Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

Disorder-specific functional abnormalities during temporal discounting in youth with Attention Deficit Hyperactivity Disorder (ADHD), Autism and comorbid ADHD and Autism

Attention Deficit Hyperactivity Disorder (ADHD) and Autism Spectrum Disorder (ASD) are often comorbid and share cognitive abnormalities in temporal foresight. A key question is whether shared cognitive phenotypes are based on common or different underlying pathophysiologies and whether comorbid patients have additive neurofunctional deficits, resemble one of the disorders or have a different pathophysiology. We compared age- and IQ-matched boys with non-comorbid ADHD (18), non-comorbid ASD (15), comorbid ADHD and ASD (13) and healthy controls (18) using functional magnetic resonance imaging (fMRI) during a temporal discounting task. Only the ASD and the comorbid groups discounted delayed rewards more steeply. The fMRI data showed both shared and disorder-specific abnormalities in the three groups relative to controls in their brain-behaviour associations. The comorbid group showed both unique and more severe brain-discounting associations than controls and the non-comorbid patient groups in temporal discounting areas of ventromedial and lateral prefrontal cortex, ventral striatum and anterior cingulate, suggesting that comorbidity is neither an endophenocopy of the two pure disorders nor an additive pathology.

Pre-conditioning the epigenetic response to high vapor pressure deficit increases the drought tolerance of Arabidopsis thaliana

Epigenetic modification of the genome via cytosine methylation is a dynamic process that responds to changes in the growing environment. This modification can also be heritable. The combination of both properties means that there is the potential for the life experiences of the parental generation to modify the methylation profiles of their offspring and so potentially to ‘pre-condition’ them to better accommodate abiotic conditions encountered by their parents. We recently identified high vapor pressure deficit (vpd)-induced DNA methylation at two gene loci in the stomatal development pathway and an associated reduction in leaf stomatal frequency.1 Here, we test whether this epigenetic modification pre-conditioned parents and their offspring to the more severe water stress of periodic drought. We found that three generations of high vpd-grown plants were better able to withstand periodic drought stress over two generations. This resistance was not directly associated with de novo methylation of the target stomata genes, but was associated with the cmt3 mutant’s inability to maintain asymmetric sequence context methylation. If our finding applies widely, it could have significant implications for evolutionary biology and breeding for stressful environments.

Varieties of semantic ‘access’ deficit in Wernicke’s aphasia and semantic aphasia

Comprehension deficits are common in stroke aphasia, including in cases with (i) semantic aphasia (SA), characterised by poor executive control of semantic processing across verbal and nonverbal modalities, and (ii) Wernicke’s aphasia (WA), associated with poor auditory-verbal comprehension and repetition, plus fluent speech with jargon. However, the varieties of these comprehension problems, and their underlying causes, are not well-understood. Both patient groups exhibit some type of semantic ‘access’ deficit, as opposed to the ‘storage’ deficits observed in semantic dementia. Nevertheless, existing descriptions suggest these patients might have different varieties of ‘access’ impairment – related to difficulty resolving competition (in SA) vs. initial activation of concepts from sensory inputs (in WA). We used a case-series design to compare WA and SA patients on Warrington’s paradigmatic assessment of semantic ‘access’ deficits. In these verbal and non-verbal matching tasks, a small set of semantically-related items are repeatedly presented over several cycles so that the target on one trial becomes a distractor on another (building up interference and eliciting semantic ‘blocking’ effects). WA and SA patients were distinguished according to lesion location in the temporal cortex, but in each group, some individuals had additional prefrontal damage. Both of these aspects of lesion variability – one that mapped onto classical ‘syndromes’ and one that did not – predicted aspects of the semantic ‘access’ deficit. Both SA and WA cases showed multimodal semantic impairment, although as expected the WA group showed greater deficits on auditory-verbal than picture judgements. Distribution of damage in the temporal lobe was crucial for predicting the initially beneficial effects of stimulus repetition: WA cases showed initial improvement with repetition of words and pictures, while in SA, semantic access was initially good but declined in the face of competition from previous targets. Prefrontal damage predicted the harmful effects of repetition: the ability to re-select both word and picture targets in the face of mounting competition was linked to left prefrontal damage in both groups. Therefore, SA and WA patients have partially distinct impairment of semantic ‘access’ but, across these syndromes, prefrontal lesions produce declining comprehension with repetition in both verbal and non-verbal tasks.

The only way is up: retail format saturation and the demise of the American five and dime store, 1914-1941

We examine a classic ‘wheel of retailing’ episode – the abandonment of the five and dime pricing formula by American variety chains. These switched from a conventional product lifecycle, focusing on cost reduction through standardisation, to a reverse path up the ‘service cost - unit value’ continuum. We show that, rather than reflecting deteriorating managerial acumen, this was a response to the continued imperative for growth following retail format saturation. Firm-specific (rather than format-specific) competitive advantages were too weak for any chain to be confident it could win a within-format price war, making inter-format competition through raising price points more attractive.