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Generative AI as a transformational logic for cognitive neuroscience. [PDF]

Commun Biol
Beste C, Safavi S.
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Learning the reaction coordinate: collective variables from physical intuition to generative models.

Digit Discov
Talmazan RA, Chen CG, Tang C, Megías A, Contreras Arredondo S, Chipot C.   +5 more
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A Variational Principle for Scattering

Physical Review, 1952
A variational principle is presented for the phase shifts ${\ensuremath{\delta}}_{l}$ of a central force scattering problem. This generalizes the principles of Schwinger and Hulth\`en for $S$-state scattering in that (a) it is applicable to states of higher angular momentum, and (b) it depends explicitly on the "inside" wave function only.
Feshbach, Herman, Rubinow, S. I.
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A variational principle in optics

Journal of the Optical Society of America A, 2004
We derive a new variational principle in optics. We first formulate the principle for paraxial waves and then generalize it to arbitrary waves. The new principle, unlike the Fermat principle, concerns both the phase and the intensity of the wave. In particular, the principle provides a method for finding the ray mapping between two surfaces in space ...
Jacob, Rubinstein, Gershon, Wolansky
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On the Generality of Variational Principles

Milan Journal of Mathematics, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Schwinger’s variational principle

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1957
Abstract The classical and quantum theories of dynamical systems whose Lagrangians are linear in the co-ordinate derivatives are studied, with a view to clarifying a number of points in relation to Schwinger’s quantum-mechanical variational principle.
Kibble, T. W. B., Polkinghorne, J. C.
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Complementary variational principles and variational-iterative principles

Journal of Physics A: Mathematical and General, 1981
Complementary variational principles for the solution of certain linear equations are developed. It is shown that these may be used iteratively for the solution of nonlinear equations. Examples are presented with applications in particle theory, electromagnetic theory, communication theory and the Thomas-Fermi statistical theory for atoms.
Burrows, B. L., Perks, A. J.
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Variational principles in elastostatics

Meccanica, 1967
In a previous paper three new variational principles of elastostatics in the theory of small displacements were added to the four principles previously known: that of the minimum potential energy, of Menabrea-Finzi, of Reissner and of Hu-Washizu. This paper presents another new principle plus a variant of Reissner's principle and of its dual and ...
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Variation Principles of Hydrodynamics

The Physics of Fluids, 1960
It is shown that the Lagrangian equations for the motion of both incompressible and compressible fluids can be derived from variation principles. As has been pointed out by C. C. Lin, an important feature of these principles is the boundary condition: The coordinates of each particle (and not merely the normal component of its velocity) must be ...
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