<p dir="ltr">In most theoretical studies on missing data analysis, data is typically assumed to be missing according to a specific probabilistic model. However, such assumption may not accurately reflect real-world situations, and sometimes missing is not purely random. In this thesis, our focus is on analyzing incomplete data matrices without relying on any probabilistic model assumptions for the missing schemes. To characterize a missing scheme deterministically, we employ a graph whose adjacency matrix is a binary matrix that indicates whether each matrix entry is observed or not. Leveraging its graph properties, we mathematically represent the missing pattern of an incomplete data matrix and conduct a theoretical analysis of how this non-random missing pattern affects the solvability of specific problems related to incomplete data. This dissertation primarily focuses on three types of incomplete data problems characterized by their low-rank nature: structured prediction, matrix completion, and sparse PCA.</p><p dir="ltr">First, we investigate a basic structured prediction problem, which involves recovering binary node labels on a fixed undirected graph, where noisy binary observations corresponding to edges are given. Essentially, this setting parallels a simple binary rank-1 symmetric matrix completion problem, where missing entries are determined by a fixed undirected graph. Our aim is to establish the fundamental limit bounds of this problem, revealing a close association between the limits and graph properties, such as connectivity.</p><p dir="ltr">Second, we move on to the general low-rank matrix completion problem. In this study, we establish provable guarantees for exact and approximate low-rank matrix completion problems that can be applied to any non-random missing pattern, by utilizing the observation graph corresponding to the missing scheme. We theoretically and experimentally show that the standard constrained nuclear norm minimization algorithm can successfully recover the true matrix when the observation graph is well-connected and has similar node degrees. We also verify that matrix completion is achievable with a near-optimal sample complexity rate when the observation graph has uniform node degrees and its adjacency matrix has a large spectral gap.</p><p dir="ltr">Finally, we address the sparse PCA problem, featuring an approximate low-rank attribute. Missing data is common in situations where sparse PCA is useful, such as single-cell RNA sequence data analysis. We propose a semidefinite relaxation of the non-convex $\ell_1$-regularized PCA problem to solve sparse PCA on incomplete data. We demonstrate that the method is particularly effective when the observation pattern has favorable properties. Our theory is substantiated through synthetic and real data analysis, showcasing the superior performance of our algorithm compared to other sparse PCA approaches, especially when the observed data pattern has specific characteristics.</p>

This study provides a qualitative examination of the role of visualization through an understanding of the thought processes that occur during visualization when Grade 9 learners engage in data handling and spatial tasks. Data were gathered in a problem-centred context from learners' written responses in order to determine the students' visuality. Visuality is defined as how often learners used visualization. In addition interviews were conducted with the learners who described the thought processes that they engaged in during visualization while involved in problem solving. The role of visualization was highlighted through the processes that learners described during the interviews. The tasks which provided manipulative materials helped learners create visual images which promoted the process of visualization. Certain recommendations were made. Knowledge of the role of visualization enables the educator to encourage the use of visualization during the teaching of mathematics. / Educational Studies / M.Ed. (Mathematical Education)

International Telemetering Conference Proceedings / October 28-31, 1996 / Town and Country Hotel and Convention Center, San Diego, California / This paper reviews the performance requirements that provided the baseline for development of the onboard data system, RF transmission system, and ground segment receiving system of the Midcourse Space Experiment (MSX) spacecraft. The onboard Command and Data Handling (C&DH) System was designed to support the high data outputs of the three imaging sensor systems onboard the spacecraft and the requirement for large volumes of data storage. Because of the high data rates, it was necessary to construct a dedicated X-band ground receiver system at The Johns Hopkins University Applied Physics Laboratory (APL) and implement a tape recorder system for recording and downlinking sensor and spacecraft data. The system uses two onboard tape recorders to provide redundancy and backup capabilities. The storage capability of each tape recorder is 54 gigabits. The MSX C&DH System can record data at 25 Mbps or 5 Mbps. To meet the redundancy requirements of the high-priority experiments, the data can also be recorded in parallel on both tape recorders. To provide longer onboard recording, the data can also be recorded serially on the two recorders. The reproduce (playback) mode is at 25 Mbps. A unique requirement of the C&DH System is to multiplex and commutate the different output rates of the sensors and housekeeping signals into a common data stream for recording. The system also supports 1-Mbps real-time sensor data and 16-kbps real-time housekeeping data transmission to the dedicated ground site and through the U.S. Air Force Satellite Control Network ground stations. The primary ground receiving site for the telemetry is the MSX Tracking System (MTS) at APL. A dedicated 10-m X-band antenna is used to track the satellite during overhead passes and acquire the 25-Mbps telemetry downlinks, along with the 1-Mbps and 16-kbps real-time transmissions. This paper discusses some of the key technology trade-offs that were made in the design of the system to meet requirements for reliability, performance, and development schedule. It also presents some of the lessons learned during development and the impact these lessons will have on development of future systems.

