Topological data analysis emerged as a field in the 2000s and has proven very useful for examining the shape of data sets. Using persistent homology as their main methodology researchers has succesfully applied the theory presented in this paper to study as varied subjects as robot motion, brain connectivity, network theory, finger print analysis and computer vision.  The mathematical theory behind persistent homology has traditionally required training far beyond what an average engineer would have. Therefore much theory is usually left out of presentations meant for an audience outside of a mathematics department. This paper contains a novel approach to the presentation of this theory, maintaining mathematical rigour while only using linear algebra as its building blocks.

Persistent homology is a technique of topological data analysis that seeks to understand the shape of data. We study the effectiveness of a single-layer perceptron and gradient boosted classification trees in classifying perhaps the most well-known data set in machine learning, the MNIST-Digits, or MNIST. An alternative representation is constructed, called MNIST-PD. This construction captures the topology of the digits using persistence diagrams, a product of persistent homology. We show that the models are more effective when trained on MNIST compared to MNIST-PD. Promising evidence reveals that the topology is learned by the algorithms. / Thesis / Master of Science (MSc)

In this study the problem may be stated as follows: to determine persistent life situations in a Public Relations Program. The problem involves a survey of school-community-public relations in the areas of family living, recreational living, occupational living and community living as developed in practice and in educational literature; the establishing of sound criteria for such a program; the application of the criteria to the techniques of the program; and the evaluation of the program once it has been established.

Yes / This paper examines whether major media advertising expenditures help in predicting future earnings. We consider the role of media advertising in firms’ marketing efforts and posit that persistent advertisers are more likely to benefit from advertising activities in creating long‐lived intangible assets. Employing a sample of persistent UK advertisers over the period 1997–2013, we find that advertising expenditures are significantly positively associated with firms’ future earnings and market value. We also report size and sector‐based differences in the association between advertising and firms’ future earnings. Our additional analysis provides support for the arguments that despite the recent rise in digital advertising budgets, traditional advertising media are still effective in positively influencing firms’ performance. Overall, the results of this study are consistent with the view that advertising expenditures produce intangible assets, at least for firms in certain sectors. These findings have implications for marketers in providing evidence of the value generated by firms’ advertising budgets, for investors in validating the relevance of advertising information in influencing future earnings, and for accounting regulators in relation to the provision of useful insights for any future deliberations on financial reporting policies for advertising expenditures.

Structural material fatigue is a leading cause of failure and has motivated fatigue-resistant design to eliminate risks to human lives. Intrinsic microstructural features alter fatigue deformation mechanisms so profoundly that, essentially, fatigue properties of structural materials become deviant. With this in mind, we initiated this project to investigate the microstructural effect on fatigue behavior of potential structural high entropy alloys. With a better understanding of the effect of microstructure features on fatigue properties, the ultimate goal was to engineer the microstructure to enhance the fatigue life of structural materials. The effects of two major deformation mechanisms presented here are twinning-induced fatigue crack retardation, and transformation-induced fatigue crack retardation. The fundamental principle of both mechanisms is to delay the fatigue crack propagation rate by altering the work hardening ability locally within the crack plastic zone. In ultrafine grained triplex Al0.3CoCrFeNi, nano-sized deformation twins were observed during cyclic loading in FCC matrix due to low stacking fault energy (SFE). The work-hardening ability of the material near the crack was sustained with the formation of twins according to Considere's criteria. Further, due to the ultrafine-grained (UFG) nature of the material, fatigue runout stress was enhanced. In a coarse-grained, dual-phase high entropy alloy, persistent slip bands formed in FCC matrix during cyclic loading due mainly to the slight composition change that affects the SFE in the FCC matrix and eventually alters the deformation mechanism. Another way known to alter an alloy's work hardening (WH) ability is transformation-induced plasticity (TRIP). In some alloys, phase transformation happens due to strain localization, which alters the work-hardening ability. iii In a fine-grained, dual-phase metastable high entropy alloy, gamma (f.c.c.) to epsilon (h.c.p.) transformation occurred in the plastic zone that was induced from cracks. Thus, we designed a Cu-containing FeMnCoCrSi high entropy alloy that exhibited a normalized fatigue ratio of ~ 0.62 UTS (ultimate tensile strength). Our design approach was based on (a) engineering the gamma phase stability to attain sustained work hardening through delayed gamma (f.c.c.) to epsilon (h.c.p.) transformation to hinder fatigue crack propagation, (b) incorporating an ultrafine-grained microstructure to delay crack initiation, and (c) forming deformation twins to reduce the crack propagation rate. We verified that a UFG gamma dominant microstructure could provide opportunities for exceptional fatigue resistance, as sustained WH activity strengthened the material locally in the crack plastic zone, thereby validating our expectation that the combination of UFG and TRIP is a path to design the next generation of fatigue-resistant alloys.

