Embedded Vortices

We present a discussion of embedded vortices in general Yang-Mills theories. The origin of a family structure of solutions is shown to be group theoretic in nature and a procedure for its determination is developed. Vortex stability can be quantified into three types: Abelian topological stability, non-Abelian topological stability, and dynamical stability; we relate these to the family structure of vortices, in particular discussing how Abelian topological and dynamical stability are related. The formalism generally encompasses embedded domain walls and embedded monopoles also.Comment: final corrections. latex fil

A future of living machines? International trends and prospects in biomimetic and biohybrid systems

Research in the fields of biomimetic and biohybrid systems is developing at an accelerating rate. Biomimetics can be understood as the development of new technologies using principles abstracted from the study of biological systems, however, biomimetics can also be viewed from an alternate perspective as an important methodology for improving our understanding of the world we live in and of ourselves as biological organisms. A biohybrid entity comprises at least one artificial (engineered) component combined with a biological one. With technologies such as microscale mobile computing, prosthetics and implants, humankind is moving towards a more biohybrid future in which biomimetics helps us to engineer biocompatible technologies. This paper reviews recent progress in the development of biomimetic and biohybrid systems focusing particularly on technologies that emulate living organisms—living machines. Based on our recent bibliographic analysis [1] we examine how biomimetics is already creating life-like robots and identify some key unresolved challenges that constitute bottlenecks for the field. Drawing on our recent research in biomimetic mammalian robots, including humanoids, we review the future prospects for such machines and consider some of their likely impacts on society, including the existential risk of creating artifacts with significant autonomy that could come to match or exceed humankind in intelligence. We conclude that living machines are more likely to be a benefit than a threat but that we should also ensure that progress in biomimetics and biohybrid systems is made with broad societal consent. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

Examples of Embedded Defects (in Particle Physics and Condensed Matter)

We present a series of examples designed to clarify the formalism of the companion paper `Embedded Vortices'. After summarising this formalism in a prescriptive sense, we run through several examples: firstly, deriving the embedded defect spectrum for Weinberg-Salam theory, then discussing several examples designed to illustrate facets of the formalism. We then calculate the embedded defect spectrum for three physical Grand Unified Theories and conclude with a discussion of vortices formed in the superfluid $^3$He-A phase transition.Comment: final corrections. latex fil

Spin and Dualization of SU(5) Dyons

Motivated by the dual standard model, we study the angular momentum spectrum of stable SU(5) dyons that can be transformed into purely electric states by a suitable duality rotation i.e. are dualizable. The problem reduces to solving a Diophantine equation for the holomorphic charges in each topological sector, but the solutions also have to satisfy certain constraints. We show that these equations can be solved and sets of dualizable, half-integer spin SU(5) dyons can be found, each of which corresponds to a single family of the standard model fermions. We then find two predictions of the dual standard model. First, the family of half-integer spin, dualizable dyons is accompanied by a set of dualizable, integer-spin partner states. Secondly, the dyon corresponding to the electron must necessarily contain non-trivial color internal structure. In addition, we provide other general results regarding the spectrum of dualizable dyons and their novel properties, and extend the stability analysis of SU(5) monopoles used in the dual standard model so far to discuss the stability of the half-integer spin dyons.Comment: 9 pages, 1 figur

Storage of Correlated Patterns in Standard and Bistable Purkinje Cell Models

The cerebellum has long been considered to undergo supervised learning, with climbing fibers acting as a ‘teaching’ or ‘error’ signal. Purkinje cells (PCs), the sole output of the cerebellar cortex, have been considered as analogs of perceptrons storing input/output associations. In support of this hypothesis, a recent study found that the distribution of synaptic weights of a perceptron at maximal capacity is in striking agreement with experimental data in adult rats. However, the calculation was performed using random uncorrelated inputs and outputs. This is a clearly unrealistic assumption since sensory inputs and motor outputs carry a substantial degree of temporal correlations. In this paper, we consider a binary output neuron with a large number of inputs, which is required to store associations between temporally correlated sequences of binary inputs and outputs, modelled as Markov chains. Storage capacity is found to increase with both input and output correlations, and diverges in the limit where both go to unity. We also investigate the capacity of a bistable output unit, since PCs have been shown to be bistable in some experimental conditions. Bistability is shown to enhance storage capacity whenever the output correlation is stronger than the input correlation. Distribution of synaptic weights at maximal capacity is shown to be independent on correlations, and is also unaffected by the presence of bistability