By means of a Monte Carlo study, this paper investigates the relative performance of Listwise Deletion, the EM-algorithm and the default algorithm in the MICE-package for R (PMM) in estimating regression coefficients under a left truncated covariate with missing values. The intention is to investigate whether the three frequently used missing data techniques are robust against left truncation when missing values are MCAR or MAR. The results suggest that no technique is superior overall in all combinations of factors studied. The EM-algorithm is unaffected by left truncation under MCAR but negatively affected by strong left truncation under MAR. Compared to the default MICE-algorithm, the performance of EM is more stable across distributions and combinations of sample size and missing rate. The default MICE-algorithm is improved by left truncation but is sensitive to missingness pattern and missing rate. Compared to Listwise Deletion, the EM-algorithm is less robust against left truncation when missing values are MAR. However, the decline in performance of the EM-algorithm is not large enough for the algorithm to be completely outperformed by Listwise Deletion, especially not when the missing rate is moderate. Listwise Deletion might be robust against left truncation but is inefficient.

This study provides a qualitative examination of the role of visualization through an understanding of the thought processes that occur during visualization when Grade 9 learners engage in data handling and spatial tasks. Data were gathered in a problem-centred context from learners' written responses in order to determine the students' visuality. Visuality is defined as how often learners used visualization. In addition interviews were conducted with the learners who described the thought processes that they engaged in during visualization while involved in problem solving. The role of visualization was highlighted through the processes that learners described during the interviews. The tasks which provided manipulative materials helped learners create visual images which promoted the process of visualization. Certain recommendations were made. Knowledge of the role of visualization enables the educator to encourage the use of visualization during the teaching of mathematics. / Educational Studies / M.Ed. (Mathematical Education)

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado. / Construction projects for buildings, in the execution stage, show a variation of the real with respect to what is planned in the budget. The consequence of this lag presented usually causes large economic losses. Given this situation, in the construction industry, various control systems have been developed that have as a final deliverable a frequent management report, which serves to make decisions regarding the analyzed, whose results are applied and evaluated after a specific period of time. These management reports have good results at the time of their application; however, data processing, analysis execution, and decision making take approximately 30 days. In this sense, the present investigation proposes to develop a control system focused in real time, generated by the daily control in the execution stage. The results show a reduction of waste in the main resources of multi-family building projects, and this is in labor and materials, identifying the causes that originate them and suggesting generic solutions, at the end of the workday. / Revisión por pares

På CBH (Skolan för kemi, bioteknologi och hälsa) har en mikro-CT utvecklats, men med förbättringspotential gällande användbarheten. Målet med kandidatexamensarbetet var att förbättra mjukvaran genom att automatisera tre olika aspekter av manuell datahantering: Dels att placera filerna i en mapp med namn kopplat till valda bildtagningsinställningar. Dels att kopiera data via SCP mellan två datorer kopplade till mikro-CT:n. Samt att radera kopierade data från disken som preliminärt sparar filerna. För att möjliggöra en automatisk dataöverföring implementerades ett SSH-nyckelpar med publik nyckelautentisering mellan de två datorerna. Till den befintliga mjukvaran tillades ett skript samt en klass med handhavande över de tre automatiseringsaspekterna. Genom användargränssnittet hämtar klassen inledningsvis information om bildtagningsinställningarna till mappnamnet och när bildtagningen är klar anropar programkoden skriptfilen som utför SCP-kopieringen. Därefter kontrolleras att inga data gått förlorade under överföringen, varefter en radering av de kopierade filerna utförs på den ursprungliga disken. Den nya klassen förbättrar mikro-CT:ns användarvänlighet och underlättar hanteringen av data efter en bildtagning. / At CBH (The School of Engineering Sciences in Chemistry, Biotechnology and Health) a micro-CT has been developed, but the system has potential improvement regarding the usability. The purpose of this bachelor’s thesis was to improve the software by automatizing three aspects of manual data handling: Firstly to place the data in a folder with a name related to the obtained acquisition settings. Secondly to transfer files through SCP between the two computers connected to the micro-CT. Lastly to delete the copied data from the disk that initially saves the files. In order to automate the data transfer an SSH key pair with public key authentication was implemented between the two computers. To the existing software a script as well as a class controlling the three automation aspects were added. From the user interface, the class initially retrieves information about the acquisition settings to the folder name and when the acquisition is complete, the program code calls the script file that performs the SCP transfer. Afterwards a verification is made that no data was lost during the transfer, after which a deletion of the copied files is performed on the original disk. The new class improves the usability of the micro-CT and facilitates the handling of data after an acquisition.

