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($R_{ij}^l\cdot U,~U\cdot R_{ij}^r,~U \cdot R_{ij}^r \cdot R_{kl}^r,~R_{ij}^l \cdot R_{kl}^l \cdot U$\big ) where $R_{ij}^{l, r}$ 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($R_{12}^l\cdot U_{BM},~R_{13}^l\cdot U_{BM},~U_{TBM}\cdot R_{13}^r$ \big ) can fit the mixing data at $3\sigma$ level. However for $R_{ij}^l\cdot R_{kl}^l\cdot U$ type rotations, only \big ($R_{23}^l\cdot R_{13}^l \cdot U_{DC}$\big ) is successful to fit all neutrino mixing angles within $1\sigma$ range. For $U\cdot R_{ij}^r\cdot R_{kl}^r$ perturbative scheme, only \big($U_{BM} \cdot R_{12}^r\cdot R_{13}^r$,~$U_{DC} \cdot R_{12}^r\cdot R_{23}^r$,~$U_{TBM} \cdot R_{12}^r\cdot R_{13}^r$\big ) are consistent at $1\sigma$ level. The remaining double rotation cases are either excluded at 3$\sigma$ level or successful in producing mixing angles only at $2\sigma-3\sigma$ level. We also updated our previous analysis on PMNS matrices of the form \big($R_{ij}\cdot U \cdot R_{kl}$\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($R_{12}\cdot U_{BM}\cdot R_{13}$, $R_{23}\cdot U_{TBM}\cdot R_{13}$ and $R_{13}\cdot U_{TBM} \cdot R_{13}$\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 $\epsilon_V$. This leads us to consider the other slow roll parameter $\eta_V$ more closely, and we are lead to conjecture that the bound is not necessarily on $\epsilon_V$, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at ${\cal O}(1)$ in Planck units in any UV complete theory. A corollary is that $\epsilon_V$ need not necessarily be ${\cal O}(1)$, if $\eta_V \lesssim -{\cal O}(1)$ 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 $N$-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 $O(\log l)$ rounds with high probability, where $l$ is the length of the longest cycle, and a deterministic algorithm which terminates in $O(\log^* n \log l)$ rounds, where $n$ is the number of nodes in the graph. Both algorithms work in the synchronous distributed model and use messages of size $O(\log n)$