Function Classes That Approximate the Bayes Risk

2006 ◽  
pp. 79-93 ◽  
Author(s):  
Ingo Steinwart ◽  
Don Hush ◽  
Clint Scovel
Keyword(s):  
Bayes Risk ◽  
Function Classes

scholarly journals Nonparametric Bayes-risk estimation

1971 ◽  
Vol 17 (4) ◽  
pp. 440-444 ◽  
Author(s):  
S. Fralick ◽  
R. Scott
Keyword(s):  
Risk Estimation ◽  
Bayes Risk ◽  
Nonparametric Bayes

Introducing a Use Perspective in Product Design Theory and Methodology

1999 ◽  
Author(s):  
Anders V. Warell
Keyword(s):  
Engineering Design ◽  
Design Theory ◽  
Functional Language ◽  
Product Systems ◽  
Function Classes ◽  
Life Phase ◽  
Active User ◽  
Design Theory And Methodology ◽  
Machine Systems ◽  
And Function

Abstract In this paper it is argued that methods are needed for the design of a larger variety of product aspects than is feasible with mechanical engineering design methodology of today. Design methods found within the European schools of design are inadequate for the design of products other than machine systems of transforming character. The reason for this is that the underlying theories only describe the nature of ‘operand-transforming’ technical systems, and that the description of the process and function systems are too narrowly defined to be useful for the design of ‘non-transforming’ products, or for products where the human is involved as an active user. The paper takes as the standpoint that the functional language, in accordance with established foundation in engineering design theory, is a successful means to treat usability aspects of human-product systems. An extended process modeling view based on product life-phase thinking including a ‘use-process’ is presented, focusing the attention towards the use, and not merely the workings, of the product. Also, extended definitions of a number of concepts are proposed, and function-classes of the human-product system, leading to a more generally applicable use of functions as a modeling tool when describing products, is introduced. The proposed functional language is illustrated in a product case example.

APPROXIMATIVE PROPERTIES OF ABEL–POISSON-TYPE OPERATORS ON THE GENERALIZED HÖLDER CLASSES

2021 ◽  
Vol 1 ◽  
pp. 76-83
Author(s):  
Yuri I. Kharkevich ◽  
◽  
Alexander G. Khanin ◽  
Keyword(s):  
Modulus Of Continuity ◽  
Applied Mathematics ◽  
Continuous Functions ◽  
Elliptic Type ◽  
Periodic Functions ◽  
French Mathematician ◽  
First Order ◽  
Function Classes ◽  
In The Beginning ◽  
Poisson Type

The paper deals with topical issues of the modern applied mathematics, in particular, an investigation of approximative properties of Abel–Poisson-type operators on the so-called generalized Hölder’s function classes. It is known, that by the generalized Hölder’s function classes we mean the classes of continuous -periodic functions determined by a first-order modulus of continuity. The notion of the modulus of continuity, in turn, was formulated in the papers of famous French mathematician Lebesgue in the beginning of the last century, and since then it belongs to the most important characteristics of smoothness for continuous functions, which can describe all natural processes in mathematical modeling. At the same time, the Abel-Poisson-type operators themselves are the solutions of elliptic-type partial differential equations. That is why the results obtained in this paper are significant for subsequent research in the field of applied mathematics. The theorem proved in this paper characterizes the upper bound of deviation of continuous -periodic functions determined by a first-order modulus of continuity from their Abel–Poisson-type operators. Hence, the classical Kolmogorov–Nikol’skii problem in A.I. Stepanets sense is solved on the approximation of functions from the classes by their Abel–Poisson-type operators. We know, that the Abel–Poisson-type operators, in partial cases, turn to the well-known in applied mathematics Poisson and Jacobi–Weierstrass operators. Therefore, from the obtained theorem follow the asymptotic equalities for the upper bounds of deviation of functions from the Hölder’s classes of order from their Poisson and Jacobi–Weierstrass operators, respectively. The obtained equalities generalize the known in this direction results from the field of applied mathematics.

scholarly journals GOLD severity stratification and risk of hospitalisation for COPD exacerbations

2016 ◽  
Vol 70 (4) ◽  
Author(s):  
M. Lusuardi ◽  
C. Lucioni ◽  
F. De Benedetto ◽  
S. Mazzi ◽  
C.M. Sanguinetti ◽  
...  
Keyword(s):  
Clinical Factors ◽  
Copd Exacerbations ◽  
Telephone Interviews ◽  
Function Classes ◽  
Prospective Multicentre Study ◽  
Relative Risks ◽  
Gold Stage ◽  
Copd Patients ◽  
Oral Corticosteroids

Background and Aim. The Italian Costs for Exacerbations in COPD (“ICE”) study, following a pharmacoeconomic assessment of costs due to COPD exacerbations (primary endpoint), aimed also at evaluating (secondary endpoint) which clinical factors, among those considered for cost-analysis, may, at follow up, present a risk of new exacerbations and re-admission to hospital. Materials and methods. A prospective, multicentre study was carried out on COPD patients admitted to 25 Hospital Centres as a result of an exacerbation from October- December 2002. Following discharge, a 6-month follow- up was performed in each patient via three bi-monthly telephone interviews with a questionnaire administered by an investigator clinician. Results. 570 patients were eligible for data processing, mean age 70.6 years (± 9.5 standard deviation, SD), males 69.2%. According to GOLD, severity stratification was as follows: moderate 36.4%; severe 31.3%; very severe 32.3%. 282 patients experienced at least one exacerbation at follow up, 42% of exacerbations requiring hospitalisation. No significant association was seen between exacerbations and GOLD stage or co-morbidities or treatments except LTOT. Conversely, COPD functional severity influenced hospitalisations very significantly, with relative risks 2.6 (95% Confidence Interval, CI 1.8-3.8) and 2.0 (CI 1.3-2.8) (GOLD very severe versus moderate and severe, respectively), and 1.3 (CI 0.85-2.1) (GOLD severe versus moderate). Hospitalisations were also significantly associated with treatments denoting more severe conditions (oral corticosteroids, oral theophylline, and LTOT). Conclusions. Severity stratification of COPD patients according to respiratory function classes as outlined in GOLD guidelines and need for LTOT are confirmed as important predictors of hospitalisation for an exacerbation.

Sign in / Sign up

Export Citation Format

Share Document