京都大学 / 新制・課程博士 / 博士(人間・環境学) / 甲第25388号 / 人博第1130号 / 新制||人||263(附属図書館) / 2023||人博||1130(吉田南総合図書館) / 京都大学大学院人間・環境学研究科相関環境学専攻 / (主査)教授 田部 勢津久, 教授 吉田 寿雄, 教授 中村 敏浩, 教授 田中 勝久 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM

<p>Harnessing the power of data has been a driving force for computing in recently years. However, the non-vectorized or even non-Euclidean nature of certain data with complex structures also poses new challenges to the data science community. Topological data analysis (TDA) has proven effective in several scenarios for alleviating the challenges, by providing techniques that can reveal hidden structures and high-order connectivity for data. A central technique in TDA is called persistent homology, which provides intervals tracking the birth and death of topological features in a growing sequence of topological spaces. In this dissertation, we study the representative problem for persistent homology, motivated by the observation that persistent homology does not pinpoint a specific homology class or cycle born and dying with the persistence intervals. Furthermore, studying the representatives also leads us to new findings for related problems such as persistence computation.<br> </p> <p>First, we look into the representative problem for (standard) persistence homology and term the representatives as persistent cycles. We define persistent cycles as cycles born and dying with given persistence intervals and connect the definition to interval decomposition for persistence modules. We also look into the computation of optimal (minimum) persistent cycles which have guaranteed quality. We prove that it is NP-hard to compute minimum persistent p-cycles for the two types of intervals in persistent homology in general dimensions (p>1). In view of the NP-hardness results, we then identify a special but important class of inputs called weak (p+1)-pseudomanifolds whose minimum persistent p-cycles can be computed in polynomial time. The algorithms are based on a reduction to minimum (s,t)-cuts on dual graphs.<br> </p> <p>Second, we propose alternative persistent cycles capturing the dynamic changes of homological features born and dying with persistence intervals, which the previous persistent cycles do not reveal. We focus on persistent homology generated by piecewise linear (PL) functions and base our definition on an extension of persistence called the levelset zigzag persistence. We define a sequence of cycles called levelset persistent cycles containing a cycle between each consecutive critical points within the persistence interval. Due to the NP-harness results proven previously, we propose polynomial-time algorithms computing optimal sequences of levelset persistent p-cycles for weak (p+1)-pseudomanifolds. Our algorithms draw upon the idea of relating optimal cycles to min-cuts in a graph that we exploited earlier for standard persistent cycles. Note that levelset zigzag poses non-trivial challenges for the approach because a sequence of optimal cycles instead of a single one needs to be computed in this case.<br> </p> <p>Third, we investigate the computation of zigzag persistence on graph inputs, motivated by the fact that graphs model real-world circumstances in many applications where they may constantly change to capture dynamic behaviors of phenomena. Zigzag persistence, an extension of the standard persistence incorporating both insertions and deletions of simplices, is one appropriate instrument for analyzing such changing graph data. However, unlike standard persistence which admits nearly linear-time algorithms for graphs, such results for the zigzag version improving the general $O(m^\omega)$ time complexity are not known, where $\omega< 2.37286$ is the matrix multiplication exponent. We propose algorithms for zigzag persistence on graphs which run in near-linear time. Specifically, given a filtration of length m on a graph of size n, the algorithm for 0-dimension runs in $O(m\log^2 n+m\log m)$ time and the algorithm for 1-dimension runs in $O(m\log^4 n)$ time. The algorithm for 0-dimension draws upon another algorithm designed originally for pairing critical points of Morse functions on 2-manifolds. The correctness proof of the algorithm, which is a major contribution, is achieved with the help of representatives. The algorithm for 1-dimension pairs a negative edge with the earliest positive edge so that a representative 1-cycle containing both edges resides in all intermediate graphs.</p>

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The advent of Storage Class Memory (SCM) is driving a rethink of storage systems towards a single-level architecture where memory and storage are merged. In this context, several works have investigated how to design persistent trees in SCM as a fundamental building block for these novel systems. However, these trees are significantly slower than DRAM-based counterparts since trees are latency-sensitive and SCM exhibits higher latencies than DRAM. In this paper we propose a novel hybrid SCM-DRAM persistent and concurrent B-Tree, named Fingerprinting Persistent Tree (FPTree) that achieves similar performance to DRAM-based counterparts. In this novel design, leaf nodes are persisted in SCM while inner nodes are placed in DRAM and rebuilt upon recovery. The FPTree uses Fingerprinting, a technique that limits the expected number of in-leaf probed keys to one. In addition, we propose a hybrid concurrency scheme for the FPTree that is partially based on Hardware Transactional Memory. We conduct a thorough performance evaluation and show that the FPTree outperforms state-of-the-art persistent trees with different SCM latencies by up to a factor of 8.2. Moreover, we show that the FPTree scales very well on a machine with 88 logical cores. Finally, we integrate the evaluated trees in memcached and a prototype database. We show that the FPTree incurs an almost negligible performance overhead over using fully transient data structures, while significantly outperforming other persistent trees.

Modern operating systems have been designed around the hypotheses that (a) memory is both byte-addressable and volatile and (b) storage is block addressable and persistent. The arrival of new Persistent Memory (PM) technologies, has made these assumptions obsolete. Despite much of the recent work in this space, the need for consistently sharing PM data across multiple applications remains an urgent, unsolved problem. Furthermore, the availability of simple yet powerful operating system support remains elusive. In this dissertation, we propose and build The Region System – a high-performance operating system stack for PM that implements usable consistency and persistence for application data. The region system provides support for consistently mapping and sharing data resident in PM across user application address spaces. The region system creates a novel IPI based PMSYNC operation, which ensures atomic persistence of mapped pages across multiple address spaces. This allows applications to consume PM using the well understood and much desired memory like model with an easy-to-use interface. Next, we propose a metadata structure without any redundant metadata to reduce CPU cache flushes. The high-performance design minimizes the expensive PM ordering and durability operations by embracing a minimalistic approach to metadata construction and management. To strengthen the case for the region system, in this dissertation, we analyze different types of applications to identify their dependence on memory mapped data usage, and propose user level libraries LIBPM-R and LIBPMEMOBJ-R to support shared persistent containers. The user level libraries along with the region system demonstrate a comprehensive end-to-end software stack for consuming the PM devices.