We study a new method of generating random $d$-regular graphs by repeatedly applying an operation called pegging. The pegging algorithm, which applies the pegging operation in each step, is a method of generating large random regular graphs beginning with small ones. We prove that the limiting joint distribution of the numbers of short cycles in the resulting graph is independent Poisson. We use the coupling method to bound the total variation distance between the joint distribution of short cycle counts and its limit and thereby show that $O(\epsilon^{-1})$ is an upper bound of the $\eps$-mixing time. The coupling involves two different, though quite similar, Markov chains that are not time-homogeneous. We also show that the $\epsilon$-mixing time is not $o(\epsilon^{-1})$. This demonstrates that the upper bound is essentially tight. We study also the connectivity of random $d$-regular graphs generated by the pegging algorithm. We show that these graphs are asymptotically almost surely $d$-connected for any even constant $d\ge 4$. The problem of orientation of random hypergraphs is motivated by the classical load balancing problem. Let $h>w>0$ be two fixed integers. Let $\orH$ be a hypergraph whose hyperedges are uniformly of size $h$. To {\em $w$-orient} a hyperedge, we assign exactly $w$ of its vertices positive signs with respect to this hyperedge, and the rest negative. A $(w,k)$-orientation of $\orH$ consists of a $w$-orientation of all hyperedges of $\orH$, such that each vertex receives at most $k$ positive signs from its incident hyperedges. When $k$ is large enough, we determine the threshold of the existence of a $(w,k)$-orientation of a random hypergraph. The $(w,k)$-orientation of hypergraphs is strongly related to a general version of the off-line load balancing problem. The other topic we discuss is computing the probability of induced subgraphs in a random regular graph. Let $0<s<n$ and $H$ be a graph on $s$ vertices. For any $S\subset [n]$ with $|S|=s$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is $H$. The result holds for any $d=o(n^{1/3})$ and is further extended to $\mathcal{G}_{n,{\bf d}}$, the probability space of random graphs with given degree sequence $\bf d$. This result provides a basic tool for studying properties, for instance the existence or the counts, of certain types of induced subgraphs.

In this paper we consider optimal design of experiments in the case of correlated observations, when no replications are possible. This situation is typical when observing a random process or random field with known covariance structure. We present a theorem which demonstrates that the computation of optimum exact designs corresponds to solving minimization problems in terms of design measures. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

The transition fundions for the correlated random walk with two absorbing boundaries are derived by means of a combinatorial construction which is based on Krattenthaler's Theorem for counting lattice paths with turns. Results for walks with one boundary and for unrestricted walks are presented as special cases. Finally we give an asymptotic formula, which proves to be useful for computational purposes. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

A practical problem in computer graphics is that of representing a textured surface at arbitrary scales. I consider the underlying mathematical problem to be that of interpolating autoregressive random fields under arbitrary coordinate transformations. I examine the theoretical basis for the transformations that autoregressive parameters exhibit when the associated stationary random fields are scaled or rotated. The basic result is that the transform takes place in the continuous autocovariance domain, and that the spectral density and associated autoregressive parameters proceed directly from sampling the continuous autocovariance on a transformed grid. I show some real-world applications of these ideas, and explore how they allow us to interpolate into a random field. Along the way, I develop interesting ways to estimate simultaneous autoregressive parameters, to calculate the distorting effects of linear interpolation algorithms, and to interpolate random fields without altering their statistics.

We study a new method of generating random $d$-regular graphs by repeatedly applying an operation called pegging. The pegging algorithm, which applies the pegging operation in each step, is a method of generating large random regular graphs beginning with small ones. We prove that the limiting joint distribution of the numbers of short cycles in the resulting graph is independent Poisson. We use the coupling method to bound the total variation distance between the joint distribution of short cycle counts and its limit and thereby show that $O(\epsilon^{-1})$ is an upper bound of the $\eps$-mixing time. The coupling involves two different, though quite similar, Markov chains that are not time-homogeneous. We also show that the $\epsilon$-mixing time is not $o(\epsilon^{-1})$. This demonstrates that the upper bound is essentially tight. We study also the connectivity of random $d$-regular graphs generated by the pegging algorithm. We show that these graphs are asymptotically almost surely $d$-connected for any even constant $d\ge 4$. The problem of orientation of random hypergraphs is motivated by the classical load balancing problem. Let $h>w>0$ be two fixed integers. Let $\orH$ be a hypergraph whose hyperedges are uniformly of size $h$. To {\em $w$-orient} a hyperedge, we assign exactly $w$ of its vertices positive signs with respect to this hyperedge, and the rest negative. A $(w,k)$-orientation of $\orH$ consists of a $w$-orientation of all hyperedges of $\orH$, such that each vertex receives at most $k$ positive signs from its incident hyperedges. When $k$ is large enough, we determine the threshold of the existence of a $(w,k)$-orientation of a random hypergraph. The $(w,k)$-orientation of hypergraphs is strongly related to a general version of the off-line load balancing problem. The other topic we discuss is computing the probability of induced subgraphs in a random regular graph. Let $0<s<n$ and $H$ be a graph on $s$ vertices. For any $S\subset [n]$ with $|S|=s$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is $H$. The result holds for any $d=o(n^{1/3})$ and is further extended to $\mathcal{G}_{n,{\bf d}}$, the probability space of random graphs with given degree sequence $\bf d$. This result provides a basic tool for studying properties, for instance the existence or the counts, of certain types of induced subgraphs.

