The Rank of the Covariance Matrix of an Evanescent Field

Evanescent random fields arise as a component of the 2-D Wold decomposition of homogenous random fields. Besides their theoretical importance, evanescent random fields have a number of practical applications, such as in modeling the observed signal in the space time adaptive processing (STAP) of airborne radar data. In this paper we derive an expression for the rank of the low-rank covariance matrix of a finite dimension sample from an evanescent random field. It is shown that the rank of this covariance matrix is completely determined by the evanescent field spectral support parameters, alone. Thus, the problem of estimating the rank lends itself to a solution that avoids the need to estimate the rank from the sample covariance matrix. We show that this result can be immediately applied to considerably simplify the estimation of the rank of the interference covariance matrix in the STAP problem

Physical Bounds to the Entropy-Depolarization Relation in Random Light Scattering

We present a theoretical study of multi-mode scattering of light by optically random media, using the Mueller-Stokes formalism which permits to encode all the polarization properties of the scattering medium in a real $4 \times 4$ matrix. From this matrix two relevant parameters can be extracted: the depolarizing power $D_M$ and the polarization entropy $E_M$ of the scattering medium. By studying the relation between $E_M$ and $D_M$, we find that {\em all} scattering media must satisfy some {\em universal} constraints. These constraints apply to both classical and quantum scattering processes. The results obtained here may be especially relevant for quantum communication applications, where depolarization is synonymous with decoherence.Comment: 4 pages, 2 figure

Intrinsic Entanglement Degradation by Multi-Mode Detection

Relations between photon scattering, entanglement and multi-mode detection are investigated. We first establish a general framework in which one- and two-photon elastic scattering processes can be discussed, then we focus on the study of the intrinsic entanglement degradation caused by a multi-mode detection. We show that any multi-mode scattered state cannot maximally violate the Bell-CHSH inequality because of the momentum spread. The results presented here have general validity and can be applied to both deterministic and random scattering processes.Comment: 12 pages, 4 figures, v3: minor changes. Phys. Rev. A (2004), to be publishe

Development of a polarization resolved spectroscopic diagnostic for measurements of the vector magnetic field in the Caltech coaxial magnetized plasma jet experiment

In the Caltech coaxial magnetized plasma jet experiment, fundamental studies are carried out relevant to spheromak formation, astrophysical jet formation/propagation, solar coronal physics, and the general behavior of twisted magnetic flux tubes that intercept a boundary. In order to measure the spatial profile of the magnetic field vector for understanding the underlying physics governing the dynamical behavior, a non-perturbing visible emission spectroscopic method is implemented to observe the Zeeman splitting in emission spectra. We have designed and constructed a polarization-resolving optical system that can simultaneously detect the left- and right-circularly polarized emission. The system is applied to singly ionized nitrogen spectral lines. The magnetic field strength is measured with a precision of about ±13 mT. The radial profiles of the azimuthal and axial vector magnetic field components are resolved by using an inversion method

Wood-based beams strengthened with FRP laminates: improved performance with pre-stressed systems

Using bonded fibre-reinforced polymer (FRP) laminates for strengthening wooden structural members has been shown to be an effective and economical method. In this paper, properties of suitable FRP materials, adhesives and two ways of strengthening beams exposed to bending moment are presented. Passive or slack reinforcement is one way of strengthening. The most effective way of such a strengthening was to place reinforcement laminates on both tension and compression side of the beam. However, the FRP material is only partially utilised. The second way is to apply pre-stressing in FRP materials prior to bonding to tension side of flexural members and this way was shown to provide the most effective utilisation of these materials. The state of the art of such a strengthening and various methods are discussed. Increasing the load-bearing capacity, introducing a pre-cambering effect and thus improving serviceability which often governs the design and reducing the amount of FRP reinforcement needed are some of the main advantages. A recent development on how to avoid the requirement for anchoring the laminates at the end of the beams to avoid premature debonding is shown, and the advantage of such a system is described

Effect of frequent hemodialysis on residual kidney function.

Frequent hemodialysis can alter volume status, blood pressure, and the concentration of osmotically active solutes, each of which might affect residual kidney function (RKF). In the Frequent Hemodialysis Network Daily and Nocturnal Trials, we examined the effects of assignment to six compared with three-times-per-week hemodialysis on follow-up RKF. In both trials, baseline RKF was inversely correlated with number of years since onset of ESRD. In the Nocturnal Trial, 63 participants had non-zero RKF at baseline (mean urine volume 0.76 liter/day, urea clearance 2.3 ml/min, and creatinine clearance 4.7 ml/min). In those assigned to frequent nocturnal dialysis, these indices were all significantly lower at month 4 and were mostly so at month 12 compared with controls. In the frequent dialysis group, urine volume had declined to zero in 52% and 67% of patients at months 4 and 12, respectively, compared with 18% and 36% in controls. In the Daily Trial, 83 patients had non-zero RKF at baseline (mean urine volume 0.43 liter/day, urea clearance 1.2 ml/min, and creatinine clearance 2.7 ml/min). Here, treatment assignment did not significantly influence follow-up levels of the measured indices, although the range in baseline RKF was narrower, potentially limiting power to detect differences. Thus, frequent nocturnal hemodialysis appears to promote a more rapid loss of RKF, the mechanism of which remains to be determined. Whether RKF also declines with frequent daily treatment could not be determined

Arquitectura ANFIS del Proceso de Fermentación de Aceitunas Negras Naturales

En el proceso de obtención de aceitunas negras naturales, las condiciones inciden sobre la calidad del fruto fermentado y éstas difieren a distintas escalas. El objetivo del trabajo es generar modelos matemáticos que caractericen las propiedades de las aceitunas negras naturales obtenidas a gran escala, a partir de datos del proceso a escala piloto. Se crearon arquitecturas ANFIS con parámetros físico-químicos como entradas, y de textura y color como salidas. Dichas estructuras se entrenaron con datos obtenidos a escala piloto y se validaron con los industriales. Las redes que demostraron mejor desempeño poseen dos funciones de membresia por entrada incorporada, en forma de campana generalizada y una de salida. Las estructuras logradas demostraron habilidad para predecir la evolución del proceso a escala industrial luego de los primeros días de fermentación. Para incrementar su aptitud, sería conveniente probar otros modelos para el tratamiento de datos, tales como las redes neuronales artificiales

Adaptive Evolutionary Clustering

In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static clustering by producing clustering results that reflect long-term trends while being robust to short-term variations. Several evolutionary clustering algorithms have recently been proposed, often by adding a temporal smoothness penalty to the cost function of a static clustering method. In this paper, we introduce a different approach to evolutionary clustering by accurately tracking the time-varying proximities between objects followed by static clustering. We present an evolutionary clustering framework that adaptively estimates the optimal smoothing parameter using shrinkage estimation, a statistical approach that improves a naive estimate using additional information. The proposed framework can be used to extend a variety of static clustering algorithms, including hierarchical, k-means, and spectral clustering, into evolutionary clustering algorithms. Experiments on synthetic and real data sets indicate that the proposed framework outperforms static clustering and existing evolutionary clustering algorithms in many scenarios.Comment: To appear in Data Mining and Knowledge Discovery, MATLAB toolbox available at http://tbayes.eecs.umich.edu/xukevin/affec