28,763 research outputs found
Optimal function spaces for the weak continuity of the distributional -Hessian
In this paper we introduce the notion of distributional -Hessian
associated with Besov type functions in Euclidean -space, .
Particularly, inspired by recent work of Baer and Jerison on distributional
Hessian determinant, we show that the distributional -Hessian is weak
continuous on the Besov space , and the result is optimal
in the framework of the space , i.e., the distributional -Hessian is
well defined in if and only if .Comment: 20 page
Currents carried by the subgradient graphs of semi-convex functions and applications to Hessian measure
In this paper we study integer multiplicity rectifiable currents carried by
the subgradient (subdifferential) graphs of semi-convex functions on a
-dimensional convex domain, and show a weak continuity theorem with respect
to pointwise convergence for such currents. As an application, the -Hessian
measures are calculated by a different method in terms of currents.Comment: 15 page
Emergence of space and cosmic evolution based on entropic force
In this paper, we propose a model in which an additional pressure due to the
effects of the entropic force is added to the ideal fluid. Furthermore, we
obtain the dynamic equation in the FRW universe which contains the quantum
gravitational effects based on the description of entropic force and emergence
of space. Our model can well explain the age of the universe and the effect of
the current accelerating expansion. We give the relation between the luminosity
distance and the redshift factor, and compare this relation with that of lambda
cold dark matter model( model).Comment: 10 pages, 2 figure
Thermodynamics of the universe bounded by the cosmological event horizon and dominated by the tachyon fluid
Our aim is to investigate the thermodynamic properties of the universe
bounded by the cosmological event horizon and dominated by the tachyon fluid.
We give two different laws of evolution of our universe. Further, we show the
first law and the generalized second law of thermodynamics (GSLT) are both
satisfied in two cases, but their properties of the thermodynamic equilibrium
are totally different. Besides, under our solutions, we find the validity of
the laws of thermodynamics is irrelevant with the parameters of the tachyon
fluid. Finally, we conclude that the universe bounded by the cosmological event
horizon and dominated by the tachyon fluid has a good thermodynamic
description. In turn, the thermodynamic description can provide a good physical
interpretation for the dynamic evolution of our universe due to the equivalence
between the first law of thermodynamics and the Friedmann equation to some
extent.Comment: 12 pages, 1 figur
Generalized Content-Preserving Warps for Image Stitching
Local misalignment caused by global homography is a common issue in image
stitching task. Content-Preserving Warping (CPW) is a typical method to deal
with this issue, in which geometric and photometric constraints are imposed to
guide the warping process. One of its essential condition however, is colour
consistency, and an elusive goal in real world applications. In this paper, we
propose a Generalized Content-Preserving Warping (GCPW) method to alleviate
this problem. GCPW extends the original CPW by applying a colour model that
expresses the colour transformation between images locally, thus meeting the
photometric constraint requirements for effective image stitching. We combine
the photometric and geometric constraints and jointly estimate the colour
transformation and the warped mesh vertexes, simultaneously. We align images
locally with an optimal grid mesh generated by our GCPW method. Experiments on
both synthetic and real images demonstrate that our new method is robust to
colour variations, outperforming other state-of-the-art CPW-based image
stitching methods
Threshold Trapdoor Functions and Their Applications
We introduce a cryptographic primitive named threshold trapdoor functions
(TTDFs), from which we give generic constructions of threshold and revocation
encryptions under adaptive corruption model. Then, we show TTDF can be
instantiated under the decisional Diffie-Hellman (DDH) assumption and the
learning with errors (LWE) assumption. By combining the instantiations of TTDF
with the generic constructions, we obtain threshold and revocation encryptions
which compare favorably over existing schemes. The experimental results show
that our proposed schemes are practical.Comment: 23 pages, 1 figures, 4 table
Complete Solution for the Rainbow Numbers of Matchings
For a given graph and , let denote the maximum number
for which there is a way to color the edges of the complete graph
with colors such that every subgraph of has at least two edges of
the same color. Equivalently, any edge-coloring of with at least
colors contains a rainbow copy of , where a rainbow
subgraph of an edge-colored graph is such that no two edges of it have the same
color. The number is called the {\it rainbow number of }.
