On the equations of electrodynamics in a flat or curved spacetime and a possible interaction energy

In this paper the independent equations of continuum electrodynamics and their quantity are investigated, beginning with the standard equations used in special and general relativity. Using differential identities it is checked that there are as many independent equations as there are unknowns, for the case with given sources as well as for the general case where the motion of the charged medium producing the field is unknown. This problem is then discussed in an alternative theory of gravity with a preferred reference frame, in order to constrain an additional, “interaction” energy tensor that has to be postulated in this theory, and that would be present also outside usual matter. In order that the interaction tensor be Lorentz-invariant in special relativity, it has to depend only on a scalar fieldp. Since the system of electrodynamics is closed in the absence of the interaction tensor, just one scalar equation more is needed to close it again in the presence ofp. That equation is taken to be the equation for charge conservation. Finally, the equations that allow the determination of fieldpare derived in a given weak gravitational field and in a given electromagnetic field.

Joint Learning of Phenotypes and Diagnosis-Medication Correspondence via Hidden Interaction Tensor Factorization

Non-negative tensor factorization has been shown effective for discovering phenotypes from the EHR data with minimal human supervision. In most cases, an interaction tensor of the elements in the EHR (e.g., diagnoses and medications) has to be first established before the factorization can be applied. Such correspondence information however is often missing. While different heuristics can be used to estimate the missing correspondence, any errors introduced will in turn cause inaccuracy for the subsequent phenotype discovery task. This is especially true for patients with multiple diseases diagnosed (e.g., under critical care). To alleviate this limitation, we propose the hidden interaction tensor factorization (HITF) where the diagnosis-medication correspondence and the underlying phenotypes are inferred simultaneously. We formulate it under a Poisson non-negative tensor factorization framework and learn the HITF model via maximum likelihood estimation. For performance evaluation, we applied HITF to the MIMIC III dataset. Our empirical results show that both the phenotypes and the correspondence inferred are clinically meaningful. In addition, the inferred HITF model outperforms a number of state-of-the-art methods for mortality prediction.

Charge conservation in a gravitational field in the scalar ether theory

A modification of the Maxwell equations due to the presence of a gravitational field was formerly proposed for a scalar theory with a preferred reference frame. With this modification, the electric charge is not conserved. The aim of the present work was to numerically assess the amount of charge production or destruction. We propose an asymptotic scheme for the electromagnetic field in a weak and slowly varying gravitational field. This scheme is valid independently of the theory and the “gravitationally-modified” Maxwell equations. Then we apply this scheme to plane waves and to a group of Hertzian dipoles in the scalar ether theory. The predicted amounts of charge production/destruction discard the formerly proposed gravitationally-modified Maxwell equations. The theoretical reason for that is the assumption that the total energy tensor is the sum of the energy tensor of the medium producing the electromagnetic (e.m.) field and the e.m. energy tensor. This means that an additional, “interaction” tensor has to be present. With this assumption, the standard Maxwell equations in a curved spacetime, which predict charge conservation, are compatible with the investigated theory. We find that the interaction energy might contribute to the dark matter.