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

Nonadiabatic extension of the Heisenberg model

The localized states within the Heisenberg model of magnetism should be represented by best localized Wannier functions forming a unitary transformation of the Bloch functions of the narrowest partly filled energy bands in the metals. However, as a consequence of degeneracies between the energy bands near the Fermi level, in any metal these Wannier functions cannot be chosen symmetry-adapted to the complete paramagnetic group M^P. Therefore, it is proposed to use Wannier functions with the reduced symmetry of a magnetic subgroup M of M^P [case (a)] or spin dependent Wannier functions [case (b)]. The original Heisenberg model is reinterpreted in order to understand the pronounced symmetry of these Wannier functions. While the original model assumes that there is exactly one electron at each atom, the extended model postulates that in narrow bands there are as many as possible atoms occupied by exactly one electron. However, this state with the highest possible atomiclike character cannot be described within the adiabatic (or Born-Oppenheimer) approximation because in the (true) nonadiabatic system the electrons move on localized orbitals that are still symmetric on the average of time, but not at any moment. The nonadiabatic states have the same symmetry as the adiabatic states and determine the commutation properties of the nonadiabatic Hamiltonian H^n. The nonadiabatic Heisenberg model is a purely group- theoretical model which interprets the commutation properties of H^n that are explicitly given in this paper for the two important cases (a) and (b). There is evidence that the occurrence of these two types of Wannier functions in the band structure of a metal is connected with the occurrence of magnetism and superconductivity, respectively

Sequence and comparative analysis of the chicken genome provide unique perspectives on vertebrate evolution

We present here a draft genome sequence of the red jungle fowl, Gallus gallus. Because the chicken is a modern descendant of the dinosaurs and the first non-mammalian amniote to have its genome sequenced, the draft sequence of its genome—composed of approximately one billion base pairs of sequence and an estimated 20,000–23,000 genes—provides a new perspective on vertebrate genome evolution, while also improving the annotation of mammalian genomes. For example, the evolutionary distance between chicken and human provides high specificity in detecting functional elements, both non-coding and coding. Notably, many conserved non-coding sequences are far from genes and cannot be assigned to defined functional classes. In coding regions the evolutionary dynamics of protein domains and orthologous groups illustrate processes that distinguish the lineages leading to birds and mammals. The distinctive properties of avian microchromosomes, together with the inferred patterns of conserved synteny, provide additional insights into vertebrate chromosome architecture

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

Alignment Metric Accuracy

We propose a metric for the space of multiple sequence alignments that can be used to compare two alignments to each other. In the case where one of the alignments is a reference alignment, the resulting accuracy measure improves upon previous approaches, and provides a balanced assessment of the fidelity of both matches and gaps. Furthermore, in the case where a reference alignment is not available, we provide empirical evidence that the distance from an alignment produced by one program to predicted alignments from other programs can be used as a control for multiple alignment experiments. In particular, we show that low accuracy alignments can be effectively identified and discarded. We also show that in the case of pairwise sequence alignment, it is possible to find an alignment that maximizes the expected value of our accuracy measure. Unlike previous approaches based on expected accuracy alignment that tend to maximize sensitivity at the expense of specificity, our method is able to identify unalignable sequence, thereby increasing overall accuracy. In addition, the algorithm allows for control of the sensitivity/specificity tradeoff via the adjustment of a single parameter. These results are confirmed with simulation studies that show that unalignable regions can be distinguished from homologous, conserved sequences. Finally, we propose an extension of the pairwise alignment method to multiple alignment. Our method, which we call AMAP, outperforms existing protein sequence multiple alignment programs on benchmark datasets. A webserver and software downloads are available at http://bio.math.berkeley.edu/amap/

The m−m-dissimilarity map and representation theory of SLmSL_m

We give another proof that $m$-dissimilarity vectors of weighted trees are points on the tropical Grassmanian, as conjectured by Cools, and proved by Giraldo in response to a question of Sturmfels and Pachter. We accomplish this by relating $m$-dissimilarity vectors to the representation theory of $SL_m.$Comment: 11 pages, 8 figure

Reliable and accurate diagnostics from highly multiplexed sequencing assays

Scalable, inexpensive, and secure testing for SARS-CoV-2 infection is crucial for control of the novel coronavirus pandemic. Recently developed highly multiplexed sequencing assays (HMSAs) that rely on high-throughput sequencing can, in principle, meet these demands, and present promising alternatives to currently used RT-qPCR-based tests. However, reliable analysis, interpretation, and clinical use of HMSAs requires overcoming several computational, statistical and engineering challenges. Using recently acquired experimental data, we present and validate a computational workflow based on kallisto and bustools, that utilizes robust statistical methods and fast, memory efficient algorithms, to quickly, accurately and reliably process high-throughput sequencing data. We show that our workflow is effective at processing data from all recently proposed SARS-CoV-2 sequencing based diagnostic tests, and is generally applicable to any diagnostic HMSA