Probing a Set of Trajectories to Maximize Captured Information

We study a trajectory analysis problem we call the Trajectory Capture Problem (TCP), in which, for a given input set T of trajectories in the plane, and an integer k? 2, we seek to compute a set of k points ("portals") to maximize the total weight of all subtrajectories of T between pairs of portals. This problem naturally arises in trajectory analysis and summarization. We show that the TCP is NP-hard (even in very special cases) and give some first approximation results. Our main focus is on attacking the TCP with practical algorithm-engineering approaches, including integer linear programming (to solve instances to provable optimality) and local search methods. We study the integrality gap arising from such approaches. We analyze our methods on different classes of data, including benchmark instances that we generate. Our goal is to understand the best performing heuristics, based on both solution time and solution quality. We demonstrate that we are able to compute provably optimal solutions for real-world instances

Identifying Moderators Of Response To The Penn Resiliency Program: A Synthesis Study

To identify moderators of a cognitive-behavioral depression prevention program’s effect on depressive symptoms among youth in early adolescence, data from three randomized controlled trials of the Penn Resiliency Program (PRP) were aggregated to maximize statistical power and sample diversity (N = 1145). Depressive symptoms, measured with the Children’s Depression Inventory (CDI; Kovacs 1992), were assessed at six common time points over two-years of follow-up. Latent growth curve models evaluated whether PRP and control conditions differed in the rate of change in CDI and whether youth- and family-level characteristics moderated intervention effects. Model-based recursive partitioning was used as a supplementary analysis for identifying moderators. There was a three-way interaction of PRP, initial symptom severity, and intervention site on growth in depressive symptoms. There was considerable variability in PRP’s effects, with the nature of the interaction between PRP and initial symptom levels differing considerably across sites. PRP reduced depressive symptoms among youth with unmarried parents, but not among those with married parents. Finally, PRP’s effects differed across school grade levels. Although initial symptom severity moderated PRP’s effect on depressive symptoms, it was not a reliable indicator of how well the intervention performed, limiting its utility as a prescriptive variable. Our primary analyses suggest that PRP’s effects are limited to youth whose parents are unmarried. The small number of fifth grade students (n = 25; 2 %) showed a delayed and sustained intervention response. Our findings underscore the importance of evaluating site, family, and contextual characteristics as moderators in future studies

Efficient Media Access Control and Distributed Channel-aware Scheduling for Wireless Ad-Hoc Networks

We address the problem of channel-aware scheduling for wireless ad-hoc networks, where the channel state information (CSI) are utilized to improve the overall system performance instead of the individual link performance. In our framework, multiple links cooperate to schedule data transmission in a decentralized and opportunistic manner, where channel probing is adopted to resolve collisions in the wireless medium. In the first part of the dissertation, we study this problem under the assumption that we know the channel statistics but not the instant CSI. In this problem, channel probing is followed by a transmission scheduling procedure executed independently within each link in the network. We study this problem for the popular block-fading channel model, where channel dependencies are inevitable between different time instances during the channel probing phase. We use optimal stopping theory to formulate this problem, but at carefully chosen time instances at which effective decisions are made. The problem can then be solved by a new stopping rule problem where the observations are independent between different time instances. We first characterize the system performance assuming the stopping rule problem has infinite stages. We then develop a measure to check how well the problem can be analyzed as an infinite horizon problem, and characterize the achievable system performance if we ignore the finite horizon constraint and design stopping rules based on the infinite horizon analysis. We then analyze the problem using backward induction when the finite horizon constraint cannot be ignored. We develop one recursive approach to solve the problem and show that the computational complexity is linear with respect to network size. We present an improved protocol to reduce the probing costs which requires no additional cost. Based on our analysis on single-channel networks, we extend the problem to ad-hoc networks where the wireless spectrum can be divided into multiple independent sub-channels for better efficiency. We start with a naive multi-channel protocol where the scheduling scheme is working independently within each sub-channel. We show that the naive protocol can only marginally improve the system performance. We then develop a protocol to jointly consider the opportunistic scheduling behavior across multiple sub-channels. We characterize the optimal stopping rule and present several bounds for the network throughputs of the multi-channel protocol. We show that by joint optimization of the scheduling scheme across multiple sub-channels, the proposed protocol improves the system performance considerably in contrast to that of single-channel systems. In the second part of the dissertation, we study this problem under the assumption that neither the instant CSI nor the channel statistics are known. We formulate the channel-aware scheduling problem using multi-armed bandit (MAB). We first present a semi-distributed MAB protocol which serves as the baseline for performance comparison. We then propose two forms of distributed MAB protocols, where each link keeps a local copy of the observations and plays the MAB game independently. In Protocol I the MAB game is only played once within each block, while in Protocol II it can be played multiple times. We show that the proposed distributed protocols can be considered as a generalized MAB procedure and each link is able to update its local copy of the observations for infinitely many times. We analyze the evolution of the local observations and the regrets of the system. For Protocol I, we show by simulation results that the local observations that are held independently at each link converge to the true parameters and the regret is comparable to that of the semi-distributed protocol. For Protocol II, we prove the convergence of the local observations and show an upper bound of the regret

Solar Gamma Rays Powered by Secluded Dark Matter

Secluded dark matter models, in which WIMPs annihilate first into metastable mediators, can present novel indirect detection signatures in the form of gamma rays and fluxes of charged particles arriving from directions correlated with the centers of large astrophysical bodies within the solar system, such as the Sun and larger planets. This naturally occurs if the mean free path of the mediator is in excess of the solar (or planetary) radius. We show that existing constraints from water Cerenkov detectors already provide a novel probe of the parameter space of these models, complementary to other sources, with significant scope for future improvement from high angular resolution gamma-ray telescopes such as Fermi-LAT. Fluxes of charged particles produced in mediator decays are also capable of contributing a significant solar system component to the spectrum of energetic electrons and positrons, a possibility which can be tested with the directional and timing information of PAMELA and Fermi.Comment: 22 pages, 3 figure

Modeling the mobility of living organisms in heterogeneous landscapes: Does memory improve foraging success?

Thanks to recent technological advances, it is now possible to track with an unprecedented precision and for long periods of time the movement patterns of many living organisms in their habitat. The increasing amount of data available on single trajectories offers the possibility of understanding how animals move and of testing basic movement models. Random walks have long represented the main description for micro-organisms and have also been useful to understand the foraging behaviour of large animals. Nevertheless, most vertebrates, in particular humans and other primates, rely on sophisticated cognitive tools such as spatial maps, episodic memory and travel cost discounting. These properties call for other modeling approaches of mobility patterns. We propose a foraging framework where a learning mobile agent uses a combination of memory-based and random steps. We investigate how advantageous it is to use memory for exploiting resources in heterogeneous and changing environments. An adequate balance of determinism and random exploration is found to maximize the foraging efficiency and to generate trajectories with an intricate spatio-temporal order. Based on this approach, we propose some tools for analysing the non-random nature of mobility patterns in general.Comment: 14 pages, 4 figures, improved discussio