Berezin Transforms Attached to Landau Levels on the Complex Projective Space P^n(ℂ)

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Berezin transforms attached to Landau levels on the complex projective space CPn

8 pagesIn this paper, we construct coherent states for each generalized Bergman space on the n-dimensional complex projective space in order to apply a coherent states quantization method. Doing so allows to define the Berezin transform for these spaces. In particular, we provide a variational formula for this transform by means of the Fubini-Study Laplace operator which reduces when n = 1 and for the lowest spherical Landau level to the well-known formula previously given by Berezin himself

Maximum approximate likelihood estimation of general continuous-time state-space models

Mews S, Langrock R, Ötting M, Yaqine H, Reinecke J. Maximum approximate likelihood estimation of general continuous-time state-space models. Statistical Modelling. 2022: 1471082X211065785.Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean

The interplay of viral loads, clinical presentation, and serological responses in SARS-CoV-2 – Results from a prospective cohort of outpatient COVID-19 cases

Puchinger K, Castelletti N, Rubio-Acero R, et al. The interplay of viral loads, clinical presentation, and serological responses in SARS-CoV-2 – Results from a prospective cohort of outpatient COVID-19 cases. Virology. 2022;569:37-43