Dissertations / Theses on the topic 'Mutual independence'

This research investigates relationships between undergraduate studentsâ understanding of proof and how this understanding relates to their conceptions of mathematical definitions. Three students in an introductory proofs course were each interviewed three times in order to assess their proof schemes, understand how they think of specific mathematical concepts, and investigate how the students prove relationships between these concepts. This research used theoretical frameworks from both proof and definition literature. Findings show that studentsâ ability or inability to adapt their concept images of the mathematical concepts enhanced and impeded their proof schemes, respectively.
Master of Science

碩士
元智大學
財務金融學系
98
This study extends Gaspar, Massa and Matos (2006) by considering corporate governance of low family value funds ranked by their net style returns. By analyzing the sample combined with EDGAR and CRSP Mutual Fund Database from 2002 to 2008, the result suggests that low value fund’s ratio of board independence helps monitor the cross fund subsidization conducted by fund family relative to funds in different families. The result of board concentration on low value fund implies that independent directors sitting on many funds tend to become rubber stamps, failing to exercise fiduciary duties. But the result of an independent chairman dummy is inconsistent with my hypothesis.

No
This paper presents a novel concept to describe the couplings among the outputs of the stochastic systems which are represented by NARMA models. Compared with the traditional coupling description, the presented concept can be considered as an extension using statistical independence theory. Based on this concept, the decoupling control in statistical sense is established with the necessary and sufficient conditions for complete decoupling. Since the complete decoupling is difficult to achieve, a control algorithm has been developed using the Cauchy-Schwarz mutual information criterion. Without modifying the existing control loop, this algorithm supplies a compensative controller to minimise the statistical couplings of the system outputs and the local stability has been analysed. In addition, a further discussion illustrates the combination of the presented control algorithm and data-based mutual information estimation. Finally, a numerical example is given to show the feasibility and efficiency of the proposed algorithm.

Cette thèse est rédigée par articles. Les articles sont rédigés en anglais et le reste de la thèse est rédigée en français.
Le travail établit une équivalence en termes de puissance entre les tests basés sur la alpha-distance de covariance et sur le critère d'indépendance de Hilbert-Schmidt (HSIC) avec fonction caractéristique de distribution de probabilité stable d'indice alpha avec paramètre d'échelle suffisamment petit. Des simulations en grandes dimensions montrent la supériorité des tests de distance de covariance et des tests HSIC par rapport à certains tests utilisant les copules. Des simulations montrent également que la distribution de Pearson de type III, très utile et moins connue, approche la distribution exacte de permutation des tests et donne des erreurs de type I précises. Une nouvelle méthode de sélection adaptative des paramètres d'échelle pour les tests HSIC est proposée. Trois simulations, dont deux sont empruntées de l'apprentissage automatique, montrent que la nouvelle méthode de sélection améliore la puissance des tests HSIC. Le problème de tests d'indépendance entre deux vecteurs est généralisé au problème de tests d'indépendance mutuelle entre plusieurs vecteurs. Le travail traite aussi d'un problème très proche à savoir, le test d'indépendance sérielle d'une suite multidimensionnelle stationnaire. La décomposition de Möbius des fonctions caractéristiques est utilisée pour caractériser l'indépendance. Des tests généralisés basés sur le critère d'indépendance de Hilbert-Schmidt et sur la distance de covariance en sont obtenus. Une équivalence est également établie entre le test basé sur la distance de covariance et le test HSIC de noyau caractéristique d'une distribution stable avec des paramètres d'échelle suffisamment petits. La convergence faible du test HSIC est obtenue. Un calcul rapide et précis des valeurs-p des tests développés utilise une distribution de Pearson de type III comme approximation de la distribution exacte des tests. Un résultat fascinant est l'obtention des trois premiers moments exacts de la distribution de permutation des statistiques de dépendance. Une méthodologie similaire a été développée pour le test d'indépendance sérielle d'une suite. Des applications à des données réelles environnementales et financières sont effectuées.
The main result establishes the equivalence in terms of power between the alpha-distance covariance test and the Hilbert-Schmidt independence criterion (HSIC) test with the characteristic kernel of a stable probability distribution of index alpha with sufficiently small scale parameters. Large-scale simulations reveal the superiority of these two tests over other tests based on the empirical independence copula process. They also establish the usefulness of the lesser known Pearson type III approximation to the exact permutation distribution. This approximation yields tests with more accurate type I error rates than the gamma approximation usually used for HSIC, especially when dimensions of the two vectors are large. A new method for scale parameter selection in HSIC tests is proposed which improves power performance in three simulations, two of which are from machine learning. The problem of testing mutual independence between many random vectors is addressed. The closely related problem of testing serial independence of a multivariate stationary sequence is also considered. The Möbius transformation of characteristic functions is used to characterize independence. A generalization to p vectors of the alpha -distance covariance test and the Hilbert-Schmidt independence criterion (HSIC) test with the characteristic kernel of a stable probability distributionof index alpha is obtained. It is shown that an HSIC test with sufficiently small scale parameters is equivalent to an alpha -distance covariance test. Weak convergence of the HSIC test is established. A very fast and accurate computation of p-values uses the Pearson type III approximation which successfully approaches the exact permutation distribution of the tests. This approximation relies on the exact first three moments of the permutation distribution of any test which can be expressed as the sum of all elements of a componentwise product of p doubly-centered matrices. The alpha -distance covariance test and the HSIC test are both of this form. A new selection method is proposed for the scale parameter of the characteristic kernel of the HSIC test. It is shown in a simulation that this adaptive HSIC test has higher power than the alpha-distance covariance test when data are generated from a Student copula. Applications are given to environmental and financial data.

