Dissertations / Theses on the topic 'Symmetry testing'

Dans cette thèse, nous nous intéressons au problème de tester en grande dimension l'uniformité sur la sphère-unité $S^{p_n-1}$ (la dimension des observations, $p_n$, dépend de leur nombre, $n$, et être en grande dimension signifie que $p_n$ tend vers l'infini en même temps que $n$). Nous nous restreignons dans un premier temps à des contre-hypothèses ``monotones'' de densité croissante le long d'une direction ${\pmb \theta}_n\in S^{p_n-1}$ et dépendant d'un paramètre de concentration $\kappa_n>0$. Nous commençons par identifier le taux $\kappa_n$ auquel ces contre-hypothèses sont contiguës à l'uniformité ;nous montrons ensuite grâce à des résultats de normalité locale asymptotique, que le test d'uniformité le plus classique, le test de Rayleigh, n'est pas optimal quand ${\pmb \theta}_n$ est connu mais qu'il le devient à $p$ fixé et dans le cas FvML en grande dimension quand ${\pmb \theta}_n$ est inconnu.Dans un second temps, nous considérons des contre-hypothèses ``axiales'', attribuant la même probabilité à des points diamétralement opposés. Elles dépendent aussi d'un paramètre de position ${\pmb \theta}_n\in S^{p_n-1}$ et d'un paramètre de concentration $\kappa_n\in\R$. Le taux de contiguïté s'avère ici plus élevé et suggère un problème plus difficile que dans le cas monotone. En effet, le test de Bingham, le test classique dans le cas axial, n'est pas optimal à ${\pmb \theta}_n$ inconnu et $p$ fixé, et ne détecte pas les contre-hypothèses contiguës en grande dimension. C'est pourquoi nous nous tournons vers des tests basés sur les plus grande et plus petite valeurs propres de la matrice de variance-covariance et nous déterminons leurs distributions asymptotiques sous les contre-hypothèses contiguës à $p$ fixé.Enfin, à l'aide d'un théorème central limite pour martingales, nous montrons que sous certaines conditions et après standardisation, les statistiques de Rayleigh et de Bingham sont asymptotiquement normales sous l'hypothèse d'invariance par rotation des observations. Ce résultat permet non seulement d'identifier le taux auquel le test de Bingham détecte des contre-hypothèses axiales mais aussi celui auquel il détecte des contre-hypothèses monotones.<br>In this thesis we are interested in testing uniformity in high dimensions on the unit sphere $S^{p_n-1}$ (the dimension of the observations, $p_n$, depends on their number, and high-dimensional data are such that $p_n$ diverges to infinity with $n$).We consider first ``monotone'' alternatives whose density increases along an axis ${\pmb \theta}_n\in S^{p_n-1}$ and depends on a concentration parameter $\kappa_n>0$. We start by identifying the rate at which these alternatives are contiguous to uniformity; then we show thanks to local asymptotic normality results that the most classical test of uniformity, the Rayleigh test, is not optimal when ${\pmb \theta}_n$ is specified but becomes optimal when $p$ is fixed and in the high-dimensional FvML case when ${\pmb \theta}_n$ is unspecified.We consider next ``axial'' alternatives, assigning the same probability to antipodal points. They also depend on a location parameter ${\pmb \theta}_n\in S^{p_n-1}$ and a concentration parameter $\kappa_n\in\R$. The contiguity rate proves to be higher in that case and implies that the problem is more difficult than in the monotone case. Indeed, the Bingham test, the classical test when dealing with axial data, is not optimal when $p$ is fixed and ${\pmb \theta}_n$ is not specified, and is blind to the contiguous alternatives in high dimensions. This is why we turn to tests based on the extreme eigenvalues of the covariance matrix and establish their fixed-$p$ asymptotic distributions under contiguous alternatives.Finally, thanks to a martingale central limit theorem, we show that, under some assumptions and after standardisation, the Rayleigh and Bingham test statistics are asymptotically normal under general rotationally symmetric distributions. It enables us to identify the rate at which the Bingham test detects axial alternatives and also monotone alternatives.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished

Microarray technology allows the simultaneous measurement of thousands of gene expressions simultaneously. As a result of this, many statistical methods emerged for identifying differentially expressed genes. Kerr et al. (2001) proposed analysis of variance (ANOVA) procedure for the analysis of gene expression data. Their estimators are based on the assumption of normality, however the parameter estimates and residuals from this analysis are notably heavier-tailed than normal as they commented. Since non-normality complicates the data analysis and results in inefficient estimators, it is very important to develop statistical procedures which are efficient and robust. For this reason, in this work, we use Modified Maximum Likelihood (MML) and Adaptive Maximum Likelihood estimation method (Tiku and Suresh, 1992) and show that MML and AMML estimators are more efficient and robust. In our study we compared MML and AMML method with widely used statistical analysis methods via simulations and real microarray data sets.

