Symplectic Structures on Moduli Spaces of Parabolic Higgs Bundles and Hilbert Scheme

Parabolic triples of the form $(E_*,\theta,\sigma)$ are considered, where $(E_*,\theta)$ is a parabolic Higgs bundle on a given compact Riemann surface $X$ with parabolic structure on a fixed divisor $S$, and $\sigma$ is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle $(E_*,\theta)$ a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bundles is obtained. The pull back, by this map, of the symplectic form on the moduli space of stable parabolic Higgs bundles will be denoted by $\text{d}\Omega'$. On the other hand, there is a map from the moduli space of stable parabolic triples to a Hilbert scheme $\text{Hilb}^\delta(Z)$, where $Z$ denotes the total space of the line bundle $K_X\otimes{\mathcal O}_X(S)$, that sends a triple $(E_*,\theta,\sigma)$ to the divisor defined by the section $\sigma$ on the spectral curve corresponding to the parabolic Higgs bundle $(E_*,\theta)$. Using this map and a meromorphic one--form on $\text{Hilb}^\delta(Z)$, a natural two--form on the moduli space of stable parabolic triples is constructed. It is shown here that this form coincides with the above mentioned form $\text{d}\Omega'$.Comment: LaTex file; 11 page

Flight Departure Delay and Rerouting Under Uncertainty in En Route Convective Weather

Delays caused by uncertainty in weather forecasts can be reduced by improving traffic flow management decisions. This paper presents a methodology for traffic flow management under uncertainty in convective weather forecasts. An algorithm for assigning departure delays and reroutes to aircraft is presented. Departure delay and route assignment are executed at multiple stages, during which, updated weather forecasts and flight schedules are used. At each stage, weather forecasts up to a certain look-ahead time are treated as deterministic and flight scheduling is done to mitigate the impact of weather on four-dimensional flight trajectories. Uncertainty in weather forecasts during departure scheduling results in tactical airborne holding of flights. The amount of airborne holding depends on the accuracy of forecasts as well as the look-ahead time included in the departure scheduling. The weather forecast look-ahead time is varied systematically within the experiments performed in this paper to analyze its effect on flight delays. Based on the results, longer look-ahead times cause higher departure delays and additional flying time due to reroutes. However, the amount of airborne holding necessary to prevent weather incursions reduces when the forecast look-ahead times are higher. For the chosen day of traffic and weather, setting the look-ahead time to 90 minutes yields the lowest total delay cost

Optimizing Flight Departure Delay and Route Selection Under En Route Convective Weather

This paper presents a linear Integer Programming model for managing air traffic flow in the United States. The decision variables in the model are departure delays and predeparture reroutes of aircraft whose trajectories are predicted to cross weather-impacted regions of the National Airspace System. The model assigns delays to a set of flights while ensuring their trajectories are free of any conflicts with weather. In a deterministic setting, there is no airborne holding due to unexpected weather incursion in a flight s path. The model is applied to solve a large-scale traffic flow management problem with realistic weather data and flight schedules. Experimental results indicate that allowing rerouting can reduce departure delays by nearly 57%, but it is associated with an increase in total airborne time due to longer routes flown by aircraft. The computation times to solve this problem were significantly lower than those reported in the earlier studies

Clustering Days with Similar Airport Weather Conditions

On any given day, traffic flow managers must often rely on past experience and intuition when developing traffic flow management initiatives that mitigate imbalances between the aircraft demand and the weather impacted airport capacity. The goal of this study was to build on recent efforts to apply data mining classification and clustering algorithms to vast archives of historical weather and air traffic data to identify patterns and past decisions that can ultimately inform day-of-operations decision-making. More specifically, this study identified similar weather impacted days at select U.S. airports, and analyzed the traffic management initiatives implemented on these representative days. The identification of the similar days was accomplished by applying a decision tree algorithm to the hourly Localized Aviation Model Output Statistics Program observations and the arrival delays for Newark Liberty International Airport. The branches from the trained decision tree were subsequently pruned to identify four weather conditions that resulted in medium to high delays for the arrivals scheduled to Newark in 2012. Using these weather conditions, four, daily airport-level Weather Impacted Traffic Index values were calculated using the Localized Aviation Model Output Statistics Program observations and the 2012 scheduled arrival counts from the FAAs Aviation System Performance Metric system. The four, daily Weather Impacted Traffic Index values for 2012 were subsequently clustered using an Expectation Maximization clustering algorithm, and nine unique types of weather days at Newark were identified. By far the most prominent type of day at Newark was a day associated with relatively good weather conditions, where there was little convective activity, winds were low, ceilings and visibility were high and there was little precipitation. Moderate levels of convective activity characterized the next most prominent type of day. Days with persistently high winds or low ceiling and visibility levels were relatively rare in 2012. Lastly, the frequency at which Ground Delay Programs, Ground Stops and Miles-in-Trail restrictions were implemented on each of the typical types of days at Newark were analyzed. Based on the results, it does appear as if the usage of Miles-in-Trail, Ground Delay Program and Ground Stop restrictions correlates well with the severity of the weather associated with each unique type of weather impacted day at Newark. Furthermore, the results demonstrate that it is feasible to use historical weather and air traffic archives to provide guidance on the types of traffic management restrictions to implement in response to the weather conditions impacting an airport

