Dimensional Probability Research Articles

Information theory, wavelets, and image compression

We examine practical, theoretical, and speculative aspects of wavelet transform-based image compression. Section I summarizes objectives and compares experimental results using a JPEG-standard cosine-based algorithm with a wavelet based algorithm developed at ISS. Section II analyzes image compression requirements using information theory to explain why wavelet transform-based image compression works well. The wavelet transform is shown to be a simple transform that effectively exploits second-order image statistics. Section III speculates about next-generation image compression and pattern recognition. It outlines a research plan to develop a probabilistic image model that incorporates higher-order image statistics by using wavelet expansions to provide a convergent series of finite dimensional marginal image probability densities. Physicists have successfully used similar cell cluster expansions to analyze lattice fields, Ising models, and Euclidean quantum fields. © 1996 John Wiley & Sons, Inc.

Asymptotic confidence intervals for the length of the shortt under random censoring

A shortt of a one dimensional probability distribution is defined to be an interval which has at least probability t and minimal length. The length of a show and its obvious estimator are significant measures of scale of a distribution and the corresponding random sample, respectively. In this note a non‐parametric asymptotic confidence interval for the length of the (uniqueness is assumed) shortt is established in the random censorship from the right model. The estimator of the length of the shortt is based on the product‐limit (PL) estimator of the unknown distribution function. The proof of the result mainly follows from an appropriate combination of the Glivenko‐Cantelli theorem and the functional central limit theorem for the PL estimator.

Expected social utility of life time in the presence of a chronic disease

Interventive action aimed at reducing the incidence of an irreversible chronic noncommunicable disease in a population has various effects. Hopefully, it increases total longevity in the population and it causes the disease to develop later in time in a smaller portion of the population. In this paper a statistical model is built by which these effects can be estimated. A three dimensional probability density function that underlies this model is changed by the interventive action. It is shown how a three dimensional utility function can be defined to appropriately judge this change.

Nearest-neighbor distribution functions for impenetrable particles in one to three dimensions

In several interesting recent papers, S. Torquato and his associates presented specific expressions for the dimensional hard-sphere nearest-neighbor probability density distribution function, P NN , and the mean nearest-neighbor particle separation, R NN , for D=1, 2, and 3. These expressions, which have been known since 1981, are closely related to general expressions of scaled particle theory given by Reiss and co-workers in 1959 and 1974. Here, the consequences of four different choices for the basic probability function, G, needed in calculating P NN and R NN , are explored with particular emphasis on the D=3 situation

Uniform consistency of a class of regression function estimators for Banach-space valued random variable

This paper deals with an estimator m n of the regression function m( x) = E( Y | X = x) with X in the real line and Y in a sufficiently regular Banach space. By using infinite dimensional probability inequalities for sums, we show that m n is uniformly consistent.

不完全な低次確率データからの高次結合確率密度関数の抽出の一方法

不完全な低次確率データからの高次結合確率密度関数の抽出の一方法

Statistical analyses of the two-dimensional point pattern of silver monolayer deposition on a single crystal silver electrode

Detailed data concerning the nucleation events for the deposition of 500 monolayers of silver on a screw-dislocation-free low-index face of a silver single crystal electrode, were analysed statistically by 1 and 2 Dimensional Probability Densities, Nearest Neighbour Distribution and 1 Dimensional Transects. This statistical analysis of the two-dimensional point pattern revealed that there were several lines of apparently high nucleation density. It was possible to explain the presence of these lines of higher site density as the result of the finite spatial resolution of the nucleation sites from the experimental current-time transients. No other features were detected so it may be concluded that the pattern of the nucleation sites was random, within the limits imposed by the experimental resolution of the sites.

A Comparison of Methods for Constructing Probability Measures on Infinite Product Spaces

AbstractThe construction, from a consistent family of finite dimensional probability measures, of a probability measure on a product space when the marginal measures are perfect is shown to follow from a classical theorem due to Ionescu Tulcea and known results on the existence of regular conditional probability functions.

