Large deviation theory deals with the decay of the probability of increasingly unlikely events. It is one of the key techniques of modern probability, a role which is emphasised by the recent award of the Abel prize to S.R.S. Varadhan, one of the pioneers of the subject. The subject is intimately related to combinatorial theory and the calculus of variations. Applications of large deviation the...

Recent results on sphere packings show a remarkable relation between dense nite sphere packings and concepts of crystallography, such as the Gibbs{Curie surface energy and the Wull{shape for ideal crystals and quasicrystals ((W2], W3], S], BB], BS1] and BS2]). The previous papers mainly considered applications. Here we prove some basic properties of the tools, in particular the density deviatio...

Process deviation analysis is becoming increasingly important for companies. This paper presents a framework which structures the field of process deviation analysis and identifies new research opportunities. Application of the framework starts from managerial questions which relate to specific deviation categories and methodological steps. Finally a general outline to detect high-level process...

We discuss the computation of If], where I is a positive functional on C a; b]. Any algorithm starts with some input, in typical situations this input consists of function values (f (x 1) ; : : : ; f (x n)) and the more global information f 2 K, where K C a; b] is a given set. The algorithm which makes the fullest use of the input is called the strongly optimal algorithm. We shall show that in ...

The least absolute deviation or L1 method is a widely known alternative to the classical least squares or L2 method for statistical analysis of linear regression models. Instead of minimizing the sum of squared errors, it minimizes the sum of absolute values of errors. Despite its long history and many ground-breaking works (cf. Portnoy and Koenker (1997) and references therein), the former has...

A 50-year-old man was admitted for the acute onset of vertical diplopia worse on left gaze. The right eye appeared hypertropic. Either right fourth nerve palsy or skew deviation was possible.1,2 Nonmydriatic retinal photography revealed an excyclotorsion of the hypotropic eye associated with incyclotorsion of the hypertropic eye (figure 1, A and B) providing a key element for skew deviation. In...

A new method for evaluating the resting direction of the eyes based on the use of afterimages was developed. With this technique, the effect of gaze deviations relative to the individually determined resting direction was investigated among naive subjects. Moderate gaze deviations have no effect on reports of autokinesis. Only at extreme deviations which approach anatomical limits is the direct...

Inaccuracies, or deviations, in the measurements of monitored variables in a control system are facts of life that control software must accommodate—the software is expected to continue functioning correctly in the face of an expected range of deviations in the inputs. Deviation analysis can be used to determine how a software specification will behave in the face of such deviations in data fro...

The paper adopts from the investment behavior theory and studies the affecting factors of financial investors in investment decision-making and the investment fund behavioral deviation. At the same time, the thesis also analyzes the efficiency of asset allocation and investment behavior of China's securities investment funds, and studies its impact on China's securities market. On the basis of ...