A New Class of Weighted CUSUM Statistics

A change point is a location or time at which observations or data obey two different models: before and after. In real problems, we may know some prior information about the location of the change point, say at the right or left tail of the sequence. How does one incorporate the prior information into the current cumulative sum (CUSUM) statistics? We propose a new class of weighted CUSUM statistics with three different types of quadratic weights accounting for different prior positions of the change points. One interpretation of the weights is the mean duration in a random walk. Under the normal model with known variance, the exact distributions of these statistics are explicitly expressed in terms of eigenvalues. Theoretical results about the explicit difference of the distributions are valuable. The expansions of asymptotic distributions are compared with the expansion of the limit distributions of the Cramér-von Mises statistic and the Anderson and Darling statistic. We provide some extensions from independent normal responses to more interesting models, such as graphical models, the mixture of normals, Poisson, and weakly dependent models. Simulations suggest that the proposed test statistics have better power than the graph-based statistics. We illustrate their application to a detection problem with video data.     

Determination of the optimal cylindrical geometry heights for gamma-ray spectrometric analysis

The optimal heights (sample thickness) for samples of cylindrical geometry analyzed by gamma-spectrometry with HPGe detectors have been determined by studying the correlation between the sample thickness and the sample mass multiplied by the efficiency. For energies higher than 100 keV, the optimal thickness for a cylindrical sample with a diameter of 6.8 cm was determined to be 10 cm, regardless of the type of HPGe detector. A strong relationship was observed between the optimal sample thickness and the gamma energy line (when E < 100 keV) and the density of the sample for N-type HPGe (R.eff. 60%) detectors. For a sample density 2 g cm⁻³, the optimal thickness was determined to be 3.5 cm at 46.5 keV and 5 cm at 59.5 keV.     

基于压缩感知理论的非线性γ谱分析方法

γ谱分析是一种重要的放射性核素定量分析方法. 弱峰的检测和重叠峰的分解是γ 谱分析中的难点. 为了解决这两个问题, 基于压缩感知理论, 提出了一种新的γ 谱分析方法. 这一方法从谱仪对γ 谱调制的物理机理出发, 通过数学建模, 将γ 谱分析转化为一个以真实γ 谱为解的求逆问题, 并在压缩感知理论框架下, 运用γ 谱特征峰的稀疏性, 进行逆问题的求解, 直接获得γ 谱的估计结果. 数值模拟结果和蒙特卡洛模拟结果表明: 该方法能在降低统计涨落的同时, 有效减小谱仪调制带来的能谱展宽, 从而提高γ 谱分析精度. 关键词： γ谱分析')" href="#">γ谱分析 压缩感知 非线性 逆问题     

A package for gamma-ray spectrum analysis and routine neutron activation analysis

A package for gamma spectrum analysis (PGSA) was developed using object-oriented Borland C++ design for MS-windows. This package consists of five programs which can be used for gamma-ray spectrum analysis and routine neutron activation analysis. The advantages of PGSA are its simple algorithms and its need for only minimum amount of input information.     

用于光谱分类的光谱峰谷沿匹配算法

针对超短脉冲激光与气体相互作用产生的非线性荧光光谱的特点,提出了一种新的光谱去噪、特征提取、特征匹配的有效方法.通过对三种气体不同浓度的荧光光谱进行小波压缩去噪,得到5层664个小波系数,重构后获得除噪效果满意而特征信息保持不变的光谱.对重构后的光谱进行光谱峰/谷沿相似度的分析,构造了三种气体的特征谱.在此基础上,经对三种气体光谱进行特征峰/谷沿的匹配分析,提出一种利用同种物质不同浓度下的光谱总体相似度来构造标准特征谱新方法,通过与标准特征谱的匹配分析得到分类结果.实验结果表明,该算法的分类结果受浓度变化影响小,对低至0.05%浓度条件下的全部27条光谱均获得100%的分类识别结果.     

