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Proportional reasoning instruction is prevalent in elementary, secondary, and post-secondary schooling. The concept of proportional reasoning is used in a variety of contexts for solving real-world problems. One of these contexts is the solving of dosage calculation proportional problems in the healthcare field. On the job, nurses perform drug dosage calculations which carry fatal consequences. As a result, nursing students are required to meet minimum competencies in solving proportion problems. The goal of this research is to describe the lived experiences of nurses in connection to their use of proportional reasoning in order to impact instruction of the procedures used to solve these problems. The research begins by clarifying and defining the conceptual field of proportional reasoning. Utilizing Vergnaud*s theory of conceptual fields and synthesizing the differing organizational frameworks used in the literature on proportional reasoning, the concept is organized and explicated into three components: concepts, procedures, and situations. Through the lens of this organizational structure, data from 44 registered nurses who completed a dosage calculation proportion survey were analyzed and connected to the framework of the conceptual field of proportional reasoning. Four nurses were chosen as a focus of in-depth study based upon their procedural strategies and ability to vividly describe their experiences. These qualitative results are synthesized to describe the lived experiences of nurses related to their education and use of proportional reasoning. Procedural strategies that are supported by textbooks, instruction, and practice are developed and defined. Descriptive statistics show the distribution of procedures used by nurses on a five question dosage calculation survey. The most common procedures used are the nursing formula, cross products, and dimensional analysis. These procedures correspond to the predominate procedures found in nursing dosage calculation texts. Instructional implications focus on the transition between elementary and secondary multiplicative structures, the confusion between equality and proportionality, and the difficulty that like quantities present in dealing with proportions.

We present an implementation of a very recent approximation algorithm for scheduling jobs on a single machine with precedence constraints, minimising the total weighted completion time. We also evaluate the performance of this implementation. The algorithm was published by Shi Li in 2021 and is a (6+ε)-approximation algorithm for the multiprocessor problem P|prec|∑j wjCj. We have implemented a version which is a (2+ε)-approximation algorithm for the single processor problem 1|prec|∑j wjCj. This special case can easily be generalised to the multiprocessor case, as the two algorithms are based on the same LP relaxation of the problem. Unlike other approximation algorithms for this and similar problems, for example, those published by Hall, Schulz, Shmoys and Wein in 1997, and by Li in 2020, this algorithm has been developed with a focus on obtaining a good asymptotic run time guarantee, rather than obtaining the best possible guarantee on the quality of solutions. Li’s algorithm has run time O((n+κ) · polylog(n+κ) · log3 pmax · 1/ε2), where n is the number of jobs, κ is the number of precedence constraints and pmax is the largest of the processing times of the jobs. We also present a detailed explanation of the algorithm aimed at readers who do not necessarily have a background in scheduling and/or approximation algorithms, based on the paper by Li. Finally, we empirically evaluate how well (our implementation of) this algorithm performs in practice. The performance was measured on a set of 96 randomly generated instances, with the largest instance having 1024 jobs and 32 768 precedence constraints. We can find a solution for an instance with 512 jobs and 11 585 precedence constraints in 25 minutes. / Vi presenterar en praktisk implementation av en ny approximationsalgoritm för schemaläggning av jobb på en maskin med ordningsbivillkor, under minimering av den viktade summan av sluttider. Algoritmen, som publicerades av Shi Li år 2021, är en (6+ε)-approximationsalgoritm för multiprocessorproblemet P|prec|∑j wjCj. Vi har implementerat en version som är en (2+ε)-approximationsalgoritm för enprocessorproblemet 1|prec|∑j wjCj. Detta specialfall kan enkelt generaliseras till multiprocessorfallet, eftersom de två algoritmerna baseras på samma LP-relaxation av problemet. Till skillnad från andra approximationsalgoritmer för detta och liknande problem, exempelvis de från Hall, Schulz, Shmoys och Wein år 1997, och från Li år 2020, har denna algoritm utvecklats med fokus på att uppnå en bra garanti på asymptotisk körtid, istället för att försöka uppnå den bästa möjliga garantin på lösningarnas kvalité. Lis algoritm har körtid O((n+κ) · polylog(n+κ) · log3 pmax · 1/ε2), där n är antalet jobb, κ antalet ordningsbivillkor och pmax är den största körtiden bland jobben. En detaljerad beskrivning av algoritmen riktad till personer som inte nödvändigtvis har förkunskaper inom schemaläggning och/eller approximationsalgoritmer, baserad på artikeln, ges också. Slutligen utvärderar vi empiriskt hur väl (vår implementation av) denna algoritm presterar i praktiken. Implementationens egenskaper mättes på en uppsättning av 96 slumplässigt genererade instanser, där den största instansen har 1024 jobb och 32768 ordningsbivillkor. Med vår implementation kan vi hitta en lösning för en instans med 512 jobb och 11 585 precedencensbivillkor på 25 minuter.

