Eigenvalues of Random Power law Graphs

Many graphs arising in various information networks exhibit the "power law" behavior -the number of vertices of degree k is proportional to k^-# for some positive #. We show that if # > 2.5, the largest eigenvalue of a random power law graph is almost surely(1+ o(1))?m (1+ o(1))\sqrt{m} where m is the maximum degree. Moreover, the klargest eigenvalues of a random power law graph with exponent # have power law distribution with exponent 2# if the maximum degree is sufficiently large, where k is a function depending on #, mand d, the average degree. When 2<#< 2.5, the largest eigenvalue is heavily concentrated at cm^3-# for some constant c depending on # and the average degree. This result follows from a more general theorem which shows that the largest eigenvalue of a random graph with a given expected degree sequence is determined by m, the maximum degree, and [(d)\tilde] \tilde{d} , the weighted average of the squares of the expected degrees. We show that the k-th largest eigenvalue is almost surely (1+ o(1))?{m_k} (1+ o(1))\sqrt{m_k} where m_k is the k-th largest expected degree provided m_k is large enough. These results have implications on the usage of spectral techniques in many areas related to pattern detection and information retrieval.     

Fast and precise algorithm based on maximum radial symmetry for single molecule localization

We present an algorithm to estimate the location of single fluorescent molecule with both high speed and high precision. This algorithm is based on finding the subpixel position with maximum radial symmetry in a pixelated single molecule fluorescence image. Compared with conventional algorithms, this algorithm does not rely on point-spread-function or noise model. Through numerical simulation and experimental analysis, we found that this algorithm exhibits localization precision very close to the maximum likelihood estimator (MLE), while executes ～1000 times faster than the MLE and ～6 times faster than the fluoroBancroft algorithm.     

气体扩散方程解析解及在测定分子间势能的应用

设计了一新颖的分子动理论实验装置,根据求解在约束条件下的气体扩散方程的解析解和气体分子在升华时会对容器底部产生作用力的特点,设计了一种新颖简单的实验器材来测量分子间相互作用的势能,其实验曲线符合理论数据,误差分析后的补偿曲线所得结果可较为精确地与理论结果吻合。本实验常温下即可进行,且精度较高,适合快速材料性质测定及大学物理教学,以解决大学物理演示实验课关于学气体动理论的实验数量较少,且往往只涉及对热学微观过程的宏观模拟,而很少涉及气体动理论的实验,导致学生学习不够深入的问题。有利于学生对分子运动学问题的深入探索。     

Comparison of effects of relative carry-envelope phase on two-color few cycle pulses propagating in dense and dilute lambda-type mediums

In this paper we compared effects of relative carry-envelope phase (RCEP) of two-color few cycle pulses on propagation behavior and spectral property under the single-photon resonant condition in the dense and dilute lambda-type three-level atomic mediums. It is found that, in the dense medium, with propagation distance increasing, the compound pulse of the two-color few cycle pulses will split into two or three sub-pulses with different amplitudes and shapes, or does not split, and this is completely determined by value size of RCEP; with value of RCEP decreasing, range and strength of the spectrum (particularly the higher spectral components) increase obviously, the highest frequency is about eight times of the resonance frequency. In the corresponding dilute medium, effect of RCEP on propagating behavior and spectral property is much different from that in the dense medium; specially with value of RCEP decreasing, spectral strength increasing is evident but spectral range not, the highest frequency of the spectrum is only about two times of the resonance frequency.     

Study on the Interaction Between Water-Soluble CdTe Quantum Dots and Ovalbumin by Optical Spectroscopy

ABSTRACT

CdTe quantum dots (QDs) modified by 2-mercaptoethylamine hydrochloride (CA) and thioglycolic acid (TGA), respectively, were synthesized in aqueous medium. The interaction of CdTe QDs with ovalbumin has been investigated in depth by Fourier transform infrared spectroscopy (FTIR), UV-Vis absorption, fluorescence-quenching spectrometry, and resonance Rayleigh scattering spectroscopy (RRS). Fluorescence data show that the quenching type of ovalbumin by CA-CdTe QDs is static quenching with the binding constant being 10^?4 M^?1, and the number of binding sites being one. The calculated thermodynamic parameters demonstrate that the main binding forces are hydrophobic interaction and electrostatic attraction. In contrast, the quenching style of ovalbumin by TGA-CdTe QDs is verified to be dynamic quenching. Under suitable acidity conditions, the interaction of CA-CdTe QDs or TGA-CdTe QDs with ovalbumin leads to the remarkable enhancement of RRS, and the increments are found to be proportional to the concentration of ovalbumin in a certain range. A simple and highly sensitive RRS approach for determining ovalbumin is developed. In addition, the causes for the enhancement of RRS and the quenching of fluorescence are investigated to shed light on the quenching mechanism.     

Contracting on Average Random IFS with Repelling Fixed Point

We consider random iterated function systems which consist of strictly increasing and (not necessarily strictly) convex functions on a compact interval or on a half line. We assume that the system is contracting on average in a sense which is wide enough to permit the existence of a common fixpoint at which some functions of the system are expanding and perhaps none of them are contracting (see Fig. 1). We prove that the Hausdorff dimension of any of the possibly uncountably many invariant measures is smaller than or equal to the accumulated entropy divided by the Liapunov exponent. Mathematics Subject Classification. Primary 42A85 Secondary 11R06; 26A46; 26A30; 26A78; 28A80     

Optical properties and structures of silver thin films deposited by magnetron sputtering with different thicknesses

A series of thin Ag films with different thicknesses grown under identical conditions are analyzed by means of spectrophotometer. From these measurements the values of refractive index and extinction coefficient are calculated. The films are deposited onto BK7 glass substrates by direct current (DC) magnetron sputtering. It is found that the optical properties of the Ag films can be affected by films thickness.Below critical thickness of 17 nm, which is the thickness at which Ag films form continuous films, the optical properties and constants vary significantly with thickness increasing and then tend to a stable value up to about 40 nm. At the same time, X-ray diffraction measurement is carried out to examine the microstructure evolution of Ag films as a function of films thickness. The relation between optical properties and microstructure is discussed.     

The Initial-boundary Value Problem for the Ostrovsky-Vakhnenko Equation on the Half-line

We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (DP) equation. We show that the solution u(x,t) can be recovered from its initial and boundary values via the solution of a vector Riemann-Hilbert problem formulated in the plane of a complex spectral parameter z.