7,259 research outputs found
A Spectrometer as Simple as a CCD Detector
Spectroscopy is the most fundamental instruments in almost every field of
modern science. Conventional spectrometer is based on the dispersion elements
such as various gratings. An alternative way is based on the filters such as
interference filters, plasmonic nanoresonators, or quantum dots. However, for
any of the above two spectrometers, the high-precision grating or the
absorption filter should be elaborately designed and makes it expensive. Here,
we propose a third spectrometer principle-pupil diffraction spectrometer (PDS).
Since the high-precision grating and the elaborately designed absorption filter
are abandoned, the whole structure of the PDS is just as simple as a CCD
detector. Thus, compared with the above two spectrometer, the structure of the
spectrometer is greatly simplified and the cost of the spectrometer is sharply
reduced. In addition, the PDS can ensure the spectral range and resolution
simultaneously due to the reconstruction its reconstruction algorithm. A series
of simulation results are shown to demonstrate the feasibility of the PDS
principle. Further, the effectiveness of the PDS principle in the noisy
condition is also tested. Owing to this merits small size, light weight, and
low cost, we expect the inventions of PDS has great application potential such
as putting on the satellite to perform space exploration, and integrates to the
smartphone to realize the detection pesticide residue in the food and clinical
diagnose of the disease.Comment: 8 pages, 4 figure
Three-body force for baryons from the D0-D4/D8 matrix model
This is an extensive work to our previous paper \cite{key-08} studied on the
D0-D4/D8 holographic system. We compute the three-body force for baryons with
the D0-D4/D8 matrix model derived in \cite{key-08} with considering the
non-zero QCD vacuum. We obtain the three-body force at short distances but
modified by the appearance of the smeared D0-branes i.e. considering the
effects from the non-trivial QCD vacuum. We firstly test our matrix model in
the case of 't Hooft instanton and then in two more realistic case: (1)
three-neutrons with averaged spins and (2) proton-proton-neutron (or
proton-neutron-proton). The three-body potential vanishes in the former case
while in two latter cases it is positive i.e. repulsive and makes sense only if
the constraint for stable baryonic state is satisfied. We require all the
baryons in our computation aligned on a line. These may indicate that the cases
in dense states of neutrons such as in neutron stars, Helium-3 or Tritium
nucleus all with the non-trivial QCD vacuum.Comment: 24 page
Nonparametric Modeling of Face-Centered Cubic Metal Photocathodes
Face-centered cubic (FCC) is an important crystal structure, and there are
ten elemental FCC metals (Al, Ag, Au, Ca, Cu, Pb, Pd, Pt, Rh, and Sr) that have
this structure. Three of them could be used as photocathodes (Au, Rh, Pt, and
Pd have very high work functions; Ca and Sr are very reactive). Au has high
work function, but it is included for the sake of the completeness of noble
metals' photoemission investigation. In this paper, we will apply the
nonparametric photoemission model to investigate these four remaining FCC
photocathodes; two noble metals (Cu and Au), two p-block metals (Al and Pb).
Apart from the fact that the direct photoemission is dominant for most FCC
photocathodes, photoemission from a surface state has also been observed for
the (111)-face of noble metals. The optical properties of the (111) surface
state will be extensively reviewed both experimentally and theoretically, and a
surface state DFT evaluation will be performed to show that the photocathode
generated hollow cone illumination (HCI) can be realized.Comment: DFT Calculations, Face-Centered Cubic, Hollow Cone Illumination,
Photoemission, Photocathodes, Statistical Modelin
PbTe(111) Sub-Thermionic Photocathode: A Route to High-Quality Electron Pulses
The emission properties of PbTe(111) single crystal have been extensively
investigated to demonstrate that PbTe(111) is a promising low root mean square
transverse momentum ({\Delta}p) and high brightness photocathode. The
density functional theory (DFT) based photoemission analysis successfully
elucidates that the 'hole-like' {\Lambda} energy band in the valley
with low effective mass results in low {\Delta}p. Especially, as a
300K solid planar photocathode, Te-terminated PbTe(111) single crystal is
expected to be a potential 50K electron source.Comment: DFT Calculations, PbTe(111), Photoemission, Photocathodes,
Statistical Modeling, Band Structure, Fermi Surfac
Using shortcut to adiabatic passage for the ultrafast quantum state transfer in cavity QED system
We propose an alternative scheme to implement the quantum state transfer
between two three-level atoms based on the invariant-based inverse engineering
in cavity quantum electronic dynamics (QED) system. The quantum information can
be ultrafast transferred between the atoms by taking advantage of the cavity
field as a medium for exchanging quantum information speedily. Through
designing the time-dependent laser pulse and atom-cavity coupling, we send the
atoms through the cavity with a short time interval experiencing the two
processes of the invariant dynamics between each atom and the cavity field
simultaneously. Numerical simulation shows that the target state can be
ultrafast populated with a high fidelity even when considering the atomic
spontaneous emission and the photon leakage out of the cavity field. We also
redesign a reasonable Gaussian-type wave form in the atom-cavity coupling for
the realistic experiment operation.Comment: 7 pages, 8 figures, comments are welcom
Ground state of three qubits coupled to a harmonic oscillator with ultrastrong coupling
We study the Rabi model composed of three qubits coupled to a harmonic
