rafael Bernal herrera - Academia.edu (original) (raw)
Papers by rafael Bernal herrera
Abstract. We consider an extension of the standard model based on the group U(2) × U(3), which is... more Abstract. We consider an extension of the standard model based on the group U(2) × U(3), which is naturally compatible with the standard model interacting-particle representations and the spontaneous symmetry breaking of U(2) × U(3) to an electrostrong U(3). In its minimal version, the model only adds one extra U(1) gauge boson and it implies that the hypercharge is distributed between the factors of the hyperweak and hyperstrong forces. We show that the anomaly cancellation condition can be solved by adding exotic fermions associated with a 16-dimensional representation of U(2)×U(3). A brief discussion of the mechanism of the spontaneous breakdown of U(2) ×U(3) in the gauge boson sector is given.
We study simply-connected irreducible non-locally symmetric pseudo-Riemannian Spin(q) manifolds a... more We study simply-connected irreducible non-locally symmetric pseudo-Riemannian Spin(q) manifolds admitting parallel quaternionic spinors
Applied and Computational Mechanics, 2020
While the Discrete Exterior Calculus (DEC) discretization of the diffusive term of the Trans- por... more While the Discrete Exterior Calculus (DEC) discretization of the diffusive term of the Trans- port Equation is well understood, the DEC discretization of the convective term, as well as its stabilization, is an ongoing area of research. In this paper, we propose a local discretization for this term based on DEC and geometric arguments, assuming the particle velocity field is prescribed at the vertices of the primal mesh. Since this formulation is similar to that of the Finite Element Method with linear interpolation functions (FEML), this numerical scheme can be stabilized us- ing known stabilization techniques, such as Artificial Diffusion. Using this stabilizaton technique, numerical tests are carried out on simple problems with domains discretized with coarse and fine simplicial meshes to show numerical convergence for stationary and transient problems.
Iniciação Científica Cesumar, 2008
Originally intended for business management, THE information systems help organizations for them ... more Originally intended for business management, THE information systems help organizations for them to be competitive. Focused on analyzing information to assist in decision-making, these systems have grown, and today are evolving into information systems technology. Considering itself as a system and as a set of organized elements with a common view, several market areas can fit themselves in this definition and have the benefit. One of the areas that most need help now is dentistry, since a large number of newly trained dentists are being added to this market every year, making this area a very competitive business. The main objective of this project is to include dentistry in the current challenging market through information systems technology specially developed for this health area. It also was a bibliographical study that helped in the development of a specific information system for dentistry. This information system was built through the collection and analysis of data from a ...
Complex Manifolds, 2020
We present a binary code for spinors and Clifford multiplication using non-negative integers and ... more We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of Spin(8), explicit representations of the Lie algebras 𝔰𝔭𝔦𝔶 (8), 𝔰𝔭𝔦𝔶 (7) and 𝔤2, etc.
Numerical Linear Algebra with Applications, 2020
In this paper, we present a reliable hybrid algorithm for solving convex quadratic minimization p... more In this paper, we present a reliable hybrid algorithm for solving convex quadratic minimization problems. At the k-th iteration, two points are computed: first, an auxiliary pointẋ k is generated by performing a gradient step using an optimal steplength, and secondly, the next iterate x k+1 is obtained by means of weighted sum ofẋ k with the penultimate iterate x k−1. The coefficient of the linear combination is computed by minimizing the residual norm along the line determined by the previous points. In particular, we adopt an optimal, non-delayed steplength in the first step and then use a smoothing technique to impose a delay on the scheme. Under a modest assumption, we show that our algorithm is Q-linearly convergent to the unique solution of the problem. Finally, we report numerical experiments on strictly convex quadratic problems, showing that the proposed method is competitive in terms of CPU-time and iterations with the conjugate gradient method. KEYWORDS Gradient methods, convex quadratic optimization and linear system of equations.
Symmetry, Integrability and Geometry: Methods and Applications, 2019
We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the ... more We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special Kähler holonomy. Motivated by certain curvature identities satisfied by manifolds admitting parallel twisted pure spinors, we also introduce the Clifford monopole equations as a natural geometric generalization of the Seiberg-Witten equations. We show that they restrict to the Seiberg-Witten equations in 4 dimensions, and that they admit non-trivial solutions on manifolds with special Riemannian holonomy.
