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Totally unimodular nets.
Eon JG, Proserpio DM, Blatov VA. Eon JG, et al. Acta Crystallogr A. 2012 Mar;68(Pt 2):286-94. doi: 10.1107/S0108767312000062. Epub 2012 Feb 16. Acta Crystallogr A. 2012. PMID: 22338663
A net is called totally unimodular whenever every sub-determinant of M belongs to the set {-1, 0, 1}. ...It is shown that many totally unimodular nets frequently occur in crystal structures....
A net is called totally unimodular whenever every sub-determinant of M belongs to the set {-1, 0, 1}. ...It is shown that many totall …
First-order optical systems with unimodular eigenvalues.
Bastiaans MJ, Alieva T. Bastiaans MJ, et al. J Opt Soc Am A Opt Image Sci Vis. 2006 Aug;23(8):1875-83. doi: 10.1364/josaa.23.001875. J Opt Soc Am A Opt Image Sci Vis. 2006. PMID: 16835644 Free article.
It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices …
It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has on …
INFORMATION-THEORETIC INEQUALITIES ON UNIMODULAR LIE GROUPS.
Chirikjian GS. Chirikjian GS. J Geom Mech. 2010 Jun 1;2(2):119-158. doi: 10.3934/jgm.2010.2.119. J Geom Mech. 2010. PMID: 21113416 Free PMC article.
All commutative groups are unimodular. And even in noncommutative cases unimodular Lie groups share many of the useful features of Euclidean space. The rotation and Euclidean motion groups, which are perhaps the most relevant Lie groups to problems in geometric mech …
All commutative groups are unimodular. And even in noncommutative cases unimodular Lie groups share many of the useful feature …
Copy number evolution with weighted aberrations in cancer.
Zeira R, Raphael BJ. Zeira R, et al. Bioinformatics. 2020 Jul 1;36(Suppl_1):i344-i352. doi: 10.1093/bioinformatics/btaa470. Bioinformatics. 2020. PMID: 32657354 Free PMC article.
This algorithm is based on the observation that the constraint matrix of the underlying optimization problem is totally unimodular. ...
This algorithm is based on the observation that the constraint matrix of the underlying optimization problem is totally unimodular …
Learning by criterion optimization on a unitary unimodular matrix group.
Fiori S. Fiori S. Int J Neural Syst. 2008 Apr;18(2):87-103. doi: 10.1142/S0129065708001415. Int J Neural Syst. 2008. PMID: 18452244
The present manuscript aims at illustrating fundamental challenges and solutions arising in the design of learning theories by optimization on manifolds in the context of complex-valued neural systems. The special case of a unitary unimodular group of matrices is dealt wit …
The present manuscript aims at illustrating fundamental challenges and solutions arising in the design of learning theories by optimization …
Feature selection with redundancy-constrained class separability.
Zhou L, Wang L, Shen C. Zhou L, et al. IEEE Trans Neural Netw. 2010 May;21(5):853-8. doi: 10.1109/TNN.2010.2044189. Epub 2010 Mar 11. IEEE Trans Neural Netw. 2010. PMID: 20227975
Scatter-matrix-based class separability is a simple and efficient feature selection criterion in the literature. ...To ensure the algorithm's efficiency and scalability, we study the characteristic of the constraints with which the resulted constrained 0-1 optimization can …
Scatter-matrix-based class separability is a simple and efficient feature selection criterion in the literature. ...To ensure the alg …
Shear representations of beam transfer matrices.
Başkal S, Kim YS. Başkal S, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2001 May;63(5 Pt 2):056606. doi: 10.1103/PhysRevE.63.056606. Epub 2001 Apr 13. Phys Rev E Stat Nonlin Soft Matter Phys. 2001. PMID: 11415030
The beam transfer matrix, often called the ABCD matrix, is one of the essential mathematical instruments in optics. It is a unimodular matrix whose determinant is 1. If all the elements are real with three independent parameters, this matrix is …
The beam transfer matrix, often called the ABCD matrix, is one of the essential mathematical instruments in optics. It is a …