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Minimum Penalized Hellinger Distance for Model Selection in Small Samples  [PDF]
Papa Ngom, Bertrand Ntep
Open Journal of Statistics (OJS) , 2012, DOI: 10.4236/ojs.2012.24045
Abstract: In statistical modeling area, the Akaike information criterion AIC, is a widely known and extensively used tool for model choice. The φ-divergence test statistic is a recently developed tool for statistical model selection. The popularity of the divergence criterion is however tempered by their known lack of robustness in small sample. In this paper the penalized minimum Hellinger distance type statistics are considered and some properties are established. The limit laws of the estimates and test statistics are given under both the null and the alternative hypotheses, and approximations of the power functions are deduced. A model selection criterion relative to these divergence measures are developed for parametric inference. Our interest is in the problem to testing for choosing between two models using some informational type statistics, when independent sample are drawn from a discrete population. Here, we discuss the asymptotic properties and the performance of new procedure tests and investigate their small sample behavior.
Relativistic Gauge Invariant Wave Equation of the Electron-Neutrino  [PDF]
Claude Daviau, Jacques Bertrand
Journal of Modern Physics (JMP) , 2014, DOI: 10.4236/jmp.2014.511102

With the right and the left waves of an electron, plus the left wave of its neutrino, we write the tensorial densities coming from all associations of these three spinors. We recover the wave equation of the electro-weak theory. A new non linear mass term comes out. The wave equation is form invariant, then relativistic invariant, and it is gauge invariant under the U(1)×SU(2), Lie group of electro-weak interactions. The invariant form of the wave equation has the Lagrangian density as real scalar part. One of the real equations equivalent to the invariant form is the law of conservation of the total current.

A Wave Equation including Leptons and Quarks for the Standard Model of Quantum Physics in Clifford Algebra  [PDF]
Claude Daviau, Jacques Bertrand
Journal of Modern Physics (JMP) , 2014, DOI: 10.4236/jmp.2014.518210

A wave equation with mass term is studied for all fermionic particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks u and d with three states of color and antiquarks \"\" and \"\". This wave equation is form invariant under the \"\" group generalizing the relativistic invariance. It is gauge invariant under the U(1)×SU(2)×SU(3) group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra Cl1,5. Then many features of the standard model, charge conjugation, color, left waves, and Lagrangian formalism, are obtained in the frame of the first quantization.

Geometry of the Standard Model of Quantum Physics  [PDF]
Claude Daviau, Jacques Bertrand
Journal of Applied Mathematics and Physics (JAMP) , 2015, DOI: 10.4236/jamp.2015.31007

General relativity links gravitation to the structure of our space-time. Nowadays physics knows four types of interactions: Gravitation, electromagnetism, weak interactions, strong interactions. The theory of everything (ToE) is the unification of these four domains. We study several necessary cornerstones for such a theory: geometry and mathematics, adapted manifolds on the real domain, Clifford algebras over tangent spaces of these manifolds, the real Lagrangian density in connection with the standard model of quantum physics. The geometry of the standard model of quantum physics uses three Clifford algebras. The algebra \"\"?of the 3-dimensional physical space is sufficient to describe the wave of the electron. The algebra \"\"of space-time is sufficient to describe the wave of the pair electron-neutrino. A greater space-time with two additional dimensions of space generates the algebra \"\" . It is sufficient to get the wave equation for all fermions, electron, its neutrino and quarks u and d of the first generation, and the wave equations for the two other generations. Values of these waves allow defining, in each point of space-time, geometric transformations from one intrinsic manifold of space-time into the usual manifold. The Lagrangian density is the scalar part of the wave equation.

