Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 195-214).

<p>This thesis covers the analysis of sparse and irregular fuel consumption data of long</p><p>distance haulage articulate trucks. It is shown that this kind of data is hard to analyse with multivariate as well as with functional methods. To be able to analyse the data, Principal Components Analysis through Conditional Expectation (PACE) is used, which enables the use of observations from many trucks to compensate for the sparsity of observations in order to get continuous results. The principal component scores generated by PACE, can then be used to get rough estimates of the trajectories for single trucks as well as to detect outliers. The data centric approach of PACE is very useful to enable functional analysis of sparse and irregular data. Functional analysis is desirable for this data to sidestep feature extraction and enabling a more natural view on the data.</p>

As computers keeping advancing, many difficult problems which were unable to compute formerly now have the chance to get answered. It is always the goal of mathematicians and computer scientists to compute and get the answers of the linear systems. Since 1950s, there have been a lot of published papers discussing the issue. As the linear systems larger and larger, the computer efficiency required is higher and higher, so that it is very difficult to get the answers of large linear systems. Now, the problems are showing aurora. In this dissertation, several mathematical calculations to compute the linear systems will be discussed, as well as their background and theory. Moreover, they will also be practiced.

Many computational problems involve massive data. A reasonable solution to those problems should be able to store and process the data in a effective manner. In this thesis, we study sparse representation of data streams and metric spaces, which allows for fast and private computation of heavy hitters from distributed streams, and approximate distance queries between points in a metric space. Specifically, we consider application scenarios where an untrusted aggregator wishes to continually monitor the heavy-hitters across a set of distributed streams. Since each stream can contain sensitive data, such as the purchase history of customers, we wish to guarantee the privacy of each stream, while allowing the untrusted aggregator to accurately detect the heavy hitters and their approximate frequencies. Our protocols are scalable in settings where the volume of streaming data is large, since we guarantee low memory usage and processing overhead by each data source, and low communication overhead between the data sources and the aggregator. We also study fault-tolerant spanners in doubling metrics. A subgraph H for a metric space X is called a k-vertex-fault-tolerant t-spanner ((k; t)-VFTS or simply k-VFTS), if for any subset S _ X with |Sj|≤k, it holds that dHnS(x; y) ≤ t ∙d(x; y), for any pair of x, y ∈ X \ S. For any doubling metric, we give a basic construction of k-VFTS with stretch arbitrarily close to 1 that has optimal O(kn) edges. We also consider bounded hop-diameter, which is studied in the context of fault-tolerance for the first time even for Euclidean spanners. We provide a construction of k-VFTS with bounded hop-diameter: for m ≥2n, we can reduce the hop-diameter of the above k-VFTS to O(α(m; n)) by adding O(km) edges, where α is a functional inverse of the Ackermann's function. In addition, we construct a fault-tolerant single-sink spanner with bounded maximum degree, and use it to reduce the maximum degree of our basic k-VFTS. As a result, we get a k-VFTS with O(k^2n) edges and maximum degree O(k^2). / published_or_final_version / Computer Science / Master / Master of Philosophy

As the social networking applications become popular and have attracted more and more attention, it becomes possible (or easier) to mine information networks of a large group of people, for instance the spread of viruses, products and innovations. Researchers are also benefited from these sources, as they help to study further about the human behaviors in a social networking environment. In this thesis, we study how the opinions cascade via social links and also the sparse representation of large data sets caused by the fast growing information networks. Consider an instance of advertising products on an information network, where the objective for an advertiser is to choose a set of initially active nodes, subject to some budget constraints such that the expected number of active nodes over time is maximized. In this work, the non-progressive case where active nodes could become inactive in subsequent time steps, was considered. This setting is interesting, for people have no reason to keep using a product forever, especially when a majority of his neighbors have given it up. Another setting is the users' susceptibilities to the new behavior won't change once they are chosen initially. This is di_erent from the previous works, and we think it is also interesting. Our main result is that with a specified budget, an advertiser can achieve 1/2 -approximation on maximizing the number of active nodes over a certain period of time, and (1 - 1/e)-approximation in expectation with a randomized algorithm. In our model, users' opinions are updated according to a weighted averaging scheme, which usually leads to the consensus. When this happens, the expected influence over a long time period is dominated by the consensus value. Hence, it is interesting to study when and how the consensus will be achieved. We study the convergence time required to achieve consensus. In particular, we considered the case when the underlying network is dynamic, and gave conclusions for different averaging models. Both our analysis and experiments show that dynamic networks exhibit fast convergence behavior, even under very mild connectivity assumptions. In this work, we also studied how to maintain the pairwise distances for a large group of users, when the distances form a doubling metric space. Motivated by Elkin and Solomon's construction of spanners for doubling metrics that has constant maximum degree, hop-diameter O(log n) and lightness O(log n) (i.e., weight O(log n) ． w(MST)), we offer a simple alternative construction that is very intuitive and is based on the standard technique of net tree with cross edges. Indeed, our approach can be readily applied to our previous construction of k-fault tolerant spanners (ICALP 2012) to achieve k-fault tolerance, maximum degree O(K^2), hop-diameter O(log n) and lightness O(K^3 log n). / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

