This thesis considers the problem of detecting and estimating highly oscillatory signals from noisy measurements. These signals are often referred to as chirps in the literature; they are found everywhere in nature, and frequently arise in scientific and engineering problems. Mathematically, they can be written in the general form A(t) exp(ilambda varphi(t)), where lambda is a large constant base frequency, the phase varphi(t) is time-varying, and the envelope A(t) is slowly varying. Given a sequence of noisy measurements, we study two problems seperately: 1) the problem of testing whether or not there is a chirp hidden in the noisy data, and 2) the problem of estimating this chirp from the data.
\r\n\r\nThis thesis introduces novel, flexible and practical strategies for addressing these important nonparametric statistical problems. The main idea is to calculate correlations of the data with a rich family of local templates in a first step, the multiscale chirplets, and in a second step, search for meaningful aggregations or chains of chirplets which provide a good global fit to the data. From a physical viewpoint, these chains correspond to realistic signals since they model arbitrary chirps. From an algorithmic viewpoint, these chains are identified as paths in a convenient graph. The key point is that this important underlying graph structure allows to unleash very effective algorithms such as network flow algorithms for finding those chains which optimize a near optimal trade-off between goodness of fit and complexity.
\r\n\r\nOur estimation procedures provide provably near optimal performance over a wide range of chirps and numerical experiments show that both our detection and estimation procedures perform exceptionally well over a broad class of chirps. This thesis also introduces general strategies for extracting signals of unknown duration in long streams of data when we have no idea where these signals may be. The approach is leveraging testing methods designed to detect the presence of signals with known time support.
\r\n\r\nUnderlying our methods is a general abstraction which postulates an abstract statistical problem of detecting paths in graphs which have random variables attached to their vertices. The formulation of this problem was inspired by our chirp detection methods and is of great independent interest.
", "doi": "10.7907/SAEK-MV13", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:2025", "collection": "thesis", "collection_id": "2025", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05242007-154102", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 4630109, "license": "other", "mime_type": "application/pdf", "url": "/2025/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Essays on Causal Inference and Political Representation", "author": [ { "family_name": "Bailey", "given_name": "Delia Ruth Grigg", "clpid": "Bailey-Delia-Ruth-Grigg" } ], "thesis_advisor": [ { "family_name": "Katz", "given_name": "Jonathan N.", "orcid": "0000-0002-5287-3503", "clpid": "Katz-J-N" }, { "family_name": "Alvarez", "given_name": "R. Michael", "orcid": "0000-0002-8113-4451", "clpid": "Alvarez-R-M" } ], "thesis_committee": [ { "family_name": "Katz", "given_name": "Jonathan N.", "orcid": "0000-0002-5287-3503", "clpid": "Katz-J-N" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Alvarez", "given_name": "R. Michael", "orcid": "0000-0002-8113-4451", "clpid": "Alvarez-R-M" }, { "family_name": "Sherman", "given_name": "Robert P.", "clpid": "Sherman-R-P" } ], "local_group": [ { "literal": "div_hss" } ], "abstract": "I present three political science examples of observational studies where modern causal inferences techniques are used to improve upon previous estimates. Difference-in-differences, fixed effects estimators, and a propensity score matching model are used to demonstrate model dependence in previous studies of the impact of voting technology on residual vote rates. Measuring the incumbency advantage serves as an example of when the assumptions of matching methods fail, and given the data, a linear model is most appropriate. The impact of voter identification on turnout is properly modeled in two ways: first, a multilevel logistic regression is used to appropriately model how state and individual covariates, and their interactions, affect the decision to participate; second, a Bayesian shrinkage estimator is used to properly model the ordinal nature of the voter identification treatment variable. In each essay, the benefit of using causal inference techniques to more efficiently estimate quantities of interest in questions of political representation and policy outcomes is demonstrated.", "doi": "10.7907/56R7-4M29", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:2145", "collection": "thesis", "collection_id": "2145", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05272005-110242", "primary_object_url": { "basename": "Thesis.pdf", "content": "final", "filesize": 467398, "license": "other", "mime_type": "application/pdf", "url": "/2145/1/Thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Zeros of Random Orthogonal Polynomials on the Unit Circle", "author": [ { "family_name": "Stoiciu", "given_name": "Mihai Valentin", "clpid": "Stoiciu-Mihai-Valentin" } ], "thesis_advisor": [ { "family_name": "Simon", "given_name": "Barry M.", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" } ], "thesis_committee": [ { "family_name": "Simon", "given_name": "Barry M.", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" }, { "family_name": "Damanik", "given_name": "David", "clpid": "Damanik-D" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Killip", "given_name": "Rowan", "clpid": "Killip-R" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We study the statistical distribution of the zeros of some classes of random orthogonal polynomials on the unit circle. For each n we take the random Verblunsky coefficients alpha_0, alpha_1,...,alpha_{n-2} to be independent identically distributed random variables uniformly distributed in a disk of radius r < 1 and alpha_{n-1} to be another random variable independent of the previous ones and distributed uniformly on the unit circle. These coefficients define a sequence of random paraorthogonal polynomials Phi_n. For any n, the zeros of Phi_n are n random points on the unit circle.