Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

A Functional Role for Modality-Specific Perceptual Systems in Conceptual Representations

Theories of embodied cognition suggest that conceptual processing relies on the same neural resources that are utilized for perception and action. Evidence for these perceptual simulations comes from neuroimaging and behavioural research, such as demonstrations of somatotopic motor cortex activations following the presentation of action-related words, or facilitation of grasp responses following presentation of object names. However, the interpretation of such effects has been called into question by suggestions that neural activation in modality-specific sensorimotor regions may be epiphenomenal, and merely the result of spreading activations from “disembodied”, abstracted, symbolic representations. Here, we present two studies that focus on the perceptual modalities of touch and proprioception. We show that in a timed object-comparison task, concurrent tactile or proprioceptive stimulation to the hands facilitates conceptual processing relative to control stimulation. This facilitation occurs only for small, manipulable objects, where tactile and proprioceptive information form part of the multimodal perceptual experience of interacting with such objects, but facilitation is not observed for large, nonmanipulable objects where such perceptual information is uninformative. Importantly, these facilitation effects are independent of motor and action planning, and indicate that modality-specific perceptual information plays a functionally constitutive role in our mental representations of objects, which supports embodied assumptions that concepts are grounded in the same neural systems that govern perception and action

Applauding with Closed Hands: Neural Signature of Action-Sentence Compatibility Effects

BACKGROUND: Behavioral studies have provided evidence for an action-sentence compatibility effect (ACE) that suggests a coupling of motor mechanisms and action-sentence comprehension. When both processes are concurrent, the action sentence primes the actual movement, and simultaneously, the action affects comprehension. The aim of the present study was to investigate brain markers of bidirectional impact of language comprehension and motor processes. METHODOLOGY/PRINCIPAL FINDINGS: Participants listened to sentences describing an action that involved an open hand, a closed hand, or no manual action. Each participant was asked to press a button to indicate his/her understanding of the sentence. Each participant was assigned a hand-shape, either closed or open, which had to be used to activate the button. There were two groups (depending on the assigned hand-shape) and three categories (compatible, incompatible and neutral) defined according to the compatibility between the response and the sentence. ACEs were found in both groups. Brain markers of semantic processing exhibited an N400-like component around the Cz electrode position. This component distinguishes between compatible and incompatible, with a greater negative deflection for incompatible. Motor response elicited a motor potential (MP) and a re-afferent potential (RAP), which are both enhanced in the compatible condition. CONCLUSIONS/SIGNIFICANCE: The present findings provide the first ACE cortical measurements of semantic processing and the motor response. N400-like effects suggest that incompatibility with motor processes interferes in sentence comprehension in a semantic fashion. Modulation of motor potentials (MP and RAP) revealed a multimodal semantic facilitation of the motor response. Both results provide neural evidence of an action-sentence bidirectional relationship. Our results suggest that ACE is not an epiphenomenal post-sentence comprehension process. In contrast, motor-language integration occurring during the verb onset supports a genuine and ongoing brain motor-language interaction

Cost-effectiveness of guideline-endorsed treatments for low back pain: a systematic review

Healthcare costs for low back pain (LBP) are increasing rapidly. Hence, it is important to provide treatments that are effective and cost-effective. The purpose of this systematic review was to investigate the cost-effectiveness of guideline-endorsed treatments for LBP. We searched nine clinical and economic electronic databases and the reference list of relevant systematic reviews and included studies for eligible studies. Economic evaluations conducted alongside randomised controlled trials investigating treatments for LBP endorsed by the guideline of the American College of Physicians and the American Pain Society were included. Two independent reviewers screened search results and extracted data. Data extracted included the type and perspective of the economic evaluation, the treatment comparators, and the relative cost-effectiveness of the treatment comparators. Twenty-six studies were included. Most studies found that interdisciplinary rehabilitation, exercise, acupuncture, spinal manipulation or cognitive-behavioural therapy were cost-effective in people with sub-acute or chronic LBP. Massage alone was unlikely to be cost-effective. There were inconsistent results on the cost-effectiveness of advice, insufficient evidence on spinal manipulation for people with acute LBP, and no evidence on the cost-effectiveness of medications, yoga or relaxation. This review found evidence supporting the cost-effectiveness of the guideline-endorsed treatments of interdisciplinary rehabilitation, exercise, acupuncture, spinal manipulation and cognitive-behavioural therapy for sub-acute or chronic LBP. There is little or inconsistent evidence for other treatments endorsed in the guideline