The purpose of the study was to explore problems encountered in the teaching and learning of statistics in grade 11 and to offer ways of addressing them. A convenient sample of 100 grade 11 mathematics teachers and 448 grade 11 mathematics learners participated in the study. A descriptive survey design was used. Data were collected from the teachers using a teacher questionnaire, classroom observation schedule and teacher interview, and from learners through the use of a learner questionnaire, classroom observation schedule, diagnostic test and learner interview. The validity and reliability of all these instruments was established. Descriptive statistics and frequencies were used to analyse learner questionnaires, teacher questionnaires and learners‟ responses to a diagnostic test. Teacher and learner interviews were transcribed and classified according to themes. Classroom observations were analysed by using themes and checking for similarities and differences. The results showed that teachers had difficulty with the interpretation and calculation of measures of dispersion; representation and interpretation of data on graphs or plots; determining the five number summary; constructing and interpreting probability diagrams and tables; and interpreting probability terminology. Also, the results showed that learners experienced difficulties when using graphs to predict the results; interpreting and determining measures of dispersion; computation of quartiles when the total number of data values was even; representing data on graphs or plots; interpreting and determining measures of central tendency; constructing and interpreting probability graphs and tables; and interpreting probability terminology. The results found possible causes of the teachers‟ difficulties to be (1) their lack of statistics content knowledge; (2) inadequate textbooks; (3) in-service programmes which did not cover statistical topics, or which did not pay adequate attention to probability; and (4) teachers failure to attend these in-service teacher workshops. Further, the findings of the study were that the probable causes of learners‟ difficulties were (1) inadequate teaching of statistics topics in previous grades; (2) teachers‟ lack of content knowledge in statistics meant they had difficulty explaining concepts to learners; (3) inadequate learning material and learners‟ inability to use the statistics function mode on their calculators; and (4) learners‟ lack of conceptual knowledge of certain aspects of statistics. Lastly, the results of the study found that the possible ways to address the problems in the teaching and learning of statistics in grade 11 to be: (1) teachers should receive financial support from their schools/districts to attend in-service education and training programmes; (2) textbooks should be well written (provide thorough explanations) and contain all the information necessary to teach data handling and probability (i.e. formulae, more examples); (3) in-service teacher programmes should meet the needs of the teachers by offering topics that teachers find difficult to teach; and (4) more and longer inset programmes on probability, preferably five-day workshops, should be arranged. / Mathematics Education / M. Sc. (Mathematics, Science and Technology Education)