\r\n\r\nWe prove that, for any point p on the unit circle, the distribution of the zeros of Phi_n in intervals of size O(1/n) near p is the same as the distribution of n independent random points uniformly distributed on the unit circle (i.e., Poisson). Therefore, for large n, there is no local correlation between the zeros of the considered random paraorthogonal polynomials.\r\n\r\nThe same result holds when we take alpha_0, alpha_1,...,alpha_{n-2} to be independent identically distributed random variables uniformly distributed in a circle of radius r < 1 and alpha_{n-1} to be another random variable independent of the previous ones and distributed uniformly on the unit circle.", "doi": "10.7907/T2KB-RH17", "publication_date": "2005", "thesis_type": "phd", "thesis_year": "2005" }, { "id": "thesis:1891", "collection": "thesis", "collection_id": "1891", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05202004-133633", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 680638, "license": "other", "mime_type": "application/pdf", "url": "/1891/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Asymptotically Optimal Multistage Hypothesis Tests", "author": [ { "family_name": "Bartroff", "given_name": "Jay L.", "clpid": "Bartroff-Jay-L" } ], "thesis_advisor": [ { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" } ], "thesis_committee": [ { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Wales", "given_name": "David B.", "clpid": "Wales-D-B" }, { "family_name": "Candes", "given_name": "Emmanuel J.", "clpid": "Candes-E-J" }, { "family_name": "Sherman", "given_name": "Robert P.", "clpid": "Sherman-R-P" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis investigates variable stage size multistage hypothesis testing in three different contexts, each building on the previous.
\r\n\r\nWe first consider the problem of sampling a random process in stages until it crosses a predetermined boundary at the end of a stage -- first for Brownian motion and later for a sum of i.i.d. random variables. A multistage sampling procedure is derived and its properties are shown to be not only sufficient but also necessary for asymptotic optimality as the distance to the boundary goes to infinity.
\r\n\r\nNext we consider multistage testing of two simple hypotheses about the unknown parameter of an exponential family. Tests are derived, based on optimal multistage sampling procedures, and are shown to be asymptotically optimal.
\r\n\r\nFinally we consider multistage testing of two separated composite hypotheses about the unknown parameter of an exponential family. Tests are derived, based on optimal multistage tests of simple hypotheses, and are shown to be asymptotically optimal. Numerical simulations show marked improvement over group sequential sampling in both the simple and composite hypotheses contexts.
", "doi": "10.7907/GJAW-6P82", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:1224", "collection": "thesis", "collection_id": "1224", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03312004-100014", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 566619, "license": "other", "mime_type": "application/pdf", "url": "/1224/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Eigenvalue Inequalities in Quantum Information Processing", "author": [ { "family_name": "Daftuar", "given_name": "Sumit Kumar", "clpid": "Daftuar-Sumit-Kumar" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Damanik", "given_name": "David", "clpid": "Damanik-D" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis develops restrictions governing how a quantum system, jointly held by two parties, can be altered by the local actions of those parties, under assumptions about how they may communicate. These restrictions are expressed as constraints involving the eigenvalues of the density matrix of one of the parties. The thesis is divided into two parts.
\r\n\r\nPart I (Chapters 1-4) explores what is possible if the two parties may use only classical communication. A well-known result by M. Nielsen says that this is intimately connected to the mathematical notion of majorization. If entanglement catalysis is permitted, then the relevant notion is an extension of majorization known as the trumping relation. In Part I, we study the structure of the trumping relation.
\r\n\r\nPart II (Chapters 5-9) considers the question of how a state can change as a result of quantum communication between the parties; i.e., one party sends the other a portion of the jointly held quantum system. Given the spectrum of the initial state, it turns out that the possible spectra of the final state are given by the solutions to linear inequalities. We develop a method for deriving these inequalities, using a variational principle. In order to apply this principle, we need to know when certain subvarieties of a Grassmannian variety intersect, which can be regarded as a problem in Grassmannian cohomology. We discuss this cohomology and derive the conditions for nontrivial intersections. Finally, we illustrate how these intersections give rise to the desired inequalities.
", "doi": "10.7907/7097-1657", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:2231", "collection": "thesis", "collection_id": "2231", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05292003-133431", "primary_object_url": { "basename": "mei_thesis.pdf", "content": "final", "filesize": 411808, "license": "other", "mime_type": "application/pdf", "url": "/2231/1/mei_thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Asymptotically Optimal Methods for Sequential Change-Point Detection", "author": [ { "family_name": "Mei", "given_name": "Yajun", "orcid": "0000-0002-1015-990X", "clpid": "Mei-Yajun" } ], "thesis_advisor": [ { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" } ], "thesis_committee": [ { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Wales", "given_name": "David B.", "clpid": "Wales-D-B" }, { "family_name": "Candes", "given_name": "Emmanuel J.", "clpid": "Candes-E-J" }, { "family_name": "Sherman", "given_name": "Robert P.", "clpid": "Sherman-R-P" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis studies sequential change-point detection problems in different contexts. Our main results are as follows:
\r\n\r\n- We present a new formulation of the problem of detecting a change of the parameter value in a one-parameter exponential family. Asymptotically optimal procedures are obtained.
