Hilbert W*-modules and coherent states

Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras.

Moduli of equivariant sheaves and Kronecker-McKay modules

We extend Alvarez-Consul and King description of moduli of sheaves over projective schemes to moduli of equivariant sheaves over projective Gamma-schemes, for a finite group Gamma. We introduce the notion of Kronecker-McKay modules and construct the moduli of equivariant sheaves using a natural functor from the category of equivariant sheaves to the category of Kronecker-McKay modules. Following Alvarez-Consul and King, we also study theta functions and homogeneous co-ordinates of moduli of equivariant sheaves.

Some constructions, related to noncommutative tori; Fredholm modules and the Beilinson-Bloch regulator

A noncommutative 2-torus is one of the main toy models of noncommutative geometry, and a noncommutative n-torus is a straightforward generalization of it. In 1980, Pimsner and Voiculescu in [17] described a 6-term exact sequence, which allows for the computation of the K-theory of noncommutative tori. It follows that both even and odd K-groups of n-dimensional noncommutative tori are free abelian groups on 2^n-1 generators. In 1981, the Powers-Rieffel projector was described [19], which, together with the class of identity, generates the even K-theory of noncommutative 2-tori. In 1984, Elliott [10] computed trace and Chern character on these K-groups. According to Rieffel [20], the odd K-theory of a noncommutative n-torus coincides with the group of connected components of the elements of the algebra. In particular, generators of K-theory can be chosen to be invertible elements of the algebra. In Chapter 1, we derive an explicit formula for the First nontrivial generator of the odd K-theory of noncommutative tori. This gives the full set of generators for the odd K-theory of noncommutative 3-tori and 4-tori.

In Chapter 2, we apply the graded-commutative framework of differential geometry to the polynomial subalgebra of the noncommutative torus algebra. We use the framework of differential geometry described in [27], [14], [25], [26]. In order to apply this framework to noncommutative torus, the notion of the graded-commutative algebra has to be generalized: the "signs" should be allowed to take values in U(1), rather than just {-1,1}. Such generalization is well-known (see, e.g., [8] in the context of linear algebra). We reformulate relevant results of [27], [14], [25], [26] using this extended notion of sign. We show how this framework can be used to construct differential operators, differential forms, and jet spaces on noncommutative tori. Then, we compare the constructed differential forms to the ones, obtained from the spectral triple of the noncommutative torus. Sections 2.1-2.3 recall the basic notions from [27], [14], [25], [26], with the required change of the notion of "sign". In Section 2.4, we apply these notions to the polynomial subalgebra of the noncommutative torus algebra. This polynomial subalgebra is similar to a free graded-commutative algebra. We show that, when restricted to the polynomial subalgebra, Connes construction of differential forms gives the same answer as the one obtained from the graded-commutative differential geometry. One may try to extend these notions to the smooth noncommutative torus algebra, but this was not done in this work.

A reconstruction of the Beilinson-Bloch regulator (for curves) via Fredholm modules was given by Eugene Ha in [12]. However, the proof in [12] contains a critical gap; in Chapter 3, we close this gap. More specifically, we do this by obtaining some technical results, and by proving Property 4 of Section 3.7 (see Theorem 3.9.4), which implies that such reformulation is, indeed, possible. The main motivation for this reformulation is the longer-term goal of finding possible analogs of the second K-group (in the context of algebraic geometry and K-theory of rings) and of the regulators for noncommutative spaces. This work should be seen as a necessary preliminary step for that purpose.

For the convenience of the reader, we also give a short description of the results from [12], as well as some background material on central extensions and Connes-Karoubi character.

