Stem cells
are seen as a possible solution for organ and tissue regeneration and for the
treatment or even cure of various diseases. There are basically two types of
stem cells: embryonic and adult stem cells. Embryonic stem cells are derived
from embryos and exhibit an extensive multiplication and differentiation
potential. On the other hand, adult stem cells, which are found in bone marrow
and other tissues, have a lower multiplication and differentiation capacity but
are more easily isolated and applied. In adult stem cell therapies using bone
marrow or umbilical cord blood transplantation, the differentiation of a
certain cell type is induced and its multiplication is stimulated, followed
by the implantation of these cells into damaged tissues. Examples of the
application of stem cells include the treatment of autoimmune diseases such as
type 1 diabetes mellitus and heart diseases. Stem cells open up new prospects
for the treatment of a series of diseases. In this respect, basic knowledge of
the mechanisms of growth and differentiation of these cells is of the utmost
importance to optimize therapeutic results. In this review, we discuss the
mechanisms of stem cell differentiation and describe the clinical results
reported in the literature, mainly by Brazilian research groups.

Abstract:
We discuss unsuspected relations between Maxwell, Dirac, and the Seiberg-Witten equations. First, we present the Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F=ψγ21ψ˜, where F is a given electromagnetic field. Such task is presented and it permits to clarify some objections to the MDE which claim that no MDE may exist because F has six (real) degrees of freedom and ψ has eight (real) degrees of freedom. Also, we review the generalized Maxwell equation describing charges and monopoles. The enterprise is worth, even if there is no evidence until now for magnetic monopoles, because there are at least two faithful field equations that have the form of the generalized Maxwell equations. One is the generalized Hertz potential field equation (which we discuss in detail) associated with Maxwell theory and the other is a (nonlinear) equation (of the generalized Maxwell type) satisfied by the 2-form field part of a Dirac-Hestenes spinor field that solves the Dirac-Hestenes equation for a free electron. This is a new result which can also be called MDE of the second kind. Finally, we use the MDE of the first kind together with a reasonable hypothesis to give a derivation of the famous Seiberg-Witten equations on Minkowski spacetime. A physical interpretation for those equations is proposed.

Abstract:
In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with details several exercises involving different grades of difficult. One of the problems is to show that a recent formula appearing in the literature for the exterior covariant derivative of the Hodge dual of the torsion 2-forms is simply wrong. We believe that the paper will be useful for students (and eventually for some experts) on applications of differential geometry on physical problems. A detailed account of the issues discussed in the paper appears in the table of contents.

Abstract:
In this paper we first analyze the structure of Maxwell equations in a Lorentzian spacetime where the potential A is proportional to 1-form K physically equivalent to a Killing vector field (supposed to exist). We show that such A obeys the Lorenz gauge and also a wave equation that can be written in terms of the covariant D'Alembertian or the Ricci operator. Moreover, we determine the correct current defined by that potential showing that it is of superconducting type, being two times the product of the components of A by the Ricci 1-form fields. We also study the structure of the spacetime generated by the coupled system consisting of a electromagnetic field F = dA (A, as above), an ideal charged fluid with dynamics described by an action function S and the gravitational field. We show that Einstein equations in this situation is then equivalent to Maxwell equations with a current givn by fFAF (the product meaning the Clifford product of the corresponding form fields), where f is a scalar function which satisfies a well determined algebraic quadratic equation.

Abstract:
In this paper we show how a gravitational field generated by a given energy-momentum distribution (for all realistic cases) can be represented by distinct geometrical structures (Lorentzian, teleparallel and non null nonmetricity spacetimes) or that we even can dispense all those geometrical structures and simply represent the gravitational field as a field, in the Faraday's sense, living in Minkowski spacetime. The explicit Lagrangian density for this theory is given and the field equations (which are a set of four Maxwell's like equations) are shown to be equivalent to Einstein's equations. We also analyze if the teleparallel formulation can give a mathematical meaning to "Einstein's most happy thought", i.e. the equivalence principle. Moreover we discuss the Hamiltonian formalism for for our theory and its relation to one of the possibles concepts for energy of the gravitational field which emerges from it and the concept of ADM energy. One of the main results of the paper is the identification in our theory of a legitimate energy-mometum tensor for the gravitational field expressible through a really nice formula.

Abstract:
In this paper we discuss some unusual and unsuspected relations between Maxwell, Dirac and the Seiberg-Witten equations. First we investigatethe Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for $\Psi$(a representative on a given spinorial frame of a Dirac-Hestenes spinor field (DHSF)) the equation $F=\Psi \gamma_{21} \sim{\Psi}$, where F is a given electromagnetic field. Such task is presented in this paper and it permits to clarify some possible objections to the MDE which claims that no MDE may exist, because F has six (real) degrees of freedom and $\Psi$ has eight (real) degrees of freedom. Also, we review the generalized Maxwell equation describing charges and monopoles. The enterprise is worth even if there is no evidence until now for magnetic monopoles, because there are at least two faithful field equations that have the form that equations. One is the generalized Hertz potential field equation associated with Maxwell theory and the other is a (non linear) equation satisfied by the 2-form field, which is part of a representative of a DHSF that solves the Dirac-Hestenes equation for a free electron. This is a new and surprising result, which can also be called MDE of the second kind. It strongly suggests that the electron is a composed system with more elementary "charges" of the electric and magnetic types. Finally, we use the MDE of the first kind together with a reasonable hypothesis to give a derivation of the famous Seiberg-Witten equations on Minkowski spacetime.

Abstract:
Almost all presentations of Dirac theory in first or second quantization in Physics (and Mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of non homogeneous even multivectors fields) is used. However, a carefully analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF) and Dirac-Hestenes spinor fields (DHSF) on Minkowski spacetime as some equivalence classes of well defined pairs of mathematical objects, one of the members of the pair being an even nonhomegeneous differential form. The necessity of our definitions are shown by a carefull analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections a vector bundle called the left spin-Clifford bundle. The present paper contains also Appendices (A-E) which exhibits a truly useful collection of results concerning the theory of Clifford algebras (including many `tricks of the trade') necessary for the intelligibility of the text.

Abstract:
This paper is a set of notes that we wrote concerning the first version of Emergent Gravity [gr-qc/0602022]. It is our version of an exercise that we proposed to some of our students. The idea was to find mathematical errors and inconsistencies on some recent articles published in scientific journals and in the arXiv, and we did.

Abstract:
We show that when correctly formulated the equation $\nabla \times \mbox{\boldmath $a$} = \kappa \mbox{\boldmath $a$}$ does not exhibit some inconsistencies atributed to it, so that its solutions can represent physical fields.

Abstract:
We show that Maxwell equations and Dirac equation (with zero mass term) have both subluminal and superluminal solutions in vacuum. We also discuss the possible fundamental physical consequences of our results.