Method for obtaining minimum noise in a general purpose hot wire amplifier

It has been shown that the conventional practice of designing a compensated hot wire amplifier with a fixed ceiling to floor ratio results in considerable and unnecessary increase in noise level at compensation settings other than optimum (which is at the maximum compensation at the highest frequency of interest). The optimum ceiling to floor ratio has been estimated to be between 1.5-2.0 ωmaxM. Application of the above considerations to an amplifier in which the ceiling to floor ratio is optimized at each compensation setting (for a given amplifier band-width), shows the usefulness of the method in improving the signal to noise ratio.

The high speed water tunnel facility at the Indian Institute of Science

The present article about the high speed water tunnel facility at the Indian Institute of Science, Bangalore, provides a general description of the tunnel circuit, and brief reports on the performance of the facility and some typical results from investigations carried out in it. A unique aspect of the facility is that it has a horizontal resorber in the form of a large cylindrical tank located in the lower leg of the circuit. The facility has been used, among other things, for flow visualization studies, and investigations on marine propeller hydrodynamics and “synthetic cavitation”. The last topic has been primarily developed at the Indian Institute of Science and shows considerable promise for basic work in cavitation inception and noise.

Mammalian Mat1 subunit of Transcription Factor IIH in gene-specific and general transcription

All protein-encoding genes in eukaryotes are transcribed into messenger RNA (mRNA) by RNA Polymerase II (RNAP II), whose activity therefore needs to be tightly controlled. An important and only partially understood level of regulation is the multiple phosphorylations of RNAP II large subunit C-terminal domain (CTD). Sequential phosphorylations regulate transcription initiation and elongation, and recruit factors involved in co-transcriptional processing of mRNA. Based largely on studies in yeast models and in vitro, the kinase activity responsible for the phosphorylation of the serine-5 (Ser5) residues of RNAP II CTD has been attributed to the Mat1/Cdk7/CycH trimer as part of Transcription Factor IIH. However, due to the lack of good mammalian genetic models, the roles of both RNAP II Ser5 phosphorylation as well as TFIIH kinase in transcription have provided ambiguous results and the in vivo kinase of Ser5 has remained elusive. The primary objective of this study was to elucidate the role of mammalian TFIIH, and specifically the Mat1 subunit in CTD phosphorylation and general RNAP II-mediated transcription. The approach utilized the Cre-LoxP system to conditionally delete murine Mat1 in cardiomyocytes and hepatocytes in vivo and and in cell culture models. The results identify the TFIIH kinase as the major mammalian Ser5 kinase and demonstrate its requirement for general transcription, noted by the use of nascent mRNA labeling. Also a role for Mat1 in regulating general mRNA turnover was identified, providing a possible rationale for earlier negative findings. A secondary objective was to identify potential gene- and tissue-specific roles of Mat1 and the TFIIH kinase through the use of tissue-specific Mat1 deletion. Mat1 was found to be required for the transcriptional function of PGC-1 in cardiomyocytes. Transriptional activation of lipogenic SREBP1 target genes following Mat1 deletion in hepatocytes revealed a repressive role for Mat1apparently mediated via co-repressor DMAP1 and the DNA methyltransferase Dnmt1. Finally, Mat1 and Cdk7 were also identified as a negative regulators of adipocyte differentiation through the inhibitory phosphorylation of Peroxisome proliferator-activated receptor (PPAR) γ. Together, these results demonstrate gene- and tissue-specific roles for the Mat1 subunit of TFIIH and open up new therapeutic possibilities in the treatment of diseases such as type II diabetes, hepatosteatosis and obesity.

Changing Paradigms in Biblical Criticism : 2 Kings 22:1 23:30 in the Flux of Discourses

The subject and methodology of biblical scholarship has expanded immense-ly during the last few decades. The traditional text-, literary-, source- and form-critical approaches, labeled historical-critical scholarship , have faced the challenge of social sciences. Various new literary, synchronic readings, sometimes characterized with the vague term postmodernism, have in turn challenged historicalcritical, and social-scientific approaches. Widened limits and diverging methodologies have caused a sense of crisis in biblical criticism. This metatheoretical thesis attempts to bridge the gap between philosophical discussion about the basis of biblical criticism and practical academic biblical scholarship. The study attempts to trace those epistemological changes that have produced the wealth of methods and results within biblical criticism. The account of the cult reform of King Josiah of Judah as reported in 2 Kings 22:1 23:30 serves as the case study because of its importance for critical study of the Hebrew Bible. Various scholarly approaches embracing 2 Kings 22:1 23:30 are experimentally arranged around four methodological positions: text, author, reader, and context. The heuristic model is a tentative application of Oliver Jahraus s model of four paradigms in literary theory. The study argues for six theses: 1) Our knowledge of the world is con-structed, fallible and theory-laden. 2) Methodological plurality is the neces-sary result of changes in epistemology and culture in general. 3) Oliver Jahraus s four methodological positions in regard to literature are also an applicable model within biblical criticism to comprehend the methodological plurality embracing the study of the Hebrew Bible. 4) Underlying the methodological discourse embracing biblical criticism is the epistemological ten-sion between the natural sciences and the humanities. 5) Biblical scholars should reconsider and analyze in detail concepts such as author and editor to overcome the dichotomy between the Göttingen and Cross schools. 6) To say something about the historicity of 2 Kings 22:1 23:30 one must bring together disparate elements from various disciplines and, finally, admit that though it may be possible to draw some permanent results, our conclusions often remain provisional.