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No description available.

Cardiovascular workouts offer numerous health benefits, yet beginners often find it challenging to initiate them. Existing wearable technologies, although providing valuable feedback such as heart rate zones, often disrupt the workout flow and distract users due to the need for interaction with the wearable display. In response, we propose an alternative feedback mechanism: cadence, measured in steps per minute. This feedback mechanism uses multiplicative control to produce the correct cadence for the user’s target heart rate (HR). To model the HR and cadence relationship, a first-order system was used. The prototype implementation of this system was completed in Arduino, using a force sensitive resistor (FSR) to measure the user’s cadence and a POLAR HR strap to measure the user’s HR. The cadence is updated every 10 seconds to allow the user to sync to the cadence metronome provided by earbuds. This proposed system has shown promising experimental results for both moderate-intensity and high-intensity workouts, skipping the transition zone between them. This allows the user to avoid awkward workout intensities between a fast walk and a jog.

Non-intrusive acoustic thermometry using an acoustic impulse generator and two microphones is developed and integrated with tomographic techniques to reconstruct temperature contours. A low velocity plume at around 450 °F exiting through a rectangular duct (3.25 by 10 inches) was used for validation and reconstruction. 0.3 % static temperature relative error compared with thermocouple-measured data was achieved using a cross-correlation algorithm to calculate speed of sound. Tomographic reconstruction algorithms, the simplified multiplicative algebraic reconstruction technique (SMART) and least squares method (LSQR), are investigated for visualizing temperature contours of the heated plume. A rectangular arrangement of transmitter and microphones with a traversing mechanism collected two orthogonal sets of acoustic projection data. Both reconstruction techniques have successfully recreated the overall characteristic of the contour; however, for the future work, the integration of the refraction effect and implementation of additional angled projections are required to improve local temperature estimation accuracy. The root-mean-square percentage errors of reconstructing non-uniform, asymmetric temperature contours using the SMART and LSQR method are calculated as 20% and 19%, respectively. / Master of Science

In recent years, as the availability of remote sensing imagery of varying resolution has increased, merging images of differing spatial resolution has become a significant operation in the field of digital remote sensing. This practice, known as data fusion, is designed to enhance the spatial resolution of multispectral images by merging a relatively coarse-resolution image with a higher resolution panchromatic image of the same geographic area. This study examines properties of fused images and their ability to preserve the spectral integrity of the original image. It analyzes five current data fusion techniques for three complex scenes to assess their performance. The five data fusion models used include one spatial domain model (High-Pass Filter), two algebraic models (Multiplicative and Brovey Transform), and two spectral domain models (Principal Components Transform and Intensity-Hue-Saturation). SPOT data were chosen for both the panchromatic and multispectral data sets. These data sets were chosen for the high spatial resolution of the panchromatic (10 meters) data, the relatively high spectral resolution of the multispectral data, and the low spatial resolution ratio of two to one (2:1). After the application of the data fusion techniques, each merged image was analyzed statistically, graphically, and for increased photointerpretive potential as compared with the original multispectral images. While all of the data fusion models distorted the original multispectral imagery to an extent, both the Intensity-Hue-Saturation Model and the High-Pass Filter model maintained the original qualities of the multispectral imagery to an acceptable level. The High-Pass Filter model, designed to highlight the high frequency spatial information, provided the most noticeable increase in spatial resolution. / Master of Science

