On the expected number of equilibria in a multi-player multi-strategy evolutionary game

In this paper, we analyze the mean number $E(n,d)$ of internal equilibria in a general $d$-player $n$-strategy evolutionary game where the agents' payoffs are normally distributed. First, we give a computationally implementable formula for the general case. Next we characterize the asymptotic behavior of $E(2,d)$, estimating its lower and upper bounds as $d$ increases. Two important consequences are obtained from this analysis. On the one hand, we show that in both cases the probability of seeing the maximal possible number of equilibria tends to zero when $d$ or $n$ respectively goes to infinity. On the other hand, we demonstrate that the expected number of stable equilibria is bounded within a certain interval. Finally, for larger $n$ and $d$, numerical results are provided and discussed.Comment: 26 pages, 1 figure, 1 table. revised versio

Was the Higgs boson discovered?

The standard model has postulated the existence of a scalar boson, named the Higgs boson. This boson plays a central role in a symmetry breaking scheme called the Brout-Englert-Higgs mechanism (or the Brout-Englert-Higgs-Guralnik-Hagen-Kibble mechanism, for completeness) making the standard model realistic. However, until recently at least, the 50-year-long-sought Higgs boson had remained the only particle in the standard model not yet discovered experimentally. It is the last but very important missing ingredient of the standard model. Therefore, searching for the Higgs boson is a crucial task and an important mission of particle physics. For this purpose, many theoretical works have been done and different experiments have been organized. It may be said in particular that to search for the Higgs boson has been one of the ultimate goals of building and running the LHC, the world's largest and most powerful particle accelerator, at CERN, which is a great combination of science and technology. Recently, in the summer of 2012, ATLAS and CMS, the two biggest and general-purpose LHC collaborations, announced the discovery of a new boson with a mass around 125 GeV. Since then, for over two years, ATLAS, CMS and other collaborations have carried out intensive investigations on the newly discovered boson to confirm that this new boson is really the Higgs boson (of the standard model). It is a triumph of science and technology and international cooperation. Here, we will review the main results of these investigations following a brief introduction to the Higgs boson within the theoretical framework of the standard model and Brout-Englert-Higgs mechanism as well as a theoretical and experimental background of its search. This paper may attract interest of not only particle physicists but also a broader audience.Comment: LateX, 23 pages, 01 table, 9 figures. To appear in Commun. Phys. Version 2: Minor changes, two references adde

The informativeness of the technical conversion factor for the price ratio of processing livestock

The technical conversion factor (TCF) is a survey-based estimate of the percentage of carcass weight obtained per unit of live weight. Practitioners and researchers have used it to predict the corresponding price ratio (PR). We use both in-sample regressions and out-of-sample forecasting analysis to test the validity of this approach in case of predicting the price effects of processing livestock in Europe. By regressing the PR on the inverse value of the corresponding TCF for a large panel of European countries and animal types, we find a significant positive relation between these variables, which also has economic value in terms of improving out-of-sample forecasting precision. This result is shown to be robust to animal type, year, and country fixed effects. The TCF therefore has predictive value about the corresponding PR.(3

Scalar sextet in the 331 model with right-handed neutrinos

A Higgs sextet is introduced in order to generate Dirac and Majorana neutrino masses in the 331 model with right-handed neutrinos. As will be seen, the present sextet introduction leads to a rich neutrino mass structure. The smallness of neutrino masses can be achieved via, for example, a seesaw limit. The fact that the masses of the charged leptons are not effected by their new Yukawa couplings to the sextet is convenient for generating small neutrino masses.Comment: RevTeX4, 5 pages, no figure. To appear in Phys. Rev. D. Misprints removed (v.2