Remez-type inequalities and their applications

AbstractThe Remez inequality gives a sharp uniform bound on [−1, 1] for real algebraic polynomials p of degree at most n if the Lebesgue measure of the subset of [−1, 1], where |;p|; is at most 1, is known. Remez-type inequalities give bounds for classes of functions on a line segment, on a curve or on a region of the complex plane, given that the modulus of the functions is bounded by 1 on some subset of prescribed measure. This paper offers a survey of the extensive recent research on Remez-type inequalities for polynomials, generalized nonnegative polynomials, exponentials of logarithmic potentials and Müntz polynomials. Remez-type inequalities play a central role in proving other important inequalities for the above classes. The paper illustrates the power of Remez-type inequalities by giving a number of applications

Markov-modulated and feedback fluid queues

In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short introduction on how the stationary distribution for such a model is usually found, as well as a literature overview on Markov-modulated and related uid queues. The rest of the thesis is concerned with �nding stationary distributions for some types of fluid models that have received little or no attention until now. The two main contributions are the following.\ud 1. We focus on models in which the state space of the regulating Markov process is infinitely large, either denumerable or not. Regarding the first type, we mainly look into regulating processes that are of birth-death type. We present procedures to find the stationary distribution, using the theory of orthogonal polynomials. In the nondenumerable case, we look into simple systems of fluid queues, in which one fluid queue regulates the behaviour of another (one example being a fluid tandem queue).\ud 2. We look into models in which the state of the fluid reservoir in quences the behaviour of the regulating process, so that the latter does not constitute a Markov process. We call suchlike systems feedback fluid queues, to emphasize the two-way dependence between fluid reservoir and regulating process

Large scale queueing systems : asymptotics and insights

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 195-203).Parallel server queues are a family of stochastic models useful in a variety of applications, including service systems and telecommunication networks. A particular application that has received considerable attention in recent years is the analysis of call centers. A feature common to these models is the notion of the 'trade-off' between quality and efficiency. It is known that if the underlying system parameters scale together according to a certain 'square-root scaling law', then this trade-off can be precisely quantified, in which case the queue is said to be in the Halfin-Whitt regime. A common approach to understanding this trade-off involves restricting one's models to have exponentially distributed call lengths, and restricting one's analysis to the steady-state behavior of the system. However, these are considered shortcomings of much work in the area. Although several recent works have moved beyond these assumptions, many open questions remain, especially w.r.t. the interplay between the transient and steady-state properties of the relevant models. These questions are the primary focus of this thesis. In the first part of this thesis, we prove several results about the rate of convergence to steady-state for the A/M/rn queue, i.e. n-server queue with exponentially distributed inter-arrival and processing times, in the Halfini-Whitt regime. We identify the limiting rate of convergence to steady-state, discover an asymptotic phase transition that occurs w.r.t. this rate, and prove explicit bounds on the distance to stationarity. The results of the first part of this thesis represent an important step towards understanding how to incorporate transient effects into the analysis of parallel server queues. In the second part of this thesis, we prove several results regarding the steadystate G/G/n queue, i.e. n-server queue with generally distributed inter-arrival and processing times, in the Halfin-Whitt regime. We first prove that under minor technical conditions, the steady-state number of jobs waiting in queue scales like the square root of the number of servers. We then establish bounds for the large deviations behavior of this model, partially resolving a conjecture made by Gamarnik and Momcilovic in [431. We also derive bounds for a related process studied by Reed in [91]. We then derive the first qualitative insights into the steady-state probability that an arriving job must wait for service in the Halfin-Whitt regime, for generally distributed processing times. We partially characterize the behavior of this probability when a certain excess parameter B approaches either 0 or oo. We conclude by studying the large deviations of the number of idle servers, proving that this random variable has a Gaussian-like tail. We prove our main results by combining tools from the theory of stochastic comparison [99] with the theory of heavy-traffic approximations [113]. We compare the system of interest to a 'modified' queue, in which all servers are kept busy at all times by adding artificial arrivals whenever a server would otherwise go idle, and certain servers can permanently break down. We then analyze the modified system using heavy-traffic approximations. The proven bounds hold for all n, have representations as the suprema of certain natural processes, and may prove useful in a variety of settings. The results of the second part of this thesis enhance our understanding of how parallel server queues behave in heavy traffic, when processing times are generally distributed.by David Alan Goldberg.Ph.D

Universal semantic communication

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 325-334).Is meaningful communication possible between two intelligent parties who share no common language or background? We propose that this problem can be rigorously addressed by explicitly focusing on the goals of the communication. We propose a theoretical framework in which we can address when and to what extent such semantic communication is possible. Our starting point is a mathematical definition of a generic goal for communication, that is pursued by agents of bounded computational complexity. We then model a "lack of common language or background" by considering a class of potential partners for communication; in general, this formalism is rich enough to handle varying degrees of common language and backgrounds, but the complete lack of knowledge is modeled by simply considering the class of all partners with which some agent of similar power could achieve our goal. In this formalism, we will find that for many goals (but not all), communication without any common language or background is possible. We call the strategies for achieving goals without relying on such background universal protocols. The main intermediate notions introduced by our theory are formal notions of feedback that we call sensing. We show that sensing captures the essence of whether or not reliable universal protocols can be constructed in many natural settings of interest: we find that across settings, sensing is almost always sufficient, usually necessary, and generally a useful design principle for the construction of universal protocols. We support this last point by developing a number of examples of protocols for specific goals. Notably, we show that universal delegation of computation from a space-efficient client to a general-purpose server is possible, and we show how a variant of TCP can allow end-users on a packet network to automatically adapt to small changes in the packet format (e.g., changes in IP). The latter example above alludes to our main motivation for considering such problems, which is to develop techniques for modeling and constructing computer systems that do not require that their components strictly adhere to protocols: said differently, we hope to be able to design components that function properly with a sufficiently wide range of other components to permit a rich space of "backwards-compatible" designs for those components. We expect that in the long run, this paradigm will lead to simpler systems because "backwards compatibility" is no longer such a severe constraint, and we expect it to lead to more robust systems, partially because the components should be simpler, and partially because such components are inherently robust to deviations from any fixed protocol. Unfortunately, we find that the techniques for communication under the complete absence of any common background suffer from overhead that is too severe for such practical purposes, so we consider two natural approaches for introducing some assumed common background between components while retaining some nontrivial amount of flexibility. The first approach supposes that the designer of a component has some "belief" about what protocols would be "natural" to use to interact with other components; we show that, given sensing and some sufficient "agreement" between the beliefs of the designers of two components, the components can be made universal with some relatively modest overhead. The second approach supposes that the protocols are taken from some restricted class of functions, and we will see that for certain classes of functions and simple goals, efficient universal protocols can again be constructed from sensing. Actually, we show more: the special case of our model described in the second approach above corresponds precisely to the well-known model of mistake-bounded on-line learning first studied by Barzdirs and Frievalds, and later considered in more depth by Littlestone. This connection provides a reasonably complete picture of the conditions under which we can apply the second approach. Furthermore, it also seems that the first approach is closely related to the problem of designing good user interfaces in Human-Computer Interaction. We conclude by briefly sketching the connection, and suggest that further development of this connection may be a potentially fruitful direction for future work.by Brendan Juba.Ph.D

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion

2007 Calendar - Undergraduate

816pp. Includes an Index of Academic Programs and an Index of Courses.Contains the academic program rules and syllabuses for all University of Adelaide undergraduate programs in 2007