\r\n\r\n- We propose a new and useful definition of \"asymptotically optimal to first-order\" procedures in change-point problems when both the pre-change distribution and the post-change distribution involve unknown parameters. In a general setting, we define such procedures and prove that they are asymptotically optimal.
\r\n\r\n- We develop asymptotic theory for sequential hypothesis testing and change-point problems in decentralized decision systems and prove the asymptotic optimality of our proposed procedures under certain conditions.
\r\n\r\n- We show that a published proof that the so-called modified Shiryayev-Roberts procedure is exactly optimal is incorrect. We also clarify the issues involved by both mathematical arguments and a simulation study. The correctness of the theorem remains in doubt.
\r\n\r\n- We construct a simple counterexample to a conjecture of Pollak that states that certain procedures based on likelihood ratios are asymptotically optimal in change-point problems even for dependent observations.
", "doi": "10.7907/PY76-DM19", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:2876", "collection": "thesis", "collection_id": "2876", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-07142002-210918", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 377061, "license": "other", "mime_type": "application/pdf", "url": "/2876/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Convex Cone Conditions on the Structure of Designs", "author": [ { "family_name": "Dukes", "given_name": "Peter James", "orcid": "0000-0002-5617-083X", "clpid": "Dukes-Peter-James" } ], "thesis_advisor": [ { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" } ], "thesis_committee": [ { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" }, { "family_name": "Wales", "given_name": "David B.", "clpid": "Wales-D-B" }, { "family_name": "Ramakrishnan", "given_name": "Dinakar", "clpid": "Ramakrishnan-D" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Various known and original inequalities concerning the structure of combinatorial designs are established using polyhedral cones generated by incidence matrices. This work begins by giving definitions and elementary facts concerning t-designs. A connection with the incidence matrix W of t-subsets versus k-subsets of a finite set is mentioned. The opening chapter also discusses relevant facts about convex geometry (in particular, the Farkas Lemma) and presents an arsenal of binomial identities. The purpose of Chapter 2 is to study the cone generated by columns of W, viewed as an increasing union of cones with certain invariant automorphisms. The two subsequent chapters derive inequalities on block density and intersection patterns in t-designs. Chapter 5 outlines generalizations of W which correspond to hypergraph designs and poset designs. To conclude, an easy consequence of this theory for orthogonal arrays is used in a computing application which generalizes the method of two-point based sampling", "doi": "10.7907/V7F7-FQ47", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:6783", "collection": "thesis", "collection_id": "6783", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01262012-103823681", "primary_object_url": { "basename": "Pavelich_j_2001.pdf", "content": "final", "filesize": 25118003, "license": "other", "mime_type": "application/pdf", "url": "/6783/1/Pavelich_j_2001.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Commuting Equivalence Relations and Scales on Differentiable Functions", "author": [ { "family_name": "Pavelich", "given_name": "Janet Mary", "clpid": "Pavelich-Janet-Mary" } ], "thesis_advisor": [ { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Kechris", "given_name": "Alexander S.", "clpid": "Kechris-A-S" } ], "thesis_committee": [ { "family_name": "Kechris", "given_name": "Alexander S.", "clpid": "Kechris-A-S" }, { "family_name": "Clemens", "given_name": "John D.", "clpid": "Clemens-J-D" }, { "family_name": "Luxemburg", "given_name": "W. A. J.", "clpid": "Luxemburg-W-A-J" }, { "family_name": "Ramakrishnan", "given_name": "Dinakar", "orcid": "0000-0002-0159-087X", "clpid": "Ramakrishnan-D" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This work consists of two independent chapters:
\r\n\r\nThe first is a study of commuting countable Borel equivalence relations, where two equivalence relations R and 5 are said to commute if, as binary relations, they commute with respect to the composition operator , i.e., R \u25e6 S = S \u25e6 R. The primary problem considered is, to what extent does the complexity of E = R V S depend on the complexity of R and S , if R and S commute? This is considered both in the case where the underlying space supports no E-invariant probability measure, and the case where it supports at least one such measure. In the first case, the answer is 'not very much': any such aperiodic equivalence relation E can be written as R V S, where Rand 5 are smooth aperiodic. In the second case, we frame our study within the context of costs, a system of invariants for countable Borel equivalence relations with invariant probability measures, developed by G. Levitt [12] and D. Gaboriau [5]. One aspect of costs which is not well understood is the extent to which 'commutativity' within an equivalence relation (in a more general sense than the definition given above) trivializes its cost. We have shown that, under certain conditions, this is in fact the case. One of the consequences of these investigations is a new, elementary proof of the fact the group SL_2 (Z[^1_2]) is anti-treeable.