[Formulae and special characters can not be reproduced here. Please see the pdf version of the Abstract for an accurate reproduction.] The thesis provides a comprehensive study on the behaviour of sand with a small amount of fines [i.e.1/3 plastic fines and 2/3 non-plastic fines]. The work is carried out experimentally under axi-symmetric conditions using the triaxial apparatus. Conventional drained triaxial tests are conducted on isotropic consolidated specimens and all the tests indicate that sand with fines does not manifest any unusual behaviour under drained conditions. However in undrained shearing the so-called ???reverse behaviour??? is noted. The study demonstrates that the reverse behaviour conforms to the critical state framework because significant changes in the position and geometry of the critical state [CS] and isotropic consolidation [IL] lines are caused by the presence of fines. These changes cannot be adequately modelled by the intergranular void ratio as proposed by Thevanayagam and Mohan (2000). This study also demonstrates that the original state parameter [special character] as proposed by Been and Jefferies (1985) is not an adequate parameter to predict the undrained behaviour trend. A new parameter termed ???modified state parameter??? [special character] is proposed to account for the combined effects of density and confining pressure. The suitability of the modified state parameter to characterise the response of parent sand and sand with fines is assessed for a range of void ratios and confining pressures. The effect of drained stress history is an important factor affecting the subsequent undrained response. Drained pre-shearing to failure is found to improve considerably the subsequent undrained response to the extent that liquefaction may not occur. Different drained pre-shearing histories have different effects on the undrained response. However in these tests [special character] has limitations in quantifying the subsequent undrained stress-strain response. Hence, a new framework of ???yielding parameter??? [special character] extends the capability of [special character] and additional data is presented to demonstrate the suitability of this concept. The implementation of [special character] depends on whether the previous stress state reached during the stress history is below or at failure. The effects of drained pre-shearing on the position and movement of failure surface are investigated. It is found that drained pre-shearing to failure at larger confining pressures has the effect of shifting upwards part of the drained failure surface. The shift at larger stress ratios [special character] may be described in terms of dilatancy and modified state parameter at failure. The so-called strain path tests are conducted to study the influence of strain increment ratio on the deformation behaviour of sand with fines. It is found that the value of [special character] has significant effects on the stress-strain behaviour. Along negative [special character] paths the soil strain softens in the form of decreasing the shear resistance before reaching the failure state. In contrast, along positive [special character] paths the soil strain hardens to an asymptotic stress ratio. The asymptotic stress ratio decreases with increasing [special character] along a linear relationship. The framework of [special character] cannot quantify the stress-strain response along positive and negative strain paths. Consequently an ???instability parameter??? [special character] is proposed to extend the capabilities of [special character] and the reliability of this parameter is further assessed. The behaviour along a range of positive and negative [special character] paths is investigated on pre-sheared specimens. In negative [special character] the effective stress paths reach a surface located higher than the monotonic failure surface on which they trace downward towards the origin of stress space. The results indicate this surface may be the same as the drained failure envelope which has been shifted as a result of drained pre-shearing. In positive [special character] paths a large improvement is noted in both the strength and stiffness of the soil. Note The parameters [special character] and [special character] are all generalisations of [special character] so that the behaviour under complex conditions can be characterised.

碩士<br>淡江大學<br>數學學系<br>92<br>Two of the most popular nonparametric methods for testing symmetry are the sign test ( Hettmansperger,1984 ) and Wilcoxon signed rank test ( Wilcoxon,1945 ). Recently, many scholars have proposed new tests for this problem. For example, McWilliams ( 1990 ) presented a test statistic R* based on a run statistic. Modarres and Gastwirth ( 1996 ) presented a test statistic Mp by using Wilcoxon scores to weight the runs. Chun-ta Li and Wei-hou Cheng ( 1999 ) presented a new test statistic Ck which is very easy to apply. Most of these papers focused on the case of a known center. In this paper, we consider the situation when the center is unknown. The basic idea is to estimate the center by using sample median, and construct a test statistic like the test statistic Ck . We first use Monte Carlo simulation to find the critical point. After some comparisons of power, we found k=6 to be a good choice. Then we compare the power of our test statistic C6* with the test statistic C6 using distributions belonging to the generalized lambda family. We found that our test statistic C6* performs reasonably well.

