Investigating the sterile neutrino parameters with QLC in 3 + 1 scenario

In the scenario with four generation quarks and leptons and using a 3 + 1 neutrino model having one sterile and the three standard active neutrinos with a $4 \times 4$ unitary transformation matrix, $U_{PMNS_{4}}$, we perform a model-based analysis using the latest global data and determine bounds on the sterile neutrino parameters i.e. the neutrino mixing angles. Motivated by our previous results, where, in a quark-lepton complementarity (QLC) model we predicted the values of $\theta_{13}^{PMNS}=(9_{-2}^{+1})^{\circ}$ and $\theta_{23}^{PMNS}=(40.60_{-0.3}^{+0.1})^{\circ}$. In the QLC model the non-trivial correlation between $CKM_4$ and $PMNS_4$ mixing matrix is given by the correlation matrix $V_{c_{4}}$. Monte Carlo simulations are performed to estimate the texture of $V_{c4}$ followed by the calculation of $PMNS_4$ using the equation, $U_{PMNS_{4}}= (U_{CKM_{4}} . \psi_{4})^{-1}.V_{c_{4}}$, where $\psi_{4}$ is a diagonal phase matrix. The sterile neutrino mixing angles, $\theta_{14}^{PMNS}$, $\theta_{24}^{PMNS}$ and $\theta_{34}^{PMNS}$ are assumed to be freely varying between $(0-\pi/4)$ and obtained results which are consistent with the data available from various experiments, like No$\nu$A, MINOS, SuperK, Ice Cube-DeepCore. In further investigation, we analytically obtain approximately similar ranges for various neutrino mixing parameters $\mid{ U_{\mu 4}}\mid ^2$ and $\mid{ U_{\tau 4}}\mid ^2$.Comment: 16 pages, 4 tables, 7 figures(with subfigures, total 14 figures

The Innocence Effect

Nearly all felony convictions—about 95 percent—follow guilty pleas, suggesting that plea offers are very attractive to defendants compared to trials. Some scholars argue that plea bargains are too attractive and should be curtailed because they facilitate the wrongful conviction of innocents. Others contend that plea bargains only benefit innocent defendants, providing an alternative to the risk of a harsher sentence at trial. Hence, even while heatedly disputing their desirability, both camps in the debate believe that plea bargains commonly lead innocents to plead guilty. This Article shows, however, that the belief that innocents routinely plead guilty is overstated. We provide varied empirical evidence for the hitherto neglected innocence effect, revealing that innocents are significantly less likely to accept plea offers that appear attractive to similarly situated guilty defendants. The Article further explores the psychological causes of the innocence effect and examines its implications for plea bargaining. Positively, we identify the striking cost of innocence, wherein innocents suffer harsher average sanctions than similarly situated guilty defendants. Yet our findings also show that the innocence effect directly causes an overrepresentation of the guilty among plea bargainers and an overrepresentation of the innocent among those who choose trial. In this way, the innocence effect beneficially reduces the rate of wrongful convictions—including accepted plea bargains—even when compared to a system that does not allow plea bargaining. Normatively, our analysis finds that both detractors and supporters of plea bargaining should reevaluate, if not completely reverse, their long-held positions to account for the causes and consequences of the innocence effect. The Article concludes by outlining two proposals for minimizing false convictions, better protecting the innocent, and improving the plea bargaining process altogether by accounting for the innocence effect

ECONOMIC ANALYSIS OF LAW AND ECONOMICS

The academic world is wonderful. Like few other professionals, we can choose what we want to do and what questions we think are important, which in our line of work means choosing what topics we want to research. But what influences our choices? This paper examines what drives scholars to select Law and Economics (L&E) as a topic for research. It does so by implementing the methodology of many L&E papers - by assuming that regulation and incentives matter. Legal scholars face very different academic incentives in different parts of the world. In some countries, the academic standards for appointment, promotion and tenure encourage legal scholars to concentrate on L&E. In others, they strongly discourage such research. Thus, we should expect wide variation in the rate of participation of legal scholars in the L&E discourse across countries. On the other hand, economists are evaluated with similar yardsticks everywhere. Thus, participation of economists in the L&E discourse is likely to vary much less from one place to another. The hypothesis of this paper is that the academic incentives are a major factor in the level of participation in the L&E scholarship. This "incentives hypothesis" is presented and then examined empirically on data gathered from the list of authors in L&E journals and the list of participants in L&E conferences. The data generally supports the hypothesis. In the legal academia, the incentives to focus research on L&E topics are the strongest in Israel, they are weaker in North America and weakest in Europe. In fact, the data reveal that lawyers' authorship of L&E papers weighted by population is almost ten times higher in Israel than in North America; while in Europe it is almost ten times lower than in North America. By comparison, the weighted participation level of economists - who face relatively similar academic environments across countries - in L&E research is not significantly different across countries.Law and Economics, Legal Education, Comparative Law,

