861 research outputs found
Topological Inference via Meshing
We apply ideas from mesh generation to improve the time and space complexities of computing the full persistent homological information associated with a point cloud in Euclidean space . Classical approaches rely on the \v Cech, Rips, -complex, or witness complex filtrations of , whose complexities scale up very badly with . For instance, the -complex filtration incurs the size of the Delaunay triangulation, where is the size of . The common alternative is to truncate the filtrations when the sizes of the complexes become prohibitive, possibly before discovering the most relevant topological features. In this paper we propose a new collection of filtrations, based on the Delaunay triangulation of a carefully-chosen superset of , whose sizes are reduced to . A nice property of these filtrations is to be interleaved multiplicatively with the family of offsets of , so that the persistence diagram of can be approximated in time in theory, with a near-linear observed running time in practice (ignoring the constant factors depending exponentially on ). Thus, our approach remains tractable in medium dimensions, say 4 to 10
Multilevel MDA-Lite Paris Traceroute
Since its introduction in 2006-2007, Paris Traceroute and its Multipath
Detection Algorithm (MDA) have been used to conduct well over a billion IP
level multipath route traces from platforms such as M-Lab. Unfortunately, the
MDA requires a large number of packets in order to trace an entire topology of
load balanced paths between a source and a destination, which makes it
undesirable for platforms that otherwise deploy Paris Traceroute, such as RIPE
Atlas. In this paper we present a major update to the Paris Traceroute tool.
Our contributions are: (1) MDA-Lite, an alternative to the MDA that
significantly cuts overhead while maintaining a low failure probability; (2)
Fakeroute, a simulator that enables validation of a multipath route tracing
tool's adherence to its claimed failure probability bounds; (3) multilevel
multipath route tracing, with, for the first time, a Traceroute tool that
provides a router-level view of multipath routes; and (4) surveys at both the
IP and router levels of multipath routing in the Internet, showing, among other
things, that load balancing topologies have increased in size well beyond what
has been previously reported as recently as 2016. The data and the software
underlying these results are publicly available.Comment: Preprint. To appear in Proc. ACM Internet Measurement Conference 201
Approximating Nearest Neighbor Distances
Several researchers proposed using non-Euclidean metrics on point sets in
Euclidean space for clustering noisy data. Almost always, a distance function
is desired that recognizes the closeness of the points in the same cluster,
even if the Euclidean cluster diameter is large. Therefore, it is preferred to
assign smaller costs to the paths that stay close to the input points.
In this paper, we consider the most natural metric with this property, which
we call the nearest neighbor metric. Given a point set P and a path ,
our metric charges each point of with its distance to P. The total
charge along determines its nearest neighbor length, which is formally
defined as the integral of the distance to the input points along the curve. We
describe a -approximation algorithm and a
-approximation algorithm to compute the nearest neighbor
metric. Both approximation algorithms work in near-linear time. The former uses
shortest paths on a sparse graph using only the input points. The latter uses a
sparse sample of the ambient space, to find good approximate geodesic paths.Comment: corrected author nam
Linear-Size Approximations to the Vietoris-Rips Filtration
The Vietoris-Rips filtration is a versatile tool in topological data
analysis. It is a sequence of simplicial complexes built on a metric space to
add topological structure to an otherwise disconnected set of points. It is
widely used because it encodes useful information about the topology of the
underlying metric space. This information is often extracted from its so-called
persistence diagram. Unfortunately, this filtration is often too large to
construct in full. We show how to construct an O(n)-size filtered simplicial
complex on an -point metric space such that its persistence diagram is a
good approximation to that of the Vietoris-Rips filtration. This new filtration
can be constructed in time. The constant factors in both the size
and the running time depend only on the doubling dimension of the metric space
and the desired tightness of the approximation. For the first time, this makes
it computationally tractable to approximate the persistence diagram of the
Vietoris-Rips filtration across all scales for large data sets.
We describe two different sparse filtrations. The first is a zigzag
filtration that removes points as the scale increases. The second is a
(non-zigzag) filtration that yields the same persistence diagram. Both methods
are based on a hierarchical net-tree and yield the same guarantees
On systematic approaches for interpreted information transfer of inspection data from bridge models to structural analysis
In conjunction with the improved methods of monitoring damage and degradation processes, the interest in reliability assessment of reinforced concrete bridges is increasing in recent years. Automated imagebased inspections of the structural surface provide valuable data to extract quantitative information about deteriorations, such as crack patterns. However, the knowledge gain results from processing this information in a structural context, i.e. relating the damage artifacts to building components. This way, transformation to structural analysis is enabled. This approach sets two further requirements: availability of structural bridge information and a standardized storage for interoperability with subsequent analysis tools. Since the involved large datasets are only efficiently processed in an automated manner, the implementation of the complete workflow from damage and building data to structural analysis is targeted in this work. First, domain concepts are derived from the back-end tasks: structural analysis, damage modeling, and life-cycle assessment. The common interoperability format, the Industry Foundation Class (IFC), and processes in these domains are further assessed. The need for usercontrolled interpretation steps is identified and the developed prototype thus allows interaction at subsequent model stages. The latter has the advantage that interpretation steps can be individually separated into either a structural analysis or a damage information model or a combination of both. This approach to damage information processing from the perspective of structural analysis is then validated in different case studies
What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives
Intelligent Mesh Generation (IMG) represents a novel and promising field of
research, utilizing machine learning techniques to generate meshes. Despite its
relative infancy, IMG has significantly broadened the adaptability and
practicality of mesh generation techniques, delivering numerous breakthroughs
and unveiling potential future pathways. However, a noticeable void exists in
the contemporary literature concerning comprehensive surveys of IMG methods.
This paper endeavors to fill this gap by providing a systematic and thorough
survey of the current IMG landscape. With a focus on 113 preliminary IMG
methods, we undertake a meticulous analysis from various angles, encompassing
core algorithm techniques and their application scope, agent learning
objectives, data types, targeted challenges, as well as advantages and
limitations. We have curated and categorized the literature, proposing three
unique taxonomies based on key techniques, output mesh unit elements, and
relevant input data types. This paper also underscores several promising future
research directions and challenges in IMG. To augment reader accessibility, a
dedicated IMG project page is available at
\url{https://github.com/xzb030/IMG_Survey}
Deep learning-based surrogate model for 3-D patient-specific computational fluid dynamics
Optimization and uncertainty quantification have been playing an increasingly
important role in computational hemodynamics. However, existing methods based
on principled modeling and classic numerical techniques have faced significant
challenges, particularly when it comes to complex 3D patient-specific shapes in
the real world. First, it is notoriously challenging to parameterize the input
space of arbitrarily complex 3-D geometries. Second, the process often involves
massive forward simulations, which are extremely computationally demanding or
even infeasible. We propose a novel deep learning surrogate modeling solution
to address these challenges and enable rapid hemodynamic predictions.
Specifically, a statistical generative model for 3-D patient-specific shapes is
developed based on a small set of baseline patient-specific geometries. An
unsupervised shape correspondence solution is used to enable geometric morphing
and scalable shape synthesis statistically. Moreover, a simulation routine is
developed for automatic data generation by automatic meshing, boundary setting,
simulation, and post-processing. An efficient supervised learning solution is
proposed to map the geometric inputs to the hemodynamics predictions in latent
spaces. Numerical studies on aortic flows are conducted to demonstrate the
effectiveness and merit of the proposed techniques.Comment: 8 figures, 2 table
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