碩士<br>國立臺北大學<br>統計學系<br>91<br>This thesis aims primarily to test the symmetry in Normal Inverse Gaussian distributions which act as Normal variance-mean mixtures with an Inverse Gaussian mixing distribution. Due to the complicated structure of normal inverse gaussian distribution, two approximate large-sample tests are to be applied. One of the two methods is by way of asymptotic distribution of likelihood ratio tests, another method of constructing a large-sample test statistic is based on an estimator that has an asymptotic normal distribution. An EM type algorithm is provided for the Maximum Likelihood estimation of the Normal Inverse Gaussian distribution in the two methods. Finally, according to the simulation results some conclusions are given.

Title page, abstract and table of contents only. The complete thesis in print form is available from the University of Adelaide Library.<br>http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1274742<br>Thesis (Ph.D.) -- University of Adelaide, School of Psychology, 2007

This thesis investigated the testing effect, which is the tendency of testing to enhance learning and memory retention. Specifically, the thesis examines the extent to which test-induced retention benefits extend to the questions as well as the answers; are these benefits symmetrical? The results in the laboratory experiment (Experiment 1) demonstrated that the symmetry in retention benefits is highly dependent on the accuracy in the initial test. For the items students answered correctly in the initial test, the retention benefit was found to be symmetrical across the questions and answers supporting the retrieval hypothesis of the testing effect. However, for initially incorrect items, the retention performance was substantially better for the questions than the answers suggesting an asymmetrical effect from testing, a result that is also consistent with the retrieval hypothesis. These results were replicated using educationally-relevant materials with a delay up to five and a half months in two hybrid studies combining actual classroom experiences with controlled assessments in the laboratory (Experiment 2A & 2B). A series of follow-up studies were conducted to examine the difference in retention performance of the questions and the answers for the initial incorrect items. Particularly, the experiments focused on investigating various factors that might contribute to or eliminate the difference in retention performance, including prior study (Experiment 3), verification feedback (Experiment 4A & 4B) and answer feedback (Experiment 5). The thesis also touched upon various issues related to the temporal dimension of the testing effect. The previous notion that testing slows down forgetting rate is not supported by the data. Instead, testing seems to provide a short-term insulation against immediate forgetting, but then memory for the tested materials decays in the same way as the non-tested materials.

As part of an ongoing program to study fundamental symmetries in nuclear physics, a thorough investigation into shell-model isospin-symmetry-breaking (ISB) calculation theory has been conducted using direct reactions to observe detailed nuclear-structure information. The work presented in this Thesis focuses on the 62Ga superallowed beta-decay system, and consists of two primary experiments; 1) A 64Zn(d,t)63Zn single-neutron transfer reaction, aimed at observing spectroscopic strengths to help guide calculation model-space truncations for the beta-decay wave function radial-overlap component of ISB, and 2) A two-neutron 64Zn(p,t)62Zn transfer to search for excited 0+ states in the daughter nucleus of 62Ga. The experiments were performed at the Maier-Leibnitz-Laboratory, on the joint campuses of the Ludwig-Maximilians Universitat and the Technische Universitat Munchen, in Garching, Germany. In total, 162 states in 63Zn were populated from the 64Zn(d,t) reaction, up to an excitation energy of 4.8 MeV, including the observation of 125 new levels, and unique spin/parity assignments for 92 states. As a result, this work provides the most complete picture for low-spin states in 63Zn to date. A comparison of the extracted S values to the predicted shell-model spectroscopic factors shows an overall over-prediction of strength for the 2p3/2 orbital, and a large disagreement for the 1f7/2 orbital above ~3.5 MeV. No significant 1g9/2 strength was observed, leading to the conclusion that the importance of the 1g9/2 orbital for ISB is small. Additionally, 67 states were observed in 62Zn using the two-neutron pickup mechanism, including the observation of five 0+ states. More than 99% of the total 0+ (p,t) cross-section is observed in the ground-state reaction channel, implying a nearly maximal overlap of the wave functions with the two-nucleon transfer operator. The dominance of the ground-state-to-ground-state (p,t) cross section is strikingly similar to the dominance of the superallowed Fermi beta-decay between isobaric-analogue 0+ states. This suggests that the population of excited 0+ states in the (p,t) reaction may reflect the population in the Fermi decay process, and can be used to guide future experimental and theoretical work. Further discussion of these results as they relate to the ISB correction calculations, and the implications for future theoretical work are presented in this Thesis.<br>This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, the Ontario Ministry of Economic Development and Innovation, the DFG Cluster of Excellence `Origin and Structure of the Universe', and NSF grant PHY-1068217.

