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.

Operating cost based cruise speed reduction for ground delay programs: Effect of scope length

Ground delay programs typically involve the delaying of aircraft that are departing from origin airports within some set distance of a capacity constrained destination airport. Long haul flights are not delayed in this way. A trade-off exists when fixing the distance parameter: increasing the ‘scope’ distributes delay among more aircraft and may reduce airborne holding delay but could also result in unnecessary delay in the (frequently observed) case of early program cancellation. In order to overcome part of this drawback, a fuel based cruise speed reduction strategy aimed at realizing airborne delay, was suggested by the authors in previous publications. By flying slower, at a specific speed, aircraft that are airborne can recover part of their initially assigned delay without incurring extra fuel consumption if the ground delay program is canceled before planned. In this paper, the effect of the scope of the program is assessed when applying this strategy. A case study is presented by analyzing all the ground delay programs that took place at San Francisco, Newark Liberty and Chicago O’Hare International airports during one year. Results show that by the introduction of this technique it is possible to define larger scopes, partially reducing the amount of unrecovered delay.

Effect of wind on operating cost based cruise speed reduction for delay absorption

En route speed reduction can be used for air traffic flow management (ATFM), e.g., delaying aircraft while airborne or realizing metering at an arrival fix. In previous publications, the authors identified the flight conditions that maximize the airborne delay without incurring extra fuel consumption with respect to the nominal (not delayed) flight. In this paper, the effect of wind on this strategy is studied, and the sensitivity to wind forecast errors is also assessed. A case study done in Chicago O’Hare airport (ORD) is presented, showing that wind has a significant effect on the airborne delay that can be realized and that, in some cases, even tailwinds might lead to an increase in the maximum amount of airborne delay. The values of airborne delay are representative enough to suggest that this speed reduction technique might be useful in a real operational scenario. Moreover, the speed reduction strategy is more robust than nominal operations against fuel consumption in the presence of wind forecast uncertainties.

Departure and approach procedures for unmanned aircraft systems in a visual-flight-rule environment

This paper assesses the departure and approach operations of unmanned aircraft systems in one of the most challenging scenarios: flying under visual flight rules. Inspired by some existing procedures for (manned) general aviation, some automatic and predefined procedures for unmanned aircraft systems are proposed. Hence, standardized paths to specific waypoints close to the airport are defined for departure operations, just before starting the navigation phase. Conversely, and for the approach maneuvers, a first integration into a holding pattern near the landing runway (ideally, above it) is foreseen, followed by a standard visual-flight-rule airfield traffic pattern. This paper discuses the advantages of these operations, which aim to minimize possible conflicts with other existing aircraft while reducing the pilot-in-command workload. Finally, some preliminary simulations are shown in which these procedures have been successfully tested with simulated surrounding traffic.

Performance and prospects of smaller UK regional airports

This paper investigates the traffic and financial performance of smaller UK regional airports between 2001 and 2014. Fourteen airports that typically serve less than 5 million passengers per annum were selected for the analysis. A period of strong growth in passenger demand was experienced from 2001 to 2007, driven largely by low cost carriers. The period from 2007 to 2014 was characterised by declining demand, resulting in significant losses for many of the airports. Airline strategies, such as the use of an increased unit fleet size and average sector length, may further limit future prospects for smaller UK regional airports in favour of larger ones with greater local demand. The relationship between traffic throughput and the generation of aeronautical revenues seems to vary at airports. There is generally a strong and significant relationship between traffic throughput and the generation of commercial revenues and total operating costs at airports serving 3–5 million passengers, but the situation for airports serving fewer than 3 million is less certain.

Delay Assignment Optimization Strategies at Pre- Tactical and Tactical Levels

This paper compares different optimization strategies for the minimization of flight and passenger delays at two levels: pre-tactical, with on-ground delay at origin, and tactical, with airborne delay close to the destination airport. The optimization model is based on the ground holding problem and uses various cost functions. The scenario considered takes place in a busy European airport and includes realistic values of traffic. Uncertainty is introduced in the model for the passenger allocation, minimum time required for turnaround and tactical uncertainty. Performance of the various optimization processes is presented and compared to ratio by schedule results.

