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Joël Tossa

Université d'abomey-Calavi, Institut de Mathématiques et de Sciences Physiques (IMSP), Faculty Member

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Papers by Joël Tossa

Locally Rotationally Symmetric Bianchi Type-II Magnetized String Cosmological Model with Bulk Viscous Fluid in General Relativity

Chinese Physics Letters, 2011

The locally rotationally symmetric Bianchi type-II magnetized string cosmological model with bulk... more

L H  L M  C S P C

In this paper, we generalize the Cartan’s fundamental formula on lightlike hypersurfaces, then we... more

Gray Tensors on Lightlike Hypersurfaces

This paper introduces Gray-tensors on lightlike hypersurfaces M n+1 of signature (0, n), (n ≥ 1) ... more This paper introduces Gray-tensors on lightlike hypersurfaces M n+1 of signature (0, n), (n ≥ 1) and investigates on their basic properties in connec- tion with their null geometry. In particular, we show that there is an interplay between existence of Gray-tensors of certain type and lightlike warped product structures. As a physical relevance, we show that there exists such a tensor on both globally Killing horizons (GKH) and totally geodesic lightlike triple warped product hypersurfaces.

Automatic Localization of Five Relevant Dermoscopic Structures Based on YOLOv8 for Diagnosis Improvement

Journal of Imaging

The automatic detection of dermoscopic features is a task that provides the specialists with an i... more The automatic detection of dermoscopic features is a task that provides the specialists with an image with indications about the different patterns present in it. This information can help them fully understand the image and improve their decisions. However, the automatic analysis of dermoscopic features can be a difficult task because of their small size. Some work was performed in this area, but the results can be improved. The objective of this work is to improve the precision of the automatic detection of dermoscopic features. To achieve this goal, an algorithm named yolo-dermoscopic-features is proposed. The algorithm consists of four points: (i) generate annotations in the JSON format for supervised learning of the model; (ii) propose a model based on the latest version of Yolo; (iii) pre-train the model for the segmentation of skin lesions; (iv) train five models for the five dermoscopic features. The experiments are performed on the ISIC 2018 task2 dataset. After training, t...

Décalage de l'enseignement de ‘’direction’’ et de ‘’sens’’ et introduction du vecteur géométrique en classe de 4e

Http Www Radisma Info, Jan 27, 2014

Pour designer des ‘’vecteurs de meme direction’’, des eleves sont convaincus de mieux exprimer le... more Pour designer des ‘’vecteurs de meme direction’’, des eleves sont convaincus de mieux exprimer leur representation par ‘’vecteurs paralleles’’ que par ‘’vecteurs colineaires’’. La notion de direction est abordee depuis l’ecole primaire mais c’est seulement en classe de 4 e (soit la 3 e annee de college) que le terme est utilise. Cela serait a la base de la confusion entre les caracteristiques d’orientation du vecteur geometrique. L’utilisation des la classe de 6 e du terme ‘’direction’’ pourrait faciliter l’apprentissage du sens en classe de 4 e et eviter la confusion. Les difficultes et la lenteur de la construction des caracteristiques d’orientation du vecteur geometrique font du ‘’ temps’’ une variable didactique qui pourrait jouer un role important dans l’apprentissage de ces caracteristiques particulierement la direction.

Utilité des nombres dans l’introduction de la notion de vecteur en classe de 4 e

Http Www Radisma Info, Dec 3, 2011

Par un choix mathematique inspire de l’histoire des mathematiques, nous avons montre l’utilite de... more Par un choix mathematique inspire de l’histoire des mathematiques, nous avons montre l’utilite des nombres dans l’introduction du vecteur en classe de 4 e etant entendu que les nombres ont joue un role important dans la construction du concept. Pour atteindre cet objectif, les nombres ont ete utilises comme une variable cognitive.

