We develop a number of novel "black-bounce" spacetimes. These are specific regular black holes where the "area radius" always remains non-zero, thereby leading to "throat" that is either timelike (corresponding traversable wormhole), spacelike "bounce" into future universe), or null "one-way wormhole"). shall first perform general analysis regularity conditions for such spacetime, and then cons...

The notion of causal operators is extended to periodic boundary value problems with nonlinear boundary conditions in this paper. By utilizing the monotone iterative technique and the method of lower and upper solutions (resp. weakly coupled lower and upper solutions), we establish the existence of the extremal solutions (resp. weakly coupled extremal quasi-solutions) for nonlinear periodic boun...

We introduce a simple method to illustrate how the Lorentz transformation lead to causal loop paradoxes when they are applied to superluminal velocities. c © Electronic Journal of Theoretical Physics. All rights reserved.

Learning to perform a task in an environment with sparse feedback is a difficult problem. While several approaches for increasing feedback during learning have been taken, these methods suffer from the dependency on human knowledge and engineering to find good solutions. We propose using causal models to increase the amount of feedback that will improve learning. This approach does not require ...

Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model for the measurement-error-free variables can be identified in the presence of measurement error with unknown variance. In this paper, we study precise sufficie...

The definition and study of causal operators are based on the representation theory of group algebras. We study the structure of the spectra of causal operators, obtain conditions for causal invertibility and state criteria for a causal operator to belong to the radical.

The linear optimal ltering problems in innnite dimensional Hilbert spaces and their extensions are investigated. The quality functional is allowed to be a general quadratic functional deened by a possibly degenerate operator. We describe the solution of the stable and the causal ltering problems. In case of the causal ltering we establish the relation with a relaxed causal ltering problem in th...