Quaternionic Wave Packets

We compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. This analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations from standard quantum mechanics.Comment: 9 pages, 1 figur

Human-like Walking with Compliant Legs

This work presents a novel approach to robotic bipedal walking. Based on the bipedal spring-mass model, which is known to closely describe human-like walking behavior, a robot has been designed that approaches the ideal model as closely as possible. The compliance of the springs is controllable by means of variable stiffness actuators. The controllable stiffness allows the gait to be stabilized against external disturbances

Graphene tests of Klein phenomena

Graphene is characterized by chiral electronic excitations. As such it provides a perfect testing ground for the production of Klein pairs (electron/holes). If confirmed, the standard results for barrier phenomena must be reconsidered with, as a byproduct, the accumulation within the barrier of holes.Comment: 8 page

Sacrificing Accuracy for Reduced Computation: Cascaded Inference Based on Softmax Confidence

We study the tradeoff between computational effort and accuracy in a cascade of deep neural networks. During inference, early termination in the cascade is controlled by confidence levels derived directly from the softmax outputs of intermediate classifiers. The advantage of early termination is that classification is performed using less computation, thus adjusting the computational effort to the complexity of the input. Moreover, dynamic modification of confidence thresholds allow one to trade accuracy for computational effort without requiring retraining. Basing of early termination on softmax classifier outputs is justified by experimentation that demonstrates an almost linear relation between confidence levels in intermediate classifiers and accuracy. Our experimentation with architectures based on ResNet obtained the following results. (i) A speedup of 1.5 that sacrifices 1.4% accuracy with respect to the CIFAR-10 test set. (ii) A speedup of 1.19 that sacrifices 0.7% accuracy with respect to the CIFAR-100 test set. (iii) A speedup of 2.16 that sacrifices 1.4% accuracy with respect to the SVHN test set

Delay Time in Quaternionic Quantum Mechanics

In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.Comment: 9 pages, 5 figure

Wave and Particle Limit for Multiple Barrier Tunneling

The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the plane wave results. In particular, the existence of resonance/transparency for twin tunnelling in the wave limit is immediately obvious. The known resonances for three and four barriers are also derived. The transition from the wave limit to the particle limit is exhibit numerically.Comment: 15 pages, 3 figure

Quaternionic Diffusion by a Potential Step

In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential step. In this paper, we restrict our attention to diffusion phenomena. For the group velocity of the wave packet moving in the potential region and for the reflection and transmission times, the study shows a striking difference between the complex and quaternionic formulations which could be matter of further theoretical discussions and could represent the starting point for a possible experimental investigation.Comment: 10 pages, 1 figur

A 331 WIMPy Dark Radiation Model

Recent observations suggest that the number of relativistic degrees of freedom in the early universe might exceed what is predicted in the standard cosmological model. If even a small, percent-level fraction of dark matter particles are produced relativistically, they could mimic the effect of an extra realistic species at matter-radiation equality while obeying BBN, CMB and Structure Formation bounds. We show that this scenario is quite naturally realized with a weak-scale dark matter particle and a high-scale ``mother'' particle within a well motivated 3-3-1 gauge model, which is particularly interesting for being consistent with electroweak precision measurements, with recent LHC results, and for offering a convincing explanation for the number of generations in the Standard Model.Comment: 10 pages,7 figures. Matches Published EPJC versio

Solving simple quaternionic differential equations

The renewed interest in investigating quaternionic quantum mechanics, in particular tunneling effects, and the recent results on quaternionic differential operators motivate the study of resolution methods for quaternionic differential equations. In this paper, by using the real matrix representation of left/right acting quaternionic operators, we prove existence and uniqueness for quaternionic initial value problems, discuss the reduction of order for quaternionic homogeneous differential equations and extend to the non-commutative case the method of variation of parameters. We also show that the standard Wronskian cannot uniquely be extended to the quaternionic case. Nevertheless, the absolute value of the complex Wronskian admits a non-commutative extension for quaternionic functions of one real variable. Linear dependence and independence of solutions of homogeneous (right) H-linear differential equations is then related to this new functional. Our discussion is, for simplicity, presented for quaternionic second order differential equations. This involves no loss of generality. Definitions and results can be readily extended to the n-order case.Comment: 9 pages, AMS-Te