Erd\H{o}s, Simonovits and S\'{o}s showed that . In 2004,
Schiermeyer used some counting technique and determined the rainbow numbers
for and . It is easy to see that must be
at least . So, for , the rainbow numbers remain not
determined. In this paper we will use the Gallai-Edmonds structure theorem for
matchings to determine the exact values for rainbow numbers for
all and , giving a complete solution for the rainbow
numbers of matchings.Comment: 20 page
General Spectrum Sensing in Cognitive Radio Networks
The successful operation of cognitive radio (CR) between CR transmitter and
CR receiver (CR link) relies on reliable spectrum sensing. To network CRs
requires spectrum sensing at CR transmitter and further information regarding
the spectrum availability at CR receiver. Redefining the spectrum sensing along
with statistical inference suitable for cognitive radio networks (CRN), we
mathematically derive conditions to allow CR transmitter forwarding packets to
CR receiver under guaranteed outage probability, and prove that the correlation
of localized spectrum availability between a cooperative node and CR receiver
determines effectiveness of the cooperative scheme. Applying our novel
mathematical model to potential hidden terminals in CRN, we illustrate that the
allowable transmission region of a CR, defined as neighborhood, is no longer
circular shape even in a pure path loss channel model. This results in
asymmetric CR links to make bidirectional links generally inappropriate in CRN,
though this challenge can be alleviated by cooperative sensing. Therefore,
spectrum sensing capability determines CRN topology. For multiple cooperative
nodes, to fully utilize spectrum availability, the selection methodology of
cooperative nodes is developed due to limited overhead of information exchange.
Defining reliability as information of spectrum availability at CR receiver
provided by a cooperative node and by applying neighborhood area, we can
compare sensing capability of cooperative nodes from both link and network
perspectives. In addition, due to lack of centralized coordination in dynamic
CRN, CRs can only acquire local and partial information within limited sensing
duration, robust spectrum sensing is therefore proposed. Limits of cooperative
schemes and their impacts on network operation are also derived.Comment: 26 pages, 7 figures, 47 references, submitted to IEEE Trans. on
Information Theor
Clustering Kinetics of Granular Media in Three Dimensions
Three-dimensional molecular dynamics simulations of dissipative particles (~
10^6) are carried out for studying the clustering kinetics of granular media
during cooling. The inter-connected high particle density regions are
identified, showing tube-like structures. The energy decay rates as functions
of the particle density and the restitution coefficient are obtained. It is
found that the probability density function of the particle density obeys an
exponential distribution at late stages. Both the fluctuation of density and
the mean cluster size of the particle density have power law relations against
time during the inelastic coalescing process.Comment: 4 pages, 5 figures, revte
Sketch-pix2seq: a Model to Generate Sketches of Multiple Categories
Sketch is an important media for human to communicate ideas, which reflects
the superiority of human intelligence. Studies on sketch can be roughly
summarized into recognition and generation. Existing models on image
recognition failed to obtain satisfying performance on sketch classification.
But for sketch generation, a recent study proposed a sequence-to-sequence
variational-auto-encoder (VAE) model called sketch-rnn which was able to
generate sketches based on human inputs. The model achieved amazing results
when asked to learn one category of object, such as an animal or a vehicle.
However, the performance dropped when multiple categories were fed into the
model. Here, we proposed a model called sketch-pix2seq which could learn and
draw multiple categories of sketches. Two modifications were made to improve
the sketch-rnn model: one is to replace the bidirectional recurrent neural
network (BRNN) encoder with a convolutional neural network(CNN); the other is
to remove the Kullback-Leibler divergence from the objective function of VAE.
Experimental results showed that models with CNN encoders outperformed those
with RNN encoders in generating human-style sketches. Visualization of the
latent space illustrated that the removal of KL-divergence made the encoder
learn a posterior of latent space that reflected the features of different
categories. Moreover, the combination of CNN encoder and removal of
KL-divergence, i.e., the sketch-pix2seq model, had better performance in
learning and generating sketches of multiple categories and showed promising
results in creativity tasks
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