Physiological modules for generating discrete and rhythmic movements: action identification by a dynamic recurrent neural network

In this study we employed a dynamic recurrent neural network (DRNN) in a novel fashion to reveal characteristics of control modules underlying the generation of muscle activations when drawing figures with the outstretched arm. We asked healthy human subjects to perform four different figure-eight movements in each of two workspaces (frontal plane and sagittal plane). We then trained a DRNN to predict the movement of the wrist from information in the EMG signals from seven different muscles. We trained different instances of the same network on a single movement direction, on all four movement directions in a single movement plane, or on all eight possible movement patterns and looked at the ability of the DRNN to generalize and predict movements for trials that were not included in the training set. Within a single movement plane, a DRNN trained on one movement direction was not able to predict movements of the hand for trials in the other three directions, but a DRNN trained simultaneously on all four movement directions could generalize across movement directions within the same plane. Similarly, the DRNN was able to reproduce the kinematics of the hand for both movement planes, but only if it was trained on examples performed in each one. As we will discuss, these results indicate that there are important dynamical constraints on the mapping of EMG to hand movement that depend on both the time sequence of the movement and on the anatomical constraints of the musculoskeletal system. In a second step, we injected EMG signals constructed from different synergies derived by the PCA in order to identify the mechanical significance of each of these components. From these results, one can surmise that discrete-rhythmic movements may be constructed from three different fundamental modules, one regulating the co-activation of all muscles over the time span of the movement and two others elliciting patterns of reciprocal activation operating in orthogonal directions.

Physiological modules for generating discrete and rhythmic movements: Component analysis of EMG signals

A central question in Neuroscience is that of how the nervous system generates the spatiotemporal commands needed to realize complex gestures, such as handwriting. A key postulate is that the central nervous system (CNS) builds up complex movements from a set of simpler motor primitives or control modules. In this study we examined the control modules underlying the generation of muscle activations when performing different types of movement: discrete, point-to-point movements in eight different directions and continuous figure-eight movements in both the normal, upright orientation and rotated 90 degrees. To test for the effects of biomechanical constraints, movements were performed in the frontal-parallel or sagittal planes, corresponding to two different nominal flexion/abduction postures of the shoulder. In all cases we measured limb kinematics and surface electromyographic activity (EMB) signals for seven different muscles acting around the shoulder. We first performed principal component analysis (PCA) of the EMG signals on a movement-by-movement basis. We found a surprisingly consistent pattern of muscle groupings across movement types and movement planes, although we could detect systematic differences between the PCs derived from movements performed in each sholder posture and between the principal components associated with the different orientations of the figure. Unexpectedly we found no systematic differences between the figute eights and the point-to-point movements. The first three principal components could be associated with a general co-contraction of all seven muscles plus two patterns of reciprocal activatoin. From these results, we surmise that both "discrete-rhythmic movements" such as the figure eight, and discrete point-to-point movement may be constructed from three different fundamental modules, one regulating the impedance of the limb over the time span of the movement and two others operating to generate movement, one aligned with the vertical and the other aligned with the horizontal.

Design and implementation of fishery modules in integrated household surveys in developing countries

Fish and other aquatic animals contribute to the food security of citizens of developing countries, both as a source of income and as a component of healthy diets, yet fishing is not currently captured in most integrated household surveys. This sourcebook provides essential technical guidance on the design of statistical modules and questionnaires aimed at collecting fishery data at the household level. Background on the main policies important to the fishery sector, information on the data needed to analyze issues of policy relevance, and methodology on the construction of survey questions to collect necessary data are also provided. The document is organized to provide essential technical guidance on how to design statistical modules and questionnaires aimed at collecting fishery data at the household level. It includes an overview of the main technical and statistical challenges related to sampling fishery-dependent households. The document starts with an introductory section identifying the potential reasons why fisheries and in particular small-scale fisheries have not been adequately included in national statistical systems in a large number of countries. The report then proposes a succinct review of what is known (and what remains unknown) about small-scale fisheries and their contribution to the livelihoods of households in sub-Saharan Africa. It also provides readers with background on the main policies that are important to the fishery sector, information on the data needed to analyze issues of policy relevance, and methodology on the construction of survey questions to collect necessary data.

Lyapunov's stability and operational margin of grid-connected photovoltaic modules

Analyses of photovoltaic power generation based on Lyapunov's theorems are presented. The characteristics of the photovoltaic module and the power conditioning unit are analyzed in order to establish energy functions that assess the stability of solutions and define safe regions of operation. Furthermore, it is shown that grid-connected photovoltaic modules driven at maximum power may become unstable under normal grid transients. In such cases, stability can be maintained by allowing an operational margin defined as the energy difference between the stable and the unstable solutions of the system. Simulations show that modules cope well with grid transients when a sufficiently large margin is used.

