On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Stimulation of phosphatidylinositol hydrolysis, protein kinase C translocation, and mitogen-activated protein kinase activity by bradykinin in rat ventricular myocytes: dissociation from the hypertrophic response.

In ventricular myocytes cultured from neonatal rat hearts, bradykinin (BK), kallidin or BK(1-8) [(Des-Arg9)BK] stimulated PtdinsP2 hydrolysis by 3-4-fold. EC50 values were 6 nM (BK), 2 nM (kallidin), and 14 microM [BK(1-8)]. BK or kallidin stimulated the rapid (less than 30 s) translocation of more than 80% of the novel protein kinase C (PKC) isoforms nPKC-delta and nPKC-epsilon from the soluble to the particulate fraction. EC50 values for nPKC-delta translocation by BK or kallidin were 10 and 2 nM respectively. EC50 values for nPKC-epsilon translocation by BK or kallidin were 2 and 0.6 nM respectively. EC50 values for the translocation of nPKC-delta and nPKC-epsilon by BK(1-8) were more than 5 microM. The classical PKC, cPKC-alpha, and the atypical PKC, nPKC-zeta, did not translocate. BK caused activation and phosphorylation of p42-mitogen-activated protein kinase (MAPK) (maximal at 3-5 min, 30-35% of p42-MAPK phosphorylated). p44-MAPK was similarly activated. EC50 values for p42/p44-MAPK activation by BK were less than 1 nM whereas values for BK(1-8) were more than 10 microM. The order of potency [BK approximately equal to kallidin > BK (1-8)] for the stimulation of PtdInsP2 hydrolysis, nPKC-delta and nPKC-epsilon translocation, and p42/p44-MAPK activities suggests involvement of the B2 BK receptor subtype. In addition, stimulation of all three processes by BK was inhibited by the B2BK receptor-selective antagonist HOE140 but not by the B1-selective antagonist Leu8BK(1-8). Exposure of cells to phorbol 12-myristate 13-acetate for 24 h inhibited subsequent activation of p42/p44-MAPK by BK suggesting participation of nPKC (and possibly cPKC) isoforms in the activation process. Thus, like hypertrophic agents such as endothelin-1 (ET-1) and phenylephrine (PE), BK activates PtdInsP2 hydrolysis, translocates nPKC-delta, and nPKC-epsilon, and activates p42/p44-MAPK. However, in comparison with ET-1 and PE, BK was only weakly hypertrophic as assessed by cell morphology and patterns of gene expression. This difference could not be attributed to dissimilarities between the duration of activation of p42/p44-MAPK by BK or ET-1. Thus activation of these signalling pathways alone may be insufficient to induce a powerful hypertrophic response.

From molecules to neural morphology: understanding neuroinflammation in autism spectrum condition

Growing evidence points toward a critical role for early (prenatal) atypical neurodevelopmental processes in the aetiology of autism spectrum condition (ASC). One such process that could impact early neural development is inflammation. We review the evidence for atypical expression of molecular markers in the amniotic fluid, serum, cerebrospinal fluid (CSF), and the brain parenchyma that suggest a role for inflammation in the emergence of ASC. This is complemented with a number of neuroimaging and neuropathological studies describing microglial activation. Implications for treatment are discussed.