The density profile for the Klein-Kramers equation near an absorbing wall

We derive asymptotic series for the expansion coefficients of a function in terms of the Pagani functions, which occur in the boundary layer solutions of the Klein-Kramers equation. The results enable us to determine the density profile in the stationary solution of this equation near an absorbing wall from the numerically determined velocity distribution at the wall, with an accuracy of about 2%. We also obtain information about the analytic behavior of the density profile: this profile increases near the wall with the square root of the distance to the wall. Finally, the asymptotic analysis leads to an understanding of the slow convergence of variational approximations to the solution of the absorbing-wall problem and of the exponents that occur when one studies the variational approximations to various quantities of interest as functions of the number of terms in the variational ansatz. This is used to obtain a better variational estimate for the density at the wall.     

A gamma-ray scattering technique for estimation of density and moisture content of wood

A densitometer system, operating in a non-destructive and non-invasive way, is presented to investigate the density and moisture variation in wood samples of Pinus roxburghii (known as chir pine). The inherent ability of Compton scattering can ascertain quantitative information of electron density of the target material. A well collimated beam of 662?keV gamma rays from ¹³⁷Cs radioactive source has been used to extract the information of density from interior of sample by recording scattered spectra with NaI(Tl) scintillation detector. An inverse matrix approach for unfolding of observed pulse-height distribution to a true photon spectrum is used, by choosing bin mesh (E^1/2) of 0.025 (MeV)^1/2, for the measurements of scattered spectra. The regression lines, obtained from data of scattered spectra, provide the density and moisture content of selected wood sample. The adjusted R² value 0.984 for fitted curve, justifies the linear dependence of scattered intensity upon wood density. Also, Compton scatter measurements results that the technique is less sensitive beyond wood thickness of ～110?mm due to overlying scatter components in the measured spectrum.     

The kinetic boundary layer for the Klein-Kramers equation; A new numerical approach

We explore a numerical technique for determining the structure of the kinetic boundary layer of the Klein-Kramers equation for noninteracting Brownian particles in a fluid near a wall that absorbs the Brownian particles. The equation is of interest in the theory of diffusion-controlled reactions and of the coagulation of colloidal suspensions. By numerical simulation of the Langevin equation equivalent to the Klein-Kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities. The data can be used to construct the solutions of the standard problems at an absorbing wall, the Milne and the albedo problem. We confirm and extend earlier results by Burschka and Titulaer, obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion. We briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here.     

Polarised raman and infrared spectra and vibrational analysis forα-naphthylamine

The Raman spectrum of polycrystalline α-naphthylamine was recorded in the region 100–4000 cm⁻¹. Polarisation measurements were made in CS₂ and CHCl₃ solutions. The infrared spectrum was recorded in nujol mull in the region 200–4000 cm⁻¹. The resolution was better than 2 cm⁻¹ and the accuracy of the measurements was within ± 2 cm⁻¹ for all the spectra. Vibrational assignments have been proposed for the observed frequencies. Out of the 54 normal modes of vibrations, 51 modes could be observed experimentally.     

Multiple-plateau structure and scaling relation in photoelectron spectra of high-order above-threshold ionization

By developing a full quantum scattering theory of high-order above-threshold ionization,we study the energy spectra and the angular distributions of photoelectrons from atoms with intense laser fields shining on them.We find that real rescattering can occur many times,and even infinite times.The photoelectrons from the rescattering process form a broad plateau in the kinetic-energy spectrum.We further disclose a multiple-plateau structure formed by the high-energy photoelectrons,which absorb many photons during the rescattering process.Moreover,we find that both the angular distributions and the kinetic-energy spectra of photoelectrons obey the same scaling law as that for directly emitted photoelectrons.     

A model for the multiplicity distribution in pp-collisions from 5 to 300 GeV/c

The multiplicity distribution of charged particles in pp-collisions in the range 5–300 GeV/c is explained on the basis of a dynamical model which leads to a specific mixture of Poisson distributions.     

Heuristic approach for peak regions estimation in gamma-ray spectra measured by a NaI detector

In this paper, a heuristic approach based on Slavic＇s peak searching method has been employed to estimate the width of peak regions for background removing. Synthetic and experimental data are used to test this method. With the estimated peak regions using the proposed method in the whole spectrum, we find it is simple and effective enough to be used together with the Statistics-sensitive Nonlinear Iterative Peak-Clipping method.     

