One of the main reasons why the Hamiltonian formalism is more useful than the Lagrangian formalism is that the set of coordinate transformations that leave invariant the form of the Hamilton equations is much wider than the set of coordinate transformations that leave invariant the form of the Lagrange equations. Furthermore, each of the so-called canonical transformations leaves invariant the ...

Inputs: Source domain data: T so = {(X i , Y so i )} nso i=1, target domain data: T ta = {(X i , Y ta i )} nta i=1, transformation function: G, algorithm to train f : Aso and an algorithm to train wG: AwG . Outputs: Regression function for the target domain: f̂ . 1: Train the source domain regression function f̂ = Aso (T ). 2: Construct new data to train wG with f̂ and T : T wG = {(X i ,Wi)} nta i...

Studies show that gene acquisition through natural transformation has contributed significantly to the adaptation and ecological diversification of several bacterial species. Relatively little is still known, however, about the prevalence and phylogenetic distribution of organisms possessing this property. Thus, whether natural transformation only benefits a limited number of species or has a l...

Communicative, predatory, and reproductive behaviors rely on the auditory thalamocortical system, a key nexus that combines, transforms, and distributes virtually all acoustic information relevant to survival. The rules of connectivity for this complex network, both anatomically and functionally, are only beginning to be uncovered. Although the auditory thalamocortical system shares many featur...