\r\n\r\nThe second chapter is motivated by the well known theorem of descriptive set theory that every \u041f^1_1 subset of a Polish (separable, completely metrizable) space admits a \u041f^1_1 scale. We construct a \u041f^1_1 scale on the set of differentiable functions with domain [0,1], which is a \u041f^1_1 subset of the Polish space C([0,1]) . This construction is based on the \u041f^1_1 rank of differentiable functions given by Kechris and Woodin in [4], and, like this rank, is meant to reflect the intrinsic nature of DIFF, and so give a 'natural ' criterion for determining whether the uniform limit of differentiable functions is itself differentiable. We then attempt to further analyze this 'scale criterion' for a sequence of differentiable functions (\u0192_n) by comparing it to the criterion that the sequence (\u0192'_n) converges.
\r\n", "doi": "10.7907/RHBN-ZN06", "publication_date": "2002", "thesis_type": "phd", "thesis_year": "2002" }, { "id": "thesis:5326", "collection": "thesis", "collection_id": "5326", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10232009-113530661", "type": "thesis", "title": "Boundaries of Smooth Sets and Singular Sets of Blaschke Products in the Little Bloch Class", "author": [ { "family_name": "Hungerford", "given_name": "Gregory Jude", "clpid": "Hungerford-Gregory-Jude" } ], "thesis_advisor": [ { "family_name": "Luxemburg", "given_name": "W. A. J.", "clpid": "Luxemburg-W-A-J" }, { "family_name": "Wolff", "given_name": "Thomas H.", "clpid": "Wolff-T-H" } ], "thesis_committee": [ { "family_name": "Kechris", "given_name": "Alexander S.", "clpid": "Kechris-A-S" }, { "family_name": "Luxemburg", "given_name": "W. A. J.", "clpid": "Luxemburg-W-A-J" }, { "family_name": "Wales", "given_name": "David B.", "clpid": "Wales-D-B" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Wolff", "given_name": "Thomas H.", "clpid": "Wolff-T-H" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "A subset of R is called smooth if the integral of its characteristic function is smooth in the sense defined by Zygmund. It is shown that such a set is either trivial or its boundary has Hausdorff dimension 1. Sets are constructed here which are as close to smooth as one likes but whose boundaries do not have dimension 1.
\r\n\r\nIt was conjectured by T. Wolff that if B is Blaschke product in the Little Bloch class, its zeroes accumulate to a set of dimension 1. This conjecture is proven here.
\r\n", "doi": "10.7907/ehgq-c421", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:823", "collection": "thesis", "collection_id": "823", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03012008-131442", "primary_object_url": { "basename": "Doganata_yn_1987.pdf", "content": "final", "filesize": 4560178, "license": "other", "mime_type": "application/pdf", "url": "/823/1/Doganata_yn_1987.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Analysis of Traffic Problems of Integrated Networks", "author": [ { "family_name": "Do\u011fanata", "given_name": "Yurdaer Nezihi", "clpid": "Do\u011fanata-Yurdaer-Nezihi" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A new approach to the analysis of Markovian queueing networks is developed and applied to traffic problems of voice-data integration networks and trunked mobile radio networks. This approach is shown to be computationally much less complex for large systems compared to previous work.
\r\n\r\nIn the integrated networks we consider, two classes of users share the system facilities. If all the servers are busy, the first class of users are queued, but the second class of users are blocked and cleared from the system. The performance objective of such an integrated network is to trade the time delay performance of the first class of users against the blockage performance of the second class of users to keep the grade of service as high as possible for both classes of traffic.
\r\n\r\nThe key-state approach introduced in this thesis is what makes the analysis of the corresponding Markovian queueing network model of these integrated networks computationally less complex than that of previous work. The performance of integrated networks is investigated under several control strategies and new exact closed-form expressions are obtained for the equilibrium probabilities of the corresponding Markovian models. The results are extended to a more general Markovian process where a bulk of arrivals and departures are allowed.
\r\n\r\nThe key-state approach is expected to become a standard tool for analyzing large queueing networks such as will arise when Integrated Services Digital Networks (ISDN) become widely deployed in the next five years.
", "doi": "10.7907/d844-3g40", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:11378", "collection": "thesis", "collection_id": "11378", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02012019-085357846", "type": "thesis", "title": "Stochastic Analysis of the Seismic Response of Secondary Systems", "author": [ { "family_name": "Smith", "given_name": "Kenneth Scott", "clpid": "Smith-Kenneth-Scott" } ], "thesis_advisor": [ { "family_name": "Iwan", "given_name": "Wilfred D.", "clpid": "Iwan-W-D" } ], "thesis_committee": [ { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Kanamori", "given_name": "Hiroo", "orcid": "0000-0001-8219-9428", "clpid": "Kanamori-H" }, { "family_name": "Knowles", "given_name": "James K.", "clpid": "Knowles-J-K" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Iwan", "given_name": "Wilfred D.", "clpid": "Iwan-W-D" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis is concerned with the earthquake response of light equipment in structures. The motion of the ground during an earthquake is represented as a stochastic process in order to reflect uncertainty in the prediction of such motion. A number of different stochastic earthquake models are considered, and analytical methods are described for these models.