碩士
中原大學
應用數學研究所
99
The arrangement graph An;k, has been used as the underlying topology for many practi- cal multicomputers, and has been extensively studied in the past. In this thesis, we will prove that any An;k where n ¡ k ¸ 3, k ¸ 2, contains k(n ¡ k) mutually independent hamiltonian cycles. More speci¯cally, let N =j V (An;k) j, v(i) 2 V (An;k) for 1 · i · N and hv(1); v(2); ¢ ¢ ¢ ; v(N); v(1)i be a hamiltonian cycle of An;k. We prove that An;k con- tains k(n ¡ k) hamiltonian cycles, denoted by Cl = hv(1); vl(2); ¢ ¢ ¢ ; vl(N); v(1)i for all 1 · l · k(n ¡ k), such that vl(i) 6= vl0 (i) for all 2 · i · N whenever l 6= l0 . The result is optimal since each vertex of An;k has exactly k(n ¡ k) neighbors.

碩士
國立嘉義大學
資訊工程學系研究所
99
For optimizing the network performance, some scholars brought up the concept of mutually independent Hamiltonian cycles to solve the allocation works fairly. Let $G=(V,E)$ be a graph of order $n$. A Hamiltonian cycle of $G$ is a cycle that contains every vertex in $G$. Two Hamiltonian cycles $C_1=\langle u_1, u_2, \cdots, u_n, u_1\rangle$ and $C_2=\langle v_1, v_2, \cdots, v_n, v_1\rangle$ of $G$ are independent if $u_1=v_1$ and $u_i \neq v_i$ for $2\leq i\leq n$. A set of Hamiltonian cycles $\{C_1, C_2, \cdots, C_k\}$ of $G$ is mutually independent if its elements are pairwise independent. The mutually independent hamiltonicity $IHC(G)$ of a graph $G$ is the maximum integer $k$ such that for any vertex $u$ of $G$ there are $k$ mutually independent Hamiltonian cycles of $G$ starting at $u$. This thesis proved that $IHC(B_2)=1$ and $IHC(B_n)=n$ for $n\geq 3$ and $IHC(DL(n;1,2))=4$ for odd $n\geq 5$ and $IHC(DL(n;a,b))=4$ when $gcd(n,a)=gcd(n,b)=gcd(n,b+a)=gcd(n,b-a)=1$, for odd $n\geq 5$ and $a\leq 2$ .