Maitinimo įstaigų veikla yra gana specifinė, todėl jų veikloje kylančioms problemoms spręsti reikia specializuotos programinės įrangos. Lietuvoje yra galingų programinių paketų, skirtų stambių maitinimo įmonių verslui kompiuterizuoti. Tačiau smulkios įmonės nepanaudoja visų tokios programinės įrangos galimybių, be to, ji nėra tiksliai pritaikyta tokių įmonių specifiniams poreikiams, tačiau jos kaina yra gana aukšta ir ne visada prieinama smulkioms įmonės. . Taigi šio magistro darbo tikslas - Sukurti specializuotą sistemą, kuri būtų pritaikyta konkrečioms užduotims spręsti, t.y. sukurti smulkios maitinimo įmonės veiklos duomenų analizės IS (informacinę sistemą), maksimaliai panaudojant esamą techninę ir programinę įrangą ir neinvestuojant daugiau materialinių išteklių. . Taikant šiuolaikines technologijas, ji leistų palengvinti maitinimo įmonės vadovaujančiam personalui jų veiklos baro apskaitos, duomenų analizės ir kontrolės funkcijas. Programinės įrangos pagalba darbuotojai galėtų žymiai greičiau ir paprasčiau: 1. vesti kasdieninę maitinimo įmonės produktų bei grynųjų pinigų apyvartos apskaitą; 2. užpildyti reikiamus atskaitomybės dokumentus, 3. paskaičiuoti patiekalų savikainą bei pardavimo kainą; 4. sudaryti ir naudotis receptų aprašų ir produktų normų jiems pagaminti duomenų bazę, 5. gauti ataskaitas apie produktų ir grynųjų pinigų apyvartą per norimą laikotarpį, 6. parengti atskaitomybės dokumentus kontroliuojančioms organizacijoms. Taigi bendras šio darbo tikslas -... [toliau žr. visą tekstą] / Catering service is rather specific, that‘s why to solve arising problems special software is needed. In Lithuania there are powerful software packets, assigned to computerize business of big catering enterprises. However, small enterprises don‘t apply such software, besides it isn‘t adapted to specific needs of such enterprises. What is more, the price of it is rather high and not always affordable to small enterprises. Therefore, the aim of this graduation dissertation is to create a specialized system , adopted to solve specific tasks, that is to create data analysis IS (information system) of a small catering enterprise, maximizing the usage of available hardware and software and not investing any more material resources. Applying modern technologies would allow to ease the brief accounting, data analysis and control functions for the leading executives of the enterprise. With the help of the software, workers could more quickly and easily: 1. keep the everyday count of products of the catering facility and cash circulation; 2. fill in the documents of accountability; 3. calculate the base and sale price ; 4. make and use recipe and product norm database; 5. get reports about product and cash circulation during the desirable period; 6. get ready the documents of accountability for supervisory organizations; therefore the general aim of this work is to create work record and analysis software for a catering enterprise.

L'architecture modulaire est une caractéristique distinctive des circuits cérébraux. En particulier, il a été observé l'existence de connexions réciproques entre des zones fonctionnellement interconnectées dans le cortex, et qui par ailleurs sont hiérarchiquement organisées. De plus, le développement évolutif est une autre caractéristique distinctive des espèces vivantes ; même les virus sont capables d'adaptation pour mieux répondre à de nouvelles conditions environnementales. En tenant compte de ces deux importants aspects, nous avons construit un nouvel et unique outil de simulation permettant de modéliser et d'étudier l'évolution des circuits multi-modulaires hiérarchiques. Dans ce modèle, chaque module est représenté par des réseaux de neurones impulsionels et caractérisé à la fois par des changements d'activités neurales imbriquées et par la plasticité synaptique. La morte cellulaire, la plasticité synaptique et l'apoptose intégrés dans le modèle créent des liens auto-associatifs au sein des modules. Ces liens peuvent générer une activité zonale qui reflète l'évolution de la connectivité fonctionnelle à l'intérieur comme à l'extérieur des modules, et donc entre les plusieurs modules neuronaux. L'activité bioélectrique de chaque module est enregistrée au moyen des électrodes virtuelles. Les signaux, electrochipogrammes (EChG), sont analysés par les méthodes fréquentiels et les méthodes de potentiels évoqués afin de trouver des généralités dans le comportement émergeant. En plus de ces méthodes conventionnelles, nous proposons une nouvelle approche de régression non-linéaire structurelle afin de fournir des outils plus puissants et mieux adaptés aux données habituellement analysées dans ce domaine. Nous avons donc testé l'effet d'un stimulus externe sur le développement de liens fonctionnels d'un réseau neuronaux. Le circuit est structuré hiérarchiquement avec un unique module sensoriel et d'autres modules constitués de deux voies parallèles organisées aussi de façon hiérarchique. Nos résultats montrent que les circuits modélisés manifestent un comportement similaire que les circuits biologiques réels. En particulier, tous les éléments du circuit peuvent traiter et maintenir des patterns d'activité liés à la disparition du stimulus. Les résultats obtenus dans nos expériences apportent un éclairage sur les processus émergents et coordonnés de l'activité électrique enregistrée par des EEG de circuits inter-corticaux hiérarchiques et évolutifs qui sont artificiels ou réels. Plus généralement, notre approche concernant les signaux EEG pourrait être étendue à la modélisation d'une vaste variété des processus cognitifs et comportementaux.