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Can Uncertainty Management be Realized in a Finite Totally Ordered Probability Algebra?
[article]

2013
*
arXiv
*
pre-print

The investigation shows that

arXiv:1304.1535v1
fatcat:s6nlsga3izdwtgztityf2xcmwm
*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. ...##
###
Can Uncertainty Management Be Realized In A Finite Totally Ordered Probability Algebra?
[chapter]

1990
*
Machine Intelligence and Pattern Recognition
*

*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. ...

##
###
A probabilistic relational model and algebra

1996
*
ACM Transactions on Database Systems
*

We present

doi:10.1145/232753.232796
fatcat:4oe2e2zadfgcnp5p7y6kejsfwu
*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 ...##
###
Distributionally Robust Optimization: A review on theory and applications

2022
*
Numerical Algebra, Control and Optimization
*

<p style='text-indent:20px;'>

doi:10.3934/naco.2021057
fatcat:cluvjzkrhfbc7o2446fhjrmbji
*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*. ...##
###
Today's Computational Methods of Linear Algebra

1967
*
SIAM Review
*

The reader is assumed to have

doi:10.1137/1009071
fatcat:kgd7xb6xhnawrlmmy4s3jhv6qy
*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 . ...##
###
Quantum Algebras in Nuclear Structure
[article]

1995
*
arXiv
*
pre-print

Quantum

arXiv:nucl-th/9512017v1
fatcat:vvhrva5x35dndbpogsm7eq2czq
*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. ...##
###
At the Interface of Algebra and Statistics
[article]

2020
*
arXiv
*
pre-print

Every joint

arXiv:2004.05631v1
fatcat:emb45gx4mvcghjk4zuvrgheefe
*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. ...##
###
Fuzzy Algebraic Modeling of Spatiotemporal Timeseries' Paradoxes in Cosmic Scale Kinematics

2022
*
Mathematics
*

This paper introduces the prototype of

doi:10.3390/math10040622
fatcat:uwoqfkxgobardoehwtf44v5uly
*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. ...##
###
Classical and Quantum Mechanics via Lie algebras
[article]

2011
*
arXiv
*
pre-print

The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments

arXiv:0810.1019v2
fatcat:xnkg36c4djehpnkpbhsea2ri2q
*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. ...##
###
Applications of Algebra and Coalgebra in Scientific Modelling

2010
*
Electronical Notes in Theoretical Computer Science
*

*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. ...

##
###
Randomized Numerical Linear Algebra: Foundations Algorithms
[article]

2021
*
arXiv
*
pre-print

machine learning and

arXiv:2002.01387v3
fatcat:kaqg3j55hzf6lobdqenuakqr3i
*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. ...##
###
Linear Algebra with Disordered Sparse Matrices that have Spatial Structure: Theory and Computation
[article]

2004
*
arXiv
*
pre-print

Following this review is

arXiv:cond-mat/0411386v1
fatcat:lo2qkh5yazeubjdn6nwmmztq7e
*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. ...##
###
An algebraic theory of portfolio allocation

2003
*
Economic Theory
*

The key insight is that preferences over allocations

doi:10.1007/s00199-002-0284-9
fatcat:a7l4u4k5grhkrkavlql6il7gde
*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. ...##
###
D-algebra for composing access control policy decisions

2009
*
Proceedings of the 4th International Symposium on Information, Computer, and Communications Security - ASIACCS '09
*

Compared to other algebrabased approaches aimed at policy composition, D-

doi:10.1145/1533057.1533097
dblp:conf/ccs/NiBL09
fatcat:566vmz76jnfdrgkwsrkek2qj5i
*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. ...##
###
Twenty years of rewriting logic

2012
*
The Journal of Logic and Algebraic Programming
*

Rewriting logic is

doi:10.1016/j.jlap.2012.06.003
fatcat:5tx4a5uxlvapfpf5fajozkbboi
*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 ...
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