Proposal for a monte carlo simulation of turbulent mixing ln reactive flows

Monte Carlo methods for solving the nonlinear integro–differential equation describing the mixing in turbulent reacting flows are discussed, The Markov stochastic process whose one–dimensional probability distribution coincides with the solution of this equation is described. The Monte Carlo procedure for computer simulation of this Markov process is suggested.

Parasitic source and drain resistance in high-electron-mobility transistors

The parasitic source and drain resistances of a high-electron-mobility transistor were analyzed in terms of a two layer transmission line model. The analysis showed that a highly conductive cap layer can function as an extension of the alloyed contact provided that tunneling between the cap layer and the channel is significant. The tunneling between the cap layer and the channel was analyzed in terms of a thermionic-field emission model in which a one dimensional time-dependent WKB transmission probability for the barrier was considered as well as Maxwell-Boltzman statistics for the tunneling carrier distribution. The GaAs cap, GaAlAs layer and 2-DEG channel can then be treated as a distributed resistance element with a characteristic coupling length. A reduction of the parasitic resistance can be obtained for a device structure with a short characteristic coupling length even if there exists an ideal alloyed contact to the 2-DEG channel. A multilayer cap consisting of an undoped GaAs layer inserted between the n-type GaAs and n-type GaAlAs is also proposed to reduce the barrier height for tunneling between the cap layer and the channel. The multilayer cap structure is predicted to appreciably reduce the parasitic resistance at room temperature and still be effective at 77 K.

A second look at a controversial percolation exponent?Is ? negative in three dimensions?

Series for the three dimensional bond percolation probability are reexamined in the light of a recent evaluation of the percolation thresholdpc. We find $$\beta = 0.435 \pm 0.035$$ which implies $$\eta = - 0.01 \pm 0.09$$

The ultrasound macroscope: initial studies of breast tissue.

A system called the ultrasound macroscope has been developed to measure the ultrasonic properties of tissues. Based on the concept of the scanning acoustic microscope, it is capable of generating quantitative images of ultrasound velocity, attenuation and backscatter for macroscopic slices of tissue. By maintaining high resolution (approximately 120 microns at 13 MHz) the morphology of complex tissues is well delineated. Data from regions of interest in the tissue are transformed into three dimensional probability distributions representative of the tissue's ultrasonic characteristics. Sets of two dimensional projections of these distributions are used to display the information. As an initial study, the properties of breast tissues are analyzed. Examples of both normal and abnormal pathology are presented and the relevance of the results to clinical imaging are discussed.

The ultrasound macroscope: Initial studies of breast tissue

A system called the ultrasound macroscope has been developed to measure the ultrasonic properties of tissues. Based on the concept of the scanning acoustic microscope, it is capable of generating quantitative images of ultrasound velocity, attenuation and backscatter for macroscopic slices of tissue. By maintaining high resolution (∼ 120 μm at 13 MHz) the morphology of complex tissues is well delineated. Data from regions of interest in the tissue are transformed into three dimensional probability distributions representative of the tissue's ultrasonic characteristics. Sets of two dimensional projections of these distributions are used to display the information. As an initial study, the properties of breast tissues are analyzed. Examples of both normal and abnormal pathology are presented and the relevance of the results to clinical imaging are discussed.

Calcul des variations stochastique et processus de sauts

The purpose of this paper is to develop a stochastic calculus of variations for R n -valuedstrong Markov processes with jumps x t ,which is the analogous of the Malliavin calculus of variations on diffusions. An integration by parts formula is established on a non Gaussian infinite dimensional probability space, in order to prove regularity of the probability law on R n of x t ,for fixed time t. Diffusions with jumps are also considered. The connection between the calculus of variations and the representations of martingales for jump process is exhibited.