碩士
國立交通大學
資訊科學系所
93
We say that two paths P0= and P1= are independent if u0=v0, l(P0)=l(P1) and P0(i)!=P1(i) fro every 1=4.

碩士
中原大學
應用數學研究所
96
Dual-cubes (DC_n's), introduced by Li and Peng in 2000 [14], are shown to be superior to hypercubes (Qn's) in many aspects. For example, it is proved that even though DCn and Q_2n+1 have the number of vertices and their diameters are almost the same,DC_n consists of nearly half the number of edge of Q_2n+1. In 2008, Chen and Kao [5],introduced a new kind of graphs, called dual-cube extensive networks (DCEN's), based on the structure of DC's. Instead of using the hypercube Q_n as a basic component for any DCEN as in dual-cubes, DCEN takes any graph G as the basic component and is then obtained by the similar construction scheme as in dual-cubes. In this paper, we will prove that the n-dimensional dual-cube contains n+1 mutually independent hamiltonian cycles for n >= 2. Furthermore, if any nonbipartite graph (resp. any bipartite graph) G contains n mutually independent hamiltonian cycles and is hamiltonian connected (resp. hamiltonian laceable), then DCEN(G) contains at least n+1 mutually independent hamiltonian cycles. Keywords: hypercube, dual-cube, hamiltonian cycle, hamiltonian connected, mutually independent.

碩士
國立暨南國際大學
資訊工程學系
101
In a graph G, a cycle C = ⟨v0, v1, ..., vk, v0⟩ is defined as a sequence of adjacent vertices and for all 0 ≤ i < j ≤ k, vi ≠ vj ; a cycle is called Hamiltonian cycle if it contains all vertices of G. If there exists a Hamiltonian cycle in G, then G is a Hamiltonian graph. Two Hamiltonian cycles C1 = ⟨u0, u1, u2, ..., un−1, u0⟩ and C2 = ⟨v0, v1, v2, ..., vn−1, v0⟩ are independent if u0 = v0, ui ≠ vi for all 1 ≤ i ≤ n − 1. A set of Hamiltonian cycles C = {C1,C2, ...,Ck} of G are mutually independent if any two different Hamiltonian cycles of C are independent. The mutually independent Hamiltonianicity of graph G, namely IHC(G) = k, is the maximum integer k such that for any vertex u of G there exists k-mutually independent Hamiltonian cycles starting at u. The Cartesian product of graphs G and H, written by G×H, is the graph with vertex set V (G)×V (H) specified by putting (u, v) adjacent to (u′, v′) if and only if (1) u = u′ and vv′ ∈ E(H), or (2) v = v′ and uu′ ∈ E(G). In this thesis, we study mutually independent Hamiltonianicity on G = G1×G2, where G1 and G2 are Hamiltonian graphs. We prove that IHC(G1×G2) ≥ IHC(G1) or IHC(G1) + 2 when given some difference conditions. We refer to toroidal mesh graph and define graph Cm × Cn, where m, n are lengths of cycles. We show that IHC(Cm × Cn) = 4 for any positive integers m, n ≥ 3.

