We developed an open source software for crustal strain analysis using the least-squares collocation method based on the spherical model of the earth. The software is able to simultaneously determine the signal and noise of the velocities at the observation points with the best possible removal of the observational errors, or at any other position with no velocity observation. Furthermore, the ...

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynam-ics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equa...

Representing texts as fixed-length vectors is central to many language processing tasks. Most traditional methods build text representations based on the simple Bag-of-Words (BoW) representation, which loses the rich semantic relations between words. Recent advances in natural language processing have shown that semantically meaningful representations of words can be efficiently acquired by dis...

For the spherical model with nearest-neighbour interactions, the microcanonical entropy s(ε,m) is computed analytically in the thermodynamic limit for all accessible values of the energy ε and the magnetization m per spin. The entropy is found to be a concave function, implying that the microcanonical and the canonical ensemble are equivalent, despite the long-range nature of the spherical cons...

We prove that the quantum stress tensor for a massless scalar field in two dimensional non-self-similar Tolman-Bondi dust collapse and Vaidya radiation collapse models diverges on the Cauchy horizon, if the latter exists. The two dimensional model is obtained by suppressing angular coordinates in the corresponding four dimensional spherical model.