Fundamental principles in drawing inference from sequence analysis

Individual life courses are dynamic and can be represented as a sequence of states for some portion of their experiences. More generally, study of such sequences has been made in many fields around social science; for example, sociology, linguistics, psychology, and the conceptualisation of subjects progressing through a sequence of states is common. However, many models and sets of data allow only for the treatment of aggregates or transitions, rather than interpreting whole sequences. The temporal aspect of the analysis is fundamental to any inference about the evolution of the subjects but assumptions about time are not normally made explicit. Moreover, without a clear idea of what sequences look like, it is impossible to determine when something is not seen whether it was not actually there. Some principles are proposed which link the ideas of sequences, hypothesis, analytical framework, categorisation and representation; each one being underpinned by the consideration of time. To make inferences about sequences, one needs to: understand what these sequences represent; the hypothesis and assumptions that can be derived about sequences; identify the categories within the sequences; and data representation at each stage. These ideas are obvious in themselves but they are interlinked, imposing restrictions on each other and on the inferences which can be draw

The McKay correspondence as an equivalence of derived categories

The classical McKay correspondence relates representations of a finite subgroup G ⊂ SL(2,C) to the cohomology of the well-known minimal resolution of the Kleinian singularity C2/G. Gonzalez-Sprinberg and Verdier [10] interpreted the McKay correspondence as an isomorphism on K theory, observing that the representation ring of G is equal to the G-equivariant K theory of C2. More precisely, they identify a basis of the K theory of the resolution consisting of the classes of certain tautological sheaves associated to the irreducible representations of G

Zero reflection and transmission in graded index media

Graded index media whose electric susceptibility satisfies the spatial Kramers-Kronig relations are known to be one-way reflectionless to electromagnetic radiation, for all angles of incidence. We demonstrate how a family of these media, in addition to being reflectionless, also have negligible transmission. To this end, we discuss how the transmission coefficient for the propagation of waves through a medium whose permittivity is built from poles in the complex position plane, with residues that sum to infinity, can be controlled by tuning the positions and residues of the poles. In particular, we have shown how to make the transmission arbitrarily small, and hence maximise the absorption of the wave's energy. This behaviour is confirmed by numerical simulations.Comment: 4 pages, 3 figure

Foehn warming distributions in nonlinear and linear flow regimes: a focus on the Antarctic Peninsula

The structure of lee-side warming during foehn events is investigated as a function of cross-barrier flow regime linearity. Two contrasting cases of westerly flow over the Antarctic Peninsula (AP) are considered – one highly nonlinear, the other relatively linear. Westerly flow impinging on the AP provides one of the best natural laboratories in the world for the study of foehn, owing to its maritime setting and the Larsen C Ice Shelf (LCIS) providing an expansive, homogeneous and smooth surface on its east side. Numerical simulations with the Met Office Unified Model (at 1.5 km grid size) and aircraft observations are utilized. In case A, relatively weak southwesterly cross-Peninsula flow and an elevated upwind inversion dictate a highly nonlinear foehn event, with mountain wave breaking observed. The consequent strongly accelerated downslope flow leads to high-amplitude warming and ice-shelf melt in the immediate lee of the AP. However this foehn warming diminishes rapidly downwind due to upward ascent of the foehn flow via a hydraulic jump. In case C, strong northwesterly winds dictate a relatively linear flow regime. There is no hydraulic jump and strong foehn winds are able to flow at low levels across the entire ice shelf, mechanically mixing the near-surface flow, preventing the development of a strong surface inversion and delivering large fluxes of sensible heat to the ice shelf. Consequently, in case C ice-melt rates are considerably greater over the LCIS as a whole than in case A. Our results imply that although nonlinear foehn events cause intense warming in the immediate lee of mountains, linear foehn events will commonly cause more extensive lee-side warming and, over an ice surface, higher melt rates. This has major implications for the AP, where recent east-coast warming has led to the collapse of two ice shelves immediately north of the LCIS

Reviews

Managing Change in Higher Education: A Learning Environment Architecture by Peter Ford and eight other authors, Buckingham: Society for Research into Higher Education and the Open University Press, 1996. ISBN 0–335–19791–4. 161 pages, paperback. No price indicated

Proof appendix to accompany the paper, "From MinX to MinC: Semantics-Driven Decompilation of Recursive Datatypes"

Proof appendix to accompany the paper, "From MinX to MinC: Semantics-Driven Decompilation of Recursive Datatypes

Spatio-temporal influence of tundra snow properties on Ku-band (17.2 GHz) backscatter

During the 2010/11 boreal winter, a distributed set of backscatter measurements was collected using a ground-based Ku-band (17.2 GHz) scatterometer system at 26 open tundra sites. A standard snow-sampling procedure was completed after each scan to evaluate local variability in snow layering, depth, density and water equivalent (SWE) within the scatterometer field of view. The shallow depths and large basal depth hoar encountered presented an opportunity to evaluate backscatter under a set of previously untested conditions. Strong Ku-band response was found with increasing snow depth and snow water equivalent (SWE). In particular, co-polarized vertical backscatter increased by 0.82 dB for every 1 cm increase in SWE (R2 = 0.62). While the result indicated strong potential for Ku-band retrieval of shallow snow properties, it did not characterize the influence of sub-scan variability. An enhanced snow-sampling procedure was introduced to generate detailed characterizations of stratigraphy within the scatterometer field of view using near-infrared photography along the length of a 5m trench. Changes in snow properties along the trench were used to discuss variations in the collocated backscatter response. A pair of contrasting observation sites was used to highlight uncertainties in backscatter response related to short length scale spatial variability in the observed tundra environment