碩士
國立暨南國際大學
資訊工程學系
94
Abstract Graphs and networks are often used interchangeably. There are many conflicting requirements in designing the topology for computer networks. The n-cube is one of the most popular topologies, and the topology of star network is attractive alternative to the n-cube for interconnecting processors in parallel computers. And, we know that the topology of (n, k)-star graphs is a generalization of n-star graphs. Two Hamiltonian paths P1 = < v1, v2, …, vn(G)>and P2 = < u1, u2, …, un(G)> of G are called independent if v1 = u1, vn(G) = un(G), and vi != ui for 1 <i <n(G). A set of Hamiltonian paths {P1, P2, …, Pk} of G are called mutually independent if for any two different Hamiltonian paths selected from this set are independent. It is proved that there exist (n - 2) mutually independent Hamiltonian paths in star graphs between any two distinct nodes from different bipartite set if n >= 4 and the result is optimal. Since the topology in (n, k)-star graphs is a generalization of n-star graphs, we guess there is a similar result of (n, k)-star graphs. In this thesis, we prove that there exists only one mutually independent hamiltonian path in (4, 2)-star graphs between any two distinct nodes. Besides, there exist (n – 2) mutually independent hamiltonian paths in (n, k)-star graphs between any two distinct nodes if n – k >=2, (n, k) != (4, 2) and this result is optimal.

碩士
國立東華大學
資訊工程學系
98
The problem of whether or not there are mutually independent hamiltonian cycles in interconnection networks has attracted a great attention in recent years. In this paper, we will show that n-dimensional hypercube-like networks have two mutually indepdendent hamiltonian cycles for n&gt;=3. Moreover, we also develop some e±cient algorithms for constructing two mutually independent hamiltonian cycles in the n-dimensional hypercube, the n-dimensional crossed cube, the n-dimensional folded hypercube, and the n-dimensional augmented cube for n&gt;=3.

博士
中原大學
應用數學研究所
100
Abstract Mutually independent hamiltonian cycles, abbreviated as MIHCs, have been studied on interconnection networks widely. In this dissertation, we study MIHCs on some specific graphs. We established the existence of MIHCs in $k$-ary $n$-cubes $(Q_{n}^{k})$ when $k$ is even, cycle composition networks $(CCN_k)$, alternating group graphs $(AG_n)$ and arrangement graphs $(A_{n,k})$. The results are shown to be optimal in the sense that the number of MIHCs we constructed is maximal. In addition to the construction schemes of MIHCs for specific graphs, we intend to give some sufficient and necessary conditions for the existence of MIHCs in general graphs. A conjecture is given based on known results.

碩士
國立新竹教育大學
應用數學系碩士班
94
The recursive circulant graphs G(N, d), have been introduced in 1994 [14], are circulant graphs with N nodes and with jumps of powers of d. The subfamily of the recursive circulant graphs of the form G(2*n, 4), for some nonnegative integer n, was also presented as a new topology for multicomputer networks because of its nice properties concerning their diameter and routing schemes, and so on. In this paper, we study the mutually independent hamiltonian cycles of the recursive circulant graphs G(2*n, 4). The recursive circulant graphs G(2*n, 4) and the hypercubes Qn have many similar properties. For examples, G(2*n, 4) have the same degree as Qn of dimension n, but have a smaller diameter [21]；G(2*n, 4) have the relationship with Qn in terms of embedding [15]. Furthermore, it has been shown that the numbers of the mutually independent hamiltonian cycles of Qn are MIHC(Qn) = n-1 if n belongs to {1, 2, 3}； = n if n is bigger and equal to4. Therefore, we would guess the numbers of the mutually independent hamiltonian cycles of the recursive circulant graphs G(2*n, 4), and then have verified the results that there are n mutually independent hamiltonian cycles in G(2*n, 4), for n is bigger and equal to3.

博士
國立交通大學
資訊科學與工程研究所
100
From the application point of view, efficient algorithms and execution methods are important issues for communication patterns in networks. The study of certain topological structures on network designs provides a systematic and logical analysis for the desired performance. The problem of simulating a network by another is called embedding problem. The cycle-embedding problem is one of the most popular research problems. In this dissertation, we will introduce the bipancyclic property, bipanpositionable property, and bipanpositionable bipancyclic property, and show that some interconnection networks satisfy those properties. We also study the existence of mutually independent cycles on some interconnection networks. The existence of mutually independent cycles in communication system guarantees that there will be no waiting time for parallel processing. We propose a sufficient condition to guarantee the existence of certain number of mutually independent hamiltonian cycles. We also find the optimal number of mutually independent hamiltonian cycles in some special interconnection networks. Finally, we will introduce two new concepts called mutually independent edge-bipancyclic property and mutually independent bipanconnected property. Our result strengthens previous results such as bipancyclic property, bipanconnected property, edge-bipancyclic property, and vertex-bipancyclic property.

