Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space, parametrised by $\Psi_0$, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles ${\mathcal P}_{\Psi_0}$on the moduli space whose curvature is proportional to the symplectic forms $\Omega_{\Psi_0}$.Comment: 8 page

Program Synthesis Meets Deep Learning for Decoding Regulatory Networks

With ever growing data sets spanning DNA sequencing all the way to single-cell transcriptomics, we are now facing the question of how can we turn this vast amount of information into knowledge. How do we integrate these large data sets into a coherent whole to help understand biological programs? The last few years have seen a growing interest in machine learning methods to analyse patterns in high-throughput data sets and an increasing interest in using program synthesis techniques to reconstruct and analyse executable models of gene regulatory networks. In this review, we discuss the synergies between the two methods and share our views on how they can be combined to reconstruct executable mechanistic programs directly from large-scale genomic data

The Computational Power of Minkowski Spacetime

The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.Comment: 6 pages, LaTeX, feedback welcom

Influence of Pichia pastoris cellular material on polymerase chain reaction performance as a synthetic biology standard for genome monitoring

Advances in synthetic genomics are now well underway in yeasts due to the low cost of synthetic DNA. These new capabilities also bring greater need for quantitating the presence, loss and rearrangement of loci within synthetic yeast genomes. Methods for achieving this will ideally; i) be robust to industrial settings, ii) adhere to a global standard and iii) be sufficiently rapid to enable at-line monitoring during cell growth. The methylotrophic yeast Pichia pastoris (P. pastoris) is increasingly used for industrial production of biotherapeutic proteins so we sought to answer the following questions for this particular yeast species. Is time-consuming DNA purification necessary to obtain accurate end-point polymerase chain reaction (e-pPCR) and quantitative PCR (qPCR) data? Can the novel linear regression of efficiency qPCR method (LRE qPCR), which has properties desirable in a synthetic biology standard, match the accuracy of conventional qPCR? Does cell cultivation scale influence PCR performance? To answer these questions we performed e-pPCR and qPCR in the presence and absence of cellular material disrupted by a mild 30s sonication procedure. The e-pPCR limit of detection (LOD) for a genomic target locus was 50 pg (4.91 × 103 copies) of purified genomic DNA (gDNA) but the presence of cellular material reduced this sensitivity sixfold to 300 pg gDNA (2.95 × 104 copies). LRE qPCR matched the accuracy of a conventional standard curve qPCR method. The presence of material from bioreactor cultivation of up to OD600 = 80 did not significantly compromise the accuracy of LRE qPCR. We conclude that a simple and rapid cell disruption step is sufficient to render P. pastoris samples of up to OD600 = 80 amenable to analysis using LRE qPCR which we propose as a synthetic biology standard

The existence of time

Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.Comment: 21 pages (Reduced to clarify and focus on central argument; some calculations condensed; typos corrected