The Journal of Geometric Analysis, 2017
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we ... more We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin c,r structure carrying a partially pure spinor field. We study various integrability conditions of the almost CR structure in our spinorial setup, including the classical integrability of a CR structure as well as those implied by Killing-type conditions on the partially pure spinor field. In the codimension one case, we develop a spinorial description of strictly pseudoconvex CR manifolds, metric contact manifolds and Sasakian manifolds. Finally, we study hypersurfaces of Kähler manifolds via partially pure Spin c spinors.
Symmetry, Integrability and Geometry: Methods and Applications, 2017
We prove the rigidity and vanishing of several indices of "geometrically natural" twisted Dirac o... more We prove the rigidity and vanishing of several indices of "geometrically natural" twisted Dirac operators on almost even-Clifford Hermitian manifolds admitting circle actions by automorphisms.
The Quarterly Journal of Mathematics, 2017
We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when su... more We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures.
Journal of Differential Geometry, 2012
The article "Â-genus on non-spin manifolds with S 1 actions and the classification of positive qu... more The article "Â-genus on non-spin manifolds with S 1 actions and the classification of positive quaternion-Kähler 12-manifolds" [3] contains an error in Lemma 2 of Part I, since an assumption on the finiteness of the second homotopy group is not sufficient to reach the desired conclusion. This error stems from an incorrect application of Theorem V in [2], and we thank M. Amann and A. Dessai for pointing it out (see [1]). An additional hypothesis of finiteness of the fourth homotopy group proves to be enough to correct Lemma 2 and, therefore, Theorems 1 and 3 that depend on it. We also thank M. Amann and A. Dessai [1] for this observation. On the other hand, Theorem 2 depends on the original version of Theorem 1 and, therefore, its proof is not complete. We note that the fourth homotopy group of the real Grassmannian of oriented 4-planes in R 7 , a positive quaternion-Kähler 12-manifold, is not finite.
We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex... more We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of Le-Brun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.
Proceedings of the American Mathematical Society, 2016
We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a l... more We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a large automorphism group. We classify them when they are simply connected and the dimension of the automorphism group is maximal, and also prove a gap theorem for the dimension of the automorphism group.
We present a formula for the trace of any symmetric power of a ntimesnn\times nntimesn matrix (with coefficie... more We present a formula for the trace of any symmetric power of a ntimesnn\times nntimesn matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and n−2n-2n−2 polynomial functions defined recursively.
Journal of Geometry and Physics, 2015
We determine the centralizers of certain isomorphic copies of spin subalgebras spin(r) in so(drm)... more We determine the centralizers of certain isomorphic copies of spin subalgebras spin(r) in so(drm), where dr is the dimension of a real irreducible representation of Cl 0 r , the even Clifford algebra determined by the positive definite inner product on R r , where r, m ∈ N.
Cell growth & differentiation : the molecular biology journal of the American Association for Cancer Research, 2000
IFN-gamma-mediated growth inhibition requires signal transducers and activators of transcription ... more IFN-gamma-mediated growth inhibition requires signal transducers and activators of transcription (STAT)-1 activation and may require induction of the cyclin-dependent kinase inhibitor p21. Using an electrophoretic mobility shift assay, we identified STAT1 activation after IFN-gamma treatment in breast cancer cell lines. Accordingly, IFN-gamma inhibited proliferation of monolayer cultured MCF-7 and MDA-MB-231 breast cancer cells. Interestingly, IFN-gamma inhibited anchorage-independent growth of MCF-7 cells but had no effect on MDA-MB-231 colony formation. Because p21 has been shown to play a role in anchorage-independent growth and is a transcriptional target of STAT1, we examined the effect of IFN-gamma on p21 mRNA. We found that IFN-gamma induced p21 mRNA in MCF-7 cells but not in MDA-MB-231 cells. Furthermore, IFN-gamma induced activation of a p21 promoter-luciferase reporter construct that contained the STAT1-inducible element in MCF-7 cells, but not in MDA-MB-231 cells. IFN-gam...
Topology and its Applications, 2010
We prove the vanishing of higher A-genera, in the sense of Browder and Hsiang [4], on smooth S 1-... more We prove the vanishing of higher A-genera, in the sense of Browder and Hsiang [4], on smooth S 1-manifolds with finite π 2 and π 4 .