Cosmological evolution inf(R,T)theory with collisional matter

Physical Review D, 2015

We study the evolution of the cosmological parameters, namely, the deceleration parameter q(z) an... more We study the evolution of the cosmological parameters, namely, the deceleration parameter q(z) and the parameter of effective equation of state in a universe containing, besides the ordinary matter and dark energy, a self-interacting (collisional matter), in the generalized f (R, T) theory of gravity, where R and T are the curvature scalar and the trace of the energy-momentum tensor, respectively. We use the generalized FRW equations, the equation of continuity and obtain a differential equation in H(z), and solve it numerically for studying the evolution of the cosmological parameters. Two f (R, T) models are considered and the results with collisional matter are compared with the ones of the ΛCDM model, and also with the model where there exists only non-collisional matter. The curves show that the models are acceptable because the values found for w ef f are consistent with the observational data.

E. La question de savoir si on peut determiner un spineur connaissant les tenseurs sans derivation de la theorie de Dirac aete ¶ etudiee par plusieurs auteurs. Nous proposons ici une methode al- gebrique basee sur la representation du spineur commeelement de C 2 (dans le cas d'un spineur de Pauli...

d'un spineur de Dirac). Cette methode conduit de fa» con naturelleal a construction d'un ... more d'un spineur de Dirac). Cette methode conduit de fa» con naturelleal a construction d'un flbre de Hopf au-dessus de l'algµ ebre des observables. ABSTRACT. A spinor has bilinear covariants (the observables) satisfy- ing certain quadratic equations called Fierz identities. These identities are su-cient to reconstruct a Dirac spinor from its bilinear covari- ants, up to a phase factor. We use algebraic method to recover the spinor from its bilinear covariants for the Clifiord algebras Cl3, Cl4 and Cl(1;3). This method leads in a natural way to the Hopf flbrations S 1 ! S 3 ! S 2 and S 3 ! S 7 ! S 4 for the Euclidean cases.

Lightlike Einstein's hypersurfaces in Lorentzian manifolds with constant curvature

We study a class of light like hypersurfaces in Lorentzian manifolds of constant curvature, that ... more

Qualitative analysis of a generalized Maxwell-Einstein system - Application for a cosmological model

Comptes rendus de l'Académie des sciences. Série II, Mécanique, physique, chimie, sciences de l'univers, sciences de la terre

A methodology for studying dynamical systems is employed to qualitatively analyze the relationshi... more A methodology for studying dynamical systems is employed to qualitatively analyze the relationship between a Maxwellian field coupled to gravity and Einstein equations. The Maxwellian-type field is assumed to have n even dimensions to develop variables describing the expansion factor of the 4D universe and the variation of the gravitational constant. The resulting phase diagram is analyzed and found to have trajectories expanding from a singularity at infinity and tending toward equilibrium. This description of Minkowskian space-time is complemented by nonphysical regions in which trajectories originating from a 'big-bang' singularity tend toward an unstable singularity at infinity.

Analyse qualitative du système Maxwell-Einstein généralisé. Application au modèle cosmologique. (Qualitative analysis of a generalized Maxwell-Einstein system. Application for a cosmological model)

Comptes rendus de l'Académie des sciences. Série II, Mécanique, physique, chimie, sciences de l'univers, sciences de la terre

Le couplage de la gravitation a un champ du type maxwellien en dimension n, paire, conduit, apres... more Le couplage de la gravitation a un champ du type maxwellien en dimension n, paire, conduit, apres une reduction a quatre dimensions, aux equations d'Einstein couplees non trivialement a deux champs scalaires. Dans cette Note, ce systeme est analyse qualitativement en utilisant les methodes d'analyse des systemes dynamiques

$Research paper thumbnail of From the early to the late time universe within $f(T,\mathcal{T})$ gravity$