On the information theoretic synthesis of three dimensional vibrotational reaction probabilities from collinear results

A modified version of the Bernstein—Levine collinear to three dimensional (1D→3D) transformation is described in detail and tested. As input data, the procedure requires 1D reaction probabilities and a preassigned value of the average fraction of rotational product energy. We obtain these quantities from accurate quantum and classical trajectory calculations respectively and compare the 1D→3D vibrotational reaction probabilities with those from the trajectory calculations. We consider first the H + F2 → HF + F reaction, which previous work suggests is a favourable case. The procedure is then applied to the F + H2 → HF + H reaction at various fixed energies. It is found that the 1D→3D transformation is useful at low energies but becomes unreliable at higher energies. This may be because bent configurations play a more important role as the energy increases. The significance of almost linear surprisal plots is also discussed.

Probabilistic foundations of quantum theories and Rubin-Stone spaces

A construction of Mielnik probability spaces of dimension 2 is given in terms of Rubin-Stone functionals, and conversely it is shown that if a certain subset of a real linear space is supplied with 2 dimensional Mielnik probability space structure then the space becomes a Rubin-Stone space (in final analysis, a generalized inner product space). Analogous results are given for generalized inner product spaces in the sense of Nagumo.

Onsager-Machlup Function for one dimensional nonlinear diffusion processes

Using Ito stochastic differential equations to describe stochastic processes the Onsager-Machlup Function of a nonlinear diffusion process is calculated. It is shown that for two examples the Onsager-Machlup Function calculated directly as limit of finite dimensional probability densities agrees with the formula derived by using the Ito calculus but differs from a formula given by Graham who used the concept of Langevin equations.

Convergence in Distribution of Random Measures

Let $(S, \mathscr{I})$ be a measurable space, $M$ the set of all finite measures on $\mathscr{I}, \mathscr{F}_M$ the $\sigma$-algebra generated by the family of all measurable cylindrical sets $\cap^k_{i=1} \{\mu \in M: \mu(A_i) \leqq a_i\}$. With each probability measure $P$ on $\mathscr{F}_M$ the family $\{P_{A_1}, \cdots, A_k\}$ of all finite-dimensional probability measures of the cylidrical sets is associated. The following problem is considered: Given a sequence $P^{(n)}$ of probability measures on $\mathscr{F}_M$ such that each sequence $P^{(n)}_{A_1}, \cdots, A_k$ converges weakly to a $k$-dimensional probability measure $P_{A_1}, \cdots, A_k$, does the family $\{P_{A_1}, \cdots, A_k\}$ generate a probability measure $P$ on $\mathscr{F}_M?$ It is proved that the answer is affirmative if $(S, \mathscr{I})$ is the Euclidean $n$-space with the $\sigma$-algebra of Borel sets.

Interconnected System Spinning Reserve Requirements

There has been a considerable amount of work done in the area of static capacity reliability evaluation in interconnected systems. The first important paper in this subject1 utilized a two dimensional probability array upon which the tie line constraints were imposed. The basic generating unit statistics in static and spinning reserve studies are fundamentally different and in the latter case the problem is a question of will the capacity immediately available to the system be capable of satisfying the load in the event of possible capacity and load changes. The possible assistance under these conditions from an interconnected system cannot therefore be neglected in determining the risk of just carrying or failing to carry the system load. In a static capacity interconnected system study, the tie line is normally rated at its nominal value. In a spinning study, the tie line rating or inter-system transfer capability will depend upon the immediate and known conditions between each system, i. e., the existing transmission configuration, the scheduled generation pattern, etc. etc. These could be quite variable even over the course of a day.

Reliability of a Variance Estimate Obtained from a Sample Augmented by Multivariate Regression

A sample of size n1 of a normal random variable y is augmented by n2 regression estimates obtained from p other random variables which, along with y, follow a (p + 1) dimensional normal probability law. The sampling variance of sy2, the estimate of the variance of y obtained from the augmented sample, is derived. The relative reliability of sy2 and sy2 (n1), the variance estimate based on the original n1 observations, is found to depend on n1, n2, p, and R, the multiple correlation between y and the remaining p variables.