Empirical Mode Decomposition(EMD) is an adaptive data analysis technique for analyzing nonlinear and nonstationary data[1]. EMD decomposes the original data into a number of Intrinsic Mode Functions(IMFs)[1] for giving better physical insight of the
data. Permutation Entropy(PE) is a complexity measure[3] function which is widely used in the field of complexity theory for analyzing the local complexity of time series. In this paper we are combining the concepts of PE and EMD to resolve the mode mixing problem observed in determination of IMFs.
In this work we analyze the corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining large reactor mixing angle $theta_{13}$ and checking the consistency with other neutrino mixing angles. The corrections a
re parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrix of the form $R_{ij}cdot U cdot R_{kl}$ where $R_{ij}$ is rotation in ij sector and U is any one of these special matrices. We showed the rotations $R_{13}cdot U cdot R_{23}$, $R_{12}cdot U cdot R_{13}$ for BM and $R_{13}cdot U cdot R_{13}$ for TBM perturbative case successfully fit all neutrino mixing angles within $1sigma$ range. The perturbed PMNS matrix $R_{12}cdot U cdot R_{13}$ for DC, TBM and $R_{23}cdot U cdot R_{23}$ for TBM case is successful in producing mixing angles at 2$sigma$ level. The other rotation schemes are either excluded or successful in producing mixing angles at $3sigma$ level.
We examined the influence of additional scalar doublet on the parameter space of the Standard Model supplemented with a generation of new vector like leptons. In particular we identified the viable regions of parameter space by inspecting various con
straints especially electroweak precision (S, T and U) parameters. We demonstrated that the additional scalar assists in alleviating the tension of electroweak precision constraints and thus permitting larger Yukawa mixing and mass splittings among vector like species. We also compared and contrasted the regions of parameter space pertaining to the latest LHC Higgs to diphoton channel results in this scenario with vector like leptons in single Higgs doublet and pure two Higgs doublet model case.
In this research paper, state space representation of concurrent, linearly coupled dynamical systems is discussed. It is reasoned that the Tensor State Space Representation (TSSR) proposed in [Rama1] is directly applicable in such a problem. Also som
e discussion on linearly coupled, concurrent systems evolving on multiple time scales is included. Briefly new ideas related to distributed signal processing in cyber physical systems are included.
We analyze $e^{+}e^{-}rightarrow gammagamma$, $e^{-}gamma rightarrow e^{-}gamma$ and $gammagamma rightarrow e^{+}e^{-} $ processes within the Seiberg-Witten expanded noncommutative scenario using polarized beams. With unpolarized beams the leading or
der effects of non commutativity starts from second order in non commutative(NC) parameter i.e. $O(Theta^2)$, while with polarized beams these corrections appear at first order ($O(Theta)$) in cross section. The corrections in Compton case can probe the magnetic component($vec{Theta}_B$) while in Pair production and Pair annihilation probe the electric component($vec{Theta}_E$) of NC parameter. We include the effects of earth rotation in our analysis. This study is done by investigating the effects of non commutativity on different time averaged cross section observables. The results which also depends on the position of the collider, can provide clear and distinct signatures of the model testable at the International Linear Collider(ILC).
We derive bounds on leptonic double mass insertions of the type $delta^{l}_{i4} delta^{l}_{4j}$ in four generational MSSM, using the present limits on $l_i to l_j + gamma$. Two main features distinguish the rates of these processes in MSSM4 from MSSM
3 : (a) tan$beta$ is restricted to be very small $lesssim 3 $ and (b) the large masses for the fourth generation leptons. In spite of small $tanbeta$, there is an enhancement in amplitudes with $llrr$($delta_{i4}^{ll}delta_{4j}^{rr}$) type insertions which pick up the mass of the fourth generation lepton, $m_{tau}$. We find these bounds to be at least two orders of magnitude more stringent than those in MSSM3.
