In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression functions in a spline space are discussed and their properties developed. Three monotone estimates are defined: least-square regression splines, smoothing splines and binomial regression splines. The three estimates depend upon a "smoothing parameter": the number and location of knots in regression splines and the usual [formula omitted] in smoothing splines. Two standard techniques for choosing the smoothing parameter, GCV and AIC, are modified for monotone estimation, for the normal errors case. For answering the second question, a test statistic is proposed and its null distribution conjectured. Simulations are carried out to check the conjecture. These techniques are applied to two data sets. / Science, Faculty of / Statistics, Department of / Graduate

The effect of door and window openings on long timber framed shear walls was the subject of this thesis. Four different wall configurations containing various openings and one control wall with no openings were tested to examine ultimate load capacity and stiffness. All walls were forty feet in length and contained tie-down anchorage at the extreme ends of the wall only. Two replications of the five wall configurations were built. Each of the five wall configurations was tested using a: 1) monotonic displacement pattern and 2) sequential phased displacement pattern. A better understanding of the effect of monotonic and cyclic loading (and the relationship between the two loading types) on ultimate load capacity and stiffness for a given wall configuration were examined. To efficiently design shear walls, the effect of openings on shear wall performance must be known. This thesis adds to previous work on shear walls with openings to provide valuable information for future use. Results from this investigation are intended to provide useful information regarding performance of long shear walls with openings. Data concerning capacity, drift, elastic stiffness, and ductility are presented. Two methods of capacity prediction of shear walls with openings are examined. Sugiyama (1994) provided an empirical equation for prediction of load resistance that has been applied to capacity and is the basis for the perforated shear wall method. This thesis further validates his work to full scale long shear walls. A new method for capacity prediction was developed by the author and is also presented. / Master of Science

Alon 和Krivelevich (SIAM J. Discrete Math. 15(2): 211-227 (2002)) 證明了如果一個圖是ε -非二部圖，那麼階數為Ỡ(1/ε) 的隨機導出于圖以很大概率是非二部圖。我們進一步猜想，這個導出子圖以很大概率是Ω(ε)-非二部圖。Gonen 和Ron (RANDOM 2007) 證明了當圖的最大度不超過O (εn )時猜想成立。我們將對更一般的情形給出證明，對於任意d，所有d 正則(或幾乎d 正則)的圖猜想成立。 / 假設猜想成立的情況下，我們證明二分屬性是可以被單側誤差在O(1/ε^c ) 時間內檢驗的，其中c 是一個嚴格小於2 的常數，而這個結果也改進了Alon 和Krivelevich 的檢驗算法。由於己知對二分屬性的非適應性的檢驗算法需要Ω(1 /ε²) 的複雜性(Bogdanov 和Trevisan ， CCC 2004) ，我們的結果也得出，假設猜想成立，適應性對檢驗二分屬性是有幫助的。 / 另外一個有很多屬性檢驗問題被廣泛研究的領域是布爾函數。對布爾函數單調性的檢驗也是屬性檢驗的經典問題。給定對布爾函數f: {0,1}{U+207F} → {0,1} 的訪問，在[18]中，證明了檢驗算法複雜性的下界是Ω(√n) 。另一方面，在[21]中，作者們構造了一個複雜性為O(n) 的算法。在本文中，我們刻畫一些單調布爾函數的本質，設計算法并分析其對於一些困難例子的效果。最近，在[14] 中， 一個類似的算法被證明是非適應性，單側誤差，複雜性為Ỡ (n⁵/⁶ ε⁻⁵/³) 的算法。 / Alon and Krivelevich (SIAM J. Discrete Math. 15(2): 211-227 (2002)) show that if a graph is ε-far from bipartite, then the subgraph induced by a random subset of Ỡ (1/ε) vertices is not bipartite with high probability. We conjecture that the induced subgraph is Ω(ε)-far from bipartite with high probability. Gonen and Ron (RANDOM 2007) proved this conjecture in the case when the degrees of all vertices are at most O(εn). We give a more general proof that works for any d-regular (or almost d-regular) graph for arbitrary degree d. / Assuming this conjecture, we prove that bipartiteness is testable with one-sided error in time O(1=ε{U+1D9C}), where c is a constant strictly smaller than two, improving upon the tester of Alon and Krivelevich. As it is known that non-adaptive testers for bipartiteness require Ω(1/ε²) queries (Bogdanov and Trevisan, CCC2004), our result shows, assuming the conjecture, that adaptivity helps in testing bipartiteness. / The other area in which various properties have been well studied is boolean function. Testing monotonicity of Boolean functions is a classical question in property testing. Given oracle access to a Boolean function f : {0, 1}{U+207F} →{0, 1}, in [18], it is shown a lower bound of testing is Ω(√n). On the other hand, in [21], the authors introduced an algorithm to test monotonicity using O(n) queries. In this paper, we characterize some nature of monotone functions, design a tester and analyze the performance on some generalizations of the hard case. Recently, in [14], a similar tester is shown to be a non-adaptive, one-sided error tester making Ỡ (n⁵/⁶ ε⁻⁵/³) queries. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Li, Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 76-79). / Abstracts also in Chinese. / Abstract --- p.i / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Property Testing --- p.1 / Chapter 1.2 --- Testing Bipartiteness --- p.4 / Chapter 1.3 --- Testing Monotonicity --- p.7 / Chapter 2 --- Testing Bipartiteness --- p.11 / Chapter 2.1 --- Background --- p.11 / Chapter 2.1.1 --- Our result --- p.11 / Chapter 2.1.2 --- The algorithms of Gonen and Ron --- p.13 / Chapter 2.1.3 --- Our proof --- p.16 / Chapter 2.1.4 --- Notation --- p.19 / Chapter 2.2 --- Splitting the vertices by degree --- p.19 / Chapter 2.3 --- The algorithm for high degree vertices --- p.20 / Chapter 2.4 --- Eliminating the high degree vertices --- p.22 / Chapter 2.5 --- From an XOR game to a bipartite graph --- p.33 / Chapter 2.6 --- Proof of the main theorem --- p.35 / Chapter 2.7 --- Proof of the conjecture for regular graphs --- p.37 / Chapter 3 --- Testing Monotonicity --- p.40 / Chapter 3.1 --- Towards an improved tester --- p.40 / Chapter 3.1.1 --- Properties of Distribution D --- p.42 / Chapter 3.1.2 --- An Alternative Representation of D --- p.46 / Chapter 3.1.3 --- Performance of D on Decreasing Functions --- p.51 / Chapter 3.1.4 --- Functions Containing Ω(2{U+207F}) Disjoint Violating Edges --- p.54 / Chapter 3.2 --- A o(n) Monotonicity Tester [14] and Some Improvements --- p.62 / Chapter 3.2.1 --- A o(n) Monotonicity Tester [14] --- p.62 / Chapter 3.2.2 --- An Alternative Proof of Theorem 3.2.2 --- p.65 / Chapter 4 --- Other Related Results --- p.67 / Chapter 4.1 --- Short Odd Cycles in Graphs that are Far From Bipartiteness --- p.67 / Chapter 4.2 --- Fourier Analysis on Boolean Functions --- p.69 / Bibliography --- p.76

