Non-archimedean Yomdin-Gromov parametrizations and points of bounded height

We prove an analogue of the Yomdin-Gromov Lemma for $p$-adic definable sets and more broadly in a non-archimedean, definable context. This analogue keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconnected case. We apply this result to bound the number of rational points of bounded height on the transcendental part of $p$-adic subanalytic sets, and to bound the dimension of the set of complex polynomials of bounded degree lying on an algebraic variety defined over $\mathbb{C} ((t))$, in analogy to results by Pila and Wilkie, resp. by Bombieri and Pila. Along the way we prove, for definable functions in a general context of non-archimedean geometry, that local Lipschitz continuity implies piecewise global Lipschitz continuity.Comment: 54 pages; revised, section 5.6 adde

Quasi maximum likelihood estimation for strongly mixing state space models and multivariate L\'evy-driven CARMA processes

We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate L\'evy-driven continuoustime autoregressive moving average (MCARMA) processes. In the discrete-time setting, we prove strong consistency and asymptotic normality of the QML estimator under standard moment assumptions and a strong-mixing condition on the output process of the state space model. In the second part of the paper, we investigate probabilistic and analytical properties of equidistantly sampled continuous-time state space models and apply our results from the discrete-time setting to derive the asymptotic properties of the QML estimator of discretely recorded MCARMA processes. Under natural identifiability conditions, the estimators are again consistent and asymptotically normally distributed for any sampling frequency. We also demonstrate the practical applicability of our method through a simulation study and a data example from econometrics

Symmetry Energy II: Isobaric Analog States

Using excitation energies to isobaric analog states (IAS) and charge invariance, we extract nuclear symmetry coefficients, from a mass formula, on a nucleus-by-nucleus basis. Consistently with charge invariance, the coefficients vary weakly across an isobaric chain. However, they change strongly with nuclear mass and range from a_a~10 MeV at mass A~10 to a_a~22 MeV at A~240. Following the considerations of a Hohenberg-Kohn functional for nuclear systems, we determine how to find in practice the symmetry coefficient using neutron and proton densities, even when those densities are simultaneously affected by significant symmetry-energy and Coulomb effects. These results facilitate extracting the symmetry coefficients from Skyrme-Hartree-Fock (SHF) calculations, that we carry out using a variety of Skyrme parametrizations in the literature. For the parametrizations, we catalog novel short-wavelength instabilities. In comparing the SHF and IAS results for the symmetry coefficients, we arrive at narrow (+-2.4 MeV) constraints on the symmetry energy values S(rho) at 0.04<rho<0.13 fm^-3. Towards normal density the constraints significantly widen, but the normal value of energy a_a^V and the slope parameter L are found to be strongly correlated. To narrow the constraints, we reach for the measurements of asymmetry skins and arrive at a_a^V=(30.2-33.7) MeV and L=(35-70) MeV, with those values being again strongly positively correlated along the diagonal of their combined region. Inclusion of the skin constraints allows to narrow the constraints on S(rho), at 0.04<rho<0.13 fm^-3, down to +-1.1 MeV. Several microscopic calculations, including variational, Bruckner-Hartree-Fock and Dirac-Bruckner-Hartree-Fock, are consistent with our constraint region on S(rho).Comment: 101 pages, 27 figures, 2 tables; submitted to Nuclear Physics

Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations

We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g.~as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDE) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE). The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.Comment: 16 pages, 6 figure

Interpretation of the evolution parameter of the Feynman parametrization of the Dirac equation

The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The Stueckelberg interpretation of antiparticles naturally arises from the formalism.Comment: 6 pages, RevTex, no figures, submitted to Phys. Lett.