Topology and its Applications, 2004
We prove the vanishing of various characteristic numbers, such as the signature and the A-genus, ... more We prove the vanishing of various characteristic numbers, such as the signature and the A-genus, on manifolds with finite second homotopy group and which admit smooth S 1-actions. More precisely, we prove the vanishing of various coefficientes of the elliptic genus on non-spin π 2-finite manifolds when the S 1-action either satisfies a "parity" condition or has isolated fixed points only.
![Research paper thumbnail of Erratum to “The signature and the elliptic genus of -finite manifolds with circle actions” [Topology Appl. 136 (1–3) (2004) 251–259]](https://attachments.academia-assets.com/102806214/thumbnails/1.jpg)
](Topology and its Applications, 2010
Erratum Erratum to "The signature and the elliptic genus of π 2-finite manifolds with circle acti... more Erratum Erratum to "The signature and the elliptic genus of π 2-finite manifolds with circle actions" [Topology Appl. 136 (1-3) (2004) 251-259]
Molecular Endocrinology, 2003
Repression of the transcriptional activities of the estrogen receptor (ER) is a main goal in the ... more Repression of the transcriptional activities of the estrogen receptor (ER) is a main goal in the treatment of breast cancer. The antiestrogen tamoxifen is an effective therapy for breast cancer patients because it inhibits estrogen-stimulated gene expression and cell proliferation. Previous studies have implicated a complex containing the nuclear receptor corepressor (N-CoR) in the mechanism by which tamoxifen represses ER-mediated transcriptional activity. In the present study a truncated N-CoR construct was used to inhibit endogenous N-CoR activity in an ER-positive breast cancer cell line. This dominant-negative N-CoR was successful in relieving repression conferred by the unliganded retinoic acid receptor, but it failed to affect the transcriptional activity of the ER in the presence of tamoxifen. Correspondingly, the histone acetylation levels of nucleosomes on endogenous estrogen-responsive genes were unaltered in cells expressing the N-CoR dominant-negative, regardless of ligand. In addition, in vitro cell proliferation and in vivo tumor growth were unchanged in cells that express dominant-negative N-CoR. In conclusion, these results may reveal that N-CoR affects tamoxifen-liganded ER in a manner distinct from its influence on retinoic acid receptor-mediated transcriptional activity or that corepressors other than N-CoR may be involved in the ability of tamoxifen to repress estrogen-responsive transcription and tumor growth.
Abstract. We consider an extension of the standard model based on the group U(2) × U(3), which is... more Abstract. We consider an extension of the standard model based on the group U(2) × U(3), which is naturally compatible with the standard model interacting-particle representations and the spontaneous symmetry breaking of U(2) × U(3) to an electrostrong U(3). In its minimal version, the model only adds one extra U(1) gauge boson and it implies that the hypercharge is distributed between the factors of the hyperweak and hyperstrong forces. We show that the anomaly cancellation condition can be solved by adding exotic fermions associated with a 16-dimensional representation of U(2)×U(3). A brief discussion of the mechanism of the spontaneous breakdown of U(2) ×U(3) in the gauge boson sector is given.
We study simply-connected irreducible non-locally symmetric pseudo-Riemannian Spin(q) manifolds a... more We study simply-connected irreducible non-locally symmetric pseudo-Riemannian Spin(q) manifolds admitting parallel quaternionic spinors
Applied and Computational Mechanics, 2020
While the Discrete Exterior Calculus (DEC) discretization of the diffusive term of the Trans- por... more While the Discrete Exterior Calculus (DEC) discretization of the diffusive term of the Trans- port Equation is well understood, the DEC discretization of the convective term, as well as its stabilization, is an ongoing area of research. In this paper, we propose a local discretization for this term based on DEC and geometric arguments, assuming the particle velocity field is prescribed at the vertices of the primal mesh. Since this formulation is similar to that of the Finite Element Method with linear interpolation functions (FEML), this numerical scheme can be stabilized us- ing known stabilization techniques, such as Artificial Diffusion. Using this stabilizaton technique, numerical tests are carried out on simple problems with domains discretized with coarse and fine simplicial meshes to show numerical convergence for stationary and transient problems.
