A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid

We provide a constructive characterisation of circuits in the simple (2,2)-sparsity matroid. A circuit is a simple graph G=(V,E) with |E|=2|V|-1 and the number of edges induced by any $X \subsetneq V$ is at most 2|X|-2. Insisting on simplicity results in the Henneberg operation being enough only when the graph is sufficiently connected. Thus we introduce 3 different join operations to complete the characterisation. Extensions are discussed to when the sparsity matroid is connected and this is applied to the theory of frameworks on surfaces to provide a conjectured characterisation of when frameworks on an infinite circular cylinder are generically globally rigid.Comment: 22 pages, 6 figures. Changes to presentatio

Enrich: improving integration between an institutional repository and a CRIS at the University of Glasgow

This paper provide details of the work and the lessons learned by the JISC funded Enrich project run by the University of Glasgow in the United Kingdom. Enrich provided a clear focus for the integration and enhancement of the University of Glasgow’s repository, Enlighten, with other institutional systems, including our Research System [CRIS] (for funder data) and our Data Vault (for staff records). The Enrich project has demonstrated that partnership between the University Library and the Research Office, in conjunction with researchers, administrators and IT Services is critical to ensuring the successful integration of a repository and a CRIS. Enrich is part of a wider JISC funded programme in the UK: “Information Environment 2009-11” which focuses on the management, discovery and use of information resources. It was completed at the end of March 2010

Beyond the Circle of Life

It seems certain to me that I will die and stay dead. By “I”, I mean me, Greg Nixon, this person, this self-identity. I am so intertwined with the chiasmus of lives, bodies, ecosystems, symbolic intersubjectivity, and life on this particular planet that I cannot imagine this identity continuing alone without them. However, one may survive one’s life by believing in universal awareness, perfection, and the peace that passes all understanding. Perhaps, we bring this back with us to the Source from which we began, changing it, enriching it. Once we have lived – if we don’t choose the eternal silence of oblivion by life denial, vanity, indifference, or simple weariness – the Source learns and we awaken within it. Awareness, consciousness, is universal – it comes with the territory – so maybe you will be one of the few prepared to become unexpectedly enlightened after the loss of body and self. You may discover your own apotheosis – something you always were, but after a lifetime of primate experience, now much more. Since you are of the Source and since you have changed from life experience and yet retained the dream of ultimate awakening, plus you have brought those chaotic emotions and memories back to the Source with you (though no longer yours), your life & memories will have mattered. Those who awaken beyond the death of self will have changed Reality

Breaking Out of One’s Head (& Awakening to the World)

Herein, I review the shattering moment in my life when I awoke from the dream of self to find being as part of the living world and not in my head, discovering my perspectival center to be literally everywhere. Since awakening to the world takes one beyond thought and language thus also beyond the symbolic construction of time, it is strange to place this event and its aftermath as happening long ago in my life. It is forever present. This fact puts into question the reality of my daily journey from dawn to dusk with all the mundane tasks I must complete. My linear march into aging and death inexorably continues, yet it seems somehow unreal, worth a smile as the inevitable changes ensue. Still, I write of the events leading up to my time out of mind and then review the serious repercussions that followed when I was drawn back into ego only to find I did not have the conceptual tools or the maturity to understand what had occurred. I close by looking back with theories that might explain what happened. I am now ready to allow the memory to sink into peaceful oblivion and reference it from within my mind no more. Ironically, the memory itself with its façade of knowledge may prevent me from a new, unexpected mystical experience. Only by forgetting can I hope to leave a crack in the verbal armament of self, so the world soul may break through and free me once again

Stable counteralignment of a circumbinary disc

In general, when gas accretes on to a supermassive black hole binary it is likely to have no prior knowledge of the binary angular momentum. Therefore a circumbinary disc forms with a random inclination angle, theta, to the binary. It is known that for theta < 90 degrees the disc will coalign wrt the binary. If theta > 90 degrees the disc wholly counteraligns if it satisfies cos(theta) < -J_d/2J_b, where J_d and J_b are the magnitudes of the disc and binary angular momentum vectors respectively. If however theta > 90 degrees and this criterion is not satisfied the same disc may counteralign its inner regions and, on longer timescales, coalign its outer regions. I show that for typical disc parameters, describing an accretion event on to a supermassive black hole binary, a misaligned circumbinary disc is likely to wholly co-- or counter--align with the binary plane. This is because the binary angular momentum dominates the disc angular momentum. However with extreme parameters (binary mass ratio M_2/M_1 << 1 or binary eccentricity e ~ 1) the same disc may simultaneously co- and counter-align. It is known that coplanar prograde circumbinary discs are stable. I show that coplanar retrograde circumbinary discs are also stable. A chaotic accretion event on to an SMBH binary will therefore result in a coplanar circumbinary disc that is either prograde or retrograde with respect to the binary plane.Comment: 5 pages, 4 figures. Accepted for publication in MNRA

Consciousness, Origins

To explain the origin of anything, we must be clear about that which we are explaining. There seem to be two main meanings for the term consciousness. One might be called open in that it equates consciousness with awareness and experience and considers rudimentary sensations to have evolved at a specific point in the evolution of increasing complexity. But certainly the foundation for such sensation is a physical body. It is unclear, however, exactly what the physical requirements are for a “central experiencer” to emerge in the course of evolution. Some suggest that it would require a basic brain, others a central nervous system, and others stipulate only a cellular membrane. The open definition is most often assumed by the so-called hard sciences. The closed meaning of consciousness differentiates between a special sort of experience, i.e., conscious experience, and a special sort of awareness (i.e., self-awareness). This is the approach of psychoanalysis and psychology that accepts the existence of an unconscious mind. It is also the view of most phenomenological philosophers and psychologists (Martin Heidegger, Maurice Merleau-Ponty, Jacques Lacan, etc.). This entry discusses several scientific and philosophical views of consciousness and its origins