Measurement of small-signal and large-signal responses of packaged laser modules at high temperature

In this paper, the pulsed injection method is extended to measure the chip temperature of various packaged laser modules, such as the DFB laser modules, the FP laser modules, and the EML laser modules. An optimal injection condition is obtained by investigating the dependence of the lasing wavelength on the width and period of the injection pulse in a relatively wide temperature range. The small-signal frequency responses and large-signal performances of packaged laser modules at different chip temperature are measured. The adiabatic small-signal modulation characteristics of packaged LD are first extracted. In the large-signal measurement, the effects of chip temperature, bias current and driving signal on the performances of the laser modules are discussed. It has been found that the large-signal performances of the EML modules depend on the different red-shift speeds of the DFB and EAM sections as chip temperature varying, and the optimal characteristics may be achieved at higher temperature.

Extraction and separation of cadmium(II), iron(III), zinc(II), and europium(III) by Cyanex302 solutions using hollow fiber membrane modules

The mass transfer behaviors of Cd(II), Fe(III), Zn(II), and Eu(III) in sulfuric acid solution using microporous hollow fiber membrane (HFM) containing bis(2,4,4-trimethylpentyl)monothiophosphinic acid (commercial name Cyanex302) were investigated in this paper. The experimental results showed that the values of the mass transfer coefficients (K-w) decreased with an increase of H+ concentration and increased with an increase of extractant Cyanex302 concentration. The mass transfer resistance of Eu3+ was the largest because K-w value of Eu3+ was the smallest. The order of mass transfer rate of metal ions at low pH was Cd > Zn > Fe > Eu. Mixtures of Zn2+ and Eu3+ or of Zn2+ and Cd2+ were well separated in a counter-current circulation experiment using two modules connected in series at different initial acidity and concentration ratio. These results indicate that a hollow fiber membrane extractor is capable of separating the mixture compounds by controlling the acidity of the aqueous solution and by exploiting different mass transfer kinetics. The interfacial activity of Cyanex302 in sulfuric acid solution was measured and interfacial parameters were obtained according to Gibbs adsorption equation.

Novel smart modules for imaging, communications, and displays

This dissertation proposes and demonstrates novel smart modules to solve challenging problems in the areas of imaging, communications, and displays. The smartness of the modules is due to their ability to be able to adapt to changes in operating environment and application using programmable devices, specifically, electronically variable focus lenses (ECVFLs) and digital micromirror devices (DMD). The proposed modules include imagers for laser characterization and general purpose imaging which smartly adapt to changes in irradiance, optical wireless communication systems which can adapt to the number of users and to changes in link length, and a smart laser projection display that smartly adjust the pixel size to achieve a high resolution projected image at each screen distance. The first part of the dissertation starts with the proposal of using an ECVFL to create a novel multimode laser beam characterizer for coherent light. This laser beam characterizer uses the ECVFL and a DMD so that no mechanical motion of optical components along the optical axis is required. This reduces the mechanical motion overhead that traditional laser beam characterizers have, making this laser beam characterizer more accurate and reliable. The smart laser beam characterizer is able to account for irradiance fluctuations in the source. Using image processing, the important parameters that describe multimode laser beam propagation have been successfully extracted for a multi-mode laser test source. Specifically, the laser beam analysis parameters measured are the M2 parameter, w0 the minimum beam waist, and zR the Rayleigh range. Next a general purpose incoherent light imager that has a high dynamic range (>100 dB) and automatically adjusts for variations in irradiance in the scene is proposed. Then a data efficient image sensor is demonstrated. The idea of this smart image sensor is to reduce the bandwidth needed for transmitting data from the sensor by only sending the information which is required for the specific application while discarding the unnecessary data. In this case, the imager demonstrated sends only information regarding the boundaries of objects in the image so that after transmission to a remote image viewing location, these boundaries can be used to map out objects in the original image. The second part of the dissertation proposes and demonstrates smart optical communications systems using ECVFLs. This starts with the proposal and demonstration of a zero propagation loss optical wireless link using visible light with experiments covering a 1 to 4 m range. By adjusting the focal length of the ECVFLs for this directed line-of-sight link (LOS) the laser beam propagation parameters are adjusted such that the maximum amount of transmitted optical power is captured by the receiver for each link length. This power budget saving enables a longer achievable link range, a better SNR/BER, or higher power efficiency since more received power means the transmitted power can be reduced. Afterwards, a smart dual mode optical wireless link is proposed and demonstrated using a laser and LED coupled to the ECVFL to provide for the first time features of high bandwidths and wide beam coverage. This optical wireless link combines the capabilities of smart directed LOS link from the previous section with a diffuse optical wireless link, thus achieving high data rates and robustness to blocking. The proposed smart system can switch from LOS mode to Diffuse mode when blocking occurs or operate in both modes simultaneously to accommodate multiple users and operate a high speed link if one of the users requires extra bandwidth. The last part of this section presents the design of fibre optic and free-space optical switches which use ECVFLs to deflect the beams to achieve switching operation. These switching modules can be used in the proposed optical wireless indoor network. The final section of the thesis presents a novel smart laser scanning display. The ECVFL is used to create the smallest beam spot size possible for the system designed at the distance of the screen. The smart laser scanning display increases the spatial resoluti on of the display for any given distance. A basic smart display operation has been tested for red light and a 4X improvement in pixel resolution for the image has been demonstrated.

