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We implement an algorithm for the computation of Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems: Maple, Reduce and Mathematica. This class of Hamiltonian operators encompass almost all the examples coming from the theory of (1+1)-integrable evolutionary PDEs

To evaluate the diagnostic performance of semi-supervised learning models for aggressive prostate cancer detection on MRI compared to fully supervised models trained with additional expert annotations.

There is considerable need to improve and increase the detection and measurement of depression. The use of speech as a digital biomarker of depression represents a considerable opportunity for transforming and accelerating depression identification and treatment; however, research to date has primarily consisted of small-sample feasibility or pilot studies incorporating highly controlled applications and settings. There has been limited examination of the technology in real-world use contexts.

It is shown that a Dirac bracket algebra is isomorphic to the original Poisson bracket algebra of first class functions subject to first class constraints. The isomorphic image of the Dirac bracket algebra in the star-product commutator algebra is found.

Background