\r\n\r\nThe response of equipment in a structure to stochastic ground motion is derived, in the case of a single-degree-of-freedom secondary system (equipment) attached to a single-degree-of-freedom structure. The distribution of the envelope of the secondary system displacement is obtained for general transient ground motion. Closed form expressions are computed for the transient response to stationary ground motion.
\r\n\r\nThe effect of the interaction of equipment with the structure is described by the introduction of an equivalent non-interacting system. However, this method applies only to classically damped systems.
\r\n\r\nThe results are applied in a simple way to the problem of the computation of floor spectra. It is found that the ground spectrum is amplified in a simple way, except near resonance, where special considerations must be addressed.
", "doi": "10.7907/w4cj-w767", "publication_date": "1985", "thesis_type": "phd", "thesis_year": "1985" }, { "id": "thesis:11310", "collection": "thesis", "collection_id": "11310", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:12122018-111430579", "primary_object_url": { "basename": "Blaum_M_1985.pdf", "content": "final", "filesize": 18560893, "license": "other", "mime_type": "application/pdf", "url": "/11310/1/Blaum_M_1985.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Error-Correcting Codes for Computer Memories", "author": [ { "family_name": "Blaum", "given_name": "Mario", "clpid": "Blaum-Mario" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" }, { "family_name": "Wales", "given_name": "David B.", "clpid": "Wales-D-B" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "van Tilborg", "given_name": "Henk C.A.", "clpid": "van-Tilborg-H-C-A" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis is divided into four independent chapters and two appendices.
\r\n\r\nChapter I deals with the following generalization of the birthday surprise problem: how many people we need to interview on the average until either r birthdays occur k times each or one birthday occurs k + 1 times. If r = 1, we obtain the usual \"birthday surprise\" number. We verify that our formula generalizes previous known results. We give asymptotic estimates for the birthday surprise number using a theorem proved in appendix I.
\r\n\r\nIn chapter II, we present accurate and easily evaluated estimates for the average lifetime of a semiconductor RAM memory protected by a single error correcting, doubly error detecting (SEC-DED) code. This problem is somehow related to the one in chapter I. As an application, we give an analysis of the benefits of soft error \"scrubbing\" when both hard and soft errors are present. We also discuss two methods for increasing the lifetime of a computer memory: adding s rows of spare chips and implementing 2-ECC. We close the chapter by comparing the two methods.
\r\n\r\nIn chapter III, we describe a class of burst error correcting array codes. We prove the fundamental properties of these codes.
\r\n\r\nPatel and Hong have constructed a code that can correct any track error or two track erasures in a 9-track magnetic tape. In chapter IV, we extend the construction to codes that can correct higher numbers of track errors and erasures. The result is a new family of codes, the B(n,m)-codes.
\r\n\r\nIn appendix I, we prove an important theorem used for asymptotic estimates of integrals. This theorem is used in chapters I and II.
", "doi": "10.7907/bdd9-pr94", "publication_date": "1985", "thesis_type": "phd", "thesis_year": "1985" }, { "id": "thesis:10020", "collection": "thesis", "collection_id": "10020", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01232017-115539334", "primary_object_url": { "basename": "Crawshaw_M_1985.pdf", "content": "final", "filesize": 10835351, "license": "other", "mime_type": "application/pdf", "url": "/10020/1/Crawshaw_M_1985.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Explicit Formulas for the Jump of Q-Degrees", "author": [ { "family_name": "Crawshaw", "given_name": "Mark", "clpid": "Crawshaw-Mark" } ], "thesis_advisor": [ { "family_name": "Kechris", "given_name": "Alexander S.", "orcid": "0000-0002-2226-0423", "clpid": "Kechris-A-S" } ], "thesis_committee": [ { "family_name": "Becker", "given_name": "Howard Starr", "clpid": "Becker-Howard-Starr" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Luxemburg", "given_name": "W. A. J.", "clpid": "Luxemburg-W-A-J" }, { "family_name": "Wales", "given_name": "David B.", "clpid": "Wales-D-B" }, { "family_name": "Kechris", "given_name": "Alexander S.", "orcid": "0000-0002-2226-0423", "clpid": "Kechris-A-S" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In the context of the axiom of projective determinacy, Q-degrees have been proposed as the appropriate generalisations of the hyperdegrees to all the odd levels of the projective hierarchy. In chapter one we briefly review the basics of Q-theory.
\r\n\r\nIn the second chapter we characterise the Q-jump operation in terms of certain two-person games and derive an explicit formula for the Q-jump. This makes clear the similarities between the Q-degrees and the constructibility degrees, the Q-jump operation being a natural generalisation of the sharp operation.