Ce mémoire étudie l'algorithme d'amplification de l'amplitude et ses applications dans le domaine de test de propriété. On utilise l'amplification de l'amplitude pour proposer le plus efficace algorithme quantique à ce jour qui teste la linéarité de fonctions booléennes et on généralise notre nouvel algorithme pour tester si une fonction entre deux groupes abéliens finis est un homomorphisme. Le meilleur algorithme quantique connu qui teste la symétrie de fonctions booléennes est aussi amélioré et l'on utilise ce nouvel algorithme pour tester la quasi-symétrie de fonctions booléennes. Par la suite, on approfondit l'étude du nombre de requêtes à la boîte noire que fait l'algorithme d'amplification de l'amplitude pour amplitude initiale inconnue. Une description rigoureuse de la variable aléatoire représentant ce nombre est présentée, suivie du résultat précédemment connue de la borne supérieure sur l'espérance. Suivent de nouveaux résultats sur la variance de cette variable. Il est notamment montré que, dans le cas général, la variance est infinie, mais nous montrons aussi que, pour un choix approprié de paramètres, elle devient bornée supérieurement.<br>This thesis studies the quantum amplitude amplification algorithm and some of its applications in the field of property testing. We make use of the amplitude amplification algorithm to design an algorithm testing the linearity of Boolean functions which is more efficient than the previously best known quantum algorithm. We then generalize this new algorithm to test if a function between two finite abelian groups is a homomorphism. We improve on the previously best known algorithm for testing the symmetry of Boolean functions and use this new algorithm to test the quasi-symmetry of Boolean functions. Next, we further the study of the query complexity of the amplitude amplification algorithm for unknown initial amplitude. We give a rigorous description of the random variable representing the number of queries made by the algorithm and present the previously known result on its expected value upper bound. We then provide new results on the variance of this random variable. It is shown that, in the general case, the variance cannot be bounded above. We show, however, that it can be bounded for an appropriate choice of parameters.

Theme: Evaluation of stability level of athletes (14-15 years) by MFT S3 Check Aims: The aim of this diploma thesis is evaluation of stability level, sensomotor and pose symmetry of both-limb posture by MFT S3 Check system at a selected group of children attending an athletic club. I used the comparison of values between a group of girls and boys. Methodology: The level of stability, sensomotor and pose symmetry was measured in the course of the race season. The data was measured by MFT S3 Check system and further one leg stand test was used. Measurment was supplemented with a questionnaire survey. I used the comparison of values between a group of girls and boys Results: In the test MFT S3 Check the girls achieved above-average evaluation in the index values and stability sensomotorics than boys, who were evaluated in the test below average. The sum of the average values of divergences from the ideal ratio at both monitored levels were lower by 0.15 at boys. There was proved a medium dependence of body weight and BMI values on the level of stability. Shoe size, incidence of ankle injuries, nor the results of the one leg stand test had no impact on the level of stability. Key words: senzomotor, stability, symmetry, 14-15 years, athletics, testing

碩士<br>國立臺北科技大學<br>土木與防災研究所<br>98<br>First, the study numerically simulates a structure by use of SAP2000. According to the structural time response calculated from the simulation, the modal parameters are identified using ARX-model system identification, and then compared with the ones obtained from modal analysis. The comparison demonstrates the accuracy of the used system identification method. Next, we consider a unsymmetric structure which presents torsional behavior, and collect the time response of the structure in a real test. We find that the torsional mode can be detected by applying system identification to the collected data. Meanwhile,traditional accelerometers ( piezoelectric accelerometers ) and advanced accelerometers ( MEMS accelerometers ) are used in the test. The performance of the two sensors are compared. Finally, the modal parameters of a small-scale four-story steel frame structure are identified using ambient vibration records of the structure on which no external forces are acting. The results are compared with the ones obtained using the forced vibration records. Moreover, We conduct system identification for the structure with different damage combinations. Based on the identified mode shapes, the damage detection index ( inter-story drift mode shape, IDMS ) for each damaged structure is calculated. The results show that the system identification of ambient vibration records as well as the calculated damage detection index can effectively detect damage locations.

