18,054 research outputs found
Consistency of perturbed Tribimaximal, Bimaximal and Democratic mixing with Neutrino mixing data
We scrutinize corrections to tribimaximal (TBM), bimaximal (BM) and
democratic (DC) mixing matrices for explaining recent global fit neutrino
mixing data. These corrections are parameterized in terms of small orthogonal
rotations (R) with corresponding modified PMNS matrices of the forms
\big(\big ) where is
rotation in ij sector and U is any one of these special matrices. We showed
that for perturbative schemes dictated by single rotation, only \big( \big ) can
fit the mixing data at level. However for type rotations, only \big (\big ) is successful to fit all neutrino mixing angles within
range. For perturbative scheme, only
\big(,~,~\big ) are consistent at
level. The remaining double rotation cases are either excluded at
3 level or successful in producing mixing angles only at
level. We also updated our previous analysis on PMNS matrices
of the form \big(\big ) with recent mixing data. We
showed that the results modifies substantially with fitting accuracy level
decreases for all of the permitted cases except \big(, and \big ) in this rotation scheme.Comment: 41 pages, 102 figures, References Added. arXiv admin note:
substantial text overlap with arXiv:1308.305
Bounds on Slow Roll and the de Sitter Swampland
The recently introduced swampland criterion for de Sitter (arXiv:1806.08362)
can be viewed as a (hierarchically large) bound on the smallness of the slow
roll parameter . This leads us to consider the other slow roll
parameter more closely, and we are lead to conjecture that the bound
is not necessarily on , but on slow roll itself. A natural
refinement of the de Sitter swampland conjecture is therefore that slow roll is
violated at in Planck units in any UV complete theory. A
corollary is that need not necessarily be , if
holds. We consider various tachyonic tree level
constructions of de Sitter in IIA/IIB string theory (as well as closely related
models of inflation), which superficially violate arXiv:1806.08362, and show
that they are consistent with this refined version of the bound. The phrasing
in terms of slow roll makes it plausible why both versions of the conjecture
run into trouble when the number of e-folds during inflation is high. We
speculate that one way to evade the bound could be to have a large number of
fields, like in -flation.Comment: v2: many refs added, clarifications and comments added, improved
wording regarding single/multi-field and potential/Hubble slow roll, typos
fixe
Necessary and Sufficient Conditions on Partial Orders for Modeling Concurrent Computations
Partial orders are used extensively for modeling and analyzing concurrent
computations. In this paper, we define two properties of partially ordered
sets: width-extensibility and interleaving-consistency, and show that a partial
order can be a valid state based model: (1) of some synchronous concurrent
computation iff it is width-extensible, and (2) of some asynchronous concurrent
computation iff it is width-extensible and interleaving-consistent. We also
show a duality between the event based and state based models of concurrent
computations, and give algorithms to convert models between the two domains.
When applied to the problem of checkpointing, our theory leads to a better
understanding of some existing results and algorithms in the field. It also
leads to efficient detection algorithms for predicates whose evaluation
requires knowledge of states from all the processes in the system
Parallel and Distributed Algorithms for the Housing Allocation Problem
We give parallel and distributed algorithms for the housing allocation
problem. In this problem, there is a set of agents and a set of houses. Each
agent has a strict preference list for a subset of houses. We need to find a
matching such that some criterion is optimized. One such criterion is Pareto
Optimality. A matching is Pareto optimal if no coalition of agents can be
strictly better off by exchanging houses among themselves. We also study the
housing market problem, a variant of the housing allocation problem, where each
agent initially owns a house. In addition to Pareto optimality, we are also
interested in finding the core of a housing market. A matching is in the core
if there is no coalition of agents that can be better off by breaking away from
other agents and switching houses only among themselves.
In the first part of this work, we show that computing a Pareto optimal
matching of a house allocation is in {\bf CC} and computing the core of a
housing market is {\bf CC}-hard. Given a matching, we also show that verifying
whether it is in the core can be done in {\bf NC}. We then give an algorithm to
show that computing a maximum Pareto optimal matching for the housing
allocation problem is in {\bf RNC}^2 and quasi-{\bf NC}^2. In the second part
of this work, we present a distributed version of the top trading cycle
algorithm for finding the core of a housing market. To that end, we first
present two algorithms for finding all the disjoint cycles in a functional
graph: a Las Vegas algorithm which terminates in rounds with high
probability, where is the length of the longest cycle, and a deterministic
algorithm which terminates in rounds, where is the
number of nodes in the graph. Both algorithms work in the synchronous
distributed model and use messages of size
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