35,119 research outputs found
Diffusion Approximations for Online Principal Component Estimation and Global Convergence
In this paper, we propose to adopt the diffusion approximation tools to study
the dynamics of Oja's iteration which is an online stochastic gradient descent
method for the principal component analysis. Oja's iteration maintains a
running estimate of the true principal component from streaming data and enjoys
less temporal and spatial complexities. We show that the Oja's iteration for
the top eigenvector generates a continuous-state discrete-time Markov chain
over the unit sphere. We characterize the Oja's iteration in three phases using
diffusion approximation and weak convergence tools. Our three-phase analysis
further provides a finite-sample error bound for the running estimate, which
matches the minimax information lower bound for principal component analysis
under the additional assumption of bounded samples.Comment: Appeared in NIPS 201
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Lithium‐Metal Batteries: Enabling Rapid Charging Lithium Metal Batteries via Surface Acoustic Wave‐Driven Electrolyte Flow (Adv. Mater. 14/2020)
Pattern formation of reaction-diffusion system having self-determined flow in the amoeboid organism of Physarum plasmodium
The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on
the basis of spatio-temporal pattern formation by local
contraction-oscillators. This biological system can be regarded as a
reaction-diffusion system which has spatial interaction by active flow of
protoplasmic sol in the cell. Paying attention to the physiological evidence
that the flow is determined by contraction pattern in the plasmodium, a
reaction-diffusion system having self-determined flow arises. Such a coupling
of reaction-diffusion-advection is a characteristic of the biological system,
and is expected to relate with control mechanism of amoeboid behaviours. Hence,
we have studied effects of the self-determined flow on pattern formation of
simple reaction-diffusion systems. By weakly nonlinear analysis near a trivial
solution, the envelope dynamics follows the complex Ginzburg-Landau type
equation just after bifurcation occurs at finite wave number. The flow term
affects the nonlinear term of the equation through the critical wave number
squared. Contrary to this, wave number isn't explicitly effective with lack of
flow or constant flow. Thus, spatial size of pattern is especially important
for regulating pattern formation in the plasmodium. On the other hand, the flow
term is negligible in the vicinity of bifurcation at infinitely small wave
number, and therefore the pattern formation by simple reaction-diffusion will
also hold. A physiological role of pattern formation as above is discussed.Comment: REVTeX, one column, 7 pages, no figur
Quantum Simulator for Transport Phenomena in Fluid Flows
Transport phenomena still stand as one of the most challenging problems in
computational physics. By exploiting the analogies between Dirac and lattice
Boltzmann equations, we develop a quantum simulator based on pseudospin-boson
quantum systems, which is suitable for encoding fluid dynamics transport
phenomena within a lattice kinetic formalism. It is shown that both the
streaming and collision processes of lattice Boltzmann dynamics can be
implemented with controlled quantum operations, using a heralded quantum
protocol to encode non-unitary scattering processes. The proposed simulator is
amenable to realization in controlled quantum platforms, such as ion-trap
quantum computers or circuit quantum electrodynamics processors.Comment: 8 pages, 3 figure
Clustering Memes in Social Media
The increasing pervasiveness of social media creates new opportunities to
study human social behavior, while challenging our capability to analyze their
massive data streams. One of the emerging tasks is to distinguish between
different kinds of activities, for example engineered misinformation campaigns
versus spontaneous communication. Such detection problems require a formal
definition of meme, or unit of information that can spread from person to
person through the social network. Once a meme is identified, supervised
learning methods can be applied to classify different types of communication.
The appropriate granularity of a meme, however, is hardly captured from
existing entities such as tags and keywords. Here we present a framework for
the novel task of detecting memes by clustering messages from large streams of
social data. We evaluate various similarity measures that leverage content,
metadata, network features, and their combinations. We also explore the idea of
pre-clustering on the basis of existing entities. A systematic evaluation is
carried out using a manually curated dataset as ground truth. Our analysis
shows that pre-clustering and a combination of heterogeneous features yield the
best trade-off between number of clusters and their quality, demonstrating that
a simple combination based on pairwise maximization of similarity is as
effective as a non-trivial optimization of parameters. Our approach is fully
automatic, unsupervised, and scalable for real-time detection of memes in
streaming data.Comment: Proceedings of the 2013 IEEE/ACM International Conference on Advances
in Social Networks Analysis and Mining (ASONAM'13), 201
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