However, when we seek explanations rather than mere formal descriptions of variational principles, almost invariably we discover a combinatorial origin; the best known examples are thermodynamics and Darwinian evolution. When it comes to the least-action principle, however, it is surprising that ...
Nowadays it is obtained from a variational formulation of geometric optics.Answer and Explanation: Fermat's principle states that a light ray follows a route that minimizes the optical path length. It is a variational principle, given two fixed...Become a member and unlock all Study Answers S...
As it is shown in the first part of this short essay, duality plus conservation laws allow the violation of Bell’s inequalities for any spatio-temporal separation. To dig deeper into particle dualism, in the second part, a class of models is proposed as a working framework. It encompasses...
Boris Mordukhovich is an American mathematician recognized for his research in the areas of nonlinear analysis, optimization, and control theory. Mordukhovich is one of the founders of modern variational analysis and generalized differentiatio...
What is a variational autoencoder? Variational autoencoders (VAEs) aregenerative modelsused inmachine learning(ML) to generate new data in the form ofvariationsof the input data they’re trained on. In addition to this, they also perform tasks common to other autoencoders, such as denoising...
Neuroscience research is undergoing a minor revolution. Recent advances in machine learning and artificial intelligence research have opened up new ways of thinking about neural computation. Many researchers are excited by the possibility that deep neura
In principle, any two-dimensional set is a valid region separating ore from waste. For example, for a given function f(⋅) we could have a set defined by grade pairs (x,y) such that y≥f(x). One could also have a region defined by the union—or intersection—of two or more ...
verbs are illocutionary verbs; there is too much overlap of the categories; there is too much heterogeneity within the categories; many of the verbs listed in the categories don’t satisfy the definition given for the category; and, most important, there is no consistent principle of ...
2.4, we would like to search for a variational principle that selects families of this type. The natural idea here is to try to generalize the extrinsic curvature argument to time-dependent situations. As in Sect. 3.1, consider an arbitrary spacelike curve Cm(λ) in AdS3, with tangent ...
as they excel in various scientific applications beyond what was considered possible. Yet from a certain vantage point, they are nothing but parametrized functionsffθθ(xx)of some data vectorxx, and their ‘learning’ is nothing but an iterative, algorithmic fitting of the parameters to data. ...