Reconstruction of Convex Sets from One or Two X-rays

We consider a class of problems of Discrete Tomography which has been deeply investigated in the past: the reconstruction of convex lattice sets from their horizontal and/or vertical X-rays, i.e. from the number of points in a sequence of consecutive horizontal and vertical lines. The reconstruction of the HV-convex polyominoes works usually in two steps, first the filling step consisting in filling operations, second the convex aggregation of the switching components. We prove three results about the convex aggregation step: (1) The convex aggregation step used for the reconstruction of HV-convex polyominoes does not always provide a solution. The example yielding to this result is called \textit{the bad guy} and disproves a conjecture of the domain. (2) The reconstruction of a digital convex lattice set from only one X-ray can be performed in polynomial time. We prove it by encoding the convex aggregation problem in a Directed Acyclic Graph. (3) With the same strategy, we prove that the reconstruction of fat digital convex sets from their horizontal and vertical X-rays can be solved in polynomial time. Fatness is a property of the digital convex sets regarding the relative position of the left, right, top and bottom points of the set. The complexity of the reconstruction of the lattice sets which are not fat remains an open question.Comment: 31 pages, 24 figure

Efficient Algorithms for Battleship

We consider an algorithmic problem inspired by the Battleship game. In the variant of the problem that we investigate, there is a unique ship of shape $S \subset Z^2$ which has been translated in the lattice $Z^2$. We assume that a player has already hit the ship with a first shot and the goal is to sink the ship using as few shots as possible, that is, by minimizing the number of missed shots. While the player knows the shape $S$, which position of $S$ has been hit is not known. Given a shape $S$ of $n$ lattice points, the minimum number of misses that can be achieved in the worst case by any algorithm is called the Battleship complexity of the shape $S$ and denoted $c(S)$. We prove three bounds on $c(S)$, each considering a different class of shapes. First, we have $c(S) \leq n-1$ for arbitrary shapes and the bound is tight for parallelogram-free shapes. Second, we provide an algorithm that shows that $c(S) = O(\log n)$ if $S$ is an HV-convex polyomino. Third, we provide an algorithm that shows that $c(S) = O(\log \log n)$ if $S$ is a digital convex set. This last result is obtained through a novel discrete version of the Blaschke-Lebesgue inequality relating the area and the width of any convex body.Comment: Conference version at 10th International Conference on Fun with Algorithms (FUN 2020

Short Flip Sequences to Untangle Segments in the Plane

A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip operation. We remove a pair of crossing segments, and insert a pair of non-crossing segments, while keeping the same vertex degrees. The goal of this paper is to devise efficient strategies to flip the segments in order to obtain crossing-free segments after a small number of flips. Linear and near-linear bounds on the number of flips were only known for segments with endpoints in convex position. We generalize these results, proving linear and near-linear bounds for cases with endpoints that are not in convex position. Our results are proved in a general setting that applies to multiple problems, using multigraphs and the distinction between removal and insertion choices when performing a flip.Comment: 19 pages, 10 figure

An elementary algorithm for digital arc segmentation

International audienceThis paper concerns the digital circle recognition problem, especially in the form of the circular separation problem. General fundamentals, based on classical tools, as well as algorithmic details are given (the latter by providing pseudo-code for major steps of the algorithm). After recalling the geometrical meaning of the separating circle problem, we present an incremental algorithm to segment a discrete curve into digital arcs

Compact ring-based X-ray source with on-orbit and on-energy laser-plasma injection

We report here the results of a one week long investigation into the conceptual design of an X-ray source based on a compact ring with on-orbit and on-energy laser-plasma accelerator. We performed these studies during the June 2016 USPAS class "Physics of Accelerators, Lasers, and Plasma..." applying the art of inventiveness TRIZ. We describe three versions of the light source with the constraints of the electron beam with energy $1\,\rm{GeV}$ or $3\,\rm{GeV}$ and a magnetic lattice design being normal conducting (only for the $1\,\rm{GeV}$ beam) or superconducting (for either beam). The electron beam recirculates in the ring, to increase the effective photon flux. We describe the design choices, present relevant parameters, and describe insights into such machines.Comment: 4 pages, 1 figure, Conference Proceedings of NAPAC 201

Identifying complementary and alternative medicine recommendations for insomnia treatment and care : a systematic review and critical assessment of comprehensive clinical practice guidelines

Background: There is a need for evidence-informed guidance on the use of complementary and alternative medicine (CAM) for insomnia because of its widespread utilization and a lack of guidance on the balance of benefits and harms. This systematic review aimed to identify and summarize the CAM recommendations associated with insomnia treatment and care from existing comprehensive clinical practice guidelines (CPGs). The quality of the eligible guidelines was appraised to assess the credibility of these recommendations. Methods: Formally published CPGs incorporating CAM recommendations for insomnia management were searched for in seven databases from their inception to January 2023. The NCCIH website and six websites of international guideline developing institutions were also retrieved. The methodological and reporting quality of each included guideline was appraised using the AGREE II instrument and RIGHT statement, respectively. Results: Seventeen eligible GCPs were included, and 14 were judged to be of moderate to high methodological and reporting quality. The reporting rate of eligible CPGs ranged from 42.9 to 97.1%. Twenty-two CAM modalities were implicated, involving nutritional or natural products, physical CAM, psychological CAM, homeopathy, aromatherapy, and mindful movements. Recommendations for these modalities were mostly unclear, unambiguous, uncertain, or conflicting. Logically explained graded recommendations supporting the CAM use in the treatment and/or care of insomnia were scarce, with bibliotherapy, Tai Chi, Yoga, and auriculotherapy positively recommended based on little and weak evidence. The only consensus was that four phytotherapeutics including valerian, chamomile, kava, and aromatherapy were not recommended for insomnia management because of risk profile and/or limited benefits. Conclusions: Existing guidelines are generally limited in providing clear, evidence-informed recommendations for the use of CAM therapies for insomnia management due to a lack of high-quality evidence and multidisciplinary consultation in CPG development. More well-designed studies to provide reliable clinical evidence are therefore urgently needed. Allowing the engagement of a range of interdisciplinary stakeholders in future updates of CPGs is also warranted. Systematic review registration: https://www.crd.york.ac.uk/prospero/display_record.php?RecordID=369155, identifier: CRD42022369155. Copyright © 2023 Zhao, Xu, Kennedy, Conduit, Zhang, Wang, Fu and Zheng