oscillator without involving the rotating-wave approximation. We show that the
ground state of the three-qubit Rabi model can be analytically treated by using
the transformation method, and the transformed ground state agrees well with
the exactly numerical simulation under a wide range of qubit-oscillator
coupling strengths for different detunings. We use the pairwise entanglement to
characterize the ground-state entanglement between any two qubits and show that
it has an approximately quadratic dependence on the qubit-oscillator coupling
strength. Interestingly, we find that there is no qubit-qubit entanglement for
the ground state if the qubit-oscillator coupling strength is large enough.Comment: 5 pages, 2 figures, Physical Review A 88, 045803 (2013
Nonconvex Sparse Learning via Stochastic Optimization with Progressive Variance Reduction
We propose a stochastic variance reduced optimization algorithm for solving
sparse learning problems with cardinality constraints. Sufficient conditions
are provided, under which the proposed algorithm enjoys strong linear
convergence guarantees and optimal estimation accuracy in high dimensions. We
further extend the proposed algorithm to an asynchronous parallel variant with
a near linear speedup. Numerical experiments demonstrate the efficiency of our
algorithm in terms of both parameter estimation and computational performance
On Faster Convergence of Cyclic Block Coordinate Descent-type Methods for Strongly Convex Minimization
The cyclic block coordinate descent-type (CBCD-type) methods, which performs
iterative updates for a few coordinates (a block) simultaneously throughout the
procedure, have shown remarkable computational performance for solving strongly
convex minimization problems. Typical applications include many popular
statistical machine learning methods such as elastic-net regression, ridge
penalized logistic regression, and sparse additive regression. Existing
optimization literature has shown that for strongly convex minimization, the
CBCD-type methods attain iteration complexity of
, where is a pre-specified accuracy
of the objective value, and is the number of blocks. However, such
iteration complexity explicitly depends on , and therefore is at least
times worse than the complexity of gradient
descent (GD) methods. To bridge this theoretical gap, we propose an improved
convergence analysis for the CBCD-type methods. In particular, we first show
that for a family of quadratic minimization problems, the iteration complexity
of the CBCD-type methods matches
that of the GD methods in term of dependency on , up to a factor.
Thus our complexity bounds are sharper than the existing bounds by at least a
factor of . We also provide a lower bound to confirm that our
improved complexity bounds are tight (up to a factor), under the
assumption that the largest and smallest eigenvalues of the Hessian matrix do
not scale with . Finally, we generalize our analysis to other strongly
convex minimization problems beyond quadratic ones.Comment: Accepted by JLM
Dropping Convexity for More Efficient and Scalable Online Multiview Learning
Multiview representation learning is very popular for latent factor analysis.
It naturally arises in many data analysis, machine learning, and information
retrieval applications to model dependent structures among multiple data
sources. For computational convenience, existing approaches usually formulate
the multiview representation learning as convex optimization problems, where
global optima can be obtained by certain algorithms in polynomial time.
However, many pieces of evidence have corroborated that heuristic nonconvex
approaches also have good empirical computational performance and convergence
to the global optima, although there is a lack of theoretical justification.
Such a gap between theory and practice motivates us to study a nonconvex
formulation for multiview representation learning, which can be efficiently
solved by a simple stochastic gradient descent (SGD) algorithm. We first
illustrate the geometry of the nonconvex formulation; Then, we establish
asymptotic global rates of convergence to the global optima by diffusion
approximations. Numerical experiments are provided to support our theory.Comment: A preliminary version appears in ICML 201
On Landscape of Lagrangian Functions and Stochastic Search for Constrained Nonconvex Optimization
We study constrained nonconvex optimization problems in machine learning,
signal processing, and stochastic control. It is well-known that these problems
can be rewritten to a minimax problem in a Lagrangian form. However, due to the
lack of convexity, their landscape is not well understood and how to find the
stable equilibria of the Lagrangian function is still unknown. To bridge the
gap, we study the landscape of the Lagrangian function. Further, we define a
special class of Lagrangian functions. They enjoy two properties: 1.Equilibria
are either stable or unstable (Formal definition in Section 2); 2.Stable
equilibria correspond to the global optima of the original problem. We show
that a generalized eigenvalue (GEV) problem, including canonical correlation
analysis and other problems, belongs to the class. Specifically, we
characterize its stable and unstable equilibria by leveraging an invariant
group and symmetric property (more details in Section 3). Motivated by these
neat geometric structures, we propose a simple, efficient, and stochastic
primal-dual algorithm solving the online GEV problem. Theoretically, we provide
sufficient conditions, based on which we establish an asymptotic convergence
rate and obtain the first sample complexity result for the online GEV problem
by diffusion approximations, which are widely used in applied probability and
stochastic control. Numerical results are provided to support our theory.Comment: 29 pages, 2 figure
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