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$_T$) and high brightness photocathode. The density functional theory (DFT) based photoemission analysis successfully elucidates that the 'hole-like' {\Lambda}$^+_6$ energy band in the $L$ valley with low effective mass $m^*$ results in low {\Delta}p$_T$. 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

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 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 $\mathcal{O}(p\log(1/\epsilon))$, where $\epsilon$ is a pre-specified accuracy of the objective value, and $p$ is the number of blocks. However, such iteration complexity explicitly depends on $p$, and therefore is at least $p$ times worse than the complexity $\mathcal{O}(\log(1/\epsilon))$ 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 $\mathcal{O}(\log^2(p)\cdot\log(1/\epsilon))$ of the CBCD-type methods matches that of the GD methods in term of dependency on $p$, up to a $\log^2 p$ factor. Thus our complexity bounds are sharper than the existing bounds by at least a factor of $p/\log^2(p)$. We also provide a lower bound to confirm that our improved complexity bounds are tight (up to a $\log^2 (p)$ factor), under the assumption that the largest and smallest eigenvalues of the Hessian matrix do not scale with $p$. Finally, we generalize our analysis to other strongly convex minimization problems beyond quadratic ones.Comment: Accepted by JLM

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