The semiconductor industry has been driven by Moore's law for almost half a century. Miniaturization of device size has allowed more transistors to be packed into a smaller area while the improved transistor performance has resulted in a significant increase in frequency. Increased density of devices and rising frequency led, unfortunately, to a power density problem which became an obstacle to further integration. The processor industry responded to this problem by lowering processor frequency and integrating multiple processor cores on a die, choosing to focus on Thread Level Parallelism (TLP) for performance instead of traditional Instruction Level Parallelism (ILP). While continued scaling of devices have provided unprecedented integration, it has also unfortunately led to a few serious problems: The first problem is that of increasing rates of system failures due to soft errors and aging defects. Soft errors are caused by ionizing radiations that originate from radioactive contaminants or secondary release of charged particles from cosmic neutrons. Ionizing radiations may charge/discharge a storage node causing bit flips which may result in a system failure. In this dissertation, we propose solutions for online detection of such errors in microprocessors. A small and functionally limited core called the Sentry Core (SC) is added to the multicore. It monitors operation of the functional cores in the multicore and whenever deemed necessary, it opportunistically initiates Dual Modular redundancy (DMR) to test the operation of the cores in the multicore. This scheme thus allows detection of potential core failure and comes at a small hardware overhead. In addition to detection of soft errors, this solution is also capable of detecting errors introduced by device aging that results in failure of operation. The solution is further extended to verify cache coherence transactions. A second problem we address in this dissertation relate to power concerns. While the multicore solution addresses the power density problem, overall power dissipation is still limited by packaging and cooling technologies. This limits the number of cores that can be integrated for a given package specification. One way to improve performance within this constraint is to reduce power dissipation of individual cores without sacrificing system performance. There have been prior solutions to achieve this objective that involve Dynamic Voltage and Frequency Scaling (DVFS) and the use of sleep states. DVFS and sleep states take advantage of coarse grain variation in demand for computation. In this dissertation, we propose techniques to maximize performance-per-power of multicores at a ne grained time scale. We propose multiple alternative architectures to attain this goal. One of such architectures we explore is Asymmetric Multicore Processors (AMPs). AMPs have been shown to outperform the symmetric ones in terms of performance and Performance-per-Watt for a fixed resource and power budget. However, effectiveness of these architectures depends on accurate thread-to-core scheduling. To address this problem, we propose online thread scheduling solutions responding to changing computational requirements of the threads. Another solution we consider is for Symmetric Multicore processors (SMPs). Here we target sharing of the large and underutilized resources between pairs of cores. While such architectures have been explored in the past, the evaluations were incomplete. Due to sharing, sometimes the shared resource is a bottleneck resulting in signicant performance loss. To mitigate such loss, we propose the Dynamic Voltage and Frequency Boosting (DVFB) of the shared resources. This solution is found to significantly mitigate performance loss in times of contention. We also explore in this dissertation, performance-per-Watt improvement of individual cores in a multicore. This is based on dynamic reconfiguration of individual cores to run them alternately in out-of-order (OOO) and in-order (InO) modes adapting dynamically to workload characteristics. This solution is found to significantly improve power efficiency without compromising overall performance. Thus, in this dissertation we propose solutions for several important problems to facilitate continued scaling of processors. Specifically, we address challenges in the area of reliability of computation and propose low power design solutions to address power constraints.

This thesis is focused on hash families and cover-free families and their application to problems in cryptography. We present new necessary conditions for generalized separating hash families, and provide new explicit constructions. We then consider three cryptographic applications of hash families and cover-free families. We provide a stronger de nition of anonymity in the context of shared symmetric key primitives and give a new scheme with improved anonymity properties. Second, we observe that nding the invalid signatures in a set of digital signatures that fails batch veri cation is a group testing problem, then apply and compare many group testing algorithms to solve this problem e ciently. In particular, we apply group testing algorithms based on cover-free families. Finally, we construct a one-time signature scheme based on cover-free families with short signatures.