Math 412 - Topology with Applications

Highlights of Data Expedition: • Students explored daily observations of local climate data spanning the past 35 years. • Topological Data Analysis, or TDA for short, provides cutting-edge tools for studying the geometry of data in arbitrarily high dimensions. • Using TDA tools, students discovered intrinsic dynamical features of the data and learned how to quantify periodic phenomenon in a time-series. • Since nature invariably produces noisy data which rarely has exact periodicity, students also considered the theoretical basis of almost-periodicity and even invented and tested new mathematical definitions of almost-periodic functions. Summary The dataset we used for this data expedition comes from the Global Historical Climatology Network. “GHCN (Global Historical Climatology Network)-Daily is an integrated database of daily climate summaries from land surface stations across the globe.” Source: https://www.ncdc.noaa.gov/oa/climate/ghcn-daily/ We focused on the daily maximum and minimum temperatures from January 1, 1980 to April 1, 2015 collected from RDU International Airport. Through a guided series of exercises designed to be performed in Matlab, students explore these time-series, initially by direct visualization and basic statistical techniques. Then students are guided through a special sliding-window construction which transforms a time-series into a high-dimensional geometric curve. These high-dimensional curves can be visualized by projecting down to lower dimensions as in the figure below (Figure 1), however, our focus here was to use persistent homology to directly study the high-dimensional embedding. The shape of these curves has meaningful information but how one describes the “shape” of data depends on which scale the data is being considered. However, choosing the appropriate scale is rarely an obvious choice. Persistent homology overcomes this obstacle by allowing us to quantitatively study geometric features of the data across multiple-scales. Through this data expedition, students are introduced to numerically computing persistent homology using the rips collapse algorithm and interpreting the results. In the specific context of sliding-window constructions, 1-dimensional persistent homology can reveal the nature of periodic structure in the original data. I created a special technique to study how these high-dimensional sliding-window curves form loops in order to quantify the periodicity. Students are guided through this construction and learn how to visualize and interpret this information. Climate data is extremely complex (as anyone who has suffered from a bad weather prediction can attest) and numerous variables play a role in determining our daily weather and temperatures. This complexity coupled with imperfections of measuring devices results in very noisy data. This causes the annual seasonal periodicity to be far from exact. To this end, I have students explore existing theoretical notions of almost-periodicity and test it on the data. They find that some existing definitions are also inadequate in this context. Hence I challenged them to invent new mathematics by proposing and testing their own definition. These students rose to the challenge and suggested a number of creative definitions. While autocorrelation and spectral methods based on Fourier analysis are often used to explore periodicity, the construction here provides an alternative paradigm to quantify periodic structure in almost-periodic signals using tools from topological data analysis.

An Electric Vehicle Dispatch Module for Demand-Side Energy Participation

The penetration of the electric vehicle (EV) has increased rapidly in recent years mainly as a consequence of advances in transport technology and power electronics and in response to global pressure to reduce carbon emissions and limit fossil fuel consumption. It is widely acknowledged that inappropriate provision and dispatch of EV charging can lead to negative impacts on power system infrastructure. This paper considers EV requirements and proposes a module which uses owner participation, through mobile phone apps and on-board diagnostics II (OBD-II), for scheduled vehicle charging. A multi-EV reference and single-EV real-time response (MRS2R) online algorithm is proposed to calculate the maximum and minimum adjustable limits of necessary capacity, which forms part of decision-making support in power system dispatch. The proposed EV dispatch module is evaluated in a case study and the influence of the mobile app, EV dispatch trending and commercial impact is explored.

Global efficiency of innovative rotational mold directly heated by thermal fluid

The article is focused on analysis of global efficiency of new mold for rotational molding of plastic parts, being directly heated by thermal fluid. The overall efficiency is based on several items such as reduction of cycle time, better uniformity of heating-cooling and low energy consumption. The new tool takes advantage of additive fabrication and electroforming for making the optimal manifold and cavity shell of the mold. Experimental test of a prototype mold was carried out on an experimental rotational molding machine, developed for this purpose, measuring wall temperature, and internal air temperature, with and without plastic material inside. Results were compared with conventional mold heated into an oven and to theoretical simulations done by Computational Fluid Dynamic software (CFD). The analysis represents considerable improvement of cycle time related to conventional methods (heated by oven) and better thermal uniformity to conventional procedures by direct heating of oil with external channels. In addition to thermal analysis an energetic efficiency study was done. POLYM. ENG. SCI., 52:1998-2005, 2012. © 2012 Society of Plastics Engineers Copyright © 2012 Society of Plastics Engineers.

Avaliação da fidedignidade dos ensaios de esteróides fecais realizados no Laboratório de Medidas Hormonais do Departamento de Fisiologia da UFRN

NASCIMENTO, H. G. ; FERNANDES, L. C. ; SOUSA, M. B. C. . Avaliação da fidedignidade dos ensaios de esteróides fecais realizados no Laboratório de Medidas Hormonais do Departamento de Fisiologia da UFRN. Publica , v. 2, p. 39-48, 2006.