From the early to the late time universe within $f(T,\mathcal{T})$ gravity

In this paper we perform the reconstruction scheme of the gravitational action within $f(T,\mathc... more In this paper we perform the reconstruction scheme of the gravitational action within $f(T,\mathcal{T})$ gravity, where $T$ and $\mathcal{T}$ denote the torsion scalar and the trace of the energy momentum tensor, respectively. We particularly focus our attention on the case where the algebraic function $f(T,\mathcal{T})$ is decomposed as a sum of two functions $f_1(T)$ and $f_2(\mathcal{T})$, i.e, $f(T,\mathcal{T})=f_{1}(T)+f_{2}(\mathcal{T})$. The description is essentially based on the scale factor and then, we consider two interesting and realistic expressions of this parameter and reconstruct the action corresponding to each phase of the universe. Our results show that some $f(T,\mathcal{T})$ models are able to describe the evolution of the universe from the inflation phase to the late time dark energy dominated phase.

Pseudo-Szabó Operators and Lightlike Szabó Hypersurfaces

In this paper, the pseudo-inversion of degenerate metric is considered. We extend Szabó operators... more In this paper, the pseudo-inversion of degenerate metric is considered. We extend Szabó operators associated to algebraic covariant derivative curvature maps (tensors) to lightlike hypersurfaces. Some examples are given with explicit determination of their Szabó operators. Finally, we introduce the notion of lightlike Szabó hypersurfaces and give some characterization results of locally symmetric lightlike hypersurfaces and semi-symmetric lightlike hypersurfaces from Szabó condition.

Realisticf(T) model describing the de Sitter epoch of the dark energy dominated universe

Canadian Journal of Physics, 2015

We consider an exponential model within the so-called f(T) theory of gravity, where T denotes the... more We consider an exponential model within the so-called f(T) theory of gravity, where T denotes the torsion scalar. We focus our attention on a cosmological feature of a f(T) model, checking whether it may describe the de Sitter stage of the current universe according to the evolution of the redshift, z. Our results show that the model reproduces the de Sitter stage only for low redshifts, where the perturbation function approached zero, whereas the effective parameter of the equation of state goes to –1, which is the expected behavior for any model able to reproduce the de Sitter stage.

Cosmological viable f(R,T) dark energy model: dynamics and stability

Astrophysics and Space Science, 2014

Clifford Algebra and Gabor filter for color image texture characterization

2013 International Conference on Signal-Image Technology & Internet-Based Systems, 2013

The first texture descriptors are proposed in 1973 by Haralick[1] and in 1975 by Marie Galloway[2... more The first texture descriptors are proposed in 1973 by Haralick[1] and in 1975 by Marie Galloway[2] are still used today for image classification or segmentation in various domains. The majority of these features are defined for gray level images. Many papers have proposed different approaches among them, a parallel study of color and gray level texture characterization when other combined the two groups of features by defining joint features[3][4][5]. Combining features or defining them jointly are outperformed [6] even though these features impose some constraints such as the color system, measurement similarity methods. The aim of this paper is to use Clifford Algebra to represent multi-component images and to propose a color image texture.

Scalar Perturbations and Conformal Transformation

The non-minimal coupling of gravity to a scalar field can be transformed into a minimal coupling ... more The non-minimal coupling of gravity to a scalar field can be transformed into a minimal coupling through a conformal transformation. We show how to connect the results of a perturbation calculation, performed around a Friedmann-Robertson-Walker background solution, before and after the conformal transformation. We work in the synchronous gauge, but we discuss the implications of employing other formalisms.

Ruling out the Modified Chaplygin Gas cosmologies

Physics Letters B, 2011

Qualitative study of multidimensional cosmological models

Physics Letters B, 1992

A qualitative analysis of cosmological models induced by the multidimensional theories is perform... more A qualitative analysis of cosmological models induced by the multidimensional theories is performed. The Einstein-MaxweU system written in an arbitrary n-dimensional manifold, with n > 4 is studied. Firstly, the original system is reduced to four dimensions. The analysis of the resulting equations is made by the dynamical system method. The evolution of the corresponding solutions is represented by curves in the phase diagram. Also a comparison of the results is made with those found previously in the context of the coupling of the Einstein-Hilbert iagrangian with a conformal field in higher dimensions.