Urban land cover classification has always been crucial due to its ability to link many elements of human and physical environments. Timely, accurate, and detailed knowledge of the urban land cover information derived from remote sensing data is increasingly required among a wide variety of communities. This surge of interest has been predominately driven by the recent innovations in data, technologies, and theories in urban remote sensing. The development of light detection and ranging (LiDAR) systems, especially incorporated with high-resolution camera component, has shown great potential for urban classification. However, the performance of traditional and widely used classification methods is limited in this context, due to image interpretation complexity. On the other hand, random forests (RF), a newly developed machine learning algorithm, is receiving considerable attention in the field of image classification and pattern recognition. Several studies have shown the advantages of RF in land cover classification. However, few have focused on urban areas by fusion of LiDAR data and aerial images. The performance of the RF based feature selection and classification methods for urban areas was explored and compared to other popular feature selection approach and classifiers. Evaluation was based on several criteria: classification accuracy, impact of different training sample size, and computational speed. LiDAR data and aerial imagery with 0.5-m resolution were used to classify four land categories in the study area located in the City of Niagara Falls (ON, Canada). The results clearly demonstrate that the use of RF improved the classification performance in terms of accuracy and speed. Support vector machines (SVM) based and RF based classifiers showed similar accuracies. However, RF based classifiers were much quicker than SVM based methods. Based on the results from this work, it can be concluded that the RF based method holds great potential for recent and future urban land cover classification problem with LiDAR data and aerial images.

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Resistive Random Access Memory (RRAM) is considered as the most promising candidate for the next-generation nonvolatile memories due to their superior properties such as low operation voltage, fast operation speed, non-destructive read, simple metal-insulator-metal (MIM) sandwich structure, good scale-down ability. The main targets of this research are to clarify the corresponding physical mechanism, develop the potential material and structure of RRAM and stabilize the resistive switching characteristics, in which clarifying the physical mechanism will be the key factor for RRAM into production in the future. Recent research has suggested that variation of the low and high resistance states in RRAM could be caused due to the by instability in the formation and /disruption of the filament. In addition, the endurance and stability of RRAM may be related to the dissipation of oxygen ions in the switching layer. In this study, new material (Si Introduced) and structure (oxygen confined layer) are employed to improve RRAM performance and to clarify the physical mechanism. Furthermore, constant switching energy results can be used to select the optimal materials and structures also can be used to correctly allocate voltage and time to control RRAM. The detail physical mechanism is studied by the stable RRAM device (Ti/HfO2/TiN) which is offered from Industrial Technology Research Institute (ITRI). The switching process is proved as the formation/disruption of the filament. Furthermore, the dynamic switching behaviors during reset procedure in RRAM were analyzed by the sequential experimental design to illustrate the procedure of atomic quantized reaction at the ultra-cryogenic temperature.

The past few years have seen the rapid rise of all things “social” on the web from the growth of online social networks like Facebook, to real-time communication services like Twitter, to user-contributed content sites like Flickr and YouTube, to content aggregators like Digg. Beyond these popular Web 2.0 successes, the emer- gence of Social Information Systems is promising to fundamentally transform what information we encounter and digest, how businesses market and engage with their customers, how universities educate and train a new generation of researchers, how the government investigates terror networks, and even how political regimes interact with their citizenry. Users have moved from being passive consumers of information (via querying or browsing) to becoming active participants in the creation of data and knowledge artifacts, actively sorting, ranking, and annotating other users and artifacts. This fundamental shift to social systems places new demands on providing de- pendable capabilities for knowing whom to trust and what information to trust, given the open and unregulated nature of these systems. The emergence of large-scale user participation in Social Information Systems suggests the need for the development of user-centric approaches to information quality. As a step in this direction this research proposes an interaction-based approach for modeling the notion of user im- portance. The interaction-based model is centered around the uniquely social aspects of these systems, by treating who communicates with whom (an interaction) as a core building block in evaluating user importance. We first study the interaction characteristics of Twitter, one of the most buzzworthy recent Social Web successes, examining the usage statistics, growth patterns, and user interaction behavior of over 2 million participants on Twitter. We believe this is the first large-scale study of dynamic interactions on a real-world Social Information System. Based on the anal- ysis of the interaction structure of Twitter, the second contribution of this thesis research is an exploration of approaches for measuring user importance. As part of this exploration, we study several different approaches that build on the inherent interaction-based framework of Social Information Systems. We explore this model through an experimental study over an interaction graph consisting of 800,000 nodes and about 1.9 million interaction edges. The user importance modeling approaches that we present can be applied to any Social Information System in which interactions between users can be monitored.

Ambient noise generated by surface random processes is the primary contribution to the noise-field energy in the intermediate frequency band, and thus is important in many applications of underwater sound. In this study, the noise field is analyzed with respect to the effects of random source spectrum, waveguide structure of the water column, and seabed stratification upon the noise-field intensity as well as spatial correlation. Based upon a noise-generation model due to continuous random sources, incorporating several analytical models for seabed stratification, a formulation may then be derived to facilitate the numerical implementation. Many results shall be generated and analyzed. In this study considers the noise field generated by surface random processes in an oceanic environment with a sediment layer possessing a continuously varying density and sound-speed profile. This model closely resembles the oceanic waveguide environment and therefore enables the simulation of surface noise generation. Many results of the noise field were generated, including the noise intensity distribution, vertical and horizontal correlations. It is demonstrated that the noise intensity may be affected by the stratification mainly through the continuous spectrum, in that the continuous spectrum is equally important as the normal modes in the present analysis. Moreover, the results for the correlations show that the noise field in the horizontal direction becomes more coherent when the noise sources are more correlated, while in the vertical direction, the results tend to reverse. The horizontal correlations of the noise field due to surface random sources with non-isotropic power spectrum, such as nonisotropic Gaussian and Pierson-Moskowitz, were generated and analyzed.