20,817 research outputs found
Majorana phases in neutrino-antineutrino oscillations
If the massive neutrinos are Majorana particles, neutrinoless double beta
() decay experiments are not enough to determine the Majorana
phases. We carry out a systematic study of CP violation in
neutrino-antineutrino oscillations. In these processes, CP-conserving parts
involve six independent -like mass terms and CP-violating parts are associated with nine
independent Jarlskog-like parameters (for
and ). With the help of current
neutrino oscillation data, we illustrate the salient features of six
independent CP-violating asymmetries between
and oscillations.Comment: 4 pages, 4 figures, NUFACT 2013 proceeding
Higher-order expansions of powered extremes of normal samples
In this paper, higher-order expansions for distributions and densities of
powered extremes of standard normal random sequences are established under an
optimal choice of normalized constants. Our findings refine the related results
in Hall (1980). Furthermore, it is shown that the rate of convergence of
distributions/densities of normalized extremes depends in principle on the
power index
Totally Real Flat Minimal Surfaces in Quaternionic Projective Spaces
In this paper, we study totally real minimal surfaces in the quaternionic
projective space . We prove that the linearly full totally real
flat minimal surfaces of isotropy order in are two surfaces
in , one of which is the Clifford solution, up to symplectic
congruence
Quantum state complexity and the thermodynamic arrow of time
Why time is a one-way corridor? What's the origin of the arrow of time? We
attribute the thermodynamic arrow of time as the direction of increasing
quantum state complexity. Inspired by the work of Nielsen, Susskind and
Micadei, we checked this hypothesis on both a simple two qubit and a three
qubit quantum system. The result shows that in the two qubit system, the
thermodynamic arrow of time always points in the direction of increasing
quantum state complexity. For the three qubit system, the heat flow pattern
among subsystems is closely correlated with the quantum state complexity of the
subsystems. We propose that besides its impact on macroscopic spatial geometry,
quantum state complexity might also generate the thermodynamic arrow of time.Comment: 4 pages, 4 figure
Understanding over-parameterized deep networks by geometrization
A complete understanding of the widely used over-parameterized deep networks
is a key step for AI. In this work we try to give a geometric picture of
over-parameterized deep networks using our geometrization scheme. We show that
the Riemannian geometry of network complexity plays a key role in understanding
the basic properties of over-parameterizaed deep networks, including the
generalization, convergence and parameter sensitivity. We also point out deep
networks share lots of similarities with quantum computation systems. This can
be regarded as a strong support of our proposal that geometrization is not only
the bible for physics, it is also the key idea to understand deep learning
systems.Comment: 6 page
Quantifying Nonlocality Based on Local Hidden Variable Models
We introduce a fresh scheme based on the local hidden variable models to
quantify nonlocality for arbitrarily high-dimensional quantum systems. Our
scheme explores the minimal amount of white noise that must be added to the
system in order to make the system local and realistic. Moreover, the scheme
has a clear geometric significance and is numerically computable due to
powerful computational and theoretical methods for the class of convex
optimization problems known as semidefinite programs.Comment: 4page
Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff
We give quantitative estimates on the asymptotics of the linearized Boltzmann
collision operator and its associated equation from angular cutoff to non
cutoff. On one hand, the results disclose the link between the hyperbolic
property resulting from the Grad's cutoff assumption and the smoothing property
due to the long-range interaction. On the other hand, with the help of the
localization techniques in the phase space, we observe some new phenomenon in
the asymptotic limit process. As a consequence, we give the affirmative answer
to the question that there is no jump for the property that the collision
operator with cutoff does not have the spectrum gap but the operator without
cutoff does have for the moderate soft potentials
Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations
In this paper, we present some multi-dimensional central limit theorems and
laws of large numbers under sublinear expectations, which extend some previous
results.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1002.4546 by
other author
Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary
We investigate the influence of a shifting environment on the spreading of an
invasive species through a model given by the diffusive logistic equation with
a free boundary. When the environment is homogeneous and favourable, this model
was first studied in Du and Lin \cite{DL}, where a spreading-vanishing
dichotomy was established for the long-time dynamics of the species, and when
spreading happens, it was shown that the species invades the new territory at
some uniquely determined asymptotic speed . Here we consider the
situation that part of such an environment becomes unfavourable, and the
unfavourable range of the environment moves into the favourable part with speed
. We prove that when , the species always dies out in the
long-run, but when , the long-time behavior of the species is
determined by a trichotomy described by
(a) {\it vanishing}, (b) {\it borderline spreading}, or (c) {\it spreading}.
If the initial population is writen in the form with
fixed and a parameter, then there exists such
that vanishing happens when , borderline spreading
happens when , and spreading happens when
How deep learning works --The geometry of deep learning
Why and how that deep learning works well on different tasks remains a
mystery from a theoretical perspective. In this paper we draw a geometric
picture of the deep learning system by finding its analogies with two existing
geometric structures, the geometry of quantum computations and the geometry of
the diffeomorphic template matching. In this framework, we give the geometric
structures of different deep learning systems including convolutional neural
networks, residual networks, recursive neural networks, recurrent neural
networks and the equilibrium prapagation framework. We can also analysis the
relationship between the geometrical structures and their performance of
different networks in an algorithmic level so that the geometric framework may
guide the design of the structures and algorithms of deep learning systems.Comment: 16 pages, 13 figure
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