Classical analogous of quantum cosmological perfect fluid models

Physics Letters A, 2001

Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a so... more Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state p Q = ρ Q is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.

Locally Rotationally Symmetric Bianchi Type-II Magnetized String Cosmological Model with Bulk Viscous Fluid in General Relativity

Chinese Physics Letters, 2011

The locally rotationally symmetric Bianchi type-II magnetized string cosmological model with bulk... more

L H  L M  C S P C

In this paper, we generalize the Cartan’s fundamental formula on lightlike hypersurfaces, then we... more

Gray Tensors on Lightlike Hypersurfaces

This paper introduces Gray-tensors on lightlike hypersurfaces M n+1 of signature (0, n), (n ≥ 1) ... more This paper introduces Gray-tensors on lightlike hypersurfaces M n+1 of signature (0, n), (n ≥ 1) and investigates on their basic properties in connec- tion with their null geometry. In particular, we show that there is an interplay between existence of Gray-tensors of certain type and lightlike warped product structures. As a physical relevance, we show that there exists such a tensor on both globally Killing horizons (GKH) and totally geodesic lightlike triple warped product hypersurfaces.

Automatic Localization of Five Relevant Dermoscopic Structures Based on YOLOv8 for Diagnosis Improvement

Journal of Imaging

The automatic detection of dermoscopic features is a task that provides the specialists with an i... more The automatic detection of dermoscopic features is a task that provides the specialists with an image with indications about the different patterns present in it. This information can help them fully understand the image and improve their decisions. However, the automatic analysis of dermoscopic features can be a difficult task because of their small size. Some work was performed in this area, but the results can be improved. The objective of this work is to improve the precision of the automatic detection of dermoscopic features. To achieve this goal, an algorithm named yolo-dermoscopic-features is proposed. The algorithm consists of four points: (i) generate annotations in the JSON format for supervised learning of the model; (ii) propose a model based on the latest version of Yolo; (iii) pre-train the model for the segmentation of skin lesions; (iv) train five models for the five dermoscopic features. The experiments are performed on the ISIC 2018 task2 dataset. After training, t...

Décalage de l'enseignement de ‘’direction’’ et de ‘’sens’’ et introduction du vecteur géométrique en classe de 4e

Http Www Radisma Info, Jan 27, 2014

Pour designer des ‘’vecteurs de meme direction’’, des eleves sont convaincus de mieux exprimer le... more Pour designer des ‘’vecteurs de meme direction’’, des eleves sont convaincus de mieux exprimer leur representation par ‘’vecteurs paralleles’’ que par ‘’vecteurs colineaires’’. La notion de direction est abordee depuis l’ecole primaire mais c’est seulement en classe de 4 e (soit la 3 e annee de college) que le terme est utilise. Cela serait a la base de la confusion entre les caracteristiques d’orientation du vecteur geometrique. L’utilisation des la classe de 6 e du terme ‘’direction’’ pourrait faciliter l’apprentissage du sens en classe de 4 e et eviter la confusion. Les difficultes et la lenteur de la construction des caracteristiques d’orientation du vecteur geometrique font du ‘’ temps’’ une variable didactique qui pourrait jouer un role important dans l’apprentissage de ces caracteristiques particulierement la direction.

Utilité des nombres dans l’introduction de la notion de vecteur en classe de 4 e

Http Www Radisma Info, Dec 3, 2011

Par un choix mathematique inspire de l’histoire des mathematiques, nous avons montre l’utilite de... more Par un choix mathematique inspire de l’histoire des mathematiques, nous avons montre l’utilite des nombres dans l’introduction du vecteur en classe de 4 e etant entendu que les nombres ont joue un role important dans la construction du concept. Pour atteindre cet objectif, les nombres ont ete utilises comme une variable cognitive.