As frutíferas nativas do Brasil são subexploradas comercialmente, sendo que os programas de melhoramento genético são bastante incipientes, devido a muitas limitações associadas à fisiologia e biologia dessas espécies, embora apresentem potencial econômico tanto para o consumo in natura como para o processamento industrial. No Brasil, o maracujá-doce (Passiflora alata) está conquistando novos clientes e mercados, e tem atingido preços até três vezes maiores do que os do maracujá-azedo, amplamente cultivado no país. Os frutos do maracujá-doce são muito apreciados, embora apenas a seleção empírica tenha sido praticada. Evidentemente, seria muito vantajoso obter uma variedade geneticamente superior em termos de qualidade e produção de frutos. Nesse sentido, nosso grupo de pesquisa tem focado esforços visando a caracterizar geneticamente uma população segregante de maracujá-doce. Aqui, foram avaliados 30 genótipos desta população, previamente selecionados como superiores. Estes foram plantados sob três condições experimentais: Anhumas (2014/2015 e 2015/2016) e Piracicaba (2015/2016). Foi utilizado o delineamento em blocos casualizados, sendo que as análises genético-estatísticas tiveram por base a abordagem de modelos mistos para a predição dos valores genéticos (BLUPS). Foram estimados parâmetros genéticos e fenotípicos, herdabilidade, correlações genéticas e resposta esperada à seleção relativamente a peso (PF), comprimento (CF) diâmetro (DF) do fruto, espessura (EC) e peso (PC) da casca, peso (PP) e rendimento de polpa (RP), teor de sólidos solúveis totais (SST) e Produtividade. Os resultados mostraram haver altas correlações genéticas entre os principais atributos do fruto, assim como valores elevados de herdabilidade (desde 0,45 para PF a 0,94 para EC), valores que favorecem a prática de seleção. Em seguida, foi aplicado índice multiplicativo para fins de seleção e seis genótipos foram indicados como superiores, quais sejam: 49, 21, 107, 125, 140 e 122. Nossos resultados devem auxiliar outros estudos e iniciativas de seleção de genótipos mais produtivos, evidenciando a grande utilidade de ferramentas estatísticas modernas para se obter maior resposta à seleção. Em paralelo, foi estudada a resposta do maracujá-doce à infecção causada por Xanthomonas axonopodis. Dois genes, previamente identificados como superexpressos no maracujá-azedo, e que codificam as enzimas lipoxigenase-2 e (+)-neomentol desidrogenase foram aqui analisados via qPCR. No maracujá-doce observou-se maior expressão da (+)-neomentol desidrogenase, enzima associada à resposta de hipersensibilidade. Os sintomas da doença sugerem que a resposta de hipersensibilidade é particular no maracujá-doce, já que ocorre a queda precoce das folhas, evitando a disseminação sistêmica da bactéria. / Brazilian native fruit species are under-exploited commercially, and breeding programs are quite incipient due to many limitations associated with the physiology and biology of these species, although having economic potential both for in natura consumption as well as for industrial processing. In Brazil, the sweet passion fruit (Passiflora alata) is conquering new customers and markets, and has riched up to triple the sour passion fruit prices, widely grown in the country. The fruits of the sweet passion fruit are much appreciated, although only empirical selections have been practiced. Evidently, it would be very beneficial to obtain a genetically superior variety in terms of fruit quality and production. In this scenario, our research group has focused efforts to genetically characterize a segregating population of sweet passion fruit. Here, we evaluated 30 genotypes previously selected from this population by field-cultivating them under three experimental conditions: Anhumas (2014/2015 and 2015/2016) and Piracicaba (2015/2016). A randomized block design was used, and the genetic-statistical analyzes were based on a mixed-effects model approach in order to predict the genetic values (BLUPS). We estimated genetic and phenotypic parameters, as heritability, genetic