11,279 research outputs found
When Locally Linear Embedding Hits Boundary
Based on the Riemannian manifold model, we study the asymptotic behavior of a
widely applied unsupervised learning algorithm, locally linear embedding (LLE),
when the point cloud is sampled from a compact, smooth manifold with boundary.
We show several peculiar behaviors of LLE near the boundary that are different
from those diffusion-based algorithms. Particularly, LLE converges to a
mixed-type differential operator with degeneracy. This study leads to an
alternative boundary detection algorithm and two potential approaches to
recover the Dirichlet Laplace-Beltrami operator.Comment: 11 Figure
Think globally, fit locally under the Manifold Setup: Asymptotic Analysis of Locally Linear Embedding
Since its introduction in 2000, the locally linear embedding (LLE) has been
widely applied in data science. We provide an asymptotical analysis of the LLE
under the manifold setup. We show that for the general manifold, asymptotically
we may not obtain the Laplace-Beltrami operator, and the result may depend on
the non-uniform sampling, unless a correct regularization is chosen. We also
derive the corresponding kernel function, which indicates that the LLE is not a
Markov process. A comparison with the other commonly applied nonlinear
algorithms, particularly the diffusion map, is provided, and its relationship
with the locally linear regression is also discussed.Comment: 78 pages, 4 figures. We add a short discussion about thr relation
between espilon and the intrinsic geometry of the manifold. We add a new
section about K nearest neighborhood (KNN) and a new subsection about error
in variable. We provide more numerical example
A Question Type Driven and Copy Loss Enhanced Frameworkfor Answer-Agnostic Neural Question Generation
The answer-agnostic question generation is a significant and challenging
task, which aims to automatically generate questions for a given sentence but
without an answer. In this paper, we propose two new strategies to deal with
this task: question type prediction and copy loss mechanism. The question type
module is to predict the types of questions that should be asked, which allows
our model to generate multiple types of questions for the same source sentence.
The new copy loss enhances the original copy mechanism to make sure that every
important word in the source sentence has been copied when generating
questions. Our integrated model outperforms the state-of-the-art approach in
answer-agnostic question generation, achieving a BLEU-4 score of 13.9 on SQuAD.
Human evaluation further validates the high quality of our generated questions.
We will make our code public available for further research
A Statistical Study of H I Gas in Nearby Narrow-Line AGN-Hosting Galaxies
As a quenching mechanism, AGN feedback could suppress on-going star formation
in their host galaxies. On the basis of a sample of galaxies selected from
ALFALFA HI survey, the dependence of their HI mass M[HI], stellar mass M[*] &
HI-to-stellar mass ratio M[HI]/M[*] on various tracers of AGN activity are
presented and analyzed in this paper. Almost all the AGN-hostings in this
sample are gas-rich galaxies, and there is no any evidence to be shown to
indicate that the AGN activity could increase/decrease either M[HI] or
M[HI]/M[*]. The cold neutral gas can not be fixed positions accurately just
based on available HI data due to the large beam size of ALFALFA survey. In
addition, even though AGN-hostings are more easily detected by HI survey
compared with absorption line galaxies, these two types of galaxies show
similar star formation history. If an AGN-hosting would ultimately evolve into
an old red galaxy with few cold gas, then when and how the gas has been
exhausted have to be solved by future hypotheses and observations.Comment: 34 pages, 8 figures, published in A
Problems on Foundations of General Relativity
It was generally believed that, in general relativity, the fundamental laws
of nature should be invariant or covariant under a general coordinate
transformation. In general relativity, the equivalence principle tells us the
existence of a local inertial coordinate system and the fundamental laws in the
local inertial coordinate system which are the same as those in inertial
reference system. Then, after a general coordinate transformation, the
fundamental laws of nature in arbitrary coordinate system or in arbitrary
curved space-time can be obtained. However, through a simple example, we find
that, under a general coordinate transformation, basic physical equations in
general relativity do not transform covariantly, especially they do not
preserve their forms under the transformation from a local inertial coordinate
system to a curved space-time. The origination of the violation of the general
covariance is then studied, and a general theory on general coordinate
transformations is developed. Because of the the existence of the
non-homogeneous term, the fundamental laws of nature in arbitrary curved
space-time can not be expressed by space-time metric, physical observable and
their derivatives. In other words, basic physical equations obtained from the
equivalence principle and the principle of general covariance are different
from those in general relativity. Both the equivalence principle and the
principle of general covariance can not be treated as foundations of general
relativity. So, what are the foundations of General Relativity? Such kind of
essential problems on General Relativity can be avoided in the physical picture
of gravity. Quantum gauge theory of gravity, which is founded in the physics
picture of gravity, does not have such kind of fundamental problems.Comment: 26 pages, no figur
Energy Storage as Public Asset
Energy storage has exhibited great potential in providing flexibility in
power system to meet critical peak demand and thus reduce the overall
generation cost, which in turn stabilizes the electricity prices. In this work,
we exploit the opportunities for the independent system operator (ISO) to
invest and manage storage as public asset, which could systematically provide
benefits to the public. Assuming a quadratic generation cost structure, we
apply parametric analysis to investigate the ISO's problem of economic
dispatch, given variant quantities of storage investment. This investment is
beneficial to users on expectation. However, it may not necessarily benefit
everyone. We adopt the notion of marginal system cost impact (MCI) to measure
each user's welfare and show its relationship with the conventional locational
marginal price. We find interesting convergent characteristics for MCI.