Cosmological evolution inf(R,T)theory with collisional matter

Physical Review D, 2015

We study the evolution of the cosmological parameters, namely, the deceleration parameter q(z) an... more We study the evolution of the cosmological parameters, namely, the deceleration parameter q(z) and the parameter of effective equation of state in a universe containing, besides the ordinary matter and dark energy, a self-interacting (collisional matter), in the generalized f (R, T) theory of gravity, where R and T are the curvature scalar and the trace of the energy-momentum tensor, respectively. We use the generalized FRW equations, the equation of continuity and obtain a differential equation in H(z), and solve it numerically for studying the evolution of the cosmological parameters. Two f (R, T) models are considered and the results with collisional matter are compared with the ones of the ΛCDM model, and also with the model where there exists only non-collisional matter. The curves show that the models are acceptable because the values found for w ef f are consistent with the observational data.

E. La question de savoir si on peut determiner un spineur connaissant les tenseurs sans derivation de la theorie de Dirac aete ¶ etudiee par plusieurs auteurs. Nous proposons ici une methode al- gebrique basee sur la representation du spineur commeelement de C 2 (dans le cas d'un spineur de Pauli...

d'un spineur de Dirac). Cette methode conduit de fa» con naturelleal a construction d'un ... more d'un spineur de Dirac). Cette methode conduit de fa» con naturelleal a construction d'un flbre de Hopf au-dessus de l'algµ ebre des observables. ABSTRACT. A spinor has bilinear covariants (the observables) satisfy- ing certain quadratic equations called Fierz identities. These identities are su-cient to reconstruct a Dirac spinor from its bilinear covari- ants, up to a phase factor. We use algebraic method to recover the spinor from its bilinear covariants for the Clifiord algebras Cl3, Cl4 and Cl(1;3). This method leads in a natural way to the Hopf flbrations S 1 ! S 3 ! S 2 and S 3 ! S 7 ! S 4 for the Euclidean cases.

Lightlike Einstein's hypersurfaces in Lorentzian manifolds with constant curvature

We study a class of light like hypersurfaces in Lorentzian manifolds of constant curvature, that ... more

Qualitative analysis of a generalized Maxwell-Einstein system - Application for a cosmological model

Comptes rendus de l'Académie des sciences. Série II, Mécanique, physique, chimie, sciences de l'univers, sciences de la terre

A methodology for studying dynamical systems is employed to qualitatively analyze the relationshi... more A methodology for studying dynamical systems is employed to qualitatively analyze the relationship between a Maxwellian field coupled to gravity and Einstein equations. The Maxwellian-type field is assumed to have n even dimensions to develop variables describing the expansion factor of the 4D universe and the variation of the gravitational constant. The resulting phase diagram is analyzed and found to have trajectories expanding from a singularity at infinity and tending toward equilibrium. This description of Minkowskian space-time is complemented by nonphysical regions in which trajectories originating from a 'big-bang' singularity tend toward an unstable singularity at infinity.

Analyse qualitative du système Maxwell-Einstein généralisé. Application au modèle cosmologique. (Qualitative analysis of a generalized Maxwell-Einstein system. Application for a cosmological model)

Comptes rendus de l'Académie des sciences. Série II, Mécanique, physique, chimie, sciences de l'univers, sciences de la terre

Le couplage de la gravitation a un champ du type maxwellien en dimension n, paire, conduit, apres... more Le couplage de la gravitation a un champ du type maxwellien en dimension n, paire, conduit, apres une reduction a quatre dimensions, aux equations d'Einstein couplees non trivialement a deux champs scalaires. Dans cette Note, ce systeme est analyse qualitativement en utilisant les methodes d'analyse des systemes dynamiques

$Research paper thumbnail of From the early to the late time universe within $f(T,\mathcal{T})$ gravity$

From the early to the late time universe within $f(T,\mathcal{T})$ gravity

In this paper we perform the reconstruction scheme of the gravitational action within $f(T,\mathc... more In this paper we perform the reconstruction scheme of the gravitational action within $f(T,\mathcal{T})$ gravity, where $T$ and $\mathcal{T}$ denote the torsion scalar and the trace of the energy momentum tensor, respectively. We particularly focus our attention on the case where the algebraic function $f(T,\mathcal{T})$ is decomposed as a sum of two functions $f_1(T)$ and $f_2(\mathcal{T})$, i.e, $f(T,\mathcal{T})=f_{1}(T)+f_{2}(\mathcal{T})$. The description is essentially based on the scale factor and then, we consider two interesting and realistic expressions of this parameter and reconstruct the action corresponding to each phase of the universe. Our results show that some $f(T,\mathcal{T})$ models are able to describe the evolution of the universe from the inflation phase to the late time dark energy dominated phase.