correlations and expected response to selection for weight (WF), length (LF) diameter (DF) of the fruit, thickness (TS) and weight (WS) of the shell, weight (WP) and pulp yield (PY), total soluble solids (SS) and fruit yield. We found high genetic correlations between the main fruit attributes, as well as high values of heritability (from 0.45 for WF up to 0.94 for TS), values that may favor selection practices. Then, we applied a multiplicative selection index and six superior genotypes were selected, which are: 49, 21, 107, 125, 140 and 122. Our results may assist other studies and initiatives of selection of more productive genotypes, showing the great usefulness of modern statistical tools to obtain greater responses to selection. In parallel, we studied the response of sweet passion fruit to infection caused by Xanthomonas axonopodis. Two genes, previously identified as overexpressed in sour passion fruit, and that encode the enzymes lipoxygenase-2 and (+)-neomentol dehydrogenase were herein analyzed via qPCR. In the sweet passion fruit an increased expression of (+)- neomentol dehydrogenase, an enzyme associated with hypersensitivity response, was observed. The disease symptoms suggest that the response of hypersensitivity is particular in sweet passion fruit, since it provokes the premature fall of the leaves, thereby preventing the systemic bacterial dissemination.

Le sujet principal de cette thèse est l’étude des valeurs moyennes et corrélations de fonctions multiplicatives. Les résultats portant sur ces derniers sont subséquemment appliqués à la résolution de plusieurs problèmes. Dans le premier chapitre, on rappelle certains résultats classiques concernant les valeurs moyennes des fonctions multiplicatives. On y énonce également les théorèmes principaux de la thèse. Le deuxième chapitre consiste de l’article “Mean values of multiplicative functions over the function fields". En se basant sur des résultats classiques de Wirsing, de Hall et de Tenenbaum concernant les fonctions multiplicatives arithmétiques, on énonce et on démontre des théorèmes qui y correspondent pour les fonctions multiplicatives sur les corps des fonctions Fq[x]. Ainsi, on résoud un problème posé dans un travail récent de Granville, Harper et Soundararajan. On décrit dans notre thése certaines caractéristiques du comportement des fonctions multiplicatives sur les corps de fonctions qui ne sont pas présentes dans le contexte des corps de nombres. Entre autres, on introduit pour la première fois une notion de “simulation” pour les fonctions multiplicatives sur les corps de fonctions Fq[x]. Les chapitres 3 et 4 comprennent plusieurs résultats de l’article “Correlations of multiplicative functions and applications". Dans cet article, on détermine une formule asymptotique pour les corrélations X n6x f1(P1(n)) · · · fm(Pm(n)), où f1, . . . ,fm sont des fonctions multiplicatives de module au plus ou égal à 1 ”simulatrices” qui satisfont certaines hypothèses naturelles, et P1, . . . ,Pm sont des polynomes ayant des coefficients positifs. On déduit de cette formule plusieurs conséquences intéressantes. D’abord, on donne une classification des fonctions multiplicatives f : N ! {−1,+1} ayant des sommes partielles uniformément bornées. Ainsi, on résoud un problème d’Erdos datant de 1957 (dans la forme conjecturée par Tao). Ensuite, on démontre que si la valeur moyenne des écarts |f(n + 1) − f(n)| est zéro, alors soit |f| a une valeur moyenne de zéro, soit f(n) = ns avec iii Re(s) < 1. Ce résultat affirme une ancienne conjecture de Kátai. Enfin, notre théorème principal est utilisé pour compter le nombre de représentations d’un entier n en tant que somme a+b, où a et b proviennent de sous-ensembles multiplicatifs fixés de N. Notre démonstration de ce résultat, dû à l’origine à Brüdern, évite l’usage de la “méthode du cercle". Les chapitres 5 et 6 sont basés sur les résultats obtenus dans l’article “Effective asymptotic formulae for multilinear averages and sign patterns of multiplicative functions," un travail conjoint avec Alexander Mangerel. D’après une méthode analytique dans l’esprit du théorème des valeurs moyennes de Halász, on détermine une formule asymptotique pour les moyennes multidimensionelles x−l X n2[x]l Y 16j6k fj(Lj(n)), lorsque x ! 