Optimal paths for avoiding a radiating source

We consider the problem of navigating between points in the plane so as to minimize the exposure to a radiating source. Specifically, given two points z_1, z_2 in the complex plane, we solve the problem of finding the path C(t) (0 ≤ t ≤ 1) such that C(0)=z_1, C(1)=z_2 and ∫^1_0 |C'(t)|/|C(t)|^k dt is minimized. The parameter k specializes to a number of interesting cases: in particular k=2 pertains to the passive sensor avoidance problem and k=4 entails the active radar avoidance problem. The avoidance paths which minimize exposure may have infinite arc-length. To overcome this problem we introduce a weighted exposure and path length optimization problem whose solution requires a variational approach. The optimal trajectory results we obtain are surprisingly intuitive in the cases of interest

Pursuit on a Graph Using Partial Information

The optimal control of a "blind" pursuer searching for an evader moving on a road network and heading at a known speed toward a set of goal vertices is considered. To aid the "blind" pursuer, certain roads in the network have been instrumented with Unattended Ground Sensors (UGSs) that detect the evader's passage. When the pursuer arrives at an instrumented node, the UGS therein informs the pursuer if and when the evader visited the node. The pursuer's motion is not restricted to the road network. In addition, the pursuer can choose to wait/loiter for an arbitrary time at any UGS location/node. At time 0, the evader passes by an entry node on his way towards one of the exit nodes. The pursuer also arrives at this entry node after some delay and is thus informed about the presence of the intruder/evader in the network, whereupon the chase is on - the pursuer is tasked with capturing the evader. Because the pursuer is "blind", capture entails the pursuer and evader being collocated at an UGS location. If this happens, the UGS is triggered and this information is instantaneously relayed to the pursuer, thereby enabling capture. On the other hand, if the evader reaches one of the exit nodes without being captured, he is deemed to have escaped. We provide an algorithm that computes the maximum initial delay at the entry node for which capture is guaranteed. The algorithm also returns the corresponding optimal pursuit policy

Linear programming in R3 and the skeleton and largest incircle of a convex polygon

AbstractIn this paper the geometrical problem of constructing the largest circle inscribed in a (given) convex polygon is solved in 0(n) time. This problem is related to the construction of the skeleton of the polygon, which construction is shown to be accomplishable in 0(n log n) time

The effect of a finite roll rate on the miss-distance of a bank-to-turn missile

AbstractWe consider a three-dimensional pursuit-evasion situation where a highly maneuverable evader, which we model as a “pedestrian” á la Isaacs, is engaged by a faster-pursuer. The pursuer has limited maneuverability, that is, the pursuer has a minimal turning radius, and in order to change the spatial direction of his velocity vector, he must first re-align his thrust vector in a similar manner to a bank-to-turn missile. The state space of the ensuing differential game is three-dimensional and its complexity is intermediate between Isaac's [1] classical “Homicidal Chauffeur” and “Two Car” differential games. This new DG is solved as a game of kind, and a capture criterion for a faster but less maneuverable pursuer is analytically established in terms of the game parameters

Convex Rank Tests and Semigraphoids

Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. Each class consists of the linear extensions of a partially ordered set specified by data. Our methods refine existing rank tests of non-parametric statistics, such as the sign test and the runs test, and are useful for exploratory analysis of ordinal data. We establish a bijection between convex rank tests and probabilistic conditional independence structures known as semigraphoids. The subclass of submodular rank tests is derived from faces of the cone of submodular functions, or from Minkowski summands of the permutohedron. We enumerate all small instances of such rank tests. Of particular interest are graphical tests, which correspond to both graphical models and to graph associahedra

Lassoing and corraling rooted phylogenetic trees

The construction of a dendogram on a set of individuals is a key component of a genomewide association study. However even with modern sequencing technologies the distances on the individuals required for the construction of such a structure may not always be reliable making it tempting to exclude them from an analysis. This, in turn, results in an input set for dendogram construction that consists of only partial distance information which raises the following fundamental question. For what subset of its leaf set can we reconstruct uniquely the dendogram from the distances that it induces on that subset. By formalizing a dendogram in terms of an edge-weighted, rooted phylogenetic tree on a pre-given finite set X with |X|>2 whose edge-weighting is equidistant and a set of partial distances on X in terms of a set L of 2-subsets of X, we investigate this problem in terms of when such a tree is lassoed, that is, uniquely determined by the elements in L. For this we consider four different formalizations of the idea of "uniquely determining" giving rise to four distinct types of lassos. We present characterizations for all of them in terms of the child-edge graphs of the interior vertices of such a tree. Our characterizations imply in particular that in case the tree in question is binary then all four types of lasso must coincide

