A representation for the posterior distribution of the location of a moving target

A target moves according to a continuous stochastic process in Euclidean R_^H. A search is conducted by choosing a search strategy and by observing the state of a detection process. Methods for representing the posterior distributions for target location given no detection are discussed. In particular, methods for parameterizing Gaussian models for target motion and the transition intensity of the detection process which yield tractable representations are introduced. The methodology is discussed in terms of two examples.     

Gaussian to flat-top intensity distributing lens

A system has been designed to convert the Gaussian intensity profile of a laser beam into a more uniform distribution. This paper postulates a number of afocal lens arrangements for this purpose and details the effect of one particular combination in balancing the higher-order terms and achieving collimation of a diffraction limited output between the l/e points.     

On some continuity and differentiability properties of paths of Gaussian processes

The following path properties of real separable Gaussian processes ξ with parameter set an arbitrary interval are established. At every fixed point the paths of ξ are continuous, or differentiable, with probability zero or one. If ξ is measurable, then with probability one its paths have essentially the same points of continuity and differentiability. If ξ is measurable and not mean square continuous or differentiable at every point, then with probability one its paths are almost nowhere continuous or differentiable, respectively. If ξ harmonizable or if it is mean square continuous with stationary increments, then its paths are absolutely continuous with probability one if and only if ξ is mean square differentiable; also mean square differentiability of ξ implies path differentiability with probability one at every fixed point. If ξ is mean square differentiable and stationary, then on every interval with probability one its paths are either differentiable everywhere or nondifferentiable on countable dense subsets. Also a class of harmonizable processes is determined for which of the following are true: (i) with probability one paths are either continuous or unbounded on every interval, and (ii) mean square differentiability implies that with probability one on every interval paths are either differentiable everywhere or nondifferentiable on countable dense subsets.     

菠菜PSII核心复合物激发能传递与温度的关系

采用基于延时分次扫描单光子计数器为探测装置的皮秒时间分辨荧光光谱测试系统研究了菠菜光系统 (PSⅡ )核心复合物光能传递与温度的关系。分别对PSII核心复合物样品在 2 0℃、42℃、48℃下做温浴处理 ,然后以脉宽为 1 2 0 ps,重复率为 4MHz ,波长为 5 1 4nm的Ar+激光作为光源分别激发处理后样品的荧光。通过对测量结果进行数据处理 ,分析比较发现 :同一温度下 ,呈荧光带的激发能传递速度比副荧光带处的快 ;同一波长下 ,慢组分的时间常量随温度升高而变慢 ,而快速组分的时间常数则变化不大 ;做 42℃温浴处理的样品接近于蛋白质解体的临界状态     

The excess-mass ellipsoid

The excess-mass ellipsoid is the ellipsoid that maximizes the difference between its probability content and a constant multiple of its volume, over all ellipsoids. When an empirical distribution determines the probability content, the sample excess-mass ellipsoid is a random set that can be used in contour estimation and tests for multimodality. Algorithms for computing the ellipsoid are provided, as well as comparative simulations. The asymptotic distribution of the parameters for the sample excess-mass ellipsoid are derived. It is found that a n^1/3 normalization of the center of the ellipsoid and lengths of its axes converge in distribution to the maximizer of a Gaussian process with quadratic drift. The generalization of ellipsoids to convex sets is discussed.     

A characterization of Gaussian spaces

A characterization of Gaussian subspaces of L₂ is given. It is shown that Gaussian subspaces are essentially characterized by the property that all linear isometries are induced by measure-preserving transformations.     

Statistical mechanics of a nonlinear stochastic model

A multivariable Fokker-Planck equation (FPE) is used to investigate the equilibrium and dynamical properties of a nonlinear stochastic model. The model displays a phase transition. The equilibrium distributions are found to be non-Gaussian; the deviation from Gaussian is especially significant near the transition point. To study the nonequilibrium behavior of the model, a self-consistent dynamic mean field (SCDMF) theory is derived and used to transform the FPE to a systematic hierarchy of equations for the cumulant moments of the time-dependent distribution function. These equations are numerically solved for a variety of initial conditions. During the time evolution of the system from an initial unstable equilibrium state to the final equilibrium state, three distinct time stages are found.Supported by a grant from the National Research Council of Canada (to RCD) and by the Sherman Fairchild Foundation (to RZ).Also Sherman Fairchild Distinguished Scholar, 1974–75, at the California Institute of Technology, where the early part of this research was done.     

A remark on truncation schemes of cumulant hierarchies

We discuss some problems obtained by truncating a cumulant hierarchy at ordern > 2. We show that such a truncation scheme is not consistent witha in its whole range of definition nonnegative probability function.     

Differential real-space renormalization of thed-Dimensional Gaussian model

With the aid of the differential real-space method we derive exact renormalization group (RG) equations for the Gaussian model ind dimensions. The equations involved + 1 spatially dependent nearest-neighbor interactions. We locate a critical fixed point and obtain the exact thermal critical indexy _T = 2. A special trajectory of the full nonlinear RG transformation is found and the free energy of the corresponding initial state calculated.Supported by Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 130 Ferroelektrika.     

Block spins in the edge of an Ising ferromagnetic half-plane

The characteristic function of a block spin in the face of an Ising ferromagnetic half-plane is obtained in closed form. The distribution function for the block spin converges to a Gaussian at the critical temperature, but the normalization of the block is modified.Partially supported by NRC grant A9344.