An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Wrong sign and symmetric limits and non-decoupling in 2HDMs

We analyse the possibility that, in two Higgs doublet models, one or more of the Higgs couplings to fermions or to gauge bosons change sign, relative to the respective Higgs Standard Model couplings. Possible sign changes in the coupling of a neutral scalar to charged ones are also discussed. These wrong signs can have important physical consequences, manifesting themselves in Higgs production via gluon fusion or Higgs decay into two gluons or into two photons. We consider all possible wrong sign scenarios, and also the symmetric limit, in all possible Yukawa implementations of the two Higgs doublet model, in two different possibilities: the observed Higgs boson is the lightest CP-even scalar, or the heaviest one. We also analyse thoroughly the impact of the currently available LHC data on such scenarios. With all 8 TeV data analysed, all wrong sign scenarios are allowed in all Yukawa types, even at the 1 sigma level. However, we will show that B-physics constraints are crucial in excluding the possibility of wrong sign scenarios in the case where tan beta is below 1. We will also discuss the future prospects for probing the wrong sign scenarios at the next LHC run. Finally we will present a scenario where the alignment limit could be excluded due to non-decoupling in the case where the heavy CP-even Higgs is the one discovered at the LHC.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.