Letters in High Energy Physics 2019-09-17T18:30:24+00:00 Professor Shaaban Khalil Open Journal Systems <p>Letters in High Energy Physics (LHEP) is a quarterly, peer-reviewed, hybird open access journal which specializes in theory, phenomenological, and experimental aspects of particle physics. Additional topics covered by LHEP include astrophysics, gravity, and cosmology.&nbsp; LHEP publishes articles in the letter format.</p> <p>The goal is to provide the high energy physics community with a medium through which researchers are able to publish informative summaries of important findings in the field.</p> <p style="text-align: justify;"><span style="font-family: 'Minion W08 Regular_1167271',Times; font-size: 17px; font-variant-ligatures: normal; background-color: #ffffff;">&nbsp;</span></p> A new perspective on the Ermakov-Pinney and scalar wave equations 2019-08-06T08:43:36+00:00 Giampiero Esposito Marica Minucci, Dr. <p>The first part of the paper proves that a subset of the general set of Ermakov-Pinney equations<br>can be obtained by differentiation of a first-order non-linear differential equation. The second part<br>of the paper proves that, similarly, the equation for the amplitude function for the parametrix of<br>the scalar wave equation can be obtained by covariant differentiation of a first-order non-linear<br>equation. The construction of such a first-order non-linear equation relies upon a pair of auxiliary<br>1-forms (psi,rho). The 1-form psi satisfies the divergenceless condition div(psi) = 0, whereas the 1-form rho <br>fulfills the non-linear equation div(rho)+rho**2 = 0. The auxiliary 1-forms (psi,rho) are evaluated explicitly<br>in Kasner space-time, and hence also amplitude and phase function in the parametrix are obtained.<br>Thus, the novel method developed in this paper can be used with profit in physical applications.</p> 2019-08-06T08:41:59+00:00 ##submission.copyrightStatement## Asymmetric nonsingular bounce from a dynamic scalar field 2019-09-03T15:01:49+00:00 Frans R. Klinkhamer Ziliang L. Wang <p>We present a dynamical model for a time-asymmetric nonsingular bounce<br>with a post-bounce change of the effective equation-of-state parameter.<br>Specifically, we consider a scalar-field model with a<br>time-reversal-noninvariant effective potential.</p> 2019-09-03T14:34:33+00:00 ##submission.copyrightStatement## Connections between physics, mathematics, and deep learning 2019-09-17T18:30:24+00:00 Jean Thierry-Mieg <p>Starting from Fermat’s principle of least action, which governs classical and quantum mechanics and from<br>the theory of exterior differential forms, which governs the geometry of curved manifolds, we show how<br>to derive the equations governing neural networks in an intrinsic, coordinate-invariant way, where the loss<br>function plays the role of the Hamiltonian. To be covariant, these equations imply a layer metric which is<br>instrumental in pretraining and explains the role of conjugation when using complex numbers. The differential<br>formalism clarifies the relation of the gradient descent optimizer with Aristotelian and Newtonian<br>mechanics. The Bayesian paradigm is then analyzed as a renormalizable theory yielding a new derivation<br>of the Bayesian information criterion. We hope that this formal presentation of the differential geometry<br>of neural networks will encourage some physicists to dive into deep learning and, reciprocally, that the<br>specialists of deep learning will better appreciate the close interconnection of their subject with the foundations<br>of classical and quantum field theory.</p> 2019-09-17T16:02:42+00:00 ##submission.copyrightStatement##