A tracking-based general framework to image halftoning

Existing approches to digital halftoning of image are based primarily on thresholding. We propose a general framework fot image halftoning whcrc some function uf the output halftone tracks another function of the input gray-tone.This appcoach is shown lo unify most existing algorithms and to provide useful insights. Further, the new intcrpretation allows us to remedy problems in existing aigorithrms such as the error dlffusion, and sohsequently to achieve halftones haavmg superior quality. The proposed method is very general nature is an advantage since it offers a wide choice of three Cilters and a update rule. An intercstmg product of this framework is that equally good, or better, half-tones are possible ro be obtained by thresholding a noise proccess instead of the image itself.

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.

Distributed optimization in power networks and general multi-agent systems

The dissertation studies the general area of complex networked systems that consist of interconnected and active heterogeneous components and usually operate in uncertain environments and with incomplete information. Problems associated with those systems are typically large-scale and computationally intractable, yet they are also very well-structured and have features that can be exploited by appropriate modeling and computational methods. The goal of this thesis is to develop foundational theories and tools to exploit those structures that can lead to computationally-efficient and distributed solutions, and apply them to improve systems operations and architecture.

Specifically, the thesis focuses on two concrete areas. The first one is to design distributed rules to manage distributed energy resources in the power network. The power network is undergoing a fundamental transformation. The future smart grid, especially on the distribution system, will be a large-scale network of distributed energy resources (DERs), each introducing random and rapid fluctuations in power supply, demand, voltage and frequency. These DERs provide a tremendous opportunity for sustainability, efficiency, and power reliability. However, there are daunting technical challenges in managing these DERs and optimizing their operation. The focus of this dissertation is to develop scalable, distributed, and real-time control and optimization to achieve system-wide efficiency, reliability, and robustness for the future power grid. In particular, we will present how to explore the power network structure to design efficient and distributed market and algorithms for the energy management. We will also show how to connect the algorithms with physical dynamics and existing control mechanisms for real-time control in power networks.

The second focus is to develop distributed optimization rules for general multi-agent engineering systems. A central goal in multiagent systems is to design local control laws for the individual agents to ensure that the emergent global behavior is desirable with respect to the given system level objective. Ideally, a system designer seeks to satisfy this goal while conditioning each agent’s control on the least amount of information possible. Our work focused on achieving this goal using the framework of game theory. In particular, we derived a systematic methodology for designing local agent objective functions that guarantees (i) an equivalence between the resulting game-theoretic equilibria and the system level design objective and (ii) that the resulting game possesses an inherent structure that can be exploited for distributed learning, e.g., potential games. The control design can then be completed by applying any distributed learning algorithm that guarantees convergence to the game-theoretic equilibrium. One main advantage of this game theoretic approach is that it provides a hierarchical decomposition between the decomposition of the systemic objective (game design) and the specific local decision rules (distributed learning algorithms). This decomposition provides the system designer with tremendous flexibility to meet the design objectives and constraints inherent in a broad class of multiagent systems. Furthermore, in many settings the resulting controllers will be inherently robust to a host of uncertainties including asynchronous clock rates, delays in information, and component failures.

Where Tori fear to tread : hypermassive neutron star remnants and absolute event horizons Or topics in computational general relativity

Computational general relativity is a field of study which has reached maturity only within the last decade. This thesis details several studies that elucidate phenomena related to the coalescence of compact object binaries. Chapters 2 and 3 recounts work towards developing new analytical tools for visualizing and reasoning about dynamics in strongly curved spacetimes. In both studies, the results employ analogies with the classical theory of electricity and magnitism, first (Ch. 2) in the post-Newtonian approximation to general relativity and then (Ch. 3) in full general relativity though in the absence of matter sources. In Chapter 4, we examine the topological structure of absolute event horizons during binary black hole merger simulations conducted with the SpEC code. Chapter 6 reports on the progress of the SpEC code in simulating the coalescence of neutron star-neutron star binaries, while Chapter 7 tests the effects of various numerical gauge conditions on the robustness of black hole formation from stellar collapse in SpEC. In Chapter 5, we examine the nature of pseudospectral expansions of non-smooth functions motivated by the need to simulate the stellar surface in Chapters 6 and 7. In Chapter 8, we study how thermal effects in the nuclear equation of state effect the equilibria and stability of hypermassive neutron stars. Chapter 9 presents supplements to the work in Chapter 8, including an examination of the stability question raised in Chapter 8 in greater mathematical detail.

Multipole moments in general relativity and dynamical perturbations of black-hole magnetospheres

This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.

In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e⁺e^-) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common rest frame of the freshly created plasma and the rotating magnetic field lines. The magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) Ω_H where m is an integer and Ω_H is the hole's angular velocity.