El objetivo de esta tesis es estudiar el funcionamiento de los mercados de trabajo dónde los trabajadores son asignados a las empresas por procesos aleatorios usando modelos de asignación bilateral. En estos modelos, los agentes pertenecen a uno de dos conjuntos disjuntos -empresas y trabajadores- y cada agente tiene preferencias ordinales sobre el otro lado del mercado. El problema se reduce a una asignación de los miembros de estos dos conjuntos el uno al otro.En el segundo capítulo, titulado "On Random Matching Markets: Properties and Equilibria," se describe un algoritmo que empieza desde una asignación cualquiera y continua creando, a cada paso, una asignación provisional. En cada momento del tiempo, una empresa es elegida al azar y se considera el mejor trabajador en su lista de preferencias. Si este trabajador ya está asignado a una empresa mejor, la asignación no se altera. En caso contrario, el trabajador y la empresa quedan temporalmente juntos hasta que el trabajador reciba una propuesta de trabajo mejor. Seguidamente, se exploran algunas propiedades del algoritmo; por ejemplo, el algoritmo generaliza el famoso algoritmo de "deferred-acceptance" de Gale y Shapley. Luego se analizan los incentivos que los agentes enfrentan en el juego de revelación inducido por el algoritmo. El hecho de que las empresas son seleccionadas al azar introduce incertidumbre en el resultado final. Una vez que las preferencias de los agentes son ordinales, se utiliza un concepto de equilibrio ordinal, basado en la dominancia estocastica de primer orden.En el tercer capítulo, "Incentives in Decentralized Random Matching Markets," se considera un juego secuencial dónde los agentes actúan de acuerdo con las reglas generales del algoritmo. En este capítulo, las estrategias de los agentes pueden tomar una forma cualquiera y no tienen que coincidir con una lista de preferencias. El primer jugador es la Naturaleza, que elige una secuencia de empresas , que representa la incertidumbre existente en un mercado descentralizado. Luego, las empresas son elegidas de acuerdo con la sequencia y les es dada la oportunidad de hacer una propuesta. Ya que el juego es dinamico, se analizan los equilibrios de Nash ordinales perfectos en subjuegos.En "Random Stable Mechanisms in the College Admissions Problem," se considera el juego inducido por un mecanismo aleatorio estable. En este capítulo, se caracterizan los equilibrios de Nash ordinales. En particular, puede obtenerse una asignación en un equilibrio dónde las empresas revelan sus verdaderas preferencias si y sólo si la asignación es estable con respecto a las verdaderas preferencias.Por fin, en el último capítulo, se caracterizan los equilibrios perfectos ordinales en el juego inducido por un mecanismo aleatorio estable. / The purpose of this thesis is to explore the functioning of labor markets where workers are assigned to firms by means of random processes using two-sided matching models. In these models, agents belong to one of two disjoint sets -firms and workers- and each agent has ordinal preferences over the other side of the market. Matching reduces to assigning the members of these two sets to one another.In the second chapter, entitled "On Random Matching Markets: Properties and Equilibria," I describe an algorithm that starts with any matching situation and proceeds by creating, at each step, a provisional matching. At each moment in time, a firm is randomly chosen and the best worker on its list of preferences is considered. If this worker is already holding a firm he prefers, the matching goes unchanged. Otherwise, they are (temporarily) matched, pending the possible draw of even better firms willing to match this worker. Some features of this algorithm are explored; namely, it encompasses other algorithms in the literature, as Gale and Shapley's famous deferred-acceptance algorithm. I then analyze the incentives facing agents in the revelation game induced by the proposed algorithm. The random order in which firms are selected when the algorithm is run introduces some uncertainty in the output reached. Since agents' preferences are ordinal in nature, I use ordinal Nash equilibria, based on first-order stochastic dominance.In the third chapter, "Incentives in Decentralized Random Matching Markets," I take a step further by considering a sequential game where agents act according to the general rules of the algorithm. The original feature is that available strategies exhaust all possible forms of behavior: agents act in what they perceive to be their own best interest throughout the game, not necessarily according to a list of possible matches. The game starts with a move by Nature that determines the order of play, reflecting the inherently uncertain features of a decentralized market. Then, firms are selected according to the drawn order and given the opportunity to offer their positions. In order to account for the dynamic nature of the game, I characterize subgame perfect ordinal Nash equilibria.Following a different approach, in "Random Stable Mechanisms in the College Admissions Problem," I consider the game induced by a random stable matching mechanism. In this paper, I characterize ordinal Nash equilibria, providing simultaneously some results that extend to deterministic mechanisms. In particular, a matching can be obtained as the outcome of a play of the game where firms reveal their true preferences if and only if it is stable with respect to the true preferences.In closing, in the last chapter I characterize perfect equilibria in the game induced by a random stable mechanism.

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.

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.

No description available.

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.