Reconstructing Trees from Subtree Weights

The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phylogenetics. Our main result is an extension of the tree-metric theorem to more general dissimilarity maps. In particular, we show that a tree with n leaves is reconstructible from the weights of the m-leaf subtrees provided that n \geq 2m-1

Active Target Defense Differential Game with a Fast Defender

This paper addresses the active target defense differential game where an Attacker missile pursues a Target aircraft. A Defender missile is fired by the Target's wingman in order to intercept the Attacker before it reaches the aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the distance between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while the Attacker tries to minimize said distance. The results shown here extend previous work. We consider here the case where the Defender is faster than the Attacker. The solution to this differential game provides optimal heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker and it also provides the optimal heading angle for the Attacker to minimize the said distance.Comment: 9 pages, 8 figures. A shorter version of this paper will be presented at the 2015 American Control Conferenc

Escape Regions of the Active Target Defense Differential Game

The active target defense differential game is addressed in this paper. In this differential game an Attacker missile pursues a Target aircraft. The aircraft is however aided by a Defender missile launched by, say, the wingman, to intercept the Attacker before it reaches the Target aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the separation between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while the Attacker simultaneously tries to minimize said distance. This paper focuses on characterizing the set of coordinates such that if the Target's initial position belong to this set then its survival is guaranteed if both the Target and the Defender follow their optimal strategies. Such optimal strategies are presented in this paper as well.Comment: 19 pages, 9 figures. arXiv admin note: text overlap with arXiv:1502.0274

Identification and correction of systematic error in high-throughput sequence data

A feature common to all DNA sequencing technologies is the presence of base-call errors in the sequenced reads. The implications of such errors are application specific, ranging from minor informatics nuisances to major problems affecting biological inferences. Recently developed “next-gen” sequencing technologies have greatly reduced the cost of sequencing, but have been shown to be more error prone than previous technologies. Both position specific (depending on the location in the read) and sequence specific (depending on the sequence in the read) errors have been identified in Illumina and Life Technology sequencing platforms. We describe a new type of _systematic_ error that manifests as statistically unlikely accumulations of errors at specific genome (or transcriptome) locations. We characterize and describe systematic errors using overlapping paired reads form high-coverage data. We show that such errors occur in approximately 1 in 1000 base pairs, and that quality scores at systematic error sites do not account for the extent of errors. We identify motifs that are frequent at systematic error sites, and describe a classifier that distinguishes heterozygous sites from systematic error. Our classifier is designed to accommodate data from experiments in which the allele frequencies at heterozygous sites are not necessarily 0.5 (such as in the case of RNA-Seq). Systematic errors can easily be mistaken for heterozygous sites in individuals, or for SNPs in population analyses. Systematic errors are particularly problematic in low coverage experiments, or in estimates of allele-specific expression from RNA-Seq data. Our characterization of systematic error has allowed us to develop a program, called SysCall, for identifying and correcting such errors. We conclude that correction of systematic errors is important to consider in the design and interpretation of high-throughput sequencing experiments

Optimal Policy for Sequential Stochastic Resource Allocation

A gambler in possession of R chips/coins is allowed N(\u3eR) pulls/trials at a slot machine. Upon pulling the arm, the slot machine realizes a random state i ɛ{1, ..., M} with probability p(i) and the corresponding positive monetary reward g(i) is presented to the gambler. The gambler can accept the reward by inserting a coin in the machine. However, the dilemma facing the gambler is whether to spend the coin or keep it in reserve hoping to pick up a greater reward in the future. We assume that the gambler has full knowledge of the reward distribution function. We are interested in the optimal gambling strategy that results in the maximal cumulative reward. The problem is naturally posed as a Stochastic Dynamic Program whose solution yields the optimal policy and expected cumulative reward. We show that the optimal strategy is a threshold policy, wherein a coin is spent if and only if the number of coins r exceeds a state and stage/trial dependent threshold value. We illustrate the utility of the result on a military operational scenario

The Barrier Surface in the Cooperative Football Differential Game

This paper considers the blocking or football pursuit-evasion differential game. Two pursuers cooperate and try to capture the ball carrying evader as far as possible from the goal line. The evader wishes to be as close as possible to the goal line at the time of capture and, if possible, reach the line. In this paper the solution of the game of kind is provided: The Barrier surface that partitions the state space into two winning sets, one for the pursuer team and one for the evader, is constructed. Under optimal play, the winning team is determined by evaluating the associated Barrier function.Comment: 5 pages, 1 figur

RefShannon: A genome-guided transcriptome assembler using sparse flow decomposition

High throughput sequencing of RNA (RNA-Seq) has become a staple in modern molecular biology, with applications not only in quantifying gene expression but also in isoform-level analysis of the RNA transcripts. To enable such an isoform-level analysis, a transcriptome assembly algorithm is utilized to stitch together the observed short reads into the corresponding transcripts. This task is complicated due to the complexity of alternative splicing - a mechanism by which the same gene may generate multiple distinct RNA transcripts. We develop a novel genome-guided transcriptome assembler, RefShannon, that exploits the varying abundances of the different transcripts, in enabling an accurate reconstruction of the transcripts. Our evaluation shows RefShannon is able to improve sensitivity effectively (up to 22%) at a given specificity in comparison with other state-of-the-art assemblers. RefShannon is written in Python and is available from Github (https://github.com/shunfumao/RefShannon)

Optimal Guidance of a Relay Aircraft to Extend Small Unmanned Aircraft Range

This paper developed guidance laws to optimally and autonomously position a relay Micro Aerial Vehicle (MAV) to provide an operator with real-time Intelligence, Surveillance, and Reconnaissance (ISR) by relaying communication and video signals from a rover MAV to the base, thus extending the rover\u27s reach. The ISR system is comprised of two MAVs, the Relay and the Rover, and a Base. The Relay strives to position itself so as to minimize the radio frequency (RF) power required for maintaining communications between the Rover and the Base, while the Rover performs the ISR mission, which may maximize the required RF power. The optimal control of the Relay MAV then entails the solution of a differential game. Applying Pontryagin\u27s Maximum Principle yields a standard, albeit nonlinear, Two-Point Boundary Value Problem (TPBVP). Suboptimal solutions are first obtained as an aid in solving the TPBVP which yields the solution of the differential game. One suboptimal approach is based upon the geometry of the ISR system: The midpoint between the Rover and the Base is the ideal location which minimizes the RF power required, so the Relay heads toward that point—assuming that the Rover is stationary. At the same time, to maximize the rate of required RF power, the Rover moves in the opposite direction of the Relay—assuming the Relay is stationary. These are optimal strategies in the end-game, but it is suboptimal to use them throughout the game. Another suboptimal approach investigated envisions the Rover to remain stationary and solves for the optimal path for the Relay to minimize the RF power requirement. This one-sided optimization problem is analyzed using a Matlab-based optimization program, GPOCS, which uses the Gauss pseudospectral method of discretization. The results from GPOCS corroborated with the geometry-based suboptimal Relay strategy of heading straight toward the midpoint between the Rover and the Base. The suboptimal solutions are readily implementable for real-time operation and are used to facilitate the solutions of the TPBVP