Innovative Piloting Technique for a Semi-Autonomous UAV Lighter-Than-Air Platform Simulator

UAS design has in these years reached a point in which trends and objectives are well beyond the actual test capabilities. The tendency of the past to build and test has clearly been overridden by new design concepts for many reasons, one of these being the scarce or null possibility of testing safety-critical systems such as UAV systems. This is the context in which the Elettra-Twin-Flyer (ETF) Simulator is constantly upgraded and rearranged to incorporate new features and more advanced capabilities. In this paper it is shown how the piloting modes have been differentiated, to improve the airship autonomy and allow path following operations. Innovative piloting tools have been introduced and a new Human-Machine-Interface has been proposed along

Hot topics, urgent priorities, and ensuring success for racial/ethnic minority young investigators in academic pediatrics.

BackgroundThe number of racial/ethnic minority children will exceed the number of white children in the USA by 2018. Although 38% of Americans are minorities, only 12% of pediatricians, 5% of medical-school faculty, and 3% of medical-school professors are minorities. Furthermore, only 5% of all R01 applications for National Institutes of Health grants are from African-American, Latino, and American Indian investigators. Prompted by the persistent lack of diversity in the pediatric and biomedical research workforces, the Academic Pediatric Association Research in Academic Pediatrics Initiative on Diversity (RAPID) was initiated in 2012. RAPID targets applicants who are members of an underrepresented minority group (URM), disabled, or from a socially, culturally, economically, or educationally disadvantaged background. The program, which consists of both a research project and career and leadership development activities, includes an annual career-development and leadership conference which is open to any resident, fellow, or junior faculty member from an URM, disabled, or disadvantaged background who is interested in a career in academic general pediatrics.MethodsAs part of the annual RAPID conference, a Hot Topic Session is held in which the young investigators spend several hours developing a list of hot topics on the most useful faculty and career-development issues. These hot topics are then posed in the form of six "burning questions" to the RAPID National Advisory Committee (comprised of accomplished, nationally recognized senior investigators who are seasoned mentors), the RAPID Director and Co-Director, and the keynote speaker.Results/conclusionsThe six compelling questions posed by the 10 young investigators-along with the responses of the senior conference leadership-provide a unique resource and "survival guide" for ensuring the academic success and optimal career development of young investigators in academic pediatrics from diverse backgrounds. A rich conversation ensued on the topics addressed, consisting of negotiating for protected research time, career trajectories as academic institutions move away from an emphasis on tenure-track positions, how "non-academic" products fit into career development, racism and discrimination in academic medicine and how to address them, coping with isolation as a minority faculty member, and how best to mentor the next generation of academic physicians

Recognizing Treelike k-Dissimilarities

A k-dissimilarity D on a finite set X, |X| >= k, is a map from the set of size k subsets of X to the real numbers. Such maps naturally arise from edge-weighted trees T with leaf-set X: Given a subset Y of X of size k, D(Y) is defined to be the total length of the smallest subtree of T with leaf-set Y . In case k = 2, it is well-known that 2-dissimilarities arising in this way can be characterized by the so-called "4-point condition". However, in case k > 2 Pachter and Speyer recently posed the following question: Given an arbitrary k-dissimilarity, how do we test whether this map comes from a tree? In this paper, we provide an answer to this question, showing that for k >= 3 a k-dissimilarity on a set X arises from a tree if and only if its restriction to every 2k-element subset of X arises from some tree, and that 2k is the least possible subset size to ensure that this is the case. As a corollary, we show that there exists a polynomial-time algorithm to determine when a k-dissimilarity arises from a tree. We also give a 6-point condition for determining when a 3-dissimilarity arises from a tree, that is similar to the aforementioned 4-point condition.Comment: 18 pages, 4 figure

Evolution of Genes Neighborhood Within Reconciled Phylogenies: An Ensemble Approach

Context The reconstruction of evolutionary scenarios for whole genomes in terms of genome rearrangements is a fundamental problem in evolutionary and comparative genomics. The DeCo algorithm, recently introduced by Bérard et al., computes parsimonious evolutionary scenarios for gene adjacencies, from pairs of reconciled gene trees. However, as for many combinatorial optimization algorithms, there can exist many co-optimal, or slightly sub-optimal, evolutionary scenarios that deserve to be considered. Contribution We extend the DeCo algorithm to sample evolutionary scenarios from the whole solution space under the Boltzmann distribution, and also to compute Boltzmann probabilities for specific ancestral adjacencies. Results We apply our algorithms to a dataset of mammalian gene trees and adjacencies, and observe a significant reduction of the number of syntenic conflicts observed in the resulting ancestral gene adjacencies