1,815 research outputs found
Parallel Algorithms for Geometric Graph Problems
We give algorithms for geometric graph problems in the modern parallel models
inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem
over a set of points in the two-dimensional space, our algorithm computes a
-approximate MST. Our algorithms work in a constant number of
rounds of communication, while using total space and communication proportional
to the size of the data (linear space and near linear time algorithms). In
contrast, for general graphs, achieving the same result for MST (or even
connectivity) remains a challenging open problem, despite drawing significant
attention in recent years.
We develop a general algorithmic framework that, besides MST, also applies to
Earth-Mover Distance (EMD) and the transportation cost problem. Our algorithmic
framework has implications beyond the MapReduce model. For example it yields a
new algorithm for computing EMD cost in the plane in near-linear time,
. We note that while recently Sharathkumar and Agarwal
developed a near-linear time algorithm for -approximating EMD,
our algorithm is fundamentally different, and, for example, also solves the
transportation (cost) problem, raised as an open question in their work.
Furthermore, our algorithm immediately gives a -approximation
algorithm with space in the streaming-with-sorting model with
passes. As such, it is tempting to conjecture that the
parallel models may also constitute a concrete playground in the quest for
efficient algorithms for EMD (and other similar problems) in the vanilla
streaming model, a well-known open problem
Optimal Transport for Domain Adaptation
Domain adaptation from one data space (or domain) to another is one of the
most challenging tasks of modern data analytics. If the adaptation is done
correctly, models built on a specific data space become more robust when
confronted to data depicting the same semantic concepts (the classes), but
observed by another observation system with its own specificities. Among the
many strategies proposed to adapt a domain to another, finding a common
representation has shown excellent properties: by finding a common
representation for both domains, a single classifier can be effective in both
and use labelled samples from the source domain to predict the unlabelled
samples of the target domain. In this paper, we propose a regularized
unsupervised optimal transportation model to perform the alignment of the
representations in the source and target domains. We learn a transportation
plan matching both PDFs, which constrains labelled samples in the source domain
to remain close during transport. This way, we exploit at the same time the few
labeled information in the source and the unlabelled distributions observed in
both domains. Experiments in toy and challenging real visual adaptation
examples show the interest of the method, that consistently outperforms state
of the art approaches
One dimensional particle mover and PIC code applied to electron cyclotron resonance thruster
This project aims to describe a simplified model of the plasma-wave interaction that
occurs inside the chamber of a typical Electron Cyclotron Resonance Thruster. As
its name suggests, ECR thrusters are based on the resonance of the electron with
a given polarized electromagnetic wave, the so-called, Right Hand Polarized wave.
This is a problem known since the early 60âs, however, due to technical reasons, the
reseaech was abandoned. Recently, it has been resumed by research institutes as
Onera or universities as UC3M, in the context of MINOTOR H2020 project.
The project is devoted in the construction of a code that allows to study the interaction
of a given population of electrons with a prescribed RHP wave, which it is
assumed to be constant despite the changes on plasma properties. Different parameters
will be studied and followed along time to check how the resonance affects the
initial electron parameters.
The second second part of this project is the introduction of numerical computation
in plasma physics with the add-on of a PIC code, where particle properties are
weighted inside a grid mesh.IngenierĂa Aeroespacial (Plan 2010
Network Density of States
Spectral analysis connects graph structure to the eigenvalues and
eigenvectors of associated matrices. Much of spectral graph theory descends
directly from spectral geometry, the study of differentiable manifolds through
the spectra of associated differential operators. But the translation from
spectral geometry to spectral graph theory has largely focused on results
involving only a few extreme eigenvalues and their associated eigenvalues.
Unlike in geometry, the study of graphs through the overall distribution of
eigenvalues - the spectral density - is largely limited to simple random graph
models. The interior of the spectrum of real-world graphs remains largely
unexplored, difficult to compute and to interpret.
In this paper, we delve into the heart of spectral densities of real-world
graphs. We borrow tools developed in condensed matter physics, and add novel
adaptations to handle the spectral signatures of common graph motifs. The
resulting methods are highly efficient, as we illustrate by computing spectral
densities for graphs with over a billion edges on a single compute node. Beyond
providing visually compelling fingerprints of graphs, we show how the
estimation of spectral densities facilitates the computation of many common
centrality measures, and use spectral densities to estimate meaningful
information about graph structure that cannot be inferred from the extremal
eigenpairs alone.Comment: 10 pages, 7 figure
Improved Circular k-Mismatch Sketches
The shift distance between two strings and
of the same length is defined as the minimum Hamming distance between and
any rotation (cyclic shift) of . We study the problem of sketching the
shift distance, which is the following communication complexity problem:
Strings and of length are given to two identical players
(encoders), who independently compute sketches (summaries)
and , respectively, so that upon receiving the two sketches,
a third player (decoder) is able to compute (or approximate)
with high probability.
This paper primarily focuses on the more general -mismatch version of the
problem, where the decoder is allowed to declare a failure if
, where is a parameter known to all parties. Andoni
et al. (STOC'13) introduced exact circular -mismatch sketches of size
, where is the number of divisors of . Andoni
et al. also showed that their sketch size is optimal in the class of linear
homomorphic sketches.
We circumvent this lower bound by designing a (non-linear) exact circular
-mismatch sketch of size ; this size matches
communication-complexity lower bounds. We also design -approximate circular -mismatch sketch of size
,
which improves upon an -size sketch of
Crouch and McGregor (APPROX'11)
Newton vs. Leibniz: Intransparency vs. Inconsistency
We investigate the structure common to causal theories that attempt to
explain a (part of) the world. Causality implies conservation of identity,
itself a far from simple notion. It imposes strong demands on the
universalizing power of the theories concerned. These demands are often met by
the introduction of a metalevel which encompasses the notions of 'system' and
'lawful behaviour'. In classical mechanics, the division between universal and
particular leaves its traces in the separate treatment of cinematics and
dynamics. This analysis is applied to the mechanical theories of Newton and
Leibniz, with some surprising results
Optimal Transport for Domain Adaptation
International audienceDomain adaptation is one of the most chal- lenging tasks of modern data analytics. If the adapta- tion is done correctly, models built on a specific data representation become more robust when confronted to data depicting the same classes, but described by another observation system. Among the many strategies proposed, finding domain-invariant representations has shown excel- lent properties, in particular since it allows to train a unique classifier effective in all domains. In this paper, we propose a regularized unsupervised optimal transportation model to perform the alignment of the representations in the source and target domains. We learn a transportation plan matching both PDFs, which constrains labeled samples of the same class in the source domain to remain close during transport. This way, we exploit at the same time the labeled samples in the source and the distributions observed in both domains. Experiments on toy and challenging real visual adaptation examples show the interest of the method, that consistently outperforms state of the art approaches. In addition, numerical experiments show that our approach leads to better performances on domain invariant deep learning features and can be easily adapted to the semi- supervised case where few labeled samples are available in the target domain
Princeton Advanced Satellite Study Final Report, 8 Mar. 1965 - 15 May 1966
Development of large aperture spaceborne telescope and high resolution ultraviolet photometry for orbiting astronomical satellit
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