Adinkras From Ordered Quartets of BC4{}_4 Coxeter Group Elements and Regarding 1,358,954,496 Matrix Elements of the Gadget

We examine values of the Adinkra Holoraumy-induced Gadget representation space metric over all possible four-color, four-open node, and four-closed node adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are non-vanishing and take on one of three values: $-1/3$, $1/3$, or $1$ and thus a subspace isomorphic to a description of a body-centered tetrahedral molecule emerges.Comment: LaTeX twice, 56pp, 30 tables, 5 figures, latest version includes link to updated code, minor corrections, and additional support about inequivalent representations and tetrahedral geometry comments added along with observations about similarity with results previously found by Nekraso

Photographic reproduction of out-of-focus and distorted ocular imagery

AbstractThe necessary settings and parameters were determined for ordinary camera and lens systems to faithfully reproduce out-of-focus and distorted imagery as it falls upon the retina of the human eye. Theoretic considerations of both geometric and physical optics were used to calculate the ‘relative blur’ and distortion produced by refractive error added to ordinary camera lenses as opposed to refractive error in an arbitrary thick-lens optical system bounded by air and fluid (i.e. the eye). In both the camera and the eye, ‘relative blur’ was determined to be directly proportional to dioptric defocus and to aperture size, and effectively independent of the focal length. Distortion of imagery was also found to be independent of the focal length. Photographs corroborate the theoretic findings. A given amount of relative blur, however, appeared somewhat greater when recorded on photographic film than when appreciated by the human eye. The Stiles–Crawford effect, the chromatic aberration of the eye, and neural processing probably each contribute to this difference. Previous investigators have grossly exaggerated blur and distortion in photographs intended to simulate ocular imagery and have drawn misleading conclusions from their results

Transport properties of disordered 2D complex plasma crystal

In this work, we investigate numerically the transport properties of a 2D complex plasma crystal using diffusion of coplanar dust lattice waves. In the limit where the Hamiltonian interactions can be decoupled from the non-Hamiltonian effects, we identify two distinct types of wave transport: Anderson-type delocalization and long-distance excitation. We use a recently-developed spectral approach to evaluate the contribution of the Anderson problem and compare it to the results of the simulation. The benefit of our approach to transport problems is twofold. First, we employ a highly tunable macroscopic hexagonal crystal, which exhibits many-body interactions and allows for the investigation of transport properties at the kinetic level. Second, the analysis of the transport problem in 2D is provided using an innovative spectral approach, which avoids the use of scaling and boundary conditions. The comparison between the analytically predicted and numerically observed wave dynamics allows for the study of important characteristics of this open system. In our simulations, we observe long-distance lattice excitation, which occurs around lattice defects even when the initial perturbation does not spread from the center to the exterior of the crystal. In the decoupled Hamiltonian regime, this many-body effect can be contributed to the dust lattice interaction with the plasma environment.2D latticecomplex plasma crystaltransportAnderson localizationSpectral approachlong-distance interactio

Spectral approach to transport in the two-dimensional honeycomb lattice with substitutional disorder

The transport properties of a disordered two-dimensional (2D) honeycomb lattice are examined numerically using the spectral approach to the 2D percolation problem, characterized by an Anderson-type Hamiltonian. In our model, disorder is represented by two parameters: a distribution of random on-site energies ε_i (positional disorder) and a concentration of doping energies p (substitutional disorder). The results indicate the existence of extended energy states for nonzero disorder and the emergence of a transition towards localized behavior for critical doping concentration n_D > 0.3%, in agreement with the experimentally observed metal-to-insulator transition in a graphene sheet doped with hydrogenspectral methodtransport2D materia

Kilorobot Search and Rescue Using an Immunologically Inspired Approach

This paper presents a new concept and simulated results for cooperatively coordinating autonomous robot teams via the Immunology-derived Distributed Autonomous Robotics Architecture (IDARA) to perform autonomous search and rescue operations. Primarily designed for the coordination and control of large-scale, kilorobot colonies, this architecture uses the unique stochastic learning and response mechanisms of the immune system as a basis to yield a more astute and adaptive response so that actions are varied from being reactionary to deliberative as indicated by environmental conditions and the architecture's perceived capabilities to address them. The IDARA architecture exhibits the guided stochastic search characteristics similar to those found in the human immune system. This characteristic was exploited to develop a series of methods for performing terrain search of dynamic environments. These methods were then evaluated in a variety of domains via computer simulations with robot colonies consisting of up to 1,500 robots. These experiments show that the IDARA architecture and framework provides a simple and robust method that is computationally efficient and does not degrade when coordinating and distributing large colonies of robots in either the terrain exploration and mapping or search and rescue problem domains. By providing new levels of scalability in noisy environments IDARA enables the full potential of micro-scale robotic for intelligent exploration, mapping, and search and rescue operations in a manner not afforded by traditional methods.