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Can Uncertainty Management be Realized in a Finite Totally Ordered Probability Algebra?
[article]
2013
arXiv
pre-print
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The investigation shows that a finite probability model may be of very limited usage. ...
In this paper, the feasibility of using finite totally ordered probability models under Alelinnas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. ...
Xiang was awarded a University Fellowship during the term of this work. The authors would like to thank R. Aleli unas for helping us to gain the understanding of his TPL. ...
arXiv:1304.1535v1
fatcat:s6nlsga3izdwtgztityf2xcmwm
Can Uncertainty Management Be Realized In A Finite Totally Ordered Probability Algebra?
[chapter]
1990
Machine Intelligence and Pattern Recognition
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In this paper, the feasibility of using finite totally ordered probability models under Aleliunas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. ...
The investigation shows that a finite probability model may be of very limited usage. The semantics of TPL is given by 'possible worlds'. ...
Xiang was awarded a University Fellowship during the term of this work. The authors would like to thank R. Aleliunas for helping us to gain the understanding of his TPL. ...
doi:10.1016/b978-0-444-88738-2.50011-7
fatcat:qq6jmgr4qzhaxlavyigqxhd32q
A probabilistic relational model and algebra
1996
ACM Transactions on Database Systems
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We present a revised relational structure and extend the relational algebra. The extended algebra ]s shown to be closed. ...
Uncertainty in data values. however, is pervasive in all real-world environments and has i-eceiv[,d muc}] attent)[]n in the literature, Several methods ha}! ...
Thanks are also in order for the associate editor, Hector Garcia-Molina, and the four anonymous reviewers of ACM Transactions on Database Systems; this paper has greatly benefited from their careful reading ...
doi:10.1145/232753.232796
fatcat:4oe2e2zadfgcnp5p7y6kejsfwu
Distributionally Robust Optimization: A review on theory and applications
2022
Numerical Algebra, Control and Optimization
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<p style='text-indent:20px;'>In this paper, we survey the primary research on the theory and applications of distributionally robust optimization (DRO). ...
Then, we illustrate some applications of DRO in machine learning and operations research, and finally, we discuss the future research directions.</p> ...
Probability measures are also called probability distributions, or just distributions. The triplet (Ξ, F, P ) is called a probability space. Denote B as Borel σ-algebra. ...
doi:10.3934/naco.2021057
fatcat:cluvjzkrhfbc7o2446fhjrmbji
Today's Computational Methods of Linear Algebra
1967
SIAM Review
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The reader is assumed to have a general familiarity with the algebra and analysis of finite vectors and matrices, including norms, and to know the Gaussian elimination process. ...
Far more extensive expositions of the computational methods of linear algebra are to be found in Fox [lU], Noble [U2], Householder [28], and Wilkinson [6l]. ...
The total effect turns out to be to reduce the 5/2 round-off error bound by a factor of n . ...
doi:10.1137/1009071
fatcat:kgd7xb6xhnawrlmmy4s3jhv6qy
Quantum Algebras in Nuclear Structure
[article]
1995
arXiv
pre-print
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Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. ...
After a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su_q(2) rotator model and its extensions, the construction of deformed exactly ...
Acknowledgements The authors are grateful to Constanca Providência for a careful reading of the manuscript. One of the authors (DB) has been supported by CEC under contract ERBCHBGCT930467. ...
arXiv:nucl-th/9512017v1
fatcat:vvhrva5x35dndbpogsm7eq2czq
At the Interface of Algebra and Statistics
[article]
2020
arXiv
pre-print
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Every joint probability distribution on a finite set can be modeled as a rank one density operator. ...
The starting point is a passage from classical probability theory to quantum probability theory. ...
Every joint probability distribution on a finite set can be modeled as a rank one density operator. ...
arXiv:2004.05631v1
fatcat:emb45gx4mvcghjk4zuvrgheefe
Fuzzy Algebraic Modeling of Spatiotemporal Timeseries' Paradoxes in Cosmic Scale Kinematics
2022
Mathematics
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This paper introduces the prototype of a generic fuzzy algebraic framework, that aims to serve as a holistic modeling approach of kinematics. ...
