Intersections in genus 3 and the Boussinesq hierarchy

In this note we prove that the enlarged Witten's conjecture is true in the case of the Boussinesq hierarchy for correlators in genus 3 with descendants only at one point

The Toda hierarchy and the KdV hierarchy

The Toda hierarchy of size $N$ is well known to be analogous to the KdV hierarchy at $N$ goes to infinity. This paper shows that given $f$ a periodic function, there is a canonical way of defining the initial data for the Toda lattice equations so that the evolution of this data under the Toda lattice hierarchy looks asymptotically like the evolution of $f$ under the KdV hierarchy. Further, the conserved quantities of $f$ and those of the Toda hierarchy match.Comment: AMSTe

The need for an early anti-neutrino run of NOvA

The moderately large value of \ty, measured recently by reactor experiments, is very welcome news for the future neutrino experiments. In particular, the \nova experiment, with 3 years each of $\nu$ and \anu runs, will be able to determine the mass hierarchy if one of the following two favourable combinations is true: normal hierarchy with -180^\circ \leq \dcp \leq 0 or inverted hierarchy with 0\leq \dcp \leq 180^\circ. In this report, we study the hierarchy reach of the first 3 years of \nova data. Since \sin^2 2 \tz is measured to be non-maximal, \tz can be either in the lower or higher octant. Pure $\nu$ data is affected by \ty-hierarchy and octant-hierarchy degeneracies, which limit the hierarchy sensitivity of such data. A combination of $\nu$ and \anu data is not subject to these degeneracies and hence has much better hierarchy discrimination capability. We find that, with a 3 year $\nu$ run, hierarchy determination is possible for only two of the four octant-hierarchy combinations. Equal 1.5 year runs in $\nu$ and \anu modes give good hierarchy sensitivity for all the four combinations

The ILW hierarchy

In this paper, we present a new hierarchy which includes the intermediate long wave (ILW) equation at the lowest order. This hierarchy is thought to be a novel reduction of the 1st modified KP type hierarchy. The framework of our investigation is Sato theory.Comment: 8 pages, LaTeX2

Hierarchy from Baryogenesis

We study a recently proposed mechanism to solve the hierarchy problem in the context of the landscape, where the solution of the hierarchy problem is connected to the requirement of having baryons in our universe via Electroweak Baryogenesis. The phase transition is triggered by the fermion condensation of a new gauge sector which becomes strong at a scale Lambda determined by dimensional transmutation, and it is mediated to the standard model by a new singlet field. In a ``friendly'' neighborhood of the landscape, where only the relevant operators are ``scanned'' among the vacua, baryogenesis is effective only if the higgs mass m_h is comparable to this low scale Lambda, forcing m_h to be of order Lambda, and solving the hierarchy problem. A new CP violating phase is needed coupling the new singlet and the higgs field to new matter fields. We study the constraints on this model given by baryogenesis and by the electron electric dipole moment (EDM), and we briefly comment on gauge coupling unification and on dark matter relic abundance. We find that next generation experiments on the EDM will be sensitive to essentially the entire viable region of the parameter space, so that absence of a signal would effectively rule out the model.Comment: 28 pages, 4 figures. v2: Added comments and references. Corrected one typo in eq.(81). Conclusions unaltere

Inclusive Cognitive Hierarchy

Cognitive hierarchy theory, a collection of structural models of non-equilibrium thinking, in which players' best responses rely on heterogeneous beliefs on others' strategies including naive behavior, proved powerful in explaining observations from a wide range of games. We introduce an inclusive cognitive hierarchy model, in which players do not rule out the possibility of facing opponents at their own thinking level. Our theoretical results show that inclusiveness is crucial for asymptotic properties of deviations from equilibrium behavior in expansive games. We show that the limiting behaviors are categorized in three distinct types: naive, Savage rational with inconsistent beliefs, and sophisticated. We test the model in a laboratory experiment of collective decision-making. The data suggests that inclusiveness is indispensable with regard to explanatory power of the models of hierarchical thinking.Series: Department of Strategy and Innovation Working Paper Serie

Anarchy and Hierarchy

We advocate a new approach to study models of fermion masses and mixings, namely anarchy proposed in hep-ph/9911341. In this approach, we scan the O(1) coefficients randomly. We argue that this is the correct approach when the fundamental theory is sufficiently complicated. Assuming there is no physical distinction among three generations of neutrinos, the probability distributions in MNS mixing angles can be predicted independent of the choice of the measure. This is because the mixing angles are distributed according to the Haar measure of the Lie groups whose elements diagonalize the mass matrices. The near-maximal mixings, as observed in the atmospheric neutrino data and as required in the LMA solution to the solar neutrino problem, are highly probable. A small hierarchy between the Delta m^2 for the atmospheric and the solar neutrinos is obtained very easily; the complex seesaw case gives a hierarchy of a factor of 20 as the most probable one, even though this conclusion is more measure-dependent. U_{e3} has to be just below the current limit from the CHOOZ experiment. The CP-violating parameter sin delta is preferred to be maximal. We present a simple SU(5)-like extension of anarchy to the charged-lepton and quark sectors which works well phenomenologically.Comment: 26 page