碩士
中原大學
應用數學研究所
99
The k-ary n-cube has been used as the underlying topology for many practical multicomputers, and has been extensively studied in the past. In this thesis, we will prove that any k-ary n-cube Q(k,n), where n ≥ 2 is an integer and k ≥ 4 is an even integer, contains 2n mutually independent Hamiltonian cycles. More specifically, let N =∣V(Q(k,n))|, v(i)∈V(Q(k,n)) for 1 ≤ i ≤ N, and ⟨v(1), v(2),…, v(N), v(1)⟩ be a Hamiltonian cycle of Q(k,n). We prove that Q(k,n) contains 2n Hamiltonian cycles, denoted by Cl = ⟨v(1); vl(2),…, vl(N), v(1)⟩ for all 0 ≤ l ≤ 2n−1, such that vl(i)≠ vl′(i) for all 2 ≤ i ≤ N whenever l≠l′. The result is optimal since each vertex of Q(k,n) has exactly 2n neighbors.

碩士
中原大學
數學研究所
97
The $k$-ary $n$-cubes, $Q_{n}^{k}$, is one of the most well-known interconnection networks in parallel computers. It has been shown that any $Q_{n}^{k}$ is a $(2n)$-regular, vertex symmetric graph with a hamiltonian cycle. In this article, we will prove that any $k$-ary $n$-cube, $Q_{n}^{k}$, contains $2n$ mutually independent hamiltonian cycles, where $n ge 2$ is an integer and $k ge 3$ is an odd integer. More specifically, let $v_iin Q_{n}^{k}$ for $0le ile |Q_{n}^{k}|-1$ and let $langle v_0,v_1,ldots,v_{|Q_{n}^{k}|-1},v_0 angle$ be a hamiltonian cycle of $Q_{n}^{k}$. We prove that $Q_{n}^{k}$ contains $2n$ hamiltonian cycles of the form $langle v_0,v_1^l,ldots,v_{|Q_{n}^{k}|-1}^l,v_0 angle$ for $0le l le 2n-1$, in which $v_{i}^{l}e v_{i}^{l'}$ whenever $le l'$. The result is optimal since each vertex of $Q_{n}^{k}$ has only $2n$ neighbors.

博士
國立交通大學
資訊科學與工程研究所
99
The Menger Theorem (Menger, 1972) show that there are k-disjoint paths between any two distinct vertices of G if and only if G is k-connected. A graph G is k*-connected if there exists a k-disjoint paths between any two distinct vertices which contains all the vertices of G. The spanning connectivity of G, k*(G), is defined as the largest integer k such that G is w*-connected for 0 &lt; e w &lt; k+1 if G is a 1*-connected graph. We study the problem of spanning connectivity properties on some interconnection networks and graphs. Cycle embedding and path embedding are perhaps the most important outstanding materials in graph theory and have been defying solutions for more than a century. A hamiltonian cycle C of graph G is described as &lt; u1, u2, ..., un(G), u1 > to emphasize the order of vertices in C. Thus, u1 is the starting vertex and ui is the i-th vertex in C. Two hamiltonian cycles C1 = &lt; u1, u2, ..., un(G), u1 > and C2 = &lt; v1, v2, ..., vn(G), v1 > of G are independent if u1 = v1 and ui is not equal to vi for every i in { 2, ..., n(G) }. A set of hamiltonian cycles { C1, C2, ..., Ck } of G are mutually independent if its elements are pairwise independent. The mutually independent hamiltonianicity IHC(G) of graph G the maximum integer k such that for any vertex u of G there exist k mutually independent hamiltonian cycles of G starting at u. We study this problem on some interconnection networks and graphs.