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This paper studies and compares optimal climb and descent trajectories that conform to the Air Traffic Control (ATC) procedures and minimize fuel consumption, emissions, flight time, and/or flight distance. Tradeoffs among these different performance criteria are examined. In addition, closed-loop sensitivities are used to evaluate the likely variations of fuel burns, emissions, and flight times when optimized trajectories are tracked in actual flights. In this paper, a point-mass model of conventional commercial aircraft is used, together with available models of aircraft performance and emissions. Aircraft vertical profiles in the ATC system are described through a series of flight segments. The segment parameters are optimized to minimize fuel burn, emissions, flight time, flight distance, and/or their linear combinations, subject to aircraft equations of motion, aircraft performance limitations, and appropriate boundary conditions. A gradient method is devised for numerical solutions. In calculating the closed-loop sensitivities, the method of feedback linearization is used to model aircraft guidance strategies. NOMENCLATURE c tsfc = Thrust specific fuel consumption (C D , C L ) = (Drag, Lift) coefficient C D 0 = Parasite drag coefficient (D, L) = (Drag, Lift) force g = Acceleration of gravity H = Humidity correction h = Geometric altitude h b = Baro-corrected altitude p h = Pressure altitude K = Induced drag factor, feedback gains, weighting coefficients m = Aircraft mass n = Load factor M = Mach number p = Pressure p amb = Ambient pressure in psia p sat = Saturation vapor pressure in mbar R = Specific gas constant s = Path distance S = Aircraft wing area T = Engine thrust CAS V = Calibrated airspeed 1 Ph.D. candidate, 2 V g = Ground speed t V = True airspeed W = mg = Aircraft weight W h = Vertical wind speed W f = Weight of consumed fuel ! W f = Fuel flow rate W NO x = Weight of NOx emissions W CO 2 = Weight of CO2 emissions ẑ = Measured/estimated value of z ! = p / p SL = Pressure ratio ! = Relative humidity a γ = Air-relative flight path angle ! = Engine throttle setting ! = Humidity ratio in kg water / kg dry air ! = Air density ! = ! / ! SL = Temperature ratio ! = Air temperature ! amb = Ambient temperature in R ! ambc = Ambient temperature in C ( ) SL = Sea-level value ( ) 0 = Initial value ( ) f = Final value ( ) min , ( ) max = Minimum, maximum value ( ) c = Command, related to climb phase ( ) d = Related to descent phase ( ) cr = Related to cruise conditions

wei wang mail.tsinghua.edu.cn. † Ph.D. Candidate, wud17 mails.tsinghua.edu.cn. ‡ Professor, g.mengali ing.unipi.it. Senior Member AIAA. § Professor, a.quarta ing.unipi.it. Associate Fellow AIAA ¶ Professor, baoyin tsinghua.edu.cn. Senior Member AIAA (corresponding author).

Information diffusion model plays an important role in many real-world applications such as online marketing and e-government campaigns. Existing approaches often predict information diffusion by examining whether events are triggered by external trends or the social network itself. However, existing methods cannot take into account the semantically rich "topics" to estimate the correlations between users and messages describing some events. The main contribution of our work is the development of the Topic based Information Diffusion (TBID) model which can incorporate external trends model and topic based social descriptions to enhance the effectiveness of predicting information diffusion in online social networks. Experiments conducted based on real-world data sets confirm the distinct advantage of the proposed computational method. Our research opens the door to the development of a more effective personalized information recommendation model in online social media.