Thesis (Ph.D.)--Memorial University of Newfoundland, 2001. / Restricted until November 2003. Bibliography: leaves 170-178.

Thesis (Ph. D.)--Industrial & Systems Engineering, Georgia Institute of Technology, 2005. / Barnes, Earl, Committee Member ; Shapiro, Alex, Committee Member ; Realff, Matthew, Committee Member ; Al-Khayyal, Faiz, Committee Chair ; Ahmed, Shabbir, Committee Co-Chair. Includes bibliographical references.

Thesis (M.S.)--Duquesne University, 2005. / Title from document title page. Abstract included in electronic submission form. Includes bibliographical references (p. 21) and index.

In the present study, an analysis of plain and reinforced concrete beams under monotonic loading was made based on the Fixed Smeared Crack approach. The objectives of this research were to analyze the nonlinear behavior of the selected cases of analysis and to propose an alternative and simple model for the analysis of beams under service loadings, by means of Committee 435 of the American Concrete Institute. A brittle model for concrete and a linear-elastic behavior for steel reinforcement bars were considered. Results are presented through force-displacement curves and the sequence of cracking propagation. Also, a comparison of calculated instantaneous deflections of simply supported beams was made between the proposed model and other researches. It was verified that the proposed algorithm can predict adequately the cracking process and the deflections of beams subjected to service loadings, taking into account experimental results from other authors.

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The response of light-frame timber shear walls to lateral forces is the focus of the dissertation. The objective of this study was to obtain performance characteristics of shear walls with various aspect ratios and overturning restraint via experimental testing and analytical modeling. Presented are the test data of monotonic and cyclic tests on fifty-six light-frame timber shear walls with aspect ratios of 4:1, 2:1, 1:1, and 2:3. Overturning restraint conditions represent engineered construction and conventional construction practices. The walls representative of the engineered construction were attached to the base by means of tie-down anchors and shear bolts. As opposed to engineered construction, conventionally built walls were secured to the base by nails or shear bolts only. The specimens were tested in a horizontal position with oriented strandboard (OSB) sheathing on one side. To obtain conservative estimates, no dead load was applied in the wall plane during the tests. The nail-edge distance across the top and bottom plates varied from 10 mm (3/8 in.) to 19 mm (3/4 in.). Twelve walls were repaired after the initial tests and re-tested. A mechanics-based model was advanced to predict the racking resistance of conventional multi-panel shear walls using simple formulae. The deflections of engineered and conventional shear walls were predicted using the energy method combined with empirical formulae to account for load-deformation characteristics of sheathing-to-framing connections and overturning restraint. The proposed formulae were validated through comparison with test results obtained during this study. The results of the study serve to further development of a mechanics-based methodology for design of shear walls accounting for various wall configurations and boundary conditions. / Ph. D.

The experimental study reported upon in this thesis focused on the development of physical data characterizing the behavior of single-shear, laterally-loaded connections when loaded up to and beyond capacity (i.e., maximum resistance). Specimens included a wide array of connection configurations common in wood construction. All connections were tested monotonically in tension under displacement-controlled loading, parallel to the grain. Results of these tests are presented and discussed. Test variables of nailed connections included nail diameter, side member material type, and side member thickness. Test variables of bolted connections included bolt diameter, commercial species grouping of the main and side members, and main member thickness. Conclusions drawn from this research include mechanics-based explanations of numerous connection response trends observed with respect to test variables. Additionally, observed factors of safety and over-strengths of current design values are quantified on a capacity-basis. / Master of Science