A New Horned Crocodile from the Plio-Pleistocene Hominid Sites at Olduvai Gorge, Tanzania

BACKGROUND: The fossil record reveals surprising crocodile diversity in the Neogene of Africa, but relationships with their living relatives and the biogeographic origins of the modern African crocodylian fauna are poorly understood. A Plio-Pleistocene crocodile from Olduvai Gorge, Tanzania, represents a new extinct species and shows that high crocodylian diversity in Africa persisted after the Miocene. It had prominent triangular "horns" over the ears and a relatively deep snout, these resemble those of the recently extinct Malagasy crocodile Voay robustus, but the new species lacks features found among osteolaemines and shares derived similarities with living species of Crocodylus. METHODOLOGY/PRINCIPAL FINDINGS: The holotype consists of a partial skull and skeleton and was collected on the surface between two tuffs dated to approximately 1.84 million years (Ma), in the same interval near the type localities for the hominids Homo habilis and Australopithecus boisei. It was compared with previously-collected material from Olduvai Gorge referable to the same species. Phylogenetic analysis places the new form within or adjacent to crown Crocodylus. CONCLUSIONS/SIGNIFICANCE: The new crocodile species was the largest predator encountered by our ancestors at Olduvai Gorge, as indicated by hominid specimens preserving crocodile bite marks from these sites. The new species also reinforces the emerging view of high crocodylian diversity throughout the Neogene, and it represents one of the few extinct species referable to crown genus Crocodylus

Evolutionary Trends of the Pharyngeal Dentition in Cypriniformes (Actinopterygii: Ostariophysi)

International audienceBACKGROUND: The fish order Cypriniformes is one of the most diverse ray-finned fish groups in the world with more than 3000 recognized species. Cypriniformes are characterized by a striking distribution of their dentition: namely the absence of oral teeth and presence of pharyngeal teeth on the last gill arch (fifth ceratobranchial). Despite this limited localisation, the diversity of tooth patterns in Cypriniformes is astonishing. Here we provide a further description of this diversity using X-ray microtomography and we map the resulting dental characters on a phylogenetic tree to explore evolutionary trends. RESULTS: We performed a pilot survey of dental formulae and individual tooth shapes in 34 adult species of Cypriniformes by X-ray microtomography (using either conventional X-ray machine, or synchrotron microtomography when necessary) or by dissecting. By mapping morphological results in a phylogenetic tree, it emerges that the two super-families Cobitoidea and Cyprinoidea have followed two distinct evolutionary pathways. Furthermore, our analysis supports the hypothesis of a three-row dentition as ancestral for Cyprinoidea and a general trend in tooth row reduction in most derived lineages. Yet, this general scheme must be considered with caution as several events of tooth row gain and loss have occurred during evolutionary history of Cyprinoidea. SIGNIFICANCE: Dentition diversity in Cypriniformes constitutes an excellent model to study the evolution of complex morphological structures. This morphological survey clearly advocates for extending the use of X-ray microtomography to study tooth morphology in Cypriniformes. Yet, our survey also underlines that improved knowledge of Cypriniformes life traits, such as feeding habits, is required as current knowledge is not sufficient to conclude on the link between diet and dental morphology

Reptile remains from Tiga (Tokanod), Loyalty Islands, New Caledonia

Archaeological excavations on Tiga provide the first vouchered herpetological records for this small island between Lifou and Maré in the Loyalty Islands. Eighty-three skeletal elements from four sites yielded material assignable to skinks (Emoia loyaltiensis, Lioscincus nigrofasciolatus), geckos (Bavayia crass i-collis, B. sp., Gehyra georgpotthasti, Nactus pelagicus), and a boid snake (Candoia bihroni) all known from elsewhere in the Loyalties, as well as undetermined material consistent with these and other Loyalties lizards. Diagnostic features of geckos versus skinks for elements commonly recovered from archaeological sites and from owl pellets are discussed. Gehyra georgpotthasti has a limited distribution in the Loyalties and its occurrence on Tiga clarifies its range. The boid snake is the only reptile likely to have been harvested by human inhabitants of Tiga. The presence of gekkonid geckos in pre-European times is confirmed and contrasts with the situation of Grande Terre fossil sites, where only diplodactylid geckos have been recovered. Although it is anticipated that all species recovered from archaeological sites are still present on the island, a modern herpetofaunal survey is needed