Economic Analysis of Law and Economics

The academic world is wonderful. Like few other professionals, we can choose what we want to do and what questions we think are important, which in our line of work means choosing what topics we want to research. But what influences our choices? This paper examines what drives scholars to select Law and Economics (L&E) as a topic for research. It does so by implementing the methodology of many L&E papers – by assuming that regulation and incentives matter. Legal scholars face very different academic incentives in different parts of the world. In some countries, the academic standards for appointment, promotion and tenure encourage legal scholars to concentrate on L&E. In others, they strongly discourage such research. Thus, we should expect wide variation in the rate of participation of legal scholars in the L&E discourse across countries. On the other hand, economists are evaluated with similar yardsticks everywhere. Thus, participation of economists in the Law and Economics discourse is likely to vary much less from one place to another. The hypothesis of this paper is that the academic incentives are a major factor in the level of participation in the L&E scholarship. This incentives hypothesis is presented and then examined empirically on data gathered from the list of authors in L&E journals and the list of participants in L&E conferences. The data generally supports the hypothesis. In the legal academia, the incentives to focus research on L&E topics are the strongest in Israel, they are weaker in North America and weakest in Europe. In fact, the data reveal that lawyers\u27 authorship of L&E papers weighted by population is almost ten times higher in Israel then in North America; while in Europe it is almost ten times lower then in North America. By comparison, the weighted participation level of economists – who face relatively similar academic environments across countries – in L&E research is not significantly different across countries

Quark-lepton complementarity model based predictions for θ23PMNS\theta_{23}^{PMNS} with neutrino mass hierarchy

After the successful investigation and confirmation of non zero $\theta_{13}^{PMNS}$ by various experiments, we are standing at a square where we still encounter a number of issues, which are to be settled. In this paper, we have extended our recent work towards a precise prediction of the $\theta_{23}^{PMNS}$ mixing angle, taking into account the neutrino mass hierarchy. We parameterize the non-trivial correlation between quark (CKM) and lepton (PMNS) mixing matrices in quark-lepton complementarity (QLC) model as $V_{c}= U_{CKM}. \psi. U_{PMNS}$, where $\psi$ is a diagonal phase matrix. Monte Carlo simulations are used to estimate the texture of $V_{c}$ and compare the results with the standard Tri-Bi-Maximal (TBM) and Bi-Maximal(BM) structures of neutrino mixing matrix. We have predicted the value of $\theta_{23}^{PMNS}$ for normal and inverted neutrino mass hierarchies. The value of $\theta_{23}^{PMNS}$ obtained for two cases are about $1.3\sigma$ away from each other, implying the better precision can give us a strong hint for the type of neutrino mass hierarchy.Comment: 3 pages, 3 figure

Accuracy of Variational Estimates for Random Graph Mixture Models

International audienceL'analyse des réseaux exerce depuis quelques années un attrait croissant. Les données qui sont sous la forme de mesures de relations entre items sont de plus en plus disponibles, et abandonnent la structure usuelle d'un jeu de données de type individus-variables pour une structure de type individus-individus. Ces données "relationnelles" sont très souvent présentées sous la forme d'un graphe, même si cette représentation a ses limites, notamment quand le nombre d'individus dépasse la centaine. La représentation graphique des données des réseaux est alors attractive, mais nécessite un modèle synthétique. Le modèle de graphe le plus ancien et le plus utilisé est le modèle de Erdös-Rényi, dont les propriétés moyennes ou asymptotiques sont connues. L'écriture littérale de la vraisemblance de ce modèle est très simple, mais son temps de calcul croit de façon exponentielle avec le nombre d'individu. Une utilisation des algorithmes d'estimation usuels comme E-M n'est pas envisageable. Une approche variationnelle a été utilisée comme alternative pour implémenter un algorithme d'estimation des paramètres du modèle, et cela pour des réseaux de très grande taille (Daudin & al 2008). Les propriétés statistiques des estimateurs produits par cette approche sont cependant mal connues. L'objectif est de mener une étude sur la qualité de ces estimateurs et d'en prouver la convergence