Patterns and Symmetries in the Visual Cortex and in Natural Images

As borders between different entities, lines are an important element of natural images. Indeed, the neurons of the mammalian visual cortex are tuned to respond best to lines of a given orientation. This preferred orientation varies continuously across most of the cortex, but also has vortex-like singularities known as pinwheels. In attempting to describe such patterns of orientation preference, we are led to consider underlying rotation symmetries: Oriented segments in natural images tend to be collinear; neurons are more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underlying topography. This is verified by direct statistical tests in both natural images and in cortical maps. Using the statistics of natural scenes we construct filters that are best suited to extracting information from such images, and find qualitative similarities to mammalian vision. PACS84.35+i 89.70.+c 87.57.Nk     

Kolmogorov Width of Classes of Smooth Functions on the Sphere

Let ^d−1{(x₁,…,x_d) ^d:x²₁+···+x²_d=1} be the unit sphere of the d-dimensional Euclidean space ^d. For r>0, we denote by B^r_p (1p∞) the class of functions f on ^d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on ^d−1, and P^λ_k(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of B^r_p in L^q( ^d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces X_N of L^q( ^d−1).The main result in this paper is that for r2(d−1)²,where A_NB_N means that there exists a positive constant C, independent of N, such that C⁻¹A_NB_NCA_N.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions.     

Energy Spectrum Width and Nonequilibrium Energy of Rayleigh Waves Scattered on a Two-Dimensional Near-Surface Electron Layer

We obtain expressions for the energy spectrum widths of Rayleigh waves corresponding to their deformational coupling to Fermi and Boltzmann electrons in a two-dimensional layer near the surface of a semibounded solid. We evaluate the nonequilibrium energy of Rayleigh waves that depends on these widths and is caused by the same coupling to the corresponding hot electrons. We show that this energy is independent of the degeneracy degree of the electrons and is given by the mean energy of free Rayleigh waves heated up to temperature of the electrons. We find conditions under which the thermodynamics is determined by this nonequilibrium energy of Rayleigh waves in films of a certain thickness with Fermi electrons near the surface and by the equilibrium energy of bulk phonons in thicker samples. All the results are obtained using the Keldysh diagram technique applied to the case of semibounded media.     

A Semiconductor Laser of the Visible Range as an Exciting Source of Raman Scattering

A possibility of application of semiconductor lasers of the visible range as exciting sources for Raman spectroscopy is studied. An experimental set-up for measuring Raman spectra of polycrystalline dielectrics and broad-gap semiconductors excited by a semiconductor laser with a wavelength of 640 nm was created. The conditions under which the spectral width of the lasing line of a semiconductor laser was within 10^-3 cm^-1 in the continuous mode with a power of 10 mW are realized. The characteristics of various types of exciting sources used in Raman spectroscopy are compared. The results of studies of the characteristic Raman spectra excited with a semiconductor laser in polycrystalline sulfur are presented.     

Yb3+掺杂铝氟磷酸盐玻璃的光谱和激光性能

研究了Yb3 掺杂铝氟磷酸盐 (AFP)玻璃的吸收光谱、荧光光谱 ,测量了Yb3 离子的荧光有效线宽 (Δλeff>5 5nm)以及2 F5 2 能级的荧光寿命 (τmax=2ms)及随掺杂浓度的变化 .应用倒易法计算了Yb3 的发射截面 ,其发射截面可达 0 6 6 82 3pm2 ,且激光增益系数τfσemi达 1 2 89ms.pm2 .评估了Yb3 在AFP玻璃中的激光性能 ,发现其具有较理想的激发态最小粒子数 (0 15 )、饱和抽运强度 (8 3kW cm2 )和最小抽运强度 (1 2 4 5kW cm2 )值及良好的热稳定性 .研究结果表明掺Yb3 氟磷酸盐玻璃是实现高功率超短可调谐激光器的理想增益介质 .     

模糊全区间序结构

本文试图对模糊偏好结构及模糊全区间序结构的定义进行探讨，并讨论它们的性质．以Fodor等提出的公理为基础，给出了模糊偏好结构的定义，同时对一类重要的模糊偏好结构-模糊全区间序结构的性质进行了讨论，得出了模糊全区间序结构的一些充要条件．     

几种模糊传递关系的收敛性

本文对几种模糊传递关系进行比较 ,从一个侧面说明了用于构造偏好关系的模糊关系应是互逆关系 .文中证明了对任意的 n阶互逆传递模糊关系 R,必有 Rn=Rn+1 .     

Does the beam width affect the generalized M factor of hard-edged diffracted beams?

A detailed study of the generalized M² factor of hard-edged diffracted beams based on the truncated second-order moments method, asymptotic analysis and self-convergent beam width approach is performed. The dependence of the generalized M² factor on the parameters characterizing the spatial profile, and beam truncation, etc. is analyzed.     

射束有效宽度与成像系统MTF关系的研究

射线成像系统的射线有效宽度是评定系统成像分辨率的重要成像指标。以试验的方法,通过测试系统成像的MTF,通过对成像分辨率与射线有效宽度的关系进行研究,为射线数字成像(DR)及工业CT系统设计提供了参考。     

Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)