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|Title:||Clifford support vector machines for classification, regression, and recurrence|
De Guise, H.
Klimov, Andrei B.
De La Hoz, P.
|Abstract:||We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all of its polarization-transformed counterparts. By using the Hilbert-Schmidt metric, the resulting degree is a sum of two terms: one is the purity of the state and the other can be interpreted as a classical distinguishability, which can be experimentally determined in an interferometric setup. For transverse fields, this reduces to the standard approach, whereas it allows one to get a straight expression for nonparaxial fields. " 2014 American Physical Society.",,,,,,"10.1103/PhysRevA.90.013830",,,"http://hdl.handle.net/20.500.12104/40092","http://www.scopus.com/inward/record.url?eid=2-s2.0-84905189793&partnerID=40&md5=1fe15f223a6a0317bb79b1580c9e4236",,,,,,"1",,"Physical Review A - Atomic, Molecular, and Optical Physics",,,,"90",,"Scopus|
WOS",,,,,,,,,,,,"Classical distinguishability as an operational measure of polarization",,"Article" "41934","123456789/35008",,"Chumakov, S., Departamento de Física, Universidad de Guadalajara, Corregidora 500, Guadalajara, Jalisco, 44420, Mexico; Klimov, A.B., Departamento de Física, Universidad de Guadalajara, Corregidora 500, Guadalajara, Jalisco, 44420, Mexico; Saavedra, C., Departamento de Física, Universidad de Concepción, Casilla 4009, Concepción, Chile
Klimov, Andrei B., Universidad de Guadalajara. Centro Universitario de Ciencias Exactas e Ingenierías",,"Chumakov, S.
Klimov, Andrei B.
Saavedra, C.",,"1999",,"We have used an approximate dynamical symmetry of the Dicke model (quantum field interacting with the two-level atoms) to find an analytical solution in the presence of dissipation, see Eqs. (5.9)-(5.11) above. This solution reveals that some kind of coherent structure survives under dissipation. Namely, if the atoms are initially prepared in their semiclassical states, the state of the total system remains approximately factorized into the field and atomic parts (and thus keeps its purity). The evolution of the field part of the wave function recalls evolution of the Glauber coherent state interacting with the thermal bath at zero temperature. The evolution of an arbitrary initial atomic state can be completely described in terms of semiclassical atomic states.",,,,,,,,,"http://hdl.handle.net/20.500.12104/40155","http://www.scopus.com/inward/record.url?eid=2-s2.0-0033074631&partnerID=40&md5=ae0a10c866574cf8e922a0250baaf419",,,,,,"01-feb",,"Reports on Mathematical Physics",,"73
WOS",,,,,,,,,,,,"Coherent structures in quantum optical models with dissipation",,"Article" "41909","123456789/35008",,"García-Cruz, D., División de Genética, Guadalajara, Mexico; Cano-Colón, S., Depto. de Biología Celular, Inst. de Invest. Biomédicas, Univ. Nac. Auton. de México, México, Mexico; Sánchez-Corona, J., Div. de Medicina Molecular, Ctro. Invest. Biomedica de Occidente, Universidad de Guadalajara, Guadalajara, Mexico; Gallegos, M.P., División de Genética, Guadalajara, Mexico; Chimal-Monroy, J., Depto. de Biología Celular, Inst. de Invest. Biomédicas, Univ. Nac. Auton. de México, México, Mexico; Díaz-de-León, L., Depto. de Biología Celular, Inst. de Invest. Biomédicas, Univ. Nac. Auton. de México, México, Mexico, Depto. de Biología Celular, Inst. de Invest. Biomédicas, Univ. Nac. Auton. de México, C.U. Apartado Postal 70-228, C.P. 04510, México, Mexico",,"García-Cruz, D.
Diaz-de-Leon, L.",,"1998",,"A female with clinical features of familial articular hypermobility syndrome (FAHS) and her family were studied. The subject showed generalized hypermobility, except for a painful shoulder which presented functional limitation with a diagnosis of painful shoulder syndrome. Biochemical studies demonstrated that collagen and glycosaminoglycans (GAGs) contents from skin biopsies of the subject and her family were almost normal. Nevertheless, the densitometric analysis of electrophoretic patterns showed differences in the relative proportions of their collagenous components. They were characterized by changes in type I and III collagens and the presence of type V collagen, in the subject, her father and brother. Also, they presented changes in the types of GAGs, when compared with those of normal skin. Morphological studies revealed a general disorganization of dermal components, a loose collagen network characterized by thick bundles. Also, besides cellular elements, the presence of an abundant darkly staining material was observed. Biochemical and morphological findings permit us to suggest a connective tissue defect, initially described in the FAHS, otherwise known as Ehlers-Danlos syndrome (EDS) type XI.",,,,,,,,,"http://hdl.handle.net/20.500.12104/40130","http://www.scopus.com/inward/record.url?eid=2-s2.0-2642611094&partnerID=40&md5=5e9670fed73dbf568da5f884d3b8eca1
MEDLINE",,,,"Index Medicus;Adult;Collagen/an [Analysis];Ehlers-Danlos Syndrome/cl [Classification];Ehlers-Danlos Syndrome/pa [Pathology];Ehlers-Danlos Syndrome/pp [Physiopathology];Female;Glycosaminoglycans/an [Analysis];Humans;Joint Instability/pa [Pathology];Joint Instability/pp [Physiopathology];Male;Pedigree;Skin/ch [Chemistry];Skin/pa [Pathology]",,"Connective tissue; Ehlers-Danlos syndrome type XI; Glycosaminoglycans; Type I, III and V collagens",,,,,,"Clinical, morphological and biochemical features in the familial articular hypermobility syndrome (FAHS): A family study",,"Article" "41878","123456789/35008",,"Bayro-Corrochano, E.J., Department of Electrical Engineering and Computer Science, CINVESTAV Unidad Guadalajara, Jalisco 44430, Mexico; Arana-Daniel, N., Department of Computer Science, University of Guadalajara, Guadalajara, Jalisco 44430, Mexico",,"Bayro-Corrochano, E.J.
Arana-Daniel, N.",,"2010",,"This paper introduces the Clifford support vector machines (CSVM) as a generalization of the real and complex-valued support vector machines using the Clifford geometric algebra. In this framework, we handle the design of kernels involving the Clifford or geometric product. In this approach, one redefines the optimization variables as multivectors. This allows us to have a multivector as output. Therefore, we can represent multiple classes according to the dimension of the geometric algebra in which we work. We show that one can apply CSVM for classification and regression and also to build a recurrent CSVM. The CSVM is an attractive approach for the multiple input multiple output processing of high-dimensional geometric entities. We carried out comparisons between CSVM and the current approaches to solve multiclass classification and regression. We also study the performance of the recurrent CSVM with experiments involving time series. The authors believe that this paper can be of great use for researchers and practitioners interested in multiclass hypercomplex computing, particularly for applications in complex and quaternion signal and image processing, satellite control, neurocomputation, pattern recognition, computer vision, augmented virtual reality, robotics, and humanoids. " 2006 IEEE.
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