In the opposite case, we are gradually led to paradoxes and uncertainties. ...
The above Figure 3 clearly describes potential uncertainties and paradoxes that can be met in a CoSKiP kinematics phenomenon. ...
doi:10.3390/math10040622
fatcat:uwoqfkxgobardoehwtf44v5uly
Classical and Quantum Mechanics via Lie algebras
[article]
2011
arXiv
pre-print
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The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks ...
The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. ...
However, the exceptional simple Lie algebras can be realized as infinitesimal symmetry groups of some algebraic structure. ...
arXiv:0810.1019v2
fatcat:xnkg36c4djehpnkpbhsea2ri2q
Applications of Algebra and Coalgebra in Scientific Modelling
2010
Electronical Notes in Theoretical Computer Science
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In computer science, the algebra-coalgebra duality serves as a formal framework for connecting the perspectives of state-based and behavior-based models. ...
We explore modelling paradigms, in the sense of philosophy of science, as an intermediate step in translating the (co)algebraic framework from computer science into applications in ecology. ...
The complete space of possible behavior under human management can then be derived from its documented growth history. ...
doi:10.1016/j.entcs.2010.07.016
fatcat:vaxlidqu5rhd3fwh4i2ym3uxle
Randomized Numerical Linear Algebra: Foundations Algorithms
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2002.01387v2 fatcat:chbib4gpvbedtly2eudzhdi7tmOther Versions
machine learning and in scientific computing. ...
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. ...
application we need can be realized in Section 20.3. ...
arXiv:2002.01387v3
fatcat:kaqg3j55hzf6lobdqenuakqr3i
Linear Algebra with Disordered Sparse Matrices that have Spatial Structure: Theory and Computation
[article]
2004
arXiv
pre-print
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Following this review is a set of recommendations for better managing these problems. ...
model which generalizes Berry's model of wavefunctions in chaotic systems to include both localization and multifractality. (4) A proposal of a new sigma model for disordered systems which does not involve ...
can be managed fairly reliably. ...
arXiv:cond-mat/0411386v1
fatcat:lo2qkh5yazeubjdn6nwmmztq7e
An algebraic theory of portfolio allocation
2003
Economic Theory
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The key insight is that preferences over allocations can be partially ordered via majorized convex hulls that have been generated by group elements. ...
A diversified portfolio imposes symmetry on the allocation vector in order to balance out much of the asymmetries in the returns vector. ...
By contrast, C 3 ( r 1 , r 2 ,r 3 ) r i group generates a total ordering on the allocation vector. ...
doi:10.1007/s00199-002-0284-9
fatcat:a7l4u4k5grhkrkavlql6il7gde
D-algebra for composing access control policy decisions
2009
Proceedings of the 4th International Symposium on Information, Computer, and Communications Security - ASIACCS '09
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Compared to other algebrabased approaches aimed at policy composition, D-algebra is the only one that satisfies both functional completeness (any possible decision matrix can be expressed by a D-algebra ...
formula) and computational effectiveness (a formula can be computed efficiently given any decision matrix). ...
If there is an order, either a total order or a partial order, on D, 0 usually represents the minimal or the least element in D. ¬0 is another constant of D with a "complementary" meaning. ...
doi:10.1145/1533057.1533097
dblp:conf/ccs/NiBL09
fatcat:566vmz76jnfdrgkwsrkek2qj5i
Twenty years of rewriting logic
2012
The Journal of Logic and Algebraic Programming
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Rewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. ...
This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations ...
This work has been supported in part by NSF Grants CNS 07-16638, CNS 08-34709, CNS 08-31064, CNS 09-04749, and CCF 09-05584, AFOSR Grant FA8750-11-2-0084, and the "Programa de Apoyo a la Investigación ...
doi:10.1016/j.jlap.2012.06.003
fatcat:5tx4a5uxlvapfpf5fajozkbboi
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