The likelihood ratio and its applications in sequential analysis

The likelihood ratio is treated as a generalized Radon-Nikodym derivative for measures which need not be absolutely continuous. It is shown that a wide variety of identities and inequalities in sequential analysis follow directly from simple properties of likelihood ratios.     

The concept of sequential optimality for problems in numerical analysis

In this paper the concept of sequential optimality is introduced and discussed in a general setting for the worst-case analysis of approximately solved problems. As an example, the problem of numerical integration of monotonic functions is studied.     

Combinatorial devices for sequential analysis

Summary For Brownian motion, escape probabilities over curved boundaries have been studied in some detail. Since sequential analysis is not concerned with really large samples, the approximation by the Brownian motion is questionable; neither the central limit theorem nor the renewal theorem regulating the overshoot may be appropriate tools. The present paper shows that combinatorial results developed in fluctuation theory have some bearing on the calculation of escape probabilities. The main result is a kind of tangential approximation for random walks crossing a curved boundary.     

Nonsmooth sequential analysis in Asplund spaces

We develop a generalized differentiation theory for nonsmooth functions and sets with nonsmooth boundaries defined in Asplund spaces. This broad subclass of Banach spaces provides a convenient framework for many important applications to optimization, sensitivity, variational inequalities, etc. Our basic normal and subdifferential constructions are related to sequential weak-star limits of Fréchet normals and subdifferentials. Using a variational approach, we establish a rich calculus for these nonconvex limiting objects which turn out to be minimal among other set-valued differential constructions with natural properties. The results obtained provide new developments in infinite dimensional nonsmooth analysis and have useful applications to optimization and the geometry of Banach spaces.

     

Queuing analysis of a sequential recognizer of patterns

A recognition procedure is modelled as a queuing problem. We obtain first the steady-state distribution of probabilities of the basic process describing its evolution. Then, we derive some performance measures of the recognition procedure such as the waste time, the queue length of patterns, the classification error probabilities and so on. Stochastic comparisons are also provided. Our study extend the Viscolani's results to the non Markovian case.     

Calculus of sequential normal compactness in variational analysis

In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions.     

Asymptotic analysis for multi-objective sequential stochastic assignment problems

ABSTRACT

We provide an asymptotic analysis of multi-objective sequential stochastic assignment problems (MOSSAP). In MOSSAP, a fixed number of tasks arrive sequentially, with an n-dimensional value vector revealed upon arrival. Each task is assigned to one of a group of known workers immediately upon arrival, with the reward given by an n-dimensional product-form vector. The objective is to maximize each component of the expected reward vector. We provide expressions for the asymptotic expected reward per task for each component of the reward vector and compare the convergence rates for three classes of Pareto optimal policies.     

Strong approximations and sequential change-point analysis for diffusion processes

In this paper ergodic diffusion processes depending on a parameter in the drift are considered under the assumption that the processes can be observed continuously. Strong approximations by Wiener processes for a stochastic integral and for the estimator process constructed by the one-step procedure of Le Cam are obtained. Applying these approximations, a CUSUM-type procedure is developed for the sequential testing of changes in the parameter.     

The extensional ordering of the sequential functionals

We investigate the extensional ordering of the sequential functionals of finite types, with a focus on when the sequential functionals of a given type form a directed complete partial ordering, and on when a finite sequential functional will be the nontrivial least upper bound of an infinite chain of sequential functionals. We offer a full characterization for finite functionals of pure types.     

ONE-WAY MULTIVARIATE REPEATED MEASUREMENTS ANALYSIS OF VARIANCE MODEL

The one-way multivariate repeated measurements analysis of variance (1-way MRM ANOVA) model for complete data and the sphericity test are studied.     

Propagation of ultrasonics in bones

Conclusions The possibility has been established of determining the propagation velocity of elastic waves in bones by an ultrasonic technique in order to study the healing of fracture. An experimental apparatus of new design is described, which has been developed and made for research purposes and diagnostic measurements. The apparatus enables a numerical evaluation of the propagation velocity of ultrasonics in a bone to be automatically portrayed on the counter display, and the complete wave pattern or its details to be watched on the oscilloscope screen. The trends and principles of the exploratory measurements and practical diagnostics are discussed and, after statistical processing, certain results from our determinations are also quoted.A paper presented to the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October 28–31, 1975.Scientific-Research Institute of Traumatology, Brno, Czechoslavakian SSR. Translated from Mekhanika Polimerov, No. 6, 1084–1087, November–December, 1976.     

A planar minimax alogrithm for analysis of coordinate measurements

We characterize the solution of the following problem and describe an algorithm for numerically solving it. Two sets ofN points in the plane, labeled 1,...,N, are given: a fixed set of nominal points and a set of measured points. We wish to transform the messured points as a whole, by translation and rotation, so that the maximal distance between corresponding points in the two sets is minimized. This algorthm provides an accept-reject criterion that may be used together with a coordinate measuring machine to determine if two mating parts will fit, or if a part is sufficiently close to its ideal measurements. A weighted version, suitable for point-dependent tolerances, is also discussed, as is optimal joint scalling of the data.     

Bare bones differential evolution

The barebones differential evolution (BBDE) is a new, almost parameter-free optimization algorithm that is a hybrid of the barebones particle swarm optimizer and differential evolution. Differential evolution is used to mutate, for each particle, the attractor associated with that particle, defined as a weighted average of its personal and neighborhood best positions. The performance of the proposed approach is investigated and compared with differential evolution, a Von Neumann particle swarm optimizer and a barebones particle swarm optimizer. The experiments conducted show that the BBDE provides excellent results with the added advantage of little, almost no parameter tuning. Moreover, the performance of the barebones differential evolution using the ring and Von Neumann neighborhood topologies is investigated. Finally, the application of the BBDE to the real-world problem of unsupervised image classification is investigated. Experimental results show that the proposed approach performs very well compared to other state-of-the-art clustering algorithms in all measured criteria.     

The average value inequality in sequential effect algebras

A sequential effect algebra （E, 0, 1, ,o） is an effect algebra on which a sequential product o with certain physics properties is defined; in particular, sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Gudder asked the following problem： If a, b E （E, 0, 1, , o） and a⊥b and a o b⊥a o b, is it the case that 2（a o b） ≤ a2 b2 ？ In this paper, we construct an example to answer the problem negatively.     

An analysis of the sharpness of monotonicity results via homotopy for sequential fractional operators

We investigate the connection between the sign of $\left({\Delta }_{1-\mu +a}^{\nu }{\Delta }_a^{\mu }f\right)\left(t\right)$ and the monotone behavior of $t\mapsto f\left(t\right)$. In particular, given a function $f:{\mathbb{N}}_a\to \mathbb{R}$ we consider the homotopy $G_{\nu }:\mathbb{R}\times [0,1]\to \mathbb{R}$ defined by $G_{\nu }\left(f\left(a\right),\eta \right)≔\eta \cdot \frac{1}{2}(1-\nu )\left(\nu \right)f\left(a\right)$, and we analyze the effect of changing $\eta \in [0,1]$ in the condition $\left({\Delta }_{1-\mu +a}^{\nu }{\Delta }_a^{\mu }f\right)\left(t\right)\ge G_{\nu }\left(f\left(a\right),\eta \right)$. We show that as $\eta \to 1^{-}$ there is an increasingly strong connection between the sign of $\left({\Delta }_{1-\mu +a}^{\nu }{\Delta }_a^{\mu }f\right)\left(t\right)$ and the monotone behavior of $f$.