Iniciação Científica Cesumar, 2008
Originally intended for business management, THE information systems help organizations for them ... more Originally intended for business management, THE information systems help organizations for them to be competitive. Focused on analyzing information to assist in decision-making, these systems have grown, and today are evolving into information systems technology. Considering itself as a system and as a set of organized elements with a common view, several market areas can fit themselves in this definition and have the benefit. One of the areas that most need help now is dentistry, since a large number of newly trained dentists are being added to this market every year, making this area a very competitive business. The main objective of this project is to include dentistry in the current challenging market through information systems technology specially developed for this health area. It also was a bibliographical study that helped in the development of a specific information system for dentistry. This information system was built through the collection and analysis of data from a ...
Complex Manifolds, 2020
We present a binary code for spinors and Clifford multiplication using non-negative integers and ... more We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of Spin(8), explicit representations of the Lie algebras 𝔰𝔭𝔦𝔶 (8), 𝔰𝔭𝔦𝔶 (7) and 𝔤2, etc.
Numerical Linear Algebra with Applications, 2020
In this paper, we present a reliable hybrid algorithm for solving convex quadratic minimization p... more In this paper, we present a reliable hybrid algorithm for solving convex quadratic minimization problems. At the k-th iteration, two points are computed: first, an auxiliary pointẋ k is generated by performing a gradient step using an optimal steplength, and secondly, the next iterate x k+1 is obtained by means of weighted sum ofẋ k with the penultimate iterate x k−1. The coefficient of the linear combination is computed by minimizing the residual norm along the line determined by the previous points. In particular, we adopt an optimal, non-delayed steplength in the first step and then use a smoothing technique to impose a delay on the scheme. Under a modest assumption, we show that our algorithm is Q-linearly convergent to the unique solution of the problem. Finally, we report numerical experiments on strictly convex quadratic problems, showing that the proposed method is competitive in terms of CPU-time and iterations with the conjugate gradient method. KEYWORDS Gradient methods, convex quadratic optimization and linear system of equations.
Symmetry, Integrability and Geometry: Methods and Applications, 2019
We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the ... more We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special Kähler holonomy. Motivated by certain curvature identities satisfied by manifolds admitting parallel twisted pure spinors, we also introduce the Clifford monopole equations as a natural geometric generalization of the Seiberg-Witten equations. We show that they restrict to the Seiberg-Witten equations in 4 dimensions, and that they admit non-trivial solutions on manifolds with special Riemannian holonomy.
The Journal of Geometric Analysis, 2017
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we ... more We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin c,r structure carrying a partially pure spinor field. We study various integrability conditions of the almost CR structure in our spinorial setup, including the classical integrability of a CR structure as well as those implied by Killing-type conditions on the partially pure spinor field. In the codimension one case, we develop a spinorial description of strictly pseudoconvex CR manifolds, metric contact manifolds and Sasakian manifolds. Finally, we study hypersurfaces of Kähler manifolds via partially pure Spin c spinors.
Symmetry, Integrability and Geometry: Methods and Applications, 2017
We prove the rigidity and vanishing of several indices of "geometrically natural" twisted Dirac o... more We prove the rigidity and vanishing of several indices of "geometrically natural" twisted Dirac operators on almost even-Clifford Hermitian manifolds admitting circle actions by automorphisms.
The Quarterly Journal of Mathematics, 2017
We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when su... more We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures.
Journal of Differential Geometry, 2012
The article "Â-genus on non-spin manifolds with S 1 actions and the classification of positive qu... more The article "Â-genus on non-spin manifolds with S 1 actions and the classification of positive quaternion-Kähler 12-manifolds" [3] contains an error in Lemma 2 of Part I, since an assumption on the finiteness of the second homotopy group is not sufficient to reach the desired conclusion. This error stems from an incorrect application of Theorem V in [2], and we thank M. Amann and A. Dessai for pointing it out (see [1]). An additional hypothesis of finiteness of the fourth homotopy group proves to be enough to correct Lemma 2 and, therefore, Theorems 1 and 3 that depend on it. We also thank M. Amann and A. Dessai [1] for this observation. On the other hand, Theorem 2 depends on the original version of Theorem 1 and, therefore, its proof is not complete. We note that the fourth homotopy group of the real Grassmannian of oriented 4-planes in R 7 , a positive quaternion-Kähler 12-manifold, is not finite.
We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex... more We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of Le-Brun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.
Proceedings of the American Mathematical Society, 2016
We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a l... more We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a large automorphism group. We classify them when they are simply connected and the dimension of the automorphism group is maximal, and also prove a gap theorem for the dimension of the automorphism group.
