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

Statelessness and applications for leave to remain: a best practice guide

The UK Immigration Rules were amended in April 2013 to include a new category of leave: ‘Part 14 stateless persons’. Statelessness arises when a person is not a national of a state. The guide focuses upon the definition applied by the UK Immigration Rules: ‘a person who is not considered as a national by any State under the operation of its law’. This definition is taken from the 1954 Convention relating to the Status of Stateless Persons (the 1954 Convention). An important feature of the Immigration Rules relating to stateless persons is the scope they provide to secure recognition by the Home Office of statelessness, a legal condition which itself has important consequences in international law. The guide sets out the view of the authors on best practice in advising and representing clients considering or making an application for statelessness leave in the UK. The UK law in this area is in its infancy and is likely to develop particularly quickly. Some key questions of law and practice have yet to be addressed by the courts; the guide provides a snapshot of the state of play as at September 2016. It is aimed at those who may represent clients considering whether and when to make an application for leave to remain as a stateless person. It may also be of use to organisations working with potentially stateless persons who may refer them to legal advisers. It is a joint publication of the Immigration Law Practitioners' Association and the University of Liverpool. The authors are in-house solicitors in the Law Department's Law Clinic

Clients\u27 Internal Representations of Their Therapists

Thirteen adults in long-term individual psychotherapy were interviewed regarding their internal representations (defined as bringing to awareness the internalized image ) of their therapists. Results indicated that in the context of a good therapeutic relationship, clients\u27 internal representations combined auditory, visual, and kinesthetic (i.e., felt presence) modalities; were triggered when clients thought about past or future sessions, or when distressed; occurred in diverse locations; and varied in frequency, duration, and intensity. Clients felt positively about their representations and used them to introspect or influence therapy within sessions, beyond sessions, or both. The frequency of, comfort with, and use of clients\u27 internal representations increased over the course of therapy, and the representations benefited the therapy and therapeutic relationship. Therapists tended not to take a deliberate role in creating clients\u27 internal representations, and few clients discussed their internal representations with their therapists

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 relationship between adult attachment style and post-traumatic stress symptoms: A meta-analysis

There is increasing evidence that adult attachment plays a role in the development and perseverance of symptoms of posttraumatic stress disorder (PTSD). This meta-analysis aims to synthesise this evidence and investigate the relationship between adult attachment styles and PTSD symptoms. A random-effects model was used to analyse 46 studies (N = 9268) across a wide range of traumas. Results revealed a medium association between secure attachment and lower PTSD symptoms (ρ =-.27), and a medium association, in the opposite direction, between insecure attachment and higher PTSD symptoms (ρ =.26). Attachment categories comprised of high levels of anxiety most strongly related to PTSD symptoms, with fearful attachment displaying the largest association (ρ =.44). Dismissing attachment was not significantly associated with PTSD symptoms. The relationship between insecure attachment and PTSD was moderated by type of PTSD measure (interview or questionnaire) and specific attachment category (e.g. secure, fearful). Results have theoretical and clinical significance

Twisted geometries: A geometric parametrisation of SU(2) phase space

A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph. These are defined by the assignment to each triangle of its area, the two unit normals as seen from the two polyhedra sharing it, and an additional angle related to the extrinsic curvature. These quantities do not define a Regge geometry, since they include extrinsic data, but a looser notion of discrete geometry which is twisted in the sense that it is locally well-defined, but the local patches lack a consistent gluing among each other. We give the Poisson brackets among the new variables, and exhibit a symplectomorphism which maps them into the Poisson brackets of loop gravity. The new parametrization has the advantage of a simple description of the gauge-invariant reduced phase space, which is given by a product of phase spaces associated to edges and vertices, and it also provides an abelianisation of the SU(2) connection. The results are relevant for the construction of coherent states, and as a byproduct, contribute to clarify the connection between loop gravity and its subset corresponding to Regge geometries.Comment: 28 pages. v2 and v3 minor change

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

Geometrical aspects of integrable systems

We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko-Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting.Comment: It will appear on International Journal of Geometric Methods in Modern Physics vol.5 n.3 (May 2008) issu