\r\n\r\nIn chapter three we mix our earlier results with some\r\nforcing techniques to get a new proof of the jump inversion theorem for Q-degrees. We also extend some results about minimal covers in hyperdegrees to the Q-degrees. Many of our methods are immediately applicable to the constructible degrees and provide new proofs of old results.
", "doi": "10.7907/b0x4-c027", "publication_date": "1985", "thesis_type": "phd", "thesis_year": "1985" }, { "id": "thesis:11254", "collection": "thesis", "collection_id": "11254", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10302018-173228813", "type": "thesis", "title": "Topics in Linear Spaces and Projective Planes", "author": [ { "family_name": "Fowler", "given_name": "Joel Christopher", "clpid": "Fowler-Joel-Christopher" } ], "thesis_advisor": [ { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" } ], "thesis_committee": [ { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" }, { "family_name": "Ryser", "given_name": "Herbert J.", "clpid": "Ryser-H-J" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Dean", "given_name": "Richard A.", "clpid": "Dean-Richard-A" }, { "family_name": "Wales", "given_name": "David B.", "clpid": "Wales-D-B" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "A linear space is an incidence structure of points and lines such that every pair of points is contained in a unique line. In the first two chapters of this thesis results are presented linking structural properties to arithmetic conditions on the number of points and lines. We provide a short new proof of Jim Totten's classification of all linear spaces for which the difference between the number of points and lines does not exceed the square root of the number of points. We extend this classification when the number of points is of a certain form. Also in these chapters we have similar classification results for more specialized finite geometrical structures such as (r,l)-designs.
\r\n\r\nThe last chapter is devoted to (k,u)-arcs. A (k,u)-arc in a finite projective plane is a set of k points meeting no line of the plane in more than u points. Elementary bounds upon k can be established and we call an arc with this maximum number of points perfect. An arc not properly contained in any other is called complete. Several constructions are given for both perfect and complete arcs. The major results of this chapter concern the uniqueness of completions of a (k,u)-arc to a perfect arc.
", "doi": "10.7907/d8gp-ka37", "publication_date": "1984", "thesis_type": "phd", "thesis_year": "1984" }, { "id": "thesis:11257", "collection": "thesis", "collection_id": "11257", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10302018-181155071", "type": "thesis", "title": "Norm Constant Holomorphic Functions on Banach Spaces", "author": [ { "family_name": "Mikoli\u010d-Torreira", "given_name": "Igor", "orcid": "0000-0002-2879-4485", "clpid": "Mikoli\u010d-Torreira-Igor" } ], "thesis_advisor": [ { "family_name": "De Prima", "given_name": "Charles R.", "clpid": "De-Prima-C-R" } ], "thesis_committee": [ { "family_name": "Dean", "given_name": "Richard A.", "clpid": "Dean-Richard-A" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Luxemburg", "given_name": "W. A. J.", "clpid": "Luxemburg-W-A-J" }, { "family_name": "De Prima", "given_name": "Charles R.", "clpid": "De-Prima-C-R" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Holomorphic functions (or maps) have been defined between Banach spaces by the use of a Taylor expansion involving Frechet derivatives. When the Banach spaces in question coincide with \u2112(\u210b), the space of linear operators over a Hilbert space \u210b. the set of holomorphic functions includes those arising from the Dunford functional calculus, but is certainly not limited to these. The holomorphic functions between Banach spaces share many of the properties of ordinary holomorphic functions from the complex plane \u2104 into itself. However, in many aspects they behave differently. For example, the maximum modulus theorem implies that an ordinary holomorphic function with constant modulus must be a constant function. This is no longer true even for holomorphic functions of one complex variable taking values in a Banach space. In fact, the Thorp-Whitley Theorem states that if D is a domain in \u2104, Y a Banach space, and F:D \u2192 Y holomorphic with ||F(\u03b6)|| = 1 on D, then F is a constant function if its range contains a complex extreme point of the unit ball of Y.
\r\n\r\nIt is natural to ask which holomorphic functions between Banach spaces have constant norm. For the case where F:D \u2282 \u2104 \u2192 Y, the problem was solved by Globevnik, who also specialized the result to the case F:D \u2282 \u2104 \u2192 \u2112(\u210b). In addition, he determined under which conditions F might have constant norm in some norm equivalent to the given norm. This thesis solves the problem in the full case where F is now a holomorphic function between two Banach spaces. The following theorem analogous to Globevnik's is proved:
\r\n\r\nTheorem. Let \u03c7, Y be Banach spaces, D a domain in \u03c7 and F:D \u2192 Y holomorphic. Then ||F(x)|| will be constant for all x \u03f5D if and only if
\r\n\r\n(i) The subspace \u03b5(F(x)) is independent of x \u03f5D, i.e., \u03b5(F(x)) = \u03b5 for all x \u03f5D,
\r\n\r\n(ii) F(x) - F(y) \u03f5\u03b5 for all x, y \u03f5D, where for u \u03f5 Y the set \u03b5(u) is defined to be \u03b5(u) = {v \u03f5 Y|\u018er > 0 such that ||u+ \u03b6v|| \u2264 ||u|| for all \u03b6 \u03f5 \u2104, |\u03b6| \u2264 r}.
