1,378 research outputs found
Detecting Weakly Simple Polygons
A closed curve in the plane is weakly simple if it is the limit (in the
Fr\'echet metric) of a sequence of simple closed curves. We describe an
algorithm to determine whether a closed walk of length n in a simple plane
graph is weakly simple in O(n log n) time, improving an earlier O(n^3)-time
algorithm of Cortese et al. [Discrete Math. 2009]. As an immediate corollary,
we obtain the first efficient algorithm to determine whether an arbitrary
n-vertex polygon is weakly simple; our algorithm runs in O(n^2 log n) time. We
also describe algorithms that detect weak simplicity in O(n log n) time for two
interesting classes of polygons. Finally, we discuss subtle errors in several
previously published definitions of weak simplicity.Comment: 25 pages and 13 figures, submitted to SODA 201
Multi-criteria Anomaly Detection using Pareto Depth Analysis
We consider the problem of identifying patterns in a data set that exhibit
anomalous behavior, often referred to as anomaly detection. In most anomaly
detection algorithms, the dissimilarity between data samples is calculated by a
single criterion, such as Euclidean distance. However, in many cases there may
not exist a single dissimilarity measure that captures all possible anomalous
patterns. In such a case, multiple criteria can be defined, and one can test
for anomalies by scalarizing the multiple criteria using a linear combination
of them. If the importance of the different criteria are not known in advance,
the algorithm may need to be executed multiple times with different choices of
weights in the linear combination. In this paper, we introduce a novel
non-parametric multi-criteria anomaly detection method using Pareto depth
analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies
under multiple criteria without having to run an algorithm multiple times with
different choices of weights. The proposed PDA approach scales linearly in the
number of criteria and is provably better than linear combinations of the
criteria.Comment: Removed an unnecessary line from Algorithm
Fusible numbers and Peano Arithmetic
Inspired by a mathematical riddle involving fuses, we define the "fusible
numbers" as follows: is fusible, and whenever are fusible with
, the number is also fusible. We prove that the set of
fusible numbers, ordered by the usual order on , is well-ordered,
with order type . Furthermore, we prove that the density of the
fusible numbers along the real line grows at an incredibly fast rate: Letting
be the largest gap between consecutive fusible numbers in the interval
, we have for some constant
, where denotes the fast-growing hierarchy. Finally, we derive
some true statements that can be formulated but not proven in Peano Arithmetic,
of a different flavor than previously known such statements: PA cannot prove
the true statement "For every natural number there exists a smallest
fusible number larger than ." Also, consider the algorithm ": if
return , else return ." Then terminates on real inputs,
although PA cannot prove the statement " terminates on all natural inputs."Comment: Minor improvements. 26 pages, 5 figures, 3 table
Certifying solution geometry in random CSPs: counts, clusters and balance
An active topic in the study of random constraint satisfaction problems
(CSPs) is the geometry of the space of satisfying or almost satisfying
assignments as the function of the density, for which a precise landscape of
predictions has been made via statistical physics-based heuristics. In
parallel, there has been a recent flurry of work on refuting random constraint
satisfaction problems, via nailing refutation thresholds for spectral and
semidefinite programming-based algorithms, and also on counting solutions to
CSPs. Inspired by this, the starting point for our work is the following
question: what does the solution space for a random CSP look like to an
efficient algorithm?
In pursuit of this inquiry, we focus on the following problems about random
Boolean CSPs at the densities where they are unsatisfiable but no refutation
algorithm is known.
1. Counts. For every Boolean CSP we give algorithms that with high
probability certify a subexponential upper bound on the number of solutions. We
also give algorithms to certify a bound on the number of large cuts in a
Gaussian-weighted graph, and the number of large independent sets in a random
-regular graph.
2. Clusters. For Boolean CSPs we give algorithms that with high
probability certify an upper bound on the number of clusters of solutions.
3. Balance. We also give algorithms that with high probability certify that
there are no "unbalanced" solutions, i.e., solutions where the fraction of
s deviates significantly from .
Finally, we also provide hardness evidence suggesting that our algorithms for
counting are optimal
Multifunctional microbubbles and nanobubbles for photoacoustic and ultrasound imaging
We develop a novel dual-modal contrast agent—encapsulated-ink poly(lactic-co-glycolic acid) (PLGA) microbubbles and nanobubbles—for photoacoustic and ultrasound imaging. Soft gelatin phantoms with embedded tumor simulators of encapsulated-ink PLGA microbubbles and nanobubbles in various concentrations are clearly shown in both photoacoustic and ultrasound images. In addition, using photoacoustic imaging, we successfully image the samples positioned below 1.8-cm-thick chicken breast tissues. Potentially, simultaneous photoacoustic and ultrasound imaging enhanced by encapsulated-dye PLGA microbubbles or nanobubbles can be a valuable tool for intraoperative assessment of tumor boundaries and therapeutic margins
Toward Fine Contact Interactions: Learning to Control Normal Contact Force with Limited Information
Dexterous manipulation of objects through fine control of physical contacts
is essential for many important tasks of daily living. A fundamental ability
underlying fine contact control is compliant control, \textit{i.e.},
controlling the contact forces while moving. For robots, the most widely
explored approaches heavily depend on models of manipulated objects and
expensive sensors to gather contact location and force information needed for
real-time control. The models are difficult to obtain, and the sensors are
costly, hindering personal robots' adoption in our homes and businesses. This
study performs model-free reinforcement learning of a normal contact force
controller on a robotic manipulation system built with a low-cost,
information-poor tactile sensor. Despite the limited sensing capability, our
force controller can be combined with a motion controller to enable fine
contact interactions during object manipulation. Promising results are
demonstrated in non-prehensile, dexterous manipulation experiments
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