Brane structures in microlocal sheaf theory

Let $L$ be an exact Lagrangian submanifold of a cotangent bundle $T^* M$, asymptotic to a Legendrian submanifold $\Lambda \subset T^{\infty} M$. We study a locally constant sheaf of $\infty$-categories on $L$, called the sheaf of brane structures or $\mathrm{Brane}_L$. Its fiber is the $\infty$-category of spectra, and we construct a Hamiltonian invariant, fully faithful functor from $\Gamma(L,\mathrm{Brane}_L)$ to the $\infty$-category of sheaves of spectra on $M$ with singular support in $\Lambda$.Comment: 35 pages, 13 figure

Measurement of single electron spin with sub-micron Hall magnetometer

Submicron Hall magnetometry has been demonstrated as an efficient technique to probe extremely weak magnetic fields. In this letter, we analyze the possibility of employing it to detect single electron spin. Signal strength and readout time are estimated and discussed with respect to a number of practical issues.Comment: 4 pages, 2 figur

The signatures of the new particles h2h_2 and ZμτZ_{\mu\tau} at e-p colliders in the U(1)Lμ−LτU(1)_{L_\mu-L_\tau} model

Considering the superior performances of the future e-p colliders, LHeC and FCC-eh, we discuss the feasibility of detecting the extra neutral scalar $h_{2}$ and the light gauge boson $Z^{}_{\mu\tau}$, which are predicted by the ${U(1)}_{L^{}_{\mu} - L^{}_{\tau}}$ model. Taking into account the experimental constraints on the relevant free parameters, we consider all possible production channels of $h_{2}$ and $Z^{}_{\mu\tau}$ at e-p colliders and further investigate their observability through the optimal channels in the case of the beam polarization P($e^{-}$)= -0.8. We find that the signal significance above 5$\sigma$ of $h_{2}$ as well as $Z^{}_{\mu\tau}$ detecting can be achieved via $e^{-}p\to{e^{-}jh_{2}(\to{Z_{\mu\tau}Z_{\mu\tau}})}\to~e^{-}j+/\!\!\!\!{E}^{}_{T}$ process and a 5$\sigma$ sensitivity of $Z^{}_{\mu\tau}$ detecting can be gained via $e^{-}p\to{e^{-}jh_{1}(\to{Z^{}_{\mu\tau}Z^{}_{\mu\tau}})\to}~e^{-}j+/\!\!\!\!{E}^{}_{T}$ process at e-p colliders with appropriate parameter values and a designed integrated luminosity. However, the signals of $h_{2}$ decays into pair of SM particles are difficult to be detected.Comment: 22 pages, 9 figures, references added and typos are correcte

Modelling Realized Covariances and Returns

This paper proposes new dynamic component models of realized covariance (RCOV) matrices based on recent work in time-varying Wishart distributions. The specifications are linked to returns for a joint multivariate model of returns and covariance dynamics that is both easy to estimate and forecast. Realized covariance matrices are constructed for 5 stocks using high-frequency intraday prices based on positive semi-definite realized kernel estimates. The models are compared based on a term-structure of density forecasts of returns for multiple forecast horizons. Relative to multivariate GARCH models that use only daily returns, the joint RCOV and return models provide significant improvements in density forecasts from forecast horizons of 1 day to 3 months ahead. Global minimum variance portfolio selection is improved for forecast horizons up to 3 weeks out.eigenvalues, dynamic conditional correlation, predictive likelihoods, MCMC

Modelling Realized Covariances

This paper proposes a new dynamic model of realized covariance (RCOV) matrices based on recent work in time-varying Wishart distributions. The specifications can be linked to returns for a joint multivariate model of returns and covariance dynamics that is both easy to estimate and forecast. Realized covariance matrices are constructed for 5 stocks using high-frequency intraday prices based on positive semi-definite realized kernel estimates. We extend the model to capture the strong persistence properties in RCOV. Out-of-sample performance based on statistical and economic metrics show the importance of this. We discuss which features of the model are necessary to provide improvements over a traditional multivariate GARCH model that only uses daily returns.eigenvalues, dynamic conditional correlation, predictive likelihoods, MCMC

Modelling Realized Covariances and Returns

This paper proposes new dynamic component models of returns and realized covariance (RCOV) matrices based on time-varying Wishart distributions. Bayesian estimation and model comparison is conducted with a range of multivariate GARCH models and existing RCOV models from the literature. The main method of model comparison consists of a term-structure of density forecasts of returns for multiple forecast horizons. The new joint return-RCOV models provide superior density forecasts for returns from forecast horizons of 1 day to 3 months ahead as well as improved point forecasts for realized covariances. Global minimum variance portfolio selection is improved for forecast horizons up to 3 weeks out.Wishart distribution, predictive likelihoods, density forecasts, MCMC