Summary from Vapnik’s presentation“1. With the appearance of computers the concept of natural science, its methodology &

philosophy started a process of a paradigm change: The concepts, methodology, & philosophy of a Simple World move to very different concepts, philosophy & methodology of a Complex World.

2. In such changes an important role belongs to the mathematical facts that were discovered by analyzing the “Drosophila fly” of cognitive science the “Pattern recognition problem” & attempts to obtain their philosophical interpretation.

3. The results of these analyzes lead to methods that go beyond the classical concept of science: creating generative models of events & explain-ability of obtained rules. 4. The new paradigm introduces direct search for solution (transductive inference, instead of inductive), the meditative principle of decision making, & a unity of two languages for pattern

description: technical (rational) & holistic (irrational). This leads to the convergence of the exact science with humanities.5. The main difference between the new paradigm (developed in the computer era) & the classical one (developed before the computer era) is the claim:

To guarantee the success of inference one needs to control the complexity of algorithms for inference rather than complexity of the function that these algorithms produce. Algorithms with low complexity can create a complex function which will generalize well.”

Engagement of a Engagement of a scientist with the objectscientist with the object

The ISSUE of UNCERTAINTY for HYDROLOGIC EVENTS in The ISSUE of UNCERTAINTY for HYDROLOGIC EVENTS in the MISSOURI RIVER WATERSHED & the MISSOURI RIVER WATERSHED & the PROPERTIES of COORDINATE SYSTEM in USEthe PROPERTIES of COORDINATE SYSTEM in USE

Boris A. Shmagin, Boris A. Shmagin, Water Resources Institute, Water Resources Institute,

South Dakota State UniversitySouth Dakota State UniversityBrookings, SD 57007Brookings, SD 57007--3510, USA 3510, USA

Annual meeting: Annual meeting: South Dakota Academy of ScienceSouth Dakota Academy of ScienceApril 14, 2012April 14, 2012Vermilion, SD , USA Vermilion, SD , USA

AbstractAbstractTo deal (consider, study, describe, asses the rick) with hydrologic events (HE) such as flooding or drought the concept of uncertainty has to be clarified. The need for general theory of the uncertainty was introduced by Lofty Zadeh (2004-06). To move from the uncertainty as property for informational exchange in engineering systems (Zadeh, 2004-06) & mathematical theories (Dubois & Prade, 2009) to the uncertainty for HE, the uncertainty has to be considered as a part of knowledge & communication. We have to define the system under the consideration: researcher – object (natural as watershed & engineering as dam, levies) – models – results – stakeholder or scholar & then to trace the change of our knowledge in every of those double interactions. For the central part of this chain: “object – model –results”, - mathematical models may be used. For connections in the beginning & the end (“researcher – object” & “results – stakeholder”) concepts and approaches have to be developed. In other words, scientist working in hydrology has to define & handle the uncertainty & communicate the knowledge about time-spatial variability of the HE. The definition & properties of coordinates systems in use have to be developed and then the uncertainty of HE in given river watershed may be evaluated. The Missouri River watershed (MRW) was under the consideration with the approach of statistical learning (SL) & use of the Vapnik –Chervonkis dimension. SL allows present on the basis of mathematical models (empirical principal components, linear multi-regressions, simplified Fourier, shifts): (1) the multidimensional time-spatial variability of HE in MRW, (2) the “recovered” regionalization & seasonality of river discharge in MRW, (3) the variability & telleconnections for typical inside the units of regionalization time-series. The models affiliate with different coordinate systems to reflect 30% - 78% of variability of existed empirical data. Those numbers from mathematical models may be used to bring the concept of the knowledge & uncertainty to the stakeholders. Defining the uncertainty for HE based on use of SL opens the way for a variety of disciplines for the development of an artificial intelligence approach to analyze the interaction of HE, engineering installations & social systems in MRW including the concepts of risk assessment.

Ideal (math) axis:a : a straight line about which a body or a geometric figure

rotates or may be supposed to rotateb : a straight line with respect to which a body or figure is

symmetrical — called also axis of symmetryc : a straight line that bisects at right angles a system of parallel chords of a curve & divides the curve into two symmetrical parts

d : one of the reference lines of a coordinate system math technological (engineering) scientific

ReferencesReferencesAjami, N. K., Hornberger, G. M., & Sunding, D. L. (2008). Sustainable water resource management under hydrological uncertainty. Water Resources Research, 44(11), 1-10. Beven, K. (2007). Towards integrated environmental models of everywhere: uncertainty, data and modelling as a learning process. Hydrology and Earth System Sciences, 11(1), 460-467. Budescu, D. V., Broomell, S., & Por, H.-H. (2009). Improving communication of uncertainty in the reports of the intergovernmental panel on climate change. Psychological science, 20(3), 299-308. Hall, J., & Anderson, M. (2002). Handling uncertainty in extreme or unrepeatable hydrological processes?the need for an alternative paradigm. Hydrological Processes, 16(9), 1867-1870. Pappenberger, F., & Beven, K. J. (2006). Ignorance is bliss: Or seven reasons not to use uncertainty analysis. Water Resources Research, 42(5), 1-8. Pidgeon, N., & Fischhoff, B. (2011). The role of social and decision sciences in communicating uncertain climate risks. Nature Climate Change, 1(1), 35-41. Zadeh, L. a. (2005). Toward a generalized theory of uncertainty (GTU) - an outline. Information Sciences, 172(1-2), 1-40.

Researcher Researcher –– Object Object –– Data Data –– Models Models –– Results Results –– Stakeholder or Scholar Stakeholder or Scholar

Communication of the results Communication of the results

Mathematical modeling Mathematical modeling

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