The beginning of tourism in La Palma Island: Sixty years of the XX century

The sixties was a time of great interest for tourism development on the La Palma island. Various actions of public and private, as the policy of building a new airport, various tourist resorts, the tourism plan of 1968 or insular government also creating public entity "La Palma, Tourism SA” in 1969, will be the basis for future development of tourism on the island and will result push for private investment in this economic sector. Indeed, in the sixties, private investors had opened two hotels, while at least three others over a hundred beds each, weren´t finished.

Configurando a cidade contemporânea em Natal : os processos espaciais em Ponta Negra

This dissertation is about the spatial configuration in Natal and processes in the Ponta Negra neighborhood today. Ponta Negra has undergone a number of critical social and spatial changes due to tourism development after the 1990s. It is of special interest to consider the intensification of real estate investment after 2000, when the new airport terminal, located in the neighboring municipality of Parnamirim, was in use. Ponta Negra is the place where most tourists go to, so attracting considerable public investments. New agents of transformation have produced change in the neighborhood as well. The present study aims at analysing the spatial processes in this part of the city. Here, the spatial configuration that resulted from extended real estate investments, both public and private, in recent years, is analysed in detail. The study identifies the multually differentiated, however internally homogenous areas. The concepts of production of space, contemporanean urban development and spatial dynamics are discussed. The research is based on document analysis and field work. Results were plotted to maps and tables. A detailed analysis of the spatial processes in the Ponta Negra neighborhood is undertaken as a conclusion, considering the contemporanean global scenario

Cone penetration testing to assess slope stability in the 1979 Nice landslide area (Ligurian Margin, SE France)

In the landslide-prone area near the Nice international airport, southeastern France, an interdisciplinary approach is applied to develop realistic lithological/geometrical profiles and geotechnical/strength sub-seafloor models. Such models are indispensable for slope stability assessments using limit equilibrium or finite element methods. Regression analyses, based on the undrained shear strength (su) of intact gassy sediments are used to generate a sub-seafloor strength model based on 37 short dynamic and eight long static piezocone penetration tests, and laboratory experiments on one Calypso piston and 10 gravity cores. Significant strength variations were detected when comparing measurements from the shelf and the shelf break, with a significant drop in su to 5.5 kPa being interpreted as a weak zone at a depth between 6.5 and 8.5 m below seafloor (mbsf). Here, a 10% reduction of the in situ total unit weight compared to the surrounding sediments is found to coincide with coarse-grained layers that turn into a weak zone and detachment plane for former and present-day gravitational, retrogressive slide events, as seen in 2D chirp profiles. The combination of high-resolution chirp profiles and comprehensive geotechnical information allows us to compute enhanced 2D finite element slope stability analysis with undrained sediment response compared to previous 2D numerical and 3D limit equilibrium assessments. Those models suggest that significant portions (detachment planes at 20 m or even 55 mbsf) of the Quaternary delta and slope apron deposits may be mobilized. Given that factors of safety are equal or less than 1 when further considering the effect of free gas, a high risk for a landslide event of considerable size off Nice international airport is identified

Las infraestructuras aeroportuarias: tipo de propiedad y su relación con la eficiencia

El transporte aéreo es un sector caracterizado por ser uno de los de más rápido crecimiento en la economía mundial. Este aumento explosivo constituye un desafío para los aeropuertos en términos de desarrollo de la capacidad y la gestión. La conversión hacia la comercialización y privatización de la infraestructura aeroportuaria ha seguido los procesos de desregulación y privatización de las aerolíneas, aunque con un importante retraso. Entre los motivos que han conducido a estos procesos se encuentra la necesidad de mejorar su eficiencia para enfrentar una industria aeronáutica altamente competitiva. Este artículo de reflexión tiene como punto de partida la idea, generalmente aceptada, de que la privatización como modelo de propiedad o gestión está asociada con una mayor productividad. Los trabajos de referencia abordados hacen mención a aquellos cuyo análisis de la eficiencia es hecho a través de la técnica DEA por ser una de las más consolidadas y aceptadas en la literatura.