Display of cell surface sites for fibronectin assembly is modulated by cell adherence to (1)F3 and C-terminal modules of fibronectin.

BACKGROUND: Fibronectin-null cells assemble soluble fibronectin shortly after adherence to a substrate coated with intact fibronectin but not when adherent to the cell-binding domain of fibronectin (modules (7)F3-(10)F3). Interactions of adherent cells with regions of adsorbed fibronectin other than modules (7)F3-(10)F3, therefore, are required for early display of the cell surface sites that initiate and direct fibronectin assembly. METHODOLOGY/PRINCIPAL FINDINGS: To identify these regions, coatings of proteolytically derived or recombinant pieces of fibronectin containing modules in addition to (7)F3-(10)F3 were tested for effects on fibronectin assembly by adherent fibronectin-null fibroblasts. Pieces as large as one comprising modules (2)F3-(14)F3, which include the heparin-binding and cell adhesion domains, were not effective in supporting fibronectin assembly. Addition of module (1)F3 or the C-terminal modules to modules (2)F3-(14)F3 resulted in some activity, and addition of both (1)F3 and the C-terminal modules resulted in a construct, (1)F3-C, that best mimicked the activity of a coating of intact fibronectin. Constructs (1)F3-C V0, (1)F3-C V64, and (1)F3-C Delta(V(15)F3(10)F1) were all able to support fibronectin assembly, suggesting that (1)F3 through (11)F1 and/or (12)F1 were important for activity. Coatings in which the active parts of (1)F3-C were present in different proteins were much less active than intact (1)F3-C. CONCLUSIONS: These results suggest that (1)F3 acts together with C-terminal modules to induce display of fibronectin assembly sites on adherent cells.

Integrated reliability and prognostics prediction methodology for power electronic modules

The article consists of a PowerPoint presentation on integrated reliability and prognostics prediction methodology for power electronic modules. The areas discussed include: power electronics flagship; design for reliability; IGBT module; design for manufacture; power module components; reliability prediction techniques; failure based reliability; etc.

Predictive reliability, prognostics and risk assessment for power modules

This paper describes a framework that is being developed for the prediction and analysis of electronics power module reliability both for qualification testing and in-service lifetime prediction. Physics of failure (PoF) reliability methodology using multi-physics high-fidelity and reduced order computer modelling, as well as numerical optimization techniques, are integrated in a dedicated computer modelling environment to meet the needs of the power module designers and manufacturers as well as end-users for both design and maintenance purposes. An example of lifetime prediction for a power module solder interconnect structure is described. Another example is the lifetime prediction of a power module for a railway traction control application. Also in the paper a combined physics of failure and data trending prognostic methodology for the health monitoring of power modules is discussed.