827 research outputs found
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 which has been translated in the lattice . 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 , which position of has
been hit is not known.
Given a shape of 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 and denoted . We prove three bounds on
, each considering a different class of shapes. First, we have for arbitrary shapes and the bound is tight for parallelogram-free shapes.
Second, we provide an algorithm that shows that if is an
HV-convex polyomino. Third, we provide an algorithm that shows that if 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 or
and a magnetic lattice design being normal conducting (only for the
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
MedBench: A Large-Scale Chinese Benchmark for Evaluating Medical Large Language Models
The emergence of various medical large language models (LLMs) in the medical
domain has highlighted the need for unified evaluation standards, as manual
evaluation of LLMs proves to be time-consuming and labor-intensive. To address
this issue, we introduce MedBench, a comprehensive benchmark for the Chinese
medical domain, comprising 40,041 questions sourced from authentic examination
exercises and medical reports of diverse branches of medicine. In particular,
this benchmark is composed of four key components: the Chinese Medical
Licensing Examination, the Resident Standardization Training Examination, the
Doctor In-Charge Qualification Examination, and real-world clinic cases
encompassing examinations, diagnoses, and treatments. MedBench replicates the
educational progression and clinical practice experiences of doctors in
Mainland China, thereby establishing itself as a credible benchmark for
assessing the mastery of knowledge and reasoning abilities in medical language
learning models. We perform extensive experiments and conduct an in-depth
analysis from diverse perspectives, which culminate in the following findings:
(1) Chinese medical LLMs underperform on this benchmark, highlighting the need
for significant advances in clinical knowledge and diagnostic precision. (2)
Several general-domain LLMs surprisingly possess considerable medical
knowledge. These findings elucidate both the capabilities and limitations of
LLMs within the context of MedBench, with the ultimate goal of aiding the
medical research community.Comment: accepted by AAAI-2
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