Free Energy Wells and Overlap Gap Property in Sparse PCA

We study a variant of the sparse PCA (principal component analysis) problem in the “hard” regime, where the inference task is possible yet no polynomial-time algorithm is known to exist. Prior work, based on the low-degree likelihood ratio, has conjectured a precise expression for the best possible (subexponential) runtime throughout the hard regime. Following instead a statistical physics-inspired point of view, we show bounds on the depth of free energy wells for various Gibbs measures naturally associated to the problem. These free energy wells imply hitting time lower bounds that corroborate the low-degree conjecture: we show that a class of natural MCMC (Markov chain Monte Carlo) methods (with worst-case initialization) cannot solve sparse PCA with less than the conjectured runtime. These lower bounds apply to a wide range of values for two tuning parameters: temperature and sparsity misparametrization. Finally, we prove that the overlap gap property (OGP), a structural property that implies failure of certain local search algorithms, holds in a significant part of the hard regime. © 2022 Wiley Periodicals, Inc.     

Transition density estimates for Brownian motion on affine nested fractals

A class of affine nested fractals is introduced which have different scale factors for different similitudes but still have the symmetry assumptions of nested fractals. For these fractals estimates on the transition density for the Brownian motion are obtained using the associated Dirichlet form. An upper bound for the diagonal can be found using a Nash-type inequality, then probabilistic techniques are used to obtain the off-diagonal bound. The approach differs from previous treatments as it uses only the Dirichlet form and no estimates on the resolvent. The bounds obtained are expressed in terms of an intrinsic metric on the fractal.     

Ln7O6（BO3）（PO4）2：Eu（Ln=Al,Gd,Y）的UVU—UV激发和辐射发光

本文报道了Ln7O6(BO3)(PO4)2:Eu(Ln=La,Gd,Y)在UVU－UV区的激发光谱及Eu^3 在可见区的发射光谱,其激发光谱包括基质在真空紫外区的激发带和激活剂离子在紫外区的Eu^3 -O^2-电荷迁移带,随着La^3 ,Gd^3 ,Y^3 离子半径逐渐减小,Eu^3 -O^2-电荷迁移带的重心位置逐渐向高能量方向移动,Gd7O6(BO3)(PO4)2:Eu和Y7O6（BO3）（PO4）2：Eu在真空紫外区的吸收与Eu^3 -O^2-电荷迁移带位于紫外区的吸收的比值要高于在La7O6(BO3)(PO4)2:Eu中的这个比值,激发能可被基质吸收,传递给激活剂离子,得到Eu^3 的红光发射,在Gd7O6(BO3)(PO4)2:Eu中,^5D0→^7F1的发射强度较强,在Y7O6（BO3）（PO4）2：Eu中,^5D0→^7F2和^5D0→^7F3的跃迁较强。     

量子盘中的三阶非线性光学极化率

利用密度矩阵方法讨论了量子盘中的三阶非线性光学极化率,导出了近共振条件下的三次揩波的解析表达式,并以GaAs量子盘为例进行了具体的计算。结果表明,GaAs量子盘中的三阶非线性光学极化率要比GaAs量子阱的大几十倍。而且,选取适当的参量,可在吸收系数相对较小的情况下获得较大的折射率。     

The optical properties and energy transition process in nanocomposite of polyvinyl-pyrrolidone polymer and Mn-doped ZnS

This study has been carried out on the optical properties of polyvinyl-pyrrolidone (PVP), the energy transition process in nanocomposite of PVP capped ZnS:Mn nanocrystalline and the influence of the PVP concentration on the optical properties of the PVP capped ZnS:Mn nanocrystalline thin films synthesized by the wet chemical method. The microstructures of the samples were investigated by X-ray diffraction, the atomic absorption spectroscopy, and transmission electron microscopy. The results showed that the prepared samples belonged to the sphalerite structure with the average particle size of about 2–3 nm. The optical properties of samples are studied by measuring absorption, photoluminescence (PL) spectra and time-resolved PL spectra in the wavelength range from 200 to 700 nm at 300 K. From data of the absorption spectra, the absorption edge of PVP polymer was found about of 230 nm. The absorption edge of PVP capped ZnS:Mn nanoparticles shifted from 322 to 305 nm when the PVP concentration increases. The luminescence spectra of PVP showed a blue emission with peak maximum at 394 nm. The luminescence spectra of ZnS:Mn–PVP exhibits a blue emission with peak maximum at 437 nm and an orange–yellow emission of ion Mn²⁺ with peak maximum at 600 nm. While the PVP coating did not affect the microstructure of ZnS:Mn nanomaterial, the PL spectra of the PVP capped ZnS:Mn samples were found to be affected strongly by the PVP concentration.     

Evidence for nearby supernova explosions

Supernova (SN) explosions are one of the most energetic---and potentially lethal---phenomena in the Universe. We show that the Scorpius-Centaurus OB association, a group of young stars currently located at approximately 130 pc from the Sun, has generated 20 SN explosions during the last 11 Myr, some of them probably as close as 40 pc to our planet. The deposition on Earth of (60)Fe atoms produced by these explosions can explain the recent measurements of an excess of this isotope in deep ocean crust samples. We propose that approximately 2 Myr ago, one of the SNe exploded close enough to Earth to seriously damage the ozone layer, provoking or contributing to the Pliocene-Pleistocene boundary marine extinction.     

高能核碰撞中带电多重数快度与能量和中心度的关系

用强子–弦级联模型JPCIAE及相应的Monte Carlo事例产生器研究相对论性核–核碰撞中带电粒子多重数的赝快度密度对能量和中心度的依赖关系.无需另调任何模型参数的条件下,此模型可以同时较好地描述相对论性pp实验数据及PHOBOS和PHENIX实验组的Au+Au实验数据.本文指出:因〈N_part〉并非严格定义的物理量,致使实验上和理论上确定〈N_part〉有一定任意性,从而使得每参加者核子对的带电粒子赝快度密度随着〈N_part〉的增加可能逐渐增大,也可能逐渐减小,因此用它来区分粒子产生机制是欠妥的.     

Dynamic response of permalloy/Cu/Co magnetoresistive sandwiches

The dynamic response of trilayer magnetoresistive permalloy/Cu/Co films was studied by high-frequency permeability spectra measurements. The resonance frequency is shown to depend on the interlayer copper thickness. This dependence is related to exchange coupling between permalloy and cobalt and the interaction field is estimated using the Landau–Lifschitz–Gilbert model.     

Multi-Fractal Formalism for Quasi-Self-Similar Functions

The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs.     

Reactivity of tetrahydrochromeno[2,3‐b]indoles: chromic indicators of cyanide

The synthesis and reactivity of a tetrahydrochromeno[2,3‐b]indoles are reported. Evidence for reversible ring‐opening is based on H/D exchange and trapping experiments. These compounds readily undergo reaction with tetra‐n‐butylammonium cyanide. The cyanide reaction is 10–100× faster when the solution is irradiated with 350 nm light. Reaction with trimethylsilyl cyanide occurs only with UV irradiation demonstrating photoreactivity. The rate of tetrahydrochromeno[2,3‐b]indole ring‐opening is greater for (i) Me substitution at the hemiaminal carbon (compared to Ph), and (ii) substitution of fluorine at the 9‐position of the indole. Under acidic conditions, the ring‐opened indolium ion is observed. Copyright © 2013 John Wiley & Sons, Ltd.