Black Strings, Black Rings and State-space Manifold

State-space geometry is considered, for diverse three and four parameter non-spherical horizon rotating black brane configurations, in string theory and $M$-theory. We have explicitly examined the case of unit Kaluza-Klein momentum $D_1D_5P$ black strings, circular strings, small black rings and black supertubes. An investigation of the state-space pair correlation functions shows that there exist two classes of brane statistical configurations, {\it viz.}, the first category divulges a degenerate intrinsic equilibrium basis, while the second yields a non-degenerate, curved, intrinsic Riemannian geometry. Specifically, the solutions with finitely many branes expose that the two charged rotating $D_1D_5$ black strings and three charged rotating small black rings consort real degenerate state-space manifolds. Interestingly, arbitrary valued $M_5$-dipole charged rotating circular strings and Maldacena Strominger Witten black rings exhibit non-degenerate, positively curved, comprehensively regular state-space configurations. Furthermore, the state-space geometry of single bubbled rings admits a well-defined, positive definite, everywhere regular and curved intrinsic Riemannian manifold; except for the two finite values of conserved electric charge. We also discuss the implication and potential significance of this work for the physics of black holes in string theory.Comment: 41 pages, Keywords: Rotating Black Branes; Microscopic Configurations; State-space Geometry, PACS numbers: 04.70.-s Physics of black holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamic

On Linear Transmission Systems

This thesis is divided into two parts. Part I analyzes the information rate of single antenna, single carrier linear modulation systems. The information rate of a system is the maximum number of bits that can be transmitted during a channel usage, and is achieved by Gaussian symbols. It depends on the underlying pulse shape in a linear modulated signal and also the signaling rate, the rate at which the Gaussian symbols are transmitted. The object in Part I is to study the impact of both the signaling rate and the pulse shape on the information rate. Part II of the thesis is devoted to multiple antenna systems (MIMO), and more specifically to linear precoders for MIMO channels. Linear precoding is a practical scheme for improving the performance of a MIMO system, and has been studied intensively during the last four decades. In practical applications, the symbols to be transmitted are taken from a discrete alphabet, such as quadrature amplitude modulation (QAM), and it is of interest to find the optimal linear precoder for a certain performance measure of the MIMO channel. The design problem depends on the particular performance measure and the receiver structure. The main difficulty in finding the optimal precoders is the discrete nature of the problem, and mostly suboptimal solutions are proposed. The problem has been well investigated when linear receivers are employed, for which optimal precoders were found for many different performance measures. However, in the case of the optimal maximum likelihood (ML) receiver, only suboptimal constructions have been possible so far. Part II starts by proposing new novel, low complexity, suboptimal precoders, which provide a low bit error rate (BER) at the receiver. Later, an iterative optimization method is developed, which produces precoders improving upon the best known ones in the literature. The resulting precoders turn out to exhibit a certain structure, which is then analyzed and proved to be optimal for large alphabets

On Monte Carlo time-dependent variational principles

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Geometric, Algebraic, and Topological Combinatorics

The 2019 Oberwolfach meeting "Geometric, Algebraic and Topological Combinatorics" was organized by Gil Kalai (Jerusalem), Isabella Novik (Seattle), Francisco Santos (Santander), and Volkmar Welker (Marburg). It covered a wide variety of aspects of Discrete Geometry, Algebraic Combinatorics with geometric flavor, and Topological Combinatorics. Some of the highlights of the conference included (1) Karim Adiprasito presented his very recent proof of the $g$-conjecture for spheres (as a talk and as a "Q\&A" evening session) (2) Federico Ardila gave an overview on "The geometry of matroids", including his recent extension with Denham and Huh of previous work of Adiprasito, Huh and Katz

COMPLEX PULSE FORMING TEACHNIQUE USING AM DETECTOR TYPE CIRCUITRY AND THE APPLICATION OF CDMA TO RFID FOR THE SIMULTANEOUS READING OF MULTIPLE TAGS

A novel complex ultra wideband RF pulse forming technique has been implemented in this research, using the coefficients derived from discrete Fourier transform of a virtual pulse train. Incorporated in this technique is a multiple frequency communication systems designed such that transmitter receiver proximity and the fading effect of the individual frequencies make part of a corresponding modulation technique. A code division multiple access (CDMA) application to RFID to greatly reduce read time, while at the same time eliminating inter tag interference, has been investigated with the analysis of a typical cart aisle scenario. With the current rate of growth of inventory world wide there is a tremendous need for more efficient method of data gathering, data storage, and data retrieval. In this dissertation, the application of the CDMA RFID technology has been analyzed to demonstrate the potentials of integrating the RFID technology to the EPC global numbering system

Philosophical Aspects of Quantum Information Theory

Quantum information theory represents a rich subject of discussion for those interested in the philosphical and foundational issues surrounding quantum mechanics for a simple reason: one can cast its central concerns in terms of a long-familiar question: How does the quantum world differ from the classical one? Moreover, deployment of the concepts of information and computation in novel contexts hints at new (or better) means of understanding quantum mechanics, and perhaps even invites re-assessment of traditional material conceptions of the basic nature of the physical world. In this paper I review some of these philosophical aspects of quantum information theory, begining with an elementary survey of the theory, seeking to highlight some of the principles and heuristics involved. We move on to a discussion of the nature and definition of quantum information and deploy the findings in discussing the puzzles surrounding teleportation. The final two sections discuss, respectively, what one might learn from the development of quantum computation (both about the nature of quantum systems and about the nature of computation) and consider the impact of quantum information theory on the traditional foundational questions of quantum mechanics (treating of the views of Zeilinger, Bub and Fuchs, amongst others).Comment: LaTeX; 55pp; 3 figs. Forthcoming in Rickles (ed.) The Ashgate Companion to the New Philosophy of Physic

Minimum Description Length Model Selection - Problems and Extensions

The thesis treats a number of open problems in Minimum Description Length model selection, especially prediction problems. It is shown how techniques from the "Prediction with Expert Advice" literature can be used to improve model selection performance, which is particularly useful in nonparametric settings