1, où [x] := [1,x] et L1, . . . ,Lk sont des applications linéaires affines qui satisfont certaines hypothèses naturelles. Notre méthode rend ainsi une démonstration neuve d’un résultat de Frantzikinakis et Host avec, également, un terme principal explicite et un terme d’erreur quantitatif. On applique nos formules à la démonstration d’un phénomène local-global pour les normes de Gowers des fonctions multiplicatives. De plus, on découvre et explique certaines irrégularités dans la distribution des suites de signes de fonctions multiplicatives f : N ! {−1,+1}. Visant de tels résultats, on détermine les densités asymptotiques des ensembles d’entiers n tels que la fonction f rend une suite fixée de 3 ou 4 signes dans presque toutes les progressions arithmétiques de 3 ou 4 termes, respectivement, ayant n comme premier terme. Ceci mène à une généralisation et amélioration du travail de Buttkewitz et Elsholtz, et donne un complément à un travail récent de Matomäki, Radziwiłł et Tao sur les suites de signes de la fonction de Liouville. / The main theme of this thesis is to study mean values and correlations of multiplicative functions and apply the corresponding results to tackle some open problems. The first chapter contains discussion of several classical facts about mean values of multiplicative functions and statement of the main results of the thesis. The second chapter consists of the article “Mean values of multiplicative functions over the function fields". The main purpose of this chapter is to formulate and prove analog of several classical results due to Wirsing, Hall and Tenenbaum over the function field Fq[x], thus answering questions raised in the recent work of Granville, Harper and Soundararajan. We explain some features of the behaviour of multiplicative functions that are not present in the number field settings. This is accomplished by, among other things, introducing the notion of “pretentiousness" over the function fields. Chapter 3 and Chapter 4 include results of the article “Correlations of multiplicative functions and applications". Here, we give an asymptotic formula for correlations X n_x f1(P1(n))f2(P2(n)) · · · · · fm(Pm(n)) where f . . . ,fm are bounded “pretentious" multiplicative functions, under certain natural hypotheses. We then deduce several desirable consequences. First, we characterize all multiplicative functions f : N ! {−1,+1} with bounded partial sums. This answers a question of Erdos from 1957 in the form conjectured by Tao. Second, we show that if the average of the first divided difference of multiplicative function is zero, then either f(n) = ns for Re(s) < 1 or |f(n)| is small on average. This settles an old conjecture of Kátai. Third, we apply our theorem to count the number of representations of n = a + b where a,b belong to some multiplicative subsets of N. This gives a new "circle method-free" proof of the result of Brüdern. Chapters 5 and Chapter 6 are based on the results obtained in the article “Effective asymptotic formulae for multilinear averages and sign patterns of multiplicative functions," joint with Alexander Mangerel. Using an analytic approach in the spirit of Halász’ mean v value theorem, we compute multidimensional averages x−l X n2[x]l Y 16j6k fj(Lj(n)) as x ! 1, where [x] := [1,x] and L1, . . . ,Lk are affine linear forms that satisfy some natural conditions. Our approach gives a new proof of a result of Frantzikinakis and Host that is distinct from theirs, with explicit main and error terms. As an application of our formulae, we establish a local-to-global principle for Gowers norms of multiplicative functions. We reveal and explain irregularities in the distribution of the sign patterns of multiplicative functions by computing the asymptotic densities of the sets of integers n such that a given multiplicative function f : N ! {−1, 1} yields a fixed sign pattern of length 3 or 4 on almost all 3- and 4-term arithmetic progressions, respectively, with first term n. The latter generalizes and refines the work of Buttkewitz and Elsholtz and complements the recent work of Matomaki, Radziwiłł and Tao. We conclude this thesis by discussing some work in progress.