scholarly journals A linear-algebraic tool for conditional independence inference

2015 ◽  
Vol 6 (2) ◽  
Author(s):  
Kentaro Tanaka ◽  
Milan Studeny ◽  
Akimichi Takemura ◽  
Tomonari Sei
Keyword(s):  
Computational Result ◽  
Conditional Independence ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Positive Density ◽  
Implication Problem ◽  
Algebraic Tool ◽  
Linear Algebraic Method

In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables. 

Intersections of quotient rings and Prüfer v-multiplication domains

2016 ◽  
Vol 15 (08) ◽  
pp. 1650149 ◽  
Author(s):  
Said El Baghdadi ◽  
Marco Fontana ◽  
Muhammad Zafrullah
Keyword(s):  
Integral Domain ◽  
Algebraic Approach ◽  
Quotient Field ◽  
Topological Characterization ◽  
Locally Finite ◽  
Star Operation ◽  
Star Operations ◽  
Quotient Rings ◽  
Special Case

Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).

AN ALGEBRAIC APPROACH TO THE INTERACTION OF A THREE-LEVEL ATOM INTERACTING WITH QUANTIZED RADIATION FIELD

2000 ◽  
Vol 14 (14) ◽  
pp. 1459-1471
Author(s):  
XU-BO ZOU ◽  
JING-BO XU ◽  
XIAO-CHUN GAO ◽  
JIAN FU
Keyword(s):  
Algebraic Structure ◽  
Evolution Operator ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Time Evolution Operator ◽  
Level Atom ◽  
Unitary Transformations ◽  
Quantized Field ◽  
Quantized Radiation Field ◽  
Multiphoton Interaction

The system of a three-level atom in the Ξ configuration coupled to two quantized field modes with arbitrary detuning and density-dependent multiphoton interaction is studied by dynamical algebraic method. With the help of an su(3) algebraic structure, we diagonalize the Hamiltonian by making use of unitary transformations and obtain the eigenvalues, eigenstates and time evolution operator for the system. Based on this su(3) structure, we also show that the system of a three-level atom in the Ξ configuration can be exactly transformed to an effective two-level Hamiltonian by an unitary transformation. Finally, we show that there exist an su (N) algebraic structure in the system of a N-level atom interacting with N-1 field modes.

scholarly journals Ketercapaian dan Keterkontrolan Sistem Deskriptor Diskrit Linier Positif

2017 ◽  
Vol 3 (2) ◽  
pp. 65-73
Author(s):  
Yulia Retno Sari
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Algebraic Method ◽  
Discrete Systems ◽  
Descriptor System ◽  
Linear Algebraic Method

A positive discrete descriptor system has been widely used in modeling economics, engineering, chemistry and others. In this research, we studied the necessary conditions and sufficient conditions for a positive discrete descriptors system is achieved positive and controlled postively. In addition, it is also studied on sufficient terms and conditions which ensure that discrete systems are null controlled. By using linear algebraic method and Inverse Drazin, this research has proved several theorems for discrete descriptors system achieved positive, controlled positively and controlled null. In addition, examples are given as illustrations to reinforce the validity of the proven theorems.

scholarly journals On the conditional independence implication problem: A lattice-theoretic approach

2013 ◽  
Vol 202 ◽  
pp. 29-51 ◽  
Author(s):  
Mathias Niepert ◽  
Marc Gyssens ◽  
Bassem Sayrafi ◽  
Dirk Van Gucht
Keyword(s):  
Conditional Independence ◽  
Theoretic Approach ◽  
Implication Problem
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