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.

Commodification of health care systems: The Catalan case

Commodification of the public healthcare system has been a growing process in recent decades, especially in universal healthcare systems and in high-income countries like Spain.  There are substantial differences in the healthcare systems of each autonomous region of Spain, among which Catalonia is characterized by having a mixed healthcare system with complex partnerships and interactions between the public and private healthcare sectors.  Using a narrative review approach, this article addresses various aspects of the Catalan healthcare system, characterizing the privatization and commodification of health processes in Catalonia from a historical perspective with particular attention to recent legislative changes and austerity measures.  The article approximates, the eventual effects that commodification and austerity measures will have on the health of the population and on the structure, accessibility, effectiveness, equity and quality of healthcare services.

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.

La réappropriation du foncier et du bâti de la ville de Battambang dans le contexte (post) socialiste du Cambodge (1979-1993)

En avril 1975, les Khmers rouges prennent le pouvoir du Cambodge et forcent l’évacuation presque complète des villes du pays vers les campagnes. Le régime restreint à l’extrême les droits individuels, dont la propriété privée. À la chute du régime khmer rouge en janvier 1979, le foncier urbain est en théorie détaché de tous droits antérieurs. Par une enquête historique et ethnographique menée à Battambang, ce mémoire explore comment les relations de propriété autour des ressources foncières et immobilières préexistantes de la ville se sont développées dans ce contexte. Il examine plus précisément les mécanismes d’accès et d’exclusion, issus à la fois des normes politico-légales et de la coutume, qui ont alors légitimé la propriété sur divers types de biens immobiliers situés surtout en ville. La recherche couvre une période historique allant de 1979 à 1992-1993, années de la transition du régime socialiste vers une démocratie libérale. Les résultats montrent que plusieurs logiques d’accès et de possession se sont croisées durant ces années, souvent en marge de la loi et parfois de manière conflictuelle et violente. La diversité de relations de propriété révélée par l’éclairage historique « par en bas » nuance l’idée que l’allocation de la propriété en contexte socialiste a été essentiellement chaotique et contrôlée par un État néopatrimonial. Elle nuance aussi l’idée qu’une pleine privatisation de la propriété a eu lieu au tournant des années 1990. Les nombreuses frictions qui ont résulté de cette formalisation, particulièrement entre l’État local et les petits occupants, invitent à conceptualiser la propriété de manière plus large et à repenser les penchants normatifs pour un régime foncier strict basé sur des droits de propriété individuels et exclusifs, particulièrement dans des régimes post-conflit. En outre, le mémoire sert à donner une profondeur historique à la crise foncière que connaît actuellement le Cambodge.

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.

Analyse des impacts environnementaux des accords de libre-échange dans le secteur agricole : étude de cas de l’ALENA

La tendance internationale du commerce est actuellement basée sur une libéralisation et une ouverture des échanges entre les États. Pour faire suite à cette ouverture commerciale des frontières, plusieurs centaines d’accords de libre-échange sont ratifiés afin de réduire davantage les différents obstacles au commerce dans tous les secteurs. L’étude présente a pour objectif d’évaluer le libre-échange et plus particulièrement l’Accord de libre-échange nord-américain (ALENA) pour déterminer si les ententes commerciales sont de facto compatibles avec les objectifs environnementaux du développement durable, tout particulièrement dans le secteur agricole. L’analyse des théories du libre-échange démontre que la libéralisation du commerce mène généralement à la spécialisation et à un changement dans la composition des activités d’un pays. Cette hypothèse se concrétise dans le secteur agricole par une transition vers de grandes cultures d’une seule espèce, hautement mécanisées et dépendantes en intrants chimiques. Il résulte de ce changement de pratiques de multiples impacts environnementaux tels que la pollution de l’eau, de l’air et des sols, la perte de biodiversité, la propagation de ravageurs ainsi que la détérioration de la qualité du sol. Tous ces impacts environnementaux négatifs indiquent le manque de soutenabilité de ce modèle agricole. L’étude de cas de l’ALENA, un accord particulièrement intéressant à étudier vu son rôle décisif sur la scène des ententes commerciales, confirme ces résultats. Malgré les intentions louables d’intégrer un accord environnemental parallèle, les clauses établies ne sont pas suffisantes pour contrer les problématiques environnementales que la libéralisation des échanges a engendrées. En effet, un déplacement majeur de la production du Mexique vers les États-Unis a été constaté. Cela a entraîné une transition vers une production industrielle plus polluante. De multiples causes sont à la source de ce changement dans la production agricole, tel que le non-respect des clauses, l’asymétrie du pouvoir entre les membres, la privatisation et le pouvoir des lobbys, ainsi que le manque de pouvoir discrétionnaire des clauses environnementales. À partir de l’analyse de l’ALENA, des recommandations ont finalement été formulées afin d’offrir des pistes de solutions pour les prochains accords qui entreront en vigueur. D’abord, il est conseillé d’encourager la participation citoyenne dans le processus de négociation des accords. Ensuite, le processus d’évaluation des répercussions des accords pourrait être révisé pour obtenir des études plus détaillées. Il est aussi suggéré que le gouvernement porte une attention particulière à la production agricole de subsistance. Il est de plus proposé de se questionner collectivement sur la vision à long terme et sur le modèle de développement agricole désiré. Ensuite, il est suggéré d’analyser plus en profondeur la place du libre-échange particulièrement dans le secteur agricole. Finalement, il serait pertinent d’étudier des alternatives telles que l’économie écologique et le coopérativisme.