Left Chiral Solutions for the Hydrogen Atom of the Wave Equation for Electron + Neutrino  [PDF]
Claude Daviau, Jacques Bertrand
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.611166
Abstract: The resolution of our wave equation for electron + neutrino is made in the case of the H atom. From two non-classical potentials, we get chiral solutions with the same set of quantum numbers and the same energy levels as those coming from the Dirac equation for the lone electron. These chiral solutions are available for each electronic state in any atom. We discuss the implications of these new potentials.
Electro-Weak Gauge, Weinberg-Salam Angle  [PDF]
Claude Daviau, Jacques Bertrand
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.614215
Abstract: The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies \"\". We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neutrino. These potentials are space-time vectors whose components are amongst the tensor densities without derivative built from the three chiral spinors of the wave. The \"\"?gauge invariance allows us to identify the four potential space-time vectors of the electro-weak gauge to four of the nine possible vectors. One and only one of the nine derived bivector fields is the massless electromagnetic field. Putting back the four potentials linked to the spinor wave into the wave equation we get simplified equations. From the properties of the second-order wave equation we obtain the Weinberg-Salam angle. We discuss the implications of the simplified equations, obtained without second quantification, on mass, charge and gauge invariance. Chiral gauge, electric gauge and weak gauge are simply linked.
Symbolic calculus on the time-frequency half-plane
J. Bertrand,P. Bertrand
Physics , 1997, DOI: 10.1063/1.532484
Abstract: The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.
Search for Light New Physics at Factories
Bertrand Echenard
Advances in High Energy Physics , 2012, DOI: 10.1155/2012/514014
Abstract: Many extensions of the Standard Model include the possibility of light new particles, such as light Higgs bosons or dark matter candidates. These scenarios can be probed using the large datasets collected by B factories, complementing measurements performed at the LHC. This paper summarizes recent searches for light new physics conducted by the BABAR and Belle experiments. 1. Introduction From supersymmetry to dark matter, many extensions of the Standard Model (SM) include the possibility of light new physics. Thanks to their large luminosities, factories offer an ideal environment to explore these theories. During the last decade, the BABAR Collaboration at PEP-II [1] and the Belle Collaboration at KEKB [2, 3] have, respectively, collected about 550? and more than 1? of data at several resonances, mostly the resonance (see Table 1). These datasets have been exploited to explore many aspects of precision physics, including searches for light new particles. In the following, we review searches for light Higgs bosons, dark matter candidates, hidden sectors, sgoldstinos, and Majorana neutrinos. Table 1: Integrated luminosities ( ) collected by the factories at different center-of-mass energies. The off-resonance data were collected about 40?MeV below the resonance at BABAR and at a similar offset for the and resonances in the case of Belle. 2. Search for Light -Odd Higgs Boson in Decays A light Higgs boson is predicted by several extensions of the Standard Model, such as the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The NMSSM Higgs sector contains a total of seven states, three -even, two -odd, and two charged Higgs bosons. A -odd Higgs boson ( ) lighter than can evade present experimental constraints [4], and could be detected through radiative decays [5]. The corresponding branching fraction could be as large as a few , well above the sensitivity of factories [4, 6]. The Higgs boson decay pattern depends on its mass and couplings, as well as the NMSSM particle spectrum. In the absence of light neutralinos, the decays predominantly into a pair of muons below , while and hadronic final states become significant above this threshold. The branching fraction may be dominant if the neutralino ( ) is the lightest stable particle with [7]. In this case, the neutralino is a natural dark matter candidate. BABAR has performed searches for a light -odd Higgs boson in a variety of decay channels. These measurements are discussed in the next paragraphs, and the results are summarized in Table 2. They place stringent constraints on light -odd Higgs models.
Prognostic Ability of Practitioners of Traditional Arabic Medicine: Comparison with Western Methods through a Relative Patient Progress Scale
Bertrand Graz
Evidence-Based Complementary and Alternative Medicine , 2010, DOI: 10.1093/ecam/nen022
Abstract: The ancient Greek medical theory based on balance or imbalance of humors disappeared in the western world, but does survive elsewhere. Is this survival related to a certain degree of health care efficiency? We explored this hypothesis through a study of classical Greco-Arab medicine in Mauritania. Modern general practitioners evaluated the safety and effectiveness of classical Arabic medicine in a Mauritanian traditional clinic, with a prognosis/follow-up method allowing the following comparisons: (i) actual patient progress (clinical outcome) compared with what the traditional ‘tabib’ had anticipated (= prognostic ability) and (ii) patient progress compared with what could be hoped for if the patient were treated by a modern physician in the same neighborhood. The practice appeared fairly safe and, on average, clinical outcome was similar to what could be expected with modern medicine. In some cases, patient progress was better than expected. The ability to correctly predict an individual's clinical outcome did not seem to be better along modern or Greco-Arab theories. Weekly joint meetings (modern and traditional practitioners) were spontaneously organized with a modern health centre in the neighborhood. Practitioners of a different medical system can predict patient progress. For the patient, avoiding false expectations with health care and ensuring appropriate referral may be the most important. Prognosis and outcome studies such as the one presented here may help to develop institutions where patients find support in making their choices, not only among several treatment options, but also among several medical systems.
Survival of Exfoliated Epithelial Cells: A Delicate Balance between Anoikis and Apoptosis
Bertrand Kaeffer
Journal of Biomedicine and Biotechnology , 2011, DOI: 10.1155/2011/534139
Abstract: The recovery of exfoliated cells from biological fluids is a noninvasive technology which is in high demand in the field of translational research. Exfoliated epithelial cells can be isolated from several body fluids (i.e., breast milk, urines, and digestives fluids) as a cellular mixture (senescent, apoptotic, proliferative, or quiescent cells). The most intriguing are quiescent cells which can be used to derive primary cultures indicating that some phenotypes retain clonogenic potentials. Such exfoliated cells are believed to enter rapidly in anoikis after exfoliation. Anoikis can be considered as an autophagic state promoting epithelial cell survival after a timely loss of contact with extracellular matrix and cell neighbors. This paper presents current understanding of exfoliation along with the influence of methodology on the type of gastrointestinal epithelial cells isolated and, finally, speculates on the balance between anoikis and apoptosis to explain the survival of gastrointestinal epithelial cells in the environment.
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