On the stationarity of linearly forced turbulence in finite domains

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the `linear forcing', which amounts to a force term linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence towards a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to re-write the problem as one of decaying turbulence with a decreasing viscosity. Scaling symmetry considerations suggest that the system evolves to a stationary state, evolution that may be understood as the gradual breaking of a larger approximate symmetry to a smaller exact symmetry. The same arguments show that the finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times, as well as the consistency of this state with a high degree of isotropy imposed by the symmetries of the domain itself. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy. Indeed, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view, emphasizing the naturalness of the Taylor microscale as a self-similarity scale in this system. In this context the stationary state emerges as a stable fixed point. Self-preservation seems to be the reason behind a noted similarity of the third order structure function between the linearly forced and freely decaying turbulence, where again the finiteness of the domain plays an significant role.Comment: 15 pages, 7 figures, changes in the discussion at the end of section VI, formula (60) correcte

Classical and quantum ergodicity on orbifolds

We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdi\`ere and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow of p implies quantum ergodicity for the operator P. We also prove ergodicity of the geodesic flow on a compact Riemannian orbifold of negative sectional curvature.Comment: 14 page

Fully Automatic Expression-Invariant Face Correspondence

We consider the problem of computing accurate point-to-point correspondences among a set of human face scans with varying expressions. Our fully automatic approach does not require any manually placed markers on the scan. Instead, the approach learns the locations of a set of landmarks present in a database and uses this knowledge to automatically predict the locations of these landmarks on a newly available scan. The predicted landmarks are then used to compute point-to-point correspondences between a template model and the newly available scan. To accurately fit the expression of the template to the expression of the scan, we use as template a blendshape model. Our algorithm was tested on a database of human faces of different ethnic groups with strongly varying expressions. Experimental results show that the obtained point-to-point correspondence is both highly accurate and consistent for most of the tested 3D face models

A geometric approach to visualization of variability in functional data

We propose a new method for the construction and visualization of boxplot-type displays for functional data. We use a recent functional data analysis framework, based on a representation of functions called square-root slope functions, to decompose observed variation in functional data into three main components: amplitude, phase, and vertical translation. We then construct separate displays for each component, using the geometry and metric of each representation space, based on a novel definition of the median, the two quartiles, and extreme observations. The outlyingness of functional data is a very complex concept. Thus, we propose to identify outliers based on any of the three main components after decomposition. We provide a variety of visualization tools for the proposed boxplot-type displays including surface plots. We evaluate the proposed method using extensive simulations and then focus our attention on three real data applications including exploratory data analysis of sea surface temperature functions, electrocardiogram functions and growth curves

Crater lake cichlids individually specialize along the benthic-limnetic axis

A common pattern of adaptive diversification in freshwater fishes is the repeated evolution of elongated open water (limnetic) species and high-bodied shore (benthic) species from generalist ancestors. Studies on phenotype-diet correlations have suggested that population-wide individual specialization occurs at an early evolutionary and ecological stage of divergence and niche partitioning. This variable restricted niche use across individuals can provide the raw material for earliest stages of sympatric divergence. We investigated variation in morphology and diet as well as their correlations along the benthic-limnetic axis in an extremely young Midas cichlid species, Amphilophus tolteca, endemic to the Nicaraguan crater lake Asososca Managua. We found that A. tolteca varied continuously in ecologically relevant traits such as body shape and lower pharyngeal jaw morphology. The correlation of these phenotypes with niche suggested that individuals are specialized along the benthic-limnetic axis. No genetic differentiation within the crater lake was detected based on genotypes from 13 microsatellite loci. Overall, we found that individual specialization in this young crater lake species encompasses the limnetic- as well as the benthic macro-habitat. Yet there is no evidence for any diversification within the species, making this a candidate system for studying what might be the early stages preceding sympatric divergence

Building and Testing a Statistical Shape Model of the Human Ear Canal

Abstract. Today the design of custom in-the-ear hearing aids is based on personal experience and skills and not on a systematic description of the variation of the shape of the ear canal. In this paper it is described how a dense surface point distribution model of the human ear canal is built based on a training set of laser scanned ear impressions and a sparse set of anatomical landmarks placed by an expert. The landmarks are used to warp a template mesh onto all shapes in the training set. Using the vertices from the warped meshes, a 3D point distribution model is made. The model is used for testing for gender related differences in size and shape of the ear canal.

Returning children home from care: What can be learned from local authority data?

International Human Rights and child rights conventions as well as U.K. wide legislation and guidance require that children in care should be returned home to one or both parents wherever possible. Reunification with parents is the most common route out of care, but rates of re‐entry are often higher than for other exit routes. This study used 8 years of administrative data (on 2,208 care entrants), collected by one large English local authority, to examine how many children were returned home and to explore factors associated with stable reunification (not re‐entering care for at least 2 years). One‐third of children (36%) had been reunified, with adolescent entrants being the most likely age group to return home. Three quarters (75%) of reunified children had a stable reunification. In a fully adjusted regression model, age at entry, being on a care order prior to return home, staying longer in care, being of minority ethnicity, and having fewer placements in care were all significant in predicting chances of stable reunification. The results underline the importance of properly resourcing reunification services. The methods demonstrate the value to local authorities of analysing their own data longitudinally to understand the care pathways for children they look after

New quantitative approaches reveal the spatial preference of nuclear compartments in mammalian fibroblasts

The nuclei of higher eukaryotic cells display compartmentalization and certain nuclear compartments have been shown to follow a degree of spatial organization. To date, the study of nuclear organization has often involved simple quantitative procedures that struggle with both the irregularity of the nuclear boundary and the problem of handling replicate images. Such studies typically focus on inter-object distance, rather than spatial location within the nucleus. The concern of this paper is the spatial preference of nuclear compartments, for which we have developed statistical tools to quantitatively study and explore nuclear organization. These tools combine replicate images to generate ‘aggregate maps' which represent the spatial preferences of nuclear compartments. We present two examples of different compartments in mammalian fibroblasts (WI-38 and MRC-5) that demonstrate new knowledge of spatial preference within the cell nucleus. Specifically, the spatial preference of RNA polymerase II is preserved across normal and immortalized cells, whereas PML nuclear bodies exhibit a change in spatial preference from avoiding the centre in normal cells to exhibiting a preference for the centre in immortalized cells. In addition, we show that SC35 splicing speckles are excluded from the nuclear boundary and localize throughout the nucleoplasm and in the interchromatin space in non-transformed WI-38 cells. This new methodology is thus able to reveal the effect of large-scale perturbation on spatial architecture and preferences that would not be obvious from single cell imaging

Psychotherapy in historical perspective

This article will briefly explore some of the ways in which the past has been used as a means to talk about psychotherapy as a practice and as a profession, its impact on individuals and society, and the ethical debates at stake. It will show how, despite the multiple and competing claims about psychotherapy’s history and its meanings, historians themselves have, to a large degree, not attended to the intellectual and cultural development of many therapeutic approaches. This absence has the potential consequence of implying that therapies have emerged as value-free techniques, outside of a social, economic and political context. The relative neglect of psychotherapy, by contrast with the attention historians have paid to other professions, particularly psychiatry, has also underplayed its societal impact. This article will foreground some of the instances where psychotherapy has become an object of emerging historical interest, including the new research that forms the substance of this special issue of History of the Human Sciences