Pseudo-Szabó Operators and Lightlike Szabó Hypersurfaces

In this paper, the pseudo-inversion of degenerate metric is considered. We extend Szabó operators... more In this paper, the pseudo-inversion of degenerate metric is considered. We extend Szabó operators associated to algebraic covariant derivative curvature maps (tensors) to lightlike hypersurfaces. Some examples are given with explicit determination of their Szabó operators. Finally, we introduce the notion of lightlike Szabó hypersurfaces and give some characterization results of locally symmetric lightlike hypersurfaces and semi-symmetric lightlike hypersurfaces from Szabó condition.

Realisticf(T) model describing the de Sitter epoch of the dark energy dominated universe

Canadian Journal of Physics, 2015

We consider an exponential model within the so-called f(T) theory of gravity, where T denotes the... more We consider an exponential model within the so-called f(T) theory of gravity, where T denotes the torsion scalar. We focus our attention on a cosmological feature of a f(T) model, checking whether it may describe the de Sitter stage of the current universe according to the evolution of the redshift, z. Our results show that the model reproduces the de Sitter stage only for low redshifts, where the perturbation function approached zero, whereas the effective parameter of the equation of state goes to –1, which is the expected behavior for any model able to reproduce the de Sitter stage.

Cosmological viable f(R,T) dark energy model: dynamics and stability

Astrophysics and Space Science, 2014

Clifford Algebra and Gabor filter for color image texture characterization

2013 International Conference on Signal-Image Technology & Internet-Based Systems, 2013

The first texture descriptors are proposed in 1973 by Haralick[1] and in 1975 by Marie Galloway[2... more The first texture descriptors are proposed in 1973 by Haralick[1] and in 1975 by Marie Galloway[2] are still used today for image classification or segmentation in various domains. The majority of these features are defined for gray level images. Many papers have proposed different approaches among them, a parallel study of color and gray level texture characterization when other combined the two groups of features by defining joint features[3][4][5]. Combining features or defining them jointly are outperformed [6] even though these features impose some constraints such as the color system, measurement similarity methods. The aim of this paper is to use Clifford Algebra to represent multi-component images and to propose a color image texture.

Scalar Perturbations and Conformal Transformation

The non-minimal coupling of gravity to a scalar field can be transformed into a minimal coupling ... more The non-minimal coupling of gravity to a scalar field can be transformed into a minimal coupling through a conformal transformation. We show how to connect the results of a perturbation calculation, performed around a Friedmann-Robertson-Walker background solution, before and after the conformal transformation. We work in the synchronous gauge, but we discuss the implications of employing other formalisms.

Ruling out the Modified Chaplygin Gas cosmologies

Physics Letters B, 2011

Qualitative study of multidimensional cosmological models

Physics Letters B, 1992

A qualitative analysis of cosmological models induced by the multidimensional theories is perform... more A qualitative analysis of cosmological models induced by the multidimensional theories is performed. The Einstein-MaxweU system written in an arbitrary n-dimensional manifold, with n > 4 is studied. Firstly, the original system is reduced to four dimensions. The analysis of the resulting equations is made by the dynamical system method. The evolution of the corresponding solutions is represented by curves in the phase diagram. Also a comparison of the results is made with those found previously in the context of the coupling of the Einstein-Hilbert iagrangian with a conformal field in higher dimensions.

Classical analogous of quantum cosmological perfect fluid models

Physics Letters A, 2001

Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a so... more Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state p Q = ρ Q is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.