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

Bounds on Slow Roll at the Boundary of the Landscape

We present strong evidence that the tree level slow roll bounds of arXiv:1807.05193 and arXiv:1810.05506 are valid, even when the tachyon has overlap with the volume of the cycle wrapped by the orientifold. This extends our previous results in the volume-dilaton subspace to a semi-universal modulus. Emboldened by this and other observations, we investigate what it means to have a bound on (generalized) slow roll in a multi-field landscape. We argue that for $any$ point $\phi_0$ in an $N$-dimensional field space with $V(\phi_0) > 0$, there exists a path of monotonically decreasing potential energy to a point $\phi_1$ within a path length $\lesssim {\cal O}(1)$, such that $\sqrt{N}\ln \frac{V(\phi_1)}{V(\phi_0)} \lesssim - {\cal O} (1)$. The previous de Sitter swampland bounds are specific ways to realize this stringent non-local constraint on field space, but we show that it also incorporates (for example) the scenario where both slow roll parameters are intermediate-valued and the Universe undergoes a small number of e-folds, as in the Type IIA set up of arXiv:1310.8300. Our observations are in the context of tree level constructions, so we take the conservative viewpoint that it is a characterization of the classical "boundary" of the string landscape. To emphasize this, we argue that these bounds can be viewed as a type of Dine-Seiberg statement.Comment: v4: one more referenc

Probing the indefinite CP nature of the Higgs Boson through decay distributions in the process e+e−→ttˉΦe^+e^-\to t\bar{t}\Phi

The recently discovered scalar resonance at the LHC is now almost confirmed to be a Higgs Boson, whose CP properties are yet to be established. At the ILC with and without polarized beams, it may be possible to probe these properties at high precision. In this work, we study the possibility of probing departures from the pure CP-even case, by using the decay distributions in the process $e^+ e^- \to t \bar{t} \Phi$, with $\Phi$ mainly decaying into a $b\bar b$ pair. We have compared the case of a minimal extension of the SM case (Model I) with an additional pseudoscalar degree of freedom, with a more realistic case namely the CP-violating Two-Higgs Doublet Model (Model II) that permits a more general description of the couplings. We have considered the ILC with $\sqrt{s}=800$\,GeV and integrated luminosity of $300\, {\rm fb}^{-1}$. Our main findings are that even in the case of small departures from the CP-even case, the decay distributions are sensitive to the presence of a CP-odd component in Model II, while it is difficult to probe these departures in Model I unless the pseudoscalar component is very large. Noting that the proposed degrees of beam polarization increases the statistics, the process demonstrates the effective role of beam polarization in studies beyond the Standard Model. Further, our study shows that an indefinite CP Higgs would be a sensitive laboratory to physics beyond the SM.Comment: 14 pages using revtex, 10 figures, corresponds to version accepted for publication in Phys. Rev. D.; compared to v1, discussion extended, figure added, table added, section reorganize

Existence of Picard operator and iterated function system

[EN] In this paper, we define weak θm− contraction mappings and give a new class of Picard operators for such class of mappings on a complete metric space. Also, we obtain some new results on the existence and uniqueness of attractor for a weak θm− iterated multifunction system. Moreover, we introduce (α, β, θm)− contractions using cyclic (α, β)− admissible mappings and obtain some results for such class of mappings without the continuity of the operator. We also provide an illustrative example to support the concepts and results proved herein.The authors are thankful to the learned referee for valuable suggestions. The second author is also thankful to AISTDF, DST for the research grant vide project No. CRD/2018/000017.Garg, M.; Chandok, S. (2020). Existence of Picard operator and iterated function system. Applied General Topology. 21(1):57-70. https://doi.org/10.4995/agt.2020.11992OJS5770211S. Alizadeh, F. Moradlou and P. Salimi, Some fixed point results for (α, β) − (ψ, φ)- contractive mappings, Filomat 28 (2014), 635-647. https://doi.org/10.2298/FIL1403635AM. F. Barnsley, Fractals Everywhere, Revised with the Assistance of and with a Foreword by Hawley Rising, III. Academic Press Professional, Boston (1993).R. M. T. Bianchini, Su un problema di S. Reich riguardante la teoria dei punti fissi, Boll. Un. Mat. Ital. 5 (1972), 103-108.E. L. Fuster, A. Petrusel and J. C. Yao, Iterated function system and well-posedness, Chaos Sol. Fract. 41 (2009), 1561-1568. https://doi.org/10.1016/j.chaos.2008.06.019R. H. Haghi, Sh. Rezapour and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal. 74 (2011), 1799-1803. https://doi.org/10.1016/j.na.2010.10.052N. Hussain, V. Parvaneh, B. Samet and C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2015, 185 (2015). https://doi.org/10.1186/s13663-015-0433-zJ. E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 30, no. 5 (1981), 713-747. https://doi.org/10.1512/iumj.1981.30.30055M. Imdad, W. M. Alfaqih and I. A. Khan, Weak θ−contractions and some fixed point results with applications to fractal theory, Adv. Diff. Eq. 439 (2018). https://doi.org/10.1186/s13662-018-1900-8M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 38 (2014). https://doi.org/10.1186/1029-242X-2014-38M. Radenovic and S. Chandok, Simulation type functions and coincidence points, Filomat, 32, no. 1 (2018), 141-147. https://doi.org/10.2298/FIL1801141RB. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. American Math. Soc. 226 (1977), 257-290. https://doi.org/10.1090/S0002-9947-1977-0433430-4I. A. Rus, Picard operators and applications, Sci. Math. Jpn. 58, no. 1 (2003), 191-219.I. A. Rus, A. Petrusel and G. Petrusel, Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.N. A. Secelean, Countable Iterated Function Systems, LAP LAMBERT Academic Publishing (2013). https://doi.org/10.1186/1687-1812-2013-277N. A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. 2013, 277 (2013). https://doi.org/10.1186/1687-1812-2013-277V. M. Sehgal, On fixed and periodic points for a class of mappings, J. London Math. Soc. 5 (1972), 571-576. https://doi.org/10.1112/jlms/s2-5.3.571S.-A. Urziceanu, Alternative charaterizations of AGIFSs having attactors, Fixed Point Theory 20 (2019), 729-740. https://doi.org/10.24193/fpt-ro.2019.2.4

Naive Bayes Model with Improved Negation Handling and N-Gram Method for Sentiment Classification

Sentiment classification is turning into one of the most fundamental research areas for prediction and classification. In Sentiment mining, we basically try to analyse the results and predict outcomes that are based on customer feedback or opinions. Some work has been done to increase the accuracy of the Naive Bayes classifier. In this project we have examined different methods of improvising the accuracy and space of a Naive Bayes classifier for sentiment classification. We have used a modified negation handling method using POS tagging to decrease the number of feature in the feature set and also discovered that combining these with n-gram method results in improvement in the accuracy. So, a more accurate sentiment classifier with less space complexity can be built from Naive Bayes Classifier