Furthermore, we perform -means clustering to classify users for effective
user profiling and conduct numerical studies on both prototype and IEEE test
systems to verify our theoretical conclusions
Uncertainty Relations in the Presence of Quantum Memory for Mutually Unbiased Measurements
In [Berta 2014 Entanglement], uncertainty relations in the presence of
quantum memory was formulated for mutually unbiased bases using conditional
collision entropy. In this paper, we generalize their results to the mutually
unbiased measurements. Our primary result is an equality between the amount of
uncertainty for a set of measurements and the amount of entanglement of the
measured state, both of which are quantified by the conditional collision
entropy. Implications of this equality relation are discussed. We further show
that similar equality relation can be obtained for generalized symmetric
informationally complete measurements. We also derive an interesting equality
for arbitrary orthogonal basis of the space of Hermitian, traceless operators.Comment: 8 pages, comments are welcome
Community Evolution of Social Network: Feature, Algorithm and Model
Researchers have devoted themselves to exploring static features of social
networks and further discovered many representative characteristics, such as
power law in the degree distribution and assortative value used to
differentiate social networks from nonsocial ones. However, people are not
satisfied with these achievements and more and more attention has been paid on
how to uncover those dynamic characteristics of social networks, especially how
to track community evolution effectively. With these interests, in the paper we
firstly display some basic but dynamic features of social networks. Then on its
basis, we propose a novel core-based algorithm of tracking community evolution,
CommTracker, which depends on core nodes to establish the evolving
relationships among communities at different snapshots. With the algorithm, we
discover two unique phenomena in social networks and further propose two
representative coefficients: GROWTH and METABOLISM by which we are also able to
distinguish social networks from nonsocial ones from the dynamic aspect. At
last, we have developed a social network model which has the capabilities of
exhibiting two necessary features above.Comment: 16 pages,7 figure
Evolution of oxygen and nitrogen abundances and nitrogen production mechanism in massive star-forming galaxies
Utilizing the observational data of 55,318 star-forming galaxies (SFGs)
selected from the catalog of MPA-JHU emission-line measurements for the SDSS
DR8, we investigate the galaxy downsizing effect of their O and N enrichments,
and the nitrogen production mechanism in them. We show the redshift evolution
of O and N abundances and specific star formation rates for different galaxy
mass ranges, demonstrating the galaxy downsizing effect caused by less massive
progenitors of less massive galaxies. The O and N abundances do not remain
constant for different galaxy mass ranges, and the enrichment (and hence star
formation) decreases with increasing galaxy stellar mass. We find evidence of
the O enrichment for galaxies with stellar masses (in units
of ), i.e. and
from redshift 0.023 to 0.30. Based on the
evolutionary schematic model of N/O ratios in Coziol et al., who proposed the
scheme that the production of nitrogen is the consequence of a sequence of
bursts in SFGs, we conclude that the nitrogen production is dominated by the
intermediate-mass stars, which dominate the secondary synthesis in SFGs.
However, for galaxies with we find evidence of enhanced N/O
abundance ratios, which are significantly above the secondary synthesis line.
This suggests that outflows of massive stars, which deplete oxygen efficiently,
are more important in massive galaxies. Finally we find an excellent linear
relation between and log(N/O), indicating that the N/O abundance ratio
is a good indicator of the stellar mass in a SFG and may be used as a standard
candle for studying cosmology, if confirmed with further studies.Comment: Updated to match the published version in MNRAS. 25 pages, 12
figures, 2 table
Optimal Liquidation in a Finite Time Regime Switching Model with Permanent and Temporary Pricing Impact
In this paper we discuss the optimal liquidation over a finite time horizon
until the exit time. The drift and diffusion terms of the asset price are
general functions depending on all variables including control and market
regime. There is also a local nonlinear transaction cost associated to the
liquidation. The model deals with both the permanent impact and the temporary
impact in a regime switching framework. The problem can be solved with the
dynamic programming principle. The optimal value function is the unique
continuous viscosity solution to the HJB equation and can be computed with the
finite difference method.Comment: 17 page
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