\r\n\r\nAn immediate consequence is that the Thorp-Whitley Theorem also holds in this generality, that is, when F is a function between arbitrary Banach spaces.
\r\n\r\nWhen this theorem is applied to the case \u03c7 = Y = \u2112(\u210b) a simplified criterion is obtained. The norm constant functions are precisely those annihilated by certain projection operators on \u210b. As a corollary to this it is shown that the only holomorphic functions arising from the Dunford calculus with constant norm are the constant functions. In contrast to the above theorem, it is also shown that any holomorphic function F:D \u2282 \u2112(\u210b) \u2192 \u2112(\u210b) with Re(F) = 0 on D must be a constant function. A theorem analogous to Globevnik's for deciding when a function F:D \u2282 \u03c7 \u2192 Y can be norm constant under some equivalent norm is also obtained.
", "doi": "10.7907/smv6-ca65", "publication_date": "1984", "thesis_type": "phd", "thesis_year": "1984" }, { "id": "thesis:10101", "collection": "thesis", "collection_id": "10101", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03232017-113645091", "primary_object_url": { "basename": "HART_DR_1983.pdf", "content": "final", "filesize": 25814997, "license": "other", "mime_type": "application/pdf", "url": "/10101/1/HART_DR_1983.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Disjointness Preserving Operators", "author": [ { "family_name": "Hart", "given_name": "Dean Robert", "clpid": "Hart-Dean-Robert" } ], "thesis_advisor": [ { "family_name": "Luxemburg", "given_name": "W. A. J.", "clpid": "Luxemburg-W-A-J" } ], "thesis_committee": [ { "family_name": "Luxemburg", "given_name": "W. A. J.", "clpid": "Luxemburg-W-A-J" }, { "family_name": "De Prima", "given_name": "Charles R.", "clpid": "De-Prima-C-R" }, { "family_name": "de Pagter", "given_name": "Bernardus", "clpid": "de-Pagter-Benardus" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Ryser", "given_name": "Herbert J.", "clpid": "Ryser-H-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Let E and F be Archimedian Riesz spaces. A linear operator T : E \u2192 F is called disjointness preserving if |f| \u2227 |g| = 0 in E implies |Tf| \u2227 |Tg| = 0 in F. An order continuous disjointness preserving operator T : E \u2192 E is called bi-disjointness preserving if the order closure of |T|E is an ideal in E. If the order dual of E separates the points of E, then every order continuous disjointness preserving operator whose adjoint is disjointness preserving is bi-disjointness preserving. If E is in addition Dedekind complete, then the converse holds.
\r\n\r\nDEFINITION. Let T : E \u2192 E be a bi-disjointness preserving operator. We say that T is:
\r\n\r\n(i) quasi-invertible if T is injective and {TE}dd = E.
\r\n\r\n(ii) of forward shift type if T is injective and n=1\u2229\u221e{TnE}dd = {0}.
\r\n\r\n(iii) of backward shift type if n=1\u2228\u221e Ker Tn = E and{TE}dd = E.
\r\n\r\n(iv) hypernilpotent if n=1\u2228\u221e Ker Tn = E and n=1\u2229\u221e {TnE}dd = {0}.
\r\n\r\nThe supremum in (iii) and (iv) is taken in the Boolean algebra of bands.
\r\n\r\nThe following decomposition theorem is proved.
\r\n\r\nTHEOREM. Let T : E \u2192 E be a bi-disjointness preserving operator on a Dedekind complete Riesz space E. Then there exist T-reducing bands Ei (i = 1,2,3,4) such that i=1\u22954 Ei = E and the restriction of T to Ei satisfies the ith property listed in the preceding definition.
\r\n\r\nQuasi-invertible operators can be decomposed further in the following way. Set 0rth(E) :={T \u2208 \u2112b(E) : TB \u2282 B for every band B}. We say that a quasi-invertible operator T has strict period n (n \u2208\u2115) if Tn \u2208 0rth(E) and for every non-zero band B \u2282 E, there exists a band A s.t. {0} \u2260 A \u2282 B and A, {TA}dd, ... , {Tn-1A}dd are mutually disjoint. A quasi-invertible operator is called aperiodic if for every n \u2208\u2115 and every non-zero band B \u2282 E, there exists a band A s.t. {0} \u2260 A \u2282 B and A, {TA}dd , ... , {TnA}dd are mutually disjoint.