This thesis covers the analysis of sparse and irregular fuel consumption data of long distance haulage articulate trucks. It is shown that this kind of data is hard to analyse with multivariate as well as with functional methods. To be able to analyse the data, Principal Components Analysis through Conditional Expectation (PACE) is used, which enables the use of observations from many trucks to compensate for the sparsity of observations in order to get continuous results. The principal component scores generated by PACE, can then be used to get rough estimates of the trajectories for single trucks as well as to detect outliers. The data centric approach of PACE is very useful to enable functional analysis of sparse and irregular data. Functional analysis is desirable for this data to sidestep feature extraction and enabling a more natural view on the data.

Hyperspectral image data has long been an important tool for many areas of sci- ence. The addition of spectral data yields significant improvements in areas such as object and image classification, chemical and mineral composition detection, and astronomy. Traditional capture methods for hyperspectral data often require each wavelength to be captured individually, or by sacrificing spatial resolution. Recently there have been significant improvements in snapshot hyperspectral captures using, in particular, compressed sensing methods. As we move to a compressed sensing image formation model the need for strong image priors to shape our reconstruction, as well as sparse basis become more important. Here we compare several several methods for representing hyperspectral images including learned three dimensional dictionaries, sparse convolutional coding, and decomposable nonlocal tensor dictionaries. Addi- tionally, we further explore their parameter space to identify which parameters provide the most faithful and sparse representations.

ITC/USA 2011 Conference Proceedings / The Forty-Seventh Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2011 / Bally's Las Vegas, Las Vegas, Nevada / In this paper we study a new streaming Compressive Sensing (CS) technique that aims to replace high speed Analog to Digital Converters (ADC) for certain classes of signals and reduce the artifacts that arise from block processing when conventional CS is applied to continuous signals. We compare the performance of both streaming and block processing methods on several types of signals and quantify the signal reconstruction quality when packet loss is applied to the transmitted sampled data.

In Cryptography, computing a^xb^y mod n is the most important and the most time-consuming calculation The problem can be solved by classical binary method. Later research is based on this basis to increase computational efficiency. Furthermore, Binary signed-digit representation recoding algorithm, the Sparse Form, the DJM recoding method, and the Joint Sparse Form can be used to decrease the number of multiplication by aligning more non-zero bits. Another method is to pre-compute and store the part of the results to decrease the number of computations by shifting bits. Joint Sparse Form recording method is not a table driven algorithm in converting source codes into joint sparse form. In this paper, we first proposed a table driven algorithm for joint sparse form to simply recording concept. This algorithm can be constructed a finite state machine to denote the recording procedure. According to this finite state machine, we show that the average joint Hamming weight among joint sparse form is 0.5n when n approaches infinity. Finally, we show that the average joint Hamming weights of SS1 method and DS1 method among joint sparse form are 0.469n and 0.438n by using a similar method, respectively.

Title: Distribution functions of asteroid physical properties Author: Helena Cibulková Institute: Astronomical Institute of Charles University Supervisor: Mgr. Josef Ďurech, Ph.D., Astronomical Institute of Charles Univer- sity Abstract: In this thesis, I utilize photometric data sparse in time produced by all-sky surveys and investigate physical properties of large asteroid populations. In principle, the individual approach to asteroid modeling cannot compass all objects because new asteroids are continually discovered and we do not have enough data for them. Therefore, in this work I present an essentially different, statistical approach. In a series of papers, we developed two independent methods which use a triaxial-ellipsoid approximation, and we test their applicability and limits. We prove they can be used to the photometric databases like Lowell Observatory database or Pan-STARRS. The output quantities are distributions of the spin axis directions and shape elongations for asteroid populations, and using the Kolmogorov-Smirnov test we search for differences among them. The main result of my work is that the distribution of ecliptical longitudes of spin axes is nonuniform. Moreover, this nonuniformity is more significant for asteroids with low orbital inclinations and the distribution is dependent on...