1,137,294 research outputs found
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 is well known to be analogous to the KdV
hierarchy at goes to infinity. This paper shows that given 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 under the KdV
hierarchy. Further, the conserved quantities of 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 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 data is affected by \ty-hierarchy and
octant-hierarchy degeneracies, which limit the hierarchy sensitivity of such
data. A combination of and \anu data is not subject to these
degeneracies and hence has much better hierarchy discrimination capability. We
find that, with a 3 year run, hierarchy determination is possible for
only two of the four octant-hierarchy combinations. Equal 1.5 year runs in
and \anu modes give good hierarchy sensitivity for all the four
combinations
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
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
The sAKNS Hierarchy
We study, systematically, the properties of the supersymmetric AKNS (sAKNS)
hierarchy. In particular, we discuss the Lax representation in terms of a
bosonic Lax operator and some special features of the equations and construct
the bosonic local charges as well as the fermionic nonlocal charges associated
with the system starting from the Lax operator. We obtain the Hamiltonian
structures of the system and check the Jacobi identity through the method of
prolongation. We also show that this hierarchy of equations can equivalently be
described in terms of a fermionic Lax operator. We obtain the zero curvature
formulation as well as the conserved charges of the system starting from this
fermionic Lax operator which suggests a connection between the two. Finally,
starting from the fermionic description of the system, we construct the soliton
solutions for this system of equations through Darboux-Backlund transformations
and describe some open problems.Comment: LaTeX, 16 pg
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
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