We present a formula for the trace of any symmetric power of a ntimesnn\times nntimesn matrix (with coefficie... more We present a formula for the trace of any symmetric power of a ntimesnn\times nntimesn matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and n−2n-2n−2 polynomial functions defined recursively.
Journal of Geometry and Physics, 2015
We determine the centralizers of certain isomorphic copies of spin subalgebras spin(r) in so(drm)... more We determine the centralizers of certain isomorphic copies of spin subalgebras spin(r) in so(drm), where dr is the dimension of a real irreducible representation of Cl 0 r , the even Clifford algebra determined by the positive definite inner product on R r , where r, m ∈ N.
Cell growth & differentiation : the molecular biology journal of the American Association for Cancer Research, 2000
IFN-gamma-mediated growth inhibition requires signal transducers and activators of transcription ... more IFN-gamma-mediated growth inhibition requires signal transducers and activators of transcription (STAT)-1 activation and may require induction of the cyclin-dependent kinase inhibitor p21. Using an electrophoretic mobility shift assay, we identified STAT1 activation after IFN-gamma treatment in breast cancer cell lines. Accordingly, IFN-gamma inhibited proliferation of monolayer cultured MCF-7 and MDA-MB-231 breast cancer cells. Interestingly, IFN-gamma inhibited anchorage-independent growth of MCF-7 cells but had no effect on MDA-MB-231 colony formation. Because p21 has been shown to play a role in anchorage-independent growth and is a transcriptional target of STAT1, we examined the effect of IFN-gamma on p21 mRNA. We found that IFN-gamma induced p21 mRNA in MCF-7 cells but not in MDA-MB-231 cells. Furthermore, IFN-gamma induced activation of a p21 promoter-luciferase reporter construct that contained the STAT1-inducible element in MCF-7 cells, but not in MDA-MB-231 cells. IFN-gam...
Topology and its Applications, 2010
We prove the vanishing of higher A-genera, in the sense of Browder and Hsiang [4], on smooth S 1-... more We prove the vanishing of higher A-genera, in the sense of Browder and Hsiang [4], on smooth S 1-manifolds with finite π 2 and π 4 .
Topology and its Applications, 2004
We prove the vanishing of various characteristic numbers, such as the signature and the A-genus, ... more We prove the vanishing of various characteristic numbers, such as the signature and the A-genus, on manifolds with finite second homotopy group and which admit smooth S 1-actions. More precisely, we prove the vanishing of various coefficientes of the elliptic genus on non-spin π 2-finite manifolds when the S 1-action either satisfies a "parity" condition or has isolated fixed points only.
Topology and its Applications, 2010
Erratum Erratum to "The signature and the elliptic genus of π 2-finite manifolds with circle acti... more Erratum Erratum to "The signature and the elliptic genus of π 2-finite manifolds with circle actions" [Topology Appl. 136 (1-3) (2004) 251-259]
Molecular Endocrinology, 2003
Repression of the transcriptional activities of the estrogen receptor (ER) is a main goal in the ... more Repression of the transcriptional activities of the estrogen receptor (ER) is a main goal in the treatment of breast cancer. The antiestrogen tamoxifen is an effective therapy for breast cancer patients because it inhibits estrogen-stimulated gene expression and cell proliferation. Previous studies have implicated a complex containing the nuclear receptor corepressor (N-CoR) in the mechanism by which tamoxifen represses ER-mediated transcriptional activity. In the present study a truncated N-CoR construct was used to inhibit endogenous N-CoR activity in an ER-positive breast cancer cell line. This dominant-negative N-CoR was successful in relieving repression conferred by the unliganded retinoic acid receptor, but it failed to affect the transcriptional activity of the ER in the presence of tamoxifen. Correspondingly, the histone acetylation levels of nucleosomes on endogenous estrogen-responsive genes were unaltered in cells expressing the N-CoR dominant-negative, regardless of ligand. In addition, in vitro cell proliferation and in vivo tumor growth were unchanged in cells that express dominant-negative N-CoR. In conclusion, these results may reveal that N-CoR affects tamoxifen-liganded ER in a manner distinct from its influence on retinoic acid receptor-mediated transcriptional activity or that corepressors other than N-CoR may be involved in the ability of tamoxifen to repress estrogen-responsive transcription and tumor growth.