\r\n\r\nTHEOREM. Let T : E \u2192 E be a quasi-invertible operator on a Dedekind complete Riesz space E. Then there exist T-reducing bands En (n \u2208 \u2115 \u22c3 {\u221e}) such that the restriction of T to En (n \u2208 \u2115) has strict period n, the restriction of T to E\u221e is aperiodic and E = n\u2208\u2115 \u22c3 {\u221e}\u2295 En.
\r\n\r\nFinally, the spectrum of bi-disjointness preserving operators is considered.
\r\n\r\nTHEOREM. Let E be a Banach lattice which is either Dedekind complete or has a weak Fatou norm. Let T : E \u2192 E be a bi-disjointness preserving operator. If T is either of forward shift type, of backward shift type, hypernilpotent or aperiodic quasi-invertible, then the spectrum of T is rotationally invariant. If T is quasi-invertible with strict period n, then \u03bb \u2208 \u03c3(T) implies \u03bb\u03b1 \u2208 \u03c3(T) for any nth root of unity \u03b1.
\r\n\r\nThe above theorems can be combined to deduce results concerning the spectrum of arbitrary bi-disjointness preserving operators. One such result is given below.
\r\n\r\nTHEOREM. Let T : E \u2192 E be a bi-disjointness preserving operator on a Dedekind complete Banach lattice E. Suppose, for each 0 < r \u2208 \u211d, {z \u2208 \u2102 : |z| = r} \u22c2 \u03c3(T) lies in an open half plane. Then there exists T-reducing bands E1 and E2 such that E = E1\u2295 E2 , T|E1 is an abstract multiplication operator (i.e. is in the center of E) and T|E2 is quasi-nilpotent.
", "doi": "10.7907/88fv-2p60", "publication_date": "1983", "thesis_type": "phd", "thesis_year": "1983" }, { "id": "thesis:2703", "collection": "thesis", "collection_id": "2703", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06232005-145221", "type": "thesis", "title": "Stability Theory of Linear and Nonlinear Stochastic Difference Systems", "author": [ { "family_name": "Ma", "given_name": "Fai", "clpid": "Ma-Fai" } ], "thesis_advisor": [ { "family_name": "Caughey", "given_name": "Thomas Kirk", "clpid": "Caughey-T-K" } ], "thesis_committee": [ { "family_name": "Keller", "given_name": "Herbert Bishop", "clpid": "Keller-H-B" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Caughey", "given_name": "Thomas Kirk", "clpid": "Caughey-T-K" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this report the stability of linear and nonlinear stochastic difference systems is considered. Explicit criteria for stability are derived. An algorithm is developed for computing the moments of linear stochastic systems when a certain Lie-algebraic condition is satisfied. The relationship between various stability definitions is explored.
\r\n", "doi": "10.7907/QZ4T-R653", "publication_date": "1981", "thesis_type": "phd", "thesis_year": "1981" }, { "id": "thesis:10729", "collection": "thesis", "collection_id": "10729", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02222018-150519570", "type": "thesis", "title": "Vortex-Induced Vibrations of Structures", "author": [ { "family_name": "Hall", "given_name": "Shawn Anthony", "clpid": "Hall-Shawn-Anthony" } ], "thesis_advisor": [ { "family_name": "Iwan", "given_name": "Wilfred D.", "clpid": "Iwan-W-D" } ], "thesis_committee": [ { "family_name": "Iwan", "given_name": "Wilfred D.", "clpid": "Iwan-W-D" }, { "family_name": "Housner", "given_name": "George W.", "clpid": "Housner-G-W" }, { "family_name": "Hudson", "given_name": "Donald E.", "clpid": "Hudson-D-E" }, { "family_name": "Sabersky", "given_name": "Rolf H.", "clpid": "Sabersky-R-H" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" } ], "local_group": [ { "literal": "Earthquake Engineering Research Laboratory" }, { "literal": "div_eng" } ], "abstract": "Vortex-induced oscillations, often of concern when a bluff structure is exposed to fluid cross-flow, are considered herein using a semi-empirical modeling approach. Based on the fluid momentum theorem, the model involves a highly simplified abstraction of the complex flow field, and major assumptions concerning the nature of the coupling between the fluid and the oscillating structure.
\r\n\r\nThree prototype problems are studied, including harmonically forced cylinders, spring-mounted cylinders, and taut elastic cables; in each case the structure is assumed to be of circular cross-section and situated in a uniform cross-flow. Only oscillations transverse to the flow are considered. The problem of modal interaction for elastic cables, typically of interest when the fluid flow excites high-mode-number resonances, is given particular attention.
\r\n\r\nThe model produces a set of nonlinear, ordinary differential equations describing the coupled fluid/structure oscillations. Steady-state oscillatory solutions to these equations are found analytically and are examined for stability. Using various regression techniques, the steady-state solutions are then fit to experimental data for forced and spring-mounted cylinders. Finally, the model's predictions for elastic cables are used to postulate a qualitative picture of modal interaction, certain features of which have been observed experimentally.
", "doi": "10.7907/Y4QP-A998", "publication_date": "1981", "thesis_type": "phd", "thesis_year": "1981" } ]