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- Vladik Kreinovich, Jan Beck, +4 authors Scott A. Starks
- Reliable Computing
- 2007

In engineering applications, we need to make decisions under uncertainty. Traditionally, in engineering, statistical methods are used, methods assuming that we know the probability distribution of different uncertain parameters. Usually, we can safely linearize the dependence of the desired quantities y (e.g., stress at different structural points) on the… (More)

- S. A. Starks, V. Kreinovich, +7 authors R. Torres
- 2004

In many engineering applications, we have to combine probabilistic and interval errors. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In… (More)

- Jan Beck, Wolfgang Forstmeier
- Human nature
- 2007

The existence of superstition and religious beliefs in most, if not all, human societies is puzzling for behavioral ecology. These phenomena bring about various fitness costs ranging from burial objects to celibacy, and these costs are not outweighed by any obvious benefits. In an attempt to resolve this problem, we present a verbal model describing how… (More)

- Vladik Kreinovich, Gang Xiang, +8 authors Janos G. Hajagos
- Reliable Computing
- 2006

In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In… (More)

- Vladik Kreinovich, Luc Longpré, +6 authors Janos Hajagos
- 2004

In many areas of science and engineering, it is desirable to estimate statistical characteristics (mean, variance, covariance, etc.) under interval uncertainty. For example, we may want to use the measured values x(t) of a pollution level in a lake at different moments of time to estimate the average pollution level; however, we do not know the exact values… (More)

- Jan Beck, Marianne Böller, Andreas Erhardt, Wolfgang Schwanghart
- Ecological Informatics
- 2014

Due to measurement uncertainty, often, instead of the actual values xi of the measured quantities, we only know the intervals xi = [x̃i − ∆i, x̃i + ∆i], where x̃i is the measured value and ∆i is the upper bound on the measurement error (provided, e.g., by the manufacturer of the measuring instrument). These intervals can be viewed as random intervals, i.e.,… (More)

- J Benjamin Beck, Stuart J Rowan
- Journal of the American Chemical Society
- 2003

The use of metal ion-induced polymerizations of a ditopic ligand offers a facile route to the preparation of organic/inorganic hybrid materials. Such metallo-supramolecular polymers potentially offer the functionality of the metal ion along with the processibility of a polymer. We report, herein, the preparation of gellike metallo-supramolecular polymers… (More)

- V. Kreinovich, C. Ferregut, +4 authors S. A. Starks
- 2004

Typically, in engineering applications, we need to make decisions under uncertainty. In addition to measurement errors, some uncertainty comes from the fact that we do not know how exactly the engineering devices that we produced will be used: e.g., we have limits Li on the loads li in different rooms i, but we do not know how exactly these loads will be… (More)

- Wengui Weng, J Benjamin Beck, Alex M Jamieson, Stuart J Rowan
- Journal of the American Chemical Society
- 2006

Utilizing metal-ligand binding as the driving force for self-assembly of a ditopic ligand, which consists of a 2,6-bis-(1'-methylbenzimidazolyl)-4-oxypyridine moiety attached to either end of a penta(ethylene glycol) core, in the presence of a transition metal ion (Zn(II)) and a lanthanide metal ion (La(III)), we have achieved formation of… (More)