Brownian motion with inert drift, but without flux: A model

We study the motion of a Brownian particle which interacts with a stationary obstacle in two dimensions. The Brownian particle acquires drift proportionally to the time spent on the boundary of the obstacle. The system approaches equilibrium, and the equilibrium distribution for the location and drift magnitude has the product form. The distribution for the location is uniform, while the drift distribution depends on the shape of the obstacle, resembling a gamma function for the circular or elliptic obstacle.     

Heuristic approach for peak regions estimation in gamma-ray spectra measured by a NaI detector

In this paper, a heuristic approach based on Slavic's peak searching method has been employed to estimate the width of peak regions for background removing. Synthetic and experimental data are used to test this method. With the estimated peak regions using the proposed method in the whole spectrum, we find it is simple and effective enough to be used together with the Statistics-sensitive Nonlinear Iterative Peak-Clipping method.     

Vibrational spectra and normal coordinate analysis on structure of chlorambucil and thioguanine

A normal coordinate analysis on chlorambucil and thioguanine has been carried out with a set of symmetry coordinates following Wilson’s F-G matrix method. The potential constants evaluated for these molecules are found to be in good agreement with literature values thereby confirming the vibrational assignments. To check whether the chosen set of vibrational frequencies contribute maximum to the potential energy associated with the normal coordinates of the molecule, the potential energy distribution has been evaluated.      

The diffusion constant for two-state brownons

We calculate the diffusion constant for two-state brownons when the change of state is not, as usually assumed, Markovian. The correction to the non-interchanging species result is found to be exactly expressible in terms of the Laplace transforms of the sojourn time densities.     

Characteristics of high energy interactions I. High energy gamma-ray spectra near the top of the atmosphere

An emulsion chamber was used to study the characteristics of high energy nuclear interactions from the production spectra ofγ-rays. The emulsion chamber, which comprised of two parts, namely the detector and the graphite producer unit, was exposed to cosmic rays for about 7 hr at an atmospheric depth of 10 g cm⁻² at Hyderabad (geomagnetic latitude 7·6°N). 720 electromagnetic cascades due toγ-rays were recorded in the detector. These cascades were classified into three groups; (a)γ-rays from nuclear interactions in the detector (b)γ-rays from nuclear interactions in the producer unit and (c)γ-rays of atmospheric origin. The energies of the cascades were determined using photometric method. The spectra ofγ-rays from groups (a) and (c) were determined and compared with similar spectra obtained at greater atmospheric depths. The spectra were found to obey a power law. The spectrum ofγ-rays of atmospheric origin was found to steepen at high energies,E _r>2200 GeV.     

Stochastic diagrams for critical point spectra

A new technique for calculating the time-evolution, correlations and steady state spectra for nonlinear stochastic differential equations is presented. To illustrate the method, we consider examples involving cubic nonlinearities in an N-dimensional phase-space. These serve as a useful paradigm for describing critical point phase transitions in numerous equilibrium and non-equilibrium systems, ranging from chemistry, physics and biology, to engineering, sociology and economics. The technique consists in developing the stochastic variable as a power series in time, and using this to compute the short time expansion for the correlation functions. This is then extrapolated to large times, and Fourier transformed to obtain the spectrum. Stochastic diagrams are developed to facilitate computation of the coefficients of the relevant power series expansion. Two different types of long-time extrapolation technique, involving either simple exponentials or logarithmic rational approximations, are evaluated for third-order diagrams. The analytical results thus obtained are compared with numerical simulations, together with exact results available in special cases. The agreement is found to be excellent up to and including the neighborhood of the critical point. Exponential extrapolation works especially well even above the critical point at large N values, where the dynamics is one of phase-diffusion in the presence of a spontaneously broken symmetry. This method also enables the calculation of the steady state spectra of polynomial functions of the stochastic variables. In these cases, the final correlations can be non-bistable even above threshold. Here logarithmic rational extrapolation has the greater accuracy of the two extrapolation methods. Stochastic diagrams are also applicable to more general problems involving spatial variation, in addition to temporal variation. Received: 12 January 1998