Anchorage Arrival Scheduling Under Off-Nominal Weather Conditions

Weather can cause flight diversions, passenger delays, additional fuel consumption and schedule disruptions at any high volume airport. The impacts are particularly acute at the Ted Stevens Anchorage International Airport in Anchorage, Alaska due to its importance as a major international portal. To minimize the impacts due to weather, a multi-stage scheduling process is employed that is iteratively executed, as updated aircraft demand and/or airport capacity data become available. The strategic scheduling algorithm assigns speed adjustments for flights that originate outside of Anchorage Center to achieve the proper demand and capacity balance. Similarly, an internal departure-scheduling algorithm assigns ground holds for pre-departure flights that originate from within Anchorage Center. Tactical flight controls in the form of airborne holding are employed to reactively account for system uncertainties. Real-world scenarios that were derived from the January 16, 2012 Anchorage visibility observations and the January 12, 2012 Anchorage arrival schedule were used to test the initial implementation of the scheduling algorithm in fast-time simulation experiments. Although over 90% of the flights in the scenarios arrived at Anchorage without requiring any delay, pre-departure scheduling was the dominant form of control for Anchorage arrivals. Additionally, tactical scheduling was used extensively in conjunction with the pre-departure scheduling to reactively compensate for uncertainties in the arrival demand. For long-haul flights, the strategic scheduling algorithm performed best when the scheduling horizon was greater than 1,000 nmi. With these long scheduling horizons, it was possible to absorb between ten and 12 minutes of delay through speed control alone. Unfortunately, the use of tactical scheduling, which resulted in airborne holding, was found to increase as the strategic scheduling horizon increased because of the additional uncertainty in the arrival times of the aircraft. Findings from these initial experiments indicate that it is possible to schedule arrivals into Anchorage with minimal delays under low-visibility conditions with less disruption to high-cost, international flights

A Comparative Analysis of Application of Genetic Algorithm and Particle Swarm Optimization in Solving Traveling Tournament Problem (TTP)

Traveling Tournament Problem (TTP) has been a major area of research due to its huge application in developing smooth and healthy match schedules in a tournament. The primary objective of a similar problem is to minimize the travel distance for the participating teams. This would incur better quality of the tournament as the players would experience least travel; hence restore better energy level. Besides, there would be a great benefit to the tournament organizers from the economic point of view as well. A well constructed schedule, comprising of diverse combinations of the home and away matches in a round robin tournament would keep the fans more attracted, resulting in turnouts in a large number in the stadiums and a considerable amount of revenue generated from the match tickets. Hence, an optimal solution to the problem is necessary from all respects; although it becomes progressively harder to identify the optimal solution with increasing number of teams. In this work, we have described how to solve the problem using Genetic algorithm and particle swarm optimization

Interaction Between Strategic and Local Traffic Flow Controls

The loosely coordinated sets of traffic flow management initiatives that are operationally implemented at the national- and local-levels have the potential to under, over, and inconsistently control flights. This study is designed to explore these interactions through fast-time simulations with an emphasis on identifying inequitable situations in which flights receive multiple uncoordinated delays. Two operationally derived scenarios were considered in which flights arriving into the Dallas/Fort Worth International Airport were first controlled at the national-level, either with a Ground Delay Program or a playbook reroute. These flights were subsequently controlled at the local level. The Traffic Management Advisor assigned them arrival scheduling delays. For the Ground Delay Program scenarios, between 51% and 53% of all arrivals experience both pre-departure delays from the Ground Delay Program and arrival scheduling delays from the Traffic Management Advisor. Of the subset of flights that received multiple delays, between 5.7% and 6.4% of the internal departures were first assigned a pre-departure delay by the Ground Delay Program, followed by a second pre-departure delay as a result of the arrival scheduling. For the playbook reroute scenario, Dallas/Fort Worth International Airport arrivals were first assigned pre-departure reroutes based on the MW_2_DALLAS playbook plan, and were subsequently assigned arrival scheduling delays by the Traffic Management Advisor. Since the airport was operating well below capacity when the playbook reroute was in effect, only 7% of the arrivals were observed to receive both rerouting and arrival scheduling delays. Findings from these initial experiments confirm field observations that Ground Delay Programs operated in conjunction with arrival scheduling can result in inequitable situations in which flights receive multiple uncoordinated delays