O pedestrianismo como instrumento de valorização ecoturística dos sítios da Rede Natura 2000, nas ilhas de São Miguel e Flores

Tese de Doutoramento, Ciências do Ambiente (Ecologia), 30 de Julho de 2013, Universidade dos Açores.

Análise dos prejuízos financeiros da indústria brasileira de aviação civil : influência das forças competitivas de Porter

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2016.

MVVC - Museu virtual Viana do Castelo: Um guia turístico para a cidade

A UE tem manifestado em matéria de turismo, a necessidade de serem criados novos produtos turísticos, com base na oferta total e única de cada uma das localidades. Se existirem recursos naturais, recursos culturais, bem como uma oferta de serviços complementares que incluam uma rede viária de fácil acesso e aeroporto nas imediações, alojamento e restauração existem as condições necessárias para desenvolver (novos) produtos locais. Viana do Castelo, cidade do nordeste português localizada no topo do país, reúne os recursos naturais, culturais e os serviços descritos atrás, razão pela qual foi alvo da concepção de um guia turístico virtual, com o objectivo de desenvolver e promover os seus produtos (turísticos) na comunidade local. Denominado "MWC", Museu Virtual Viana do Castelo, o guia turístico virtual estará escrito em português. Pretende ser traduzido noutros idiomas, inclusive para língua gestual e Braille. ABSTRACT; EU defends the creation of new touristic products, underlining each country has its own potentialities. To create new touristic products, mean to develop the local opportunities there are to be worked out. If there are natural resources, cultural resources, as well services supported by a good road network including airport nearby, several kind of accommodation and catering services it is possible to create new (local) products. Viana do Castelo is a Portuguese city, located in the Norwest top of Portugal. It meets all the resources mentioned above and other more, the reason why it is being conceived a virtual touristic guide, to develop and to promete its products among its local community. Named "MWC”, the Viana do Castelo Virtual Museum will be written in Portuguese language and later on in another language, sign languages and Braille.

A percepção do consumidor do valor da marca : O caso TAP Portugal

Neste trabalho de investigação pretende-se responder à questão: qual a importância da percepção do consumidor do valor da marca TAP PORTUGAL? Para atingir os objectivos da investigação realizou-se um estudo de caso, tendo-se elaborado entrevistas junto de responsáveis pela área do marketing da companhia aérea nacional e procedeu-se à recolha de informação (publicações TAP, ANA¬ AEROPORTOS, entre outras; e, aplicou-se um questionário junto dos passageiros TAP. PORTUGAL no Aeroporto Internacional de Lisboa) de modo a se poder estudar o caso aprofundadamente. Os resultados da investigação indicam que a análise da nova imagem TAP PORTUGAL por parte dos passageiros é, de um modo geral, muito positiva, estando alinhados com os objectivos definidos no rebranding levado a cabo em 2005. A presente investigação contribui para sistematizar e clarificar as percepções dos consumidores do valor da marca TAP PORTUGAL, bem como retirar algumas ilações comparativas sobre os objectivos propostos e implementados na operação de rebranding com as percepções que os seus clientes têm desta nova imagem, contribuindo para uma melhor estratégia de gestão da marca. ABSTRACT; The present research seeks to answer the question: What is the importance of consumers' perception for the brand equity of TAP PORTUGAL? To achieve the objectives of the research a case study of methodology was done, having prepared interviews with the responsible for the marketing area of the Portuguese Airline, and proceeded to gather information (TAP, ANA-AEROPORTOS publications, among others; and, have applied a questionnaire to the TAP PORTUGAL passengers who made the check-in in the International Airport of Lisbon) to make a profound study of the case. Research results indicate that the new image analysis of TAP PORTUGAL from passengers, is generally very positive, and aligned with the objectives outlined in rebranding carried out in 2005. This research contributes to systematize and clarify the consumer's perceptions for the brand equity of TAP PORTUGAL, and draw some comparative conclusions on the objectives proposed and implemented in the rebranding operation with the customers’ perception that have the new image, contributing to improve the brand management strategy. NOTA: contém Cd em mau estado (Ilegível).