The cyclic-routing UAV problem is PSPACE-complete

© 2015, Springer-Verlag Berlin Heidelberg. Consider a finite set of targets, with each target assigned a relative deadline, and each pair of targets assigned a fixed transit flight time. Given a flock of identical UAVs, can one ensure that every target is repeatedly visited by some UAV at intervals of duration at most the target’s relative deadline? The Cyclic-Routing UAV Problem (cr-uav) is the question of whether this task has a solution. This problem can straightforwardly be solved in PSPACE by modelling it as a network of timed automata. The special case of there being a single UAV is claimed to be NP-complete in the literature. In this paper, we show that the cr-uav Problem is in fact PSPACE-complete even in the single-UAV case

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

Greedy D-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost

This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards) covering constraints, each of which constrains at most D variables of the problem. (A simple example is Vertex Cover, with D = 2.) The algorithm generalizes previous approximation algorithms for fundamental covering problems and online paging and caching problems

A large genome-wide association study of age-related macular degeneration highlights contributions of rare and common variants.

This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/ng.3448Advanced age-related macular degeneration (AMD) is the leading cause of blindness in the elderly, with limited therapeutic options. Here we report on a study of >12 million variants, including 163,714 directly genotyped, mostly rare, protein-altering variants. Analyzing 16,144 patients and 17,832 controls, we identify 52 independently associated common and rare variants (P < 5 × 10(-8)) distributed across 34 loci. Although wet and dry AMD subtypes exhibit predominantly shared genetics, we identify the first genetic association signal specific to wet AMD, near MMP9 (difference P value = 4.1 × 10(-10)). Very rare coding variants (frequency <0.1%) in CFH, CFI and TIMP3 suggest causal roles for these genes, as does a splice variant in SLC16A8. Our results support the hypothesis that rare coding variants can pinpoint causal genes within known genetic loci and illustrate that applying the approach systematically to detect new loci requires extremely large sample sizes.We thank all participants of all the studies included for enabling this research by their participation in these studies. Computer resources for this project have been provided by the high-performance computing centers of the University of Michigan and the University of Regensburg. Group-specific acknowledgments can be found in the Supplementary Note. The Center for Inherited Diseases Research (CIDR) Program contract number is HHSN268201200008I. This and the main consortium work were predominantly funded by 1X01HG006934-01 to G.R.A. and R01 EY022310 to J.L.H

The specific features of photoneutron reactions on

The reliability of experimental data on partial photoneutron reaction cross sections (γ, 1n) and (γ, 2n) for 58Ni obtained in experiments carried out using beams of both bremsstrahlung and quasimonoenergetic annihilation photons were analyzed using the objective physical criteria. It was found out that data obtained using bremsstrahlung are not reliable definitely. At the same time, it was shown that there are serious doubts in reliability of data obtained using quasimonoenergetic photons and the method of photoneutron multiplicity sorting. New reliable cross sections of partial and total photoneutron reactions were obtained using the experimental-theoretical method of evaluation basing on the joint using of the experimental neutron yield cross-section which is rather independent of neutron multiplicity and the results of calculations in the Combined PhotoNucleon Reaction Model (CPNRM). The significant disagreements between the new reliable evaluated cross sections and the experimental ones for both partial reactions (γ, 1n) and (γ, 2n) were analyzed in detail. It was shown that the main reason of disagreements is that experimental cross-section of (γ, 1n1p) reaction was unreliably (erroneously) interpreted as that of (γ, 2n) reaction

New evaluated data on

New cross sections of the partial ($$\gamma ,1n)$$, ($$\gamma ,2n)$$, and ($$\gamma$$, 3n) and total ($$\gamma$$, Sn), and ($$\gamma$$, tot) photoneutron reactions for $$^{{206,207}}$$Pb were evaluated using the experimental-theoretical method. The evaluation procedure was based on the comparison in detail of $$^{{206,207}}$$Pb data obtained only at Livermore (USA) with $$^{{208}}$$Pb data obtained at Livermore, Saclay (France) and also in other experiments. It was found that in the cases of all $$^{{206,207,208}}$$Pb isotopes clear disagreements between Livermore data and new evaluated data can be explained by the assumption of loss of many neutrons in experimental ($$\gamma$$, 1n) reaction cross sections. It was shown that Livermore experimental data for $$^{{206,207,208}}$$Pb as well as for $$^{{75}}$$As, $$^{{127}}$$I, and $$^{{181}}$$Ta investigated before are not reliable

A new approach for analysis and evaluation of partial photoneutron reaction cross sections

There are well-known systematic disagreements in partial photoneutron reaction cross sections obtained using quasimonoenergetic annihilation photons in experiments based on neutron multiplicity sorting methods. Using newly proposed criteria we demonstrate that a large part of the systematic uncertainty comes from certain shortcomings of experimental methods of neutron multiplicity sorting. To develop methods of correction of data obtained in experiments a new approach to data evaluation was developed in which a combined model of photonuclear reactions is used to decompose experimental total neutron yield reaction cross sections into partial reaction contributions. Evaluated cross sections of partial photoneutron reactions obtained using this method show a good agreement with results of alternative experiments