR) approximation of this density function, the outage probability formula of the system as well as its easily computable tight upper and lower bounds are obtained and these formulas are evaluated numerically. Numerical results show that the proposed strategy can achieve around 3 dB performance gain over comparable schemes. Furthermore, the multiplexing and diversity tradeoff formula is derived to illustrate the optimal performance of the proposed protocol, which also confirms that the SP relaying transmission does not cause any loss of data rate. Moreover, performance characterisation in terms of ergodic and outage capacities are studied and numerical results show that the proposed scheme can achieve significantly larger outage capacity than direct transmission, which is similar to other cooperative schemes. The superiority of the proposed strategy is demonstrated by the fact that it can maintain almost the same ergodic capacity as the direct transmission, whereas the ergodic capacity of other cooperative schemes would be much worse.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

A Syntax-based approach to measuring the degree of inconsistency for belief bases

Measuring the degree of inconsistency of a belief base is an important issue in many real world applications. It has been increasingly recognized that deriving syntax sensitive inconsistency measures for a belief base from its minimal inconsistent subsets is a natural way forward. Most of the current proposals along this line do not take the impact of the size of each minimal inconsistent subset into account. However, as illustrated by the well-known Lottery Paradox, as the size of a minimal inconsistent subset increases, the degree of its inconsistency decreases. Another lack in current studies in this area is about the role of free formulas of a belief base in measuring the degree of inconsistency. This has not yet been characterized well. Adding free formulas to a belief base can enlarge the set of consistent subsets of that base. However, consistent subsets of a belief base also have an impact on the syntax sensitive normalized measures of the degree of inconsistency, the reason for this is that each consistent subset can be considered as a distinctive plausible perspective reflected by that belief base,whilst eachminimal inconsistent subset projects a distinctive viewof the inconsistency. To address these two issues,we propose a normalized framework formeasuring the degree of inconsistency of a belief base which unifies the impact of both consistent subsets and minimal inconsistent subsets. We also show that this normalized framework satisfies all the properties deemed necessary by common consent to characterize an intuitively satisfactory measure of the degree of inconsistency for belief bases. Finally, we use a simple but explanatory example in equirements engineering to illustrate the application of the normalized framework.

Measuring the blame of each formula for inconsistent prioritized knowledge bases.

It is increasingly recognized that identifying the degree of blame or responsibility of each formula for inconsistency of a knowledge base (i.e. a set of formulas) is useful for making rational decisions to resolve inconsistency in that knowledge base. Most current techniques for measuring the blame of each formula with regard to an inconsistent knowledge base focus on classical knowledge bases only. Proposals for measuring the blames of formulas with regard to an inconsistent prioritized knowledge base have not yet been given much consideration. However, the notion of priority is important in inconsistency-tolerant reasoning. This article investigates this issue and presents a family of measurements for the degree of blame of each formula in an inconsistent prioritized knowledge base by using the minimal inconsistent subsets of that knowledge base. First of all, we present a set of intuitive postulates as general criteria to characterize rational measurements for the blames of formulas of an inconsistent prioritized knowledge base. Then we present a family of measurements for the blame of each formula in an inconsistent prioritized knowledge base under the guidance of the principle of proportionality, one of the intuitive postulates. We also demonstrate that each of these measurements possesses the properties that it ought to have. Finally, we use a simple but explanatory example in requirements engineering to illustrate the application of these measurements. Compared to the related works, the postulates presented in this article consider the special characteristics of minimal inconsistent subsets as well as the priority levels of formulas. This makes them more appropriate to characterizing the inconsistency measures defined from minimal inconsistent subsets for prioritized knowledge bases as well as classical knowledge bases. Correspondingly, the measures guided by these postulates can intuitively capture the inconsistency for prioritized knowledge bases.

Production of a monoclonal antibody and its application in an optical biosensor based assay for the quantitative measurement of Pantothenic Acid (Vitamin B5) in foodstuffs

Pantothenicacid (PA), vitamin B5, is an essential B vitamin that may be fortified in food and as such requires robust and accurate methods of detection to meet compliance legislation. This study reports the production and characterisation of the first monoclonalantibody (MAb) specific for PA and the subsequent development of a surface plasmon resonance (SPR) biosensorassay for the quantification of PA. The developed assay was compared with an SPR based commercial kit which utilised a polyclonal antibody (PAb). Foodstuffs, including cereals (n = 43), infant formulas and baby food (n = 10) and fruit juices (n = 48) were analysed by both the MAb and PAb biosensorassays and comparison plots showed good correlation (R2 0.77–0.99). The results indicate that the MAb basedbiosensorassay is suitable for the measurement of PA in foodstuffs and has the added advantage of facilitating a constant, long term supply of identical antibody. Preliminary matrix studies suggest the MAb basedassay is an excellent candidate for further validation studies and routine quality assurance based analysis.

Merging Knowledge Bases in Possibilistic Logic by Lexicographic Aggregation

Belief merging is an important but difficult problem in Artificial Intelligence, especially when sources of information are pervaded with uncertainty. Many merging operators have been proposed to deal with this problem in possibilistic logic, a weighted logic which is powerful for handling inconsistency and deal-ing with uncertainty. They often result in a possibilistic knowledge base which is a set of weighted formulas. Although possibilistic logic is inconsistency tolerant, it suffers from the well-known "drowning effect". Therefore, we may still want to obtain a consistent possibilistic knowledge base as the result of merging. In such a case, we argue that it is not always necessary to keep weighted information after merging. In this paper, we define a merging operator that maps a set of possibilistic knowledge bases and a formula representing the integrity constraints to a classical knowledge base by using lexicographic ordering. We show that it satisfies nine postulates that generalize basic postulates for propositional merging given in [11]. These postulates capture the principle of minimal change in some sense. We then provide an algorithm for generating the resulting knowledge base of our merging operator. Finally, we discuss the compatibility of our merging operator with propositional merging and establish the advantage of our merging operator over existing semantic merging operators in the propositional case.

Charge equilibrium of a laser-generated carbon-ion beam in warm dense matter

Using ion carbon beams generated by high intensity short pulse lasers we perform measurements of single shot mean charge equilibration in cold or isochorically heated solid density aluminum matter. We demonstrate that plasma effects in such matter heated up to 1 eV do not significantly impact the equilibration of carbon ions with energies 0.045-0.5 MeV/nucleon. Furthermore, these measurements allow for a first evaluation of semiempirical formulas or ab initio models that are being used to predict the mean of the equilibrium charge state distribution for light ions passing through warm dense matter.