Frontal networks in adults with autism spectrum disorder

It has been postulated that autism spectrum disorder is underpinned by an ‘atypical connectivity’ involving higher-order association brain regions. To test this hypothesis in a large cohort of adults with autism spectrum disorder we compared the white matter networks of 61 adult males with autism spectrum disorder and 61 neurotypical controls, using two complementary approaches to diffusion tensor magnetic resonance imaging. First, we applied tract-based spatial statistics, a ‘whole brain’ non-hypothesis driven method, to identify differences in white matter networks in adults with autism spectrum disorder. Following this we used a tract-specific analysis, based on tractography, to carry out a more detailed analysis of individual tracts identified by tract-based spatial statistics. Finally, within the autism spectrum disorder group, we studied the relationship between diffusion measures and autistic symptom severity. Tract-based spatial statistics revealed that autism spectrum disorder was associated with significantly reduced fractional anisotropy in regions that included frontal lobe pathways. Tractography analysis of these specific pathways showed increased mean and perpendicular diffusivity, and reduced number of streamlines in the anterior and long segments of the arcuate fasciculus, cingulum and uncinate—predominantly in the left hemisphere. Abnormalities were also evident in the anterior portions of the corpus callosum connecting left and right frontal lobes. The degree of microstructural alteration of the arcuate and uncinate fasciculi was associated with severity of symptoms in language and social reciprocity in childhood. Our results indicated that autism spectrum disorder is a developmental condition associated with abnormal connectivity of the frontal lobes. Furthermore our findings showed that male adults with autism spectrum disorder have regional differences in brain anatomy, which correlate with specific aspects of autistic symptoms. Overall these results suggest that autism spectrum disorder is a condition linked to aberrant developmental trajectories of the frontal networks that persist in adult life.

“Pussy cat, pussy cat where have you been..?” Evaluating the use of stable isotopes, radiogenic isotopes and trace elements for investigating the ecology of Panthera leo

1. Understanding the behaviour and ecology of large carnivores is becoming increasingly important as the list of endangered species grows, with felids such as Panthera leo in some locations heading dangerously close to extinction in the wild. In order to have more reliable and effective tools to understand animal behaviour, movement and diet, we need to develop novel, integrated approaches and effective techniques to capture a detailed profile of animal foraging and movement patterns. 2. Ecological studies have shown considerable interest in using stable isotope methods, both to investigate the nature of animal feeding habits, and to map their geographical location. However, recent work has suggested that stable isotope analyses of felid fur and bone is very complex and does not correlate directly with the isotopic composition of precipitation (and hence geographical location). 3. We present new data that suggest these previous findings may be atypical, and demonstrate that isotope analyses of Felidae are suitable for both evaluating dietary inputs and establishing geo-location as they have strong environmental referents to both food and water. These data provide new evidence of an important methodology that can be applied to the family Felidae for future research in ecology, conservation, wildlife forensics and archaeological science.

Convergence accommodation in orthoptic practice

Aims. Orthoptists are familiar with AC/A ratios and the concept that accommodation drives convergence, but the reverse relationship, that of the accommodation associated with convergence, is rarely considered. Methods. This article reviews published evidence from our laboratory which has investigated the drives to both vergence and accommodation. All studies involved a method by which accommodation and vergence were measured concurrently and objectively to a range of visual stimuli which manipulate blur, disparity and proximal/looming cues in different combinations. Results Results are summarised for both typical and atypical participants, and over development between birth and adulthood. Conclusions For the majority of typical children and adults, as well as patients with most heterophorias and intermittent exotropia, disparity is the main cue to both vergence and accommodation. Thus the convergence→accommodation relationship is more influential than that of accommodative vergence. Differences in “style” of near cue use may be a more useful way to think about responses to stimuli moving in depth, and their consequences for orthoptic patients, than either AC/A or CA/C ratios. The implications of a strong role for vergence accommodation in orthoptic practice are considered.

Le développement de la prosodie dans le syndrome de Williams et le syndrome de Down chez des enfants de langue anglaise

The aim of the present study is to investigate the developmental profile of three aspects of prosody function, i.e. affect, focus and turn-endings in children with Williams and in those with Down’s syndrome compared to typically developing English speaking children. The tasks used were part of the computer-based battery, Profiling Elements of Prosody for Speech Communication (Peppe, McCann & Gibon, 2003). Cross-sectional developmental trajectories linking chronological and non-verbal mental age and affects and turn-ending functions of prosody were constructed. The results showed an atypical profile in both clinical populations. More interestingly, the profiles were atypical for different reasons, suggesting multiple and possibly different developmental pathways to the acquisition of prosody in these two populations.