North American Monsoon GPS Transect Experiment 2013

Ten GPS-Met stations were installed in northwest Mexico from June - September 2013. Each station included a Trimble NetR9 GPS receiver for PWV and a Vaisala WXT520 surface meteorological package measuring wind speed and direction, air temperature, humidity, pressure and precipitation. The geographic location, elevation and data period for each station are provided in Serra et al. (2016). The GPS receiver at Rayon failed on July 16, 21 days after installation, thus these data are not included in the archive but are available upon request (yserra@uw.edu). Data include 1-min surface meteorological variables, while the GPS PWV is calculated at 5-min intervals. A full description of the experiment can be found in Serra et al., 2016: Bull. Am. Meteor. Soc., doi: 10.1175/BAMS-D-14-00250.1.

Oclusão percutânea do apêndice auricular esquerdo e estrutura auricular: efeito na função mecânica e endócrina auricular

Mestrado em Tecnologia de Diagnóstico e Intervenção Cardiovascular - Área de especialização: Intervenção Cardiovascular.

Avaliação da fidedignidade dos ensaios de esteróides fecais realizados no Laboratório de Medidas Hormonais do Departamento de Fisiologia da UFRN

NASCIMENTO, H. G. ; FERNANDES, L. C. ; SOUSA, M. B. C. . Avaliação da fidedignidade dos ensaios de esteróides fecais realizados no Laboratório de Medidas Hormonais do Departamento de Fisiologia da UFRN. Publica , v. 2, p. 39-48, 2006.

Organic Matter Removal from Piggery Wastewater in Waste Stabilisation Pond in Nigeria

Four (4) wastewater quality variables: chemical oxygen demand (COD), total solid (TS), total dissolved solid (TDS), and total suspended solid (TSS) were determined. Analysed samples comprises of raw influent and effluents entering and leaving the stabilisation ponds. Significant reduction in variables were obtained, maximum and minimum values obtained for COD were 917mg/l (anaerobic pond), and 13mg/l (maturation pond). For TS, TDS and TSS, maximum and minimum values obtained were 14,420mg/l, 9,180mg/l, 5,240mg/l and 3,398mg/l, 3,120mg/l, 278mg/l respectively. Removal efficiencies recorded for parameters in final effluent (maturation pond) were 98.55% (COD), 76.44% (TS), 66.01% (TDS), and 94.69% (TSS) respectively.

Structural features of the epididymal region of the domestic duck (Anas plathyrynchos)

A região epididimária do pato doméstico era composta pelos ductúlos eferentes, os quais hitotopologicamente foram caracterizados como dúctulos eferentes proximal e distal e, sequencialmente, pelo ducto epididimal. O epitélio dos dúctulos eferentes era pseudo-estratificado, formado por células colunares. O epitélio dos ductos epididimários mostrou-se também pseudo-estratificado, mas não ciliado. de acordo com as análises histomorfométricas, a média da altura epitelial foi significativamente maior nos dútulos esferentes distais, diferindo das baixas médias de altura epitelial observadas nos dúctulos eferentes proximais e ducto epididimal. A média dos diâmetros máximos e mínimos foi significativamente maior nos dúctulos eferentes proximais, comparativamente as médias dos mesmos diâmetros dos outros dúctulos.

Lo studio del microclima indoor per la conservazione preventiva del Patrimonio storico artistico e culturale

La conservazione preventiva degli edifici storici e dei beni custoditi al loro interno rappresenta una sfida ad oggi condivisa a livello internazionale. Tale conservazione dipende da numerose variabili, tra le quali il microclima indoor gioca un ruolo decisivo. Il fine di questa tesi è verificare come lo studio del microclima indoor, supportato dalla simulazione virtuale e dalla conoscenza storica delle evoluzioni dell’edificio stesso (legate a modifiche impiantistiche; architettoniche; d’uso; ecc., nel corso degli anni), costituiscano una base conoscitiva fondamentale, da cui architetti e restauratori possono partire per definire strategie specifiche, volte alla conservazione preventiva del Patrimonio. Per fare questo, l’autore presenta le indagini svolte per tre casi-studio: la Sala 33 della Reggia di Venaria Reale, in provincia di Torino, Italia; la Biblioteca Generale Storica dell’Università di Salamanca, in Spagna; il Portico della Gloria, nartece della Cattedrale di Santiago de Compostela, in Spagna. La metodologia definita e adottata per l’analisi e l’interpretazione dei dati di ciascun caso-studio ha previsto la comprensione e la messa in relazione tra: scelte costruttive; vicende evolutive delle singole architetture; fattori che ne determinano il microclima, letti (o ipotizzati) nelle relative modifiche diacroniche; degrado delle architetture e dei beni che sono custoditi in esse. Infine, uno degli esiti più innovativi della ricerca è stata la definizione di due indici di rischio: sono stati infatti definiti due nuovi indici (Heritage Microclimate Risk -HMR- e Predicted Risk of Damage -PRD-) legati al microclima degli edifici che ospitano beni e manufatti che costituiscono il patrimonio storico artistico e culturale. Tali indici sono stati definiti tenendo conto di tutte le variabili da cui il microclima dipende e dei fattori che ne determinano l’evolversi nel tempo e nello spazio.