Prolongations of Geometric Overdetermined Systems

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on the dimension of the solution space.Comment: 22 pages. In the second version, a comparison with the classical theory of prolongations was added. In this third version more details were added concerning our construction and especially the use of Kostant's computation of Lie algebra cohomolog

Radiation measurements in the new tandem accelerator FEL

The measurements of both spontaneous and stimulated emissions of radiation in the newly configured Israeli EA-FEL are made for the first time. The radiation at the W-band was measured and characterized. The results match the predictions of our earlier theoretical modeling and calculations.Comment: 4 pages, 3 figures, FEL 2003 Conference repor

Local Unit Invariance, Back-Reacting Tractors and the Cosmological Constant Problem

When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.Comment: 20 pages, 2 figure

Beta-gamma systems and the deformations of the BRST operator

We describe the relation between simple logarithmic CFTs associated with closed and open strings, and their "infinite metric" limits, corresponding to the beta-gamma systems. This relation is studied on the level of the BRST complex: we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the Lian-Zuckerman type on the vertex algebra, associated with the beta-gamma systems. The Maurer-Cartan equations corresponding to this deformed structure in the quasiclassical approximation lead to the nonlinear field equations. As an explicit example, we demonstrate, that using this construction, Yang-Mills equations can be derived. This gives rise to a nontrivial relation between the Courant-Dorfman algebroid and homotopy algebras emerging from the gauge theory. We also discuss possible algebraic approach to the study of beta-functions in sigma-models.Comment: LaTeX2e, 15 pages; minor revision, typos corrected, Journal of Physics A, in pres

Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe

The pseudo-conformal scenario is an alternative to inflation in which the early universe is described by an approximate conformal field theory on flat, Minkowski space. Some fields acquire a time-dependent expectation value, which breaks the flat space so(4,2) conformal algebra to its so(4,1) de Sitter subalgebra. As a result, weight-0 fields acquire a scale invariant spectrum of perturbations. The scenario is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. In this paper, we apply the well-known coset technique to derive the most general effective lagrangian describing the Goldstone field and matter fields, consistent with the assumed symmetries. The resulting action captures the low energy dynamics of any pseudo-conformal realization, including the U(1)-invariant quartic model and the Galilean Genesis scenario. We also derive this lagrangian using an alternative method of curvature invariants, consisting of writing down geometric scalars in terms of the conformal mode. Using this general effective action, we compute the two-point function for the Goldstone and a fiducial weight-0 field, as well as some sample three-point functions involving these fields.Comment: 49 pages. v2: minor corrections, added references. v3: minor edits, version appearing in JCA

Outside the gate: sub-urban legal practices in early medieval England

Many aspects of English early medieval (Anglo-Saxon) legal landscapes can be discerned in archaeological and toponymic evidence, ranging from the locations of legislative councils and judicial assemblies to sites of capital punishment. Among the corpus of such sites a striking group can be detected at the periphery of urban spaces. Gates into a number of towns appear to have functioned as legislative meeting-places, and even gave their names to some legally constituted communities, while suburban locations also feature prominently as sites of gallows and public punishment. In this paper historical, archaeological and toponymic evidence is used to examine this phenomenon of suburban legal practices and to pose questions about the wider dimensions of the early medieval legal landscape

A quantum analogue of the first fundamental theorem of invariant theory

We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For each quantum group associated with a classical Lie algebra, we construct a noncommutative associative algebra whose underlying vector space forms a module for the quantum group and whose algebraic structure is preserved by the quantum group action. The subspace of invariants is shown to form a subalgebra, which is finitely generated. We determine generators of this subalgebra of invariants and determine their commutation relations. In each case considered, the noncommutative modules we construct are flat deformations of their classical commutative analogues. Thus by taking the limit as $q\to 1$, our results imply the first fundamental theorem of classical invariant theory, and therefore generalise them to the noncommutative case.Comment: 44 pages, 3 figure

Reconsidering the Tribal-State Compact Process

This essay evaluates the tribal‐state compact process, as one of several alternative, nonadversarial processes, warranting attention. It argues that, because of its binding character and relatively low cost (in contrast to litigation), and because it is based in the idea of tribes and states exhibiting mutual respect, the compact process is an advanced version of negotiation and bargaining that tribes and states should consider where appropriate

Increased indoleamine-2,3-dioxygenase activity is associated with poor clinical outcome in adults hospitalized with influenza in the INSIGHT FLU003Plus study

BACKGROUND: Indoleamine-2,3-dioxygenase (IDO) mediated tryptophan (TRP) depletion has antimicrobial and immuno-regulatory effects. Increased kynurenine (KYN)-to-TRP (KT) ratios, reflecting increased IDO activity, have been associated with poorer outcomes from several infections. METHODS: We performed a case-control (1:2; age and sex matched) analysis of adults hospitalized with influenza A(H1N1)pdm09 with protocol-defined disease progression (died/transferred to ICU/mechanical ventilation) after enrollment (cases) or survived without progression (controls) over 60 days of follow-up. Conditional logistic regression was used to analyze the relationship between baseline KT ratio and other metabolites and disease progression. RESULTS: We included 32 cases and 64 controls with a median age of 52 years; 41% were female, and the median durations of influenza symptoms prior to hospitalization were 8 and 6 days for cases and controls, respectively (P = .04). Median baseline KT ratios were 2-fold higher in cases (0.24 mM/M; IQR, 0.13-0.40) than controls (0.12; IQR, 0.09-0.17; P ≤ .001). When divided into tertiles, 59% of cases vs 20% of controls had KT ratios in the highest tertile (0.21-0.84 mM/M). When adjusted for symptom duration, the odds ratio for disease progression for those in the highest vs lowest tertiles of KT ratio was 9.94 (95% CI, 2.25-43.90). CONCLUSIONS: High KT ratio was associated with poor outcome in adults hospitalized with influenza A(H1N1)pdm09. The clinical utility of this biomarker in this setting merits further exploration. CLINICALTRIALSGOV IDENTIFIER: NCT01056185

Historic landscape character and sense of place

This is an Author's Accepted Manuscript of an article published in Landscape Research, 2013, Vol. 38, Issue 2 pp.179-202, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/01426397.2012.672642.Most studies of landscape character within archaeology and historical geography have focused on morphological features such as whether settlement patterns were nucleated or dispersed, but this paper discusses how adding depth to this, for example by studying place-names, vernacular architecture, and the territorial structures within which a landscape was managed in the past, gives us a far greater understanding of its texture and meaning to local communities. In two case-studies in southern Essex, for example, it is shown how the connections that once existed between inland and coastal communities can be used today to promote public access to the countryside. A further case study, in southwest England, shows how field-/place-names and vernacular architecture also make an important contribution to our appreciation of the time depth and complexity of landscape character.Arts and Humanities Research Council (AHRC)Southend-on-Sea Borough Counci