1. 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 aEngagement of a
scientist with the objectscientist with the object
The ISSUE of UNCERTAINTY for HYDROLOGIC EVENTS inThe 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 University
Brookings, SD 57007Brookings, SD 57007--3510, USA3510, USA
Annual meeting:Annual meeting:
South Dakota Academy of ScienceSouth Dakota Academy of Science
April 14, 2012April 14, 2012
Vermilion, SD , USAVermilion, SD , USA
AbstractAbstract
To 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 rotate
b : a straight line with respect to which a body or figure is
symmetrical — called also axis of symmetry
c : 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
ReferencesReferences
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Hall, J., & Anderson, M. (2002). Handling uncertainty in extreme or unrepeatable hydrological
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Pappenberger, F., & Beven, K. J. (2006). Ignorance is bliss: Or seven reasons not to use
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Pidgeon, N., & Fischhoff, B. (2011). The role of social and decision sciences in communicating
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ResearcherResearcher –– ObjectObject –– DataData –– ModelsModels –– ResultsResults –– Stakeholder or ScholarStakeholder or Scholar
Communication of the resultsCommunication of the results
Mathematical modelingMathematical modeling
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