Quasireversibility Methods for Non-Well-Posed Problems

The nal value problem, ae u t + Au = 0 ; 0 ! t ! T u(T ) = f with positive self-adjoint unbounded A is known to be ill-posed. One approach to dealing with this has been the method of quasireversibility, where the operator is perturbed to obtain a well-posed problem which approximates the original problem. In this work, we will use a quasi-boundary-value method, where we perturb the nal condition to form an approximate non-local problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions u converge on 0; T] if and only if the original problem has a classical solution. We obtain several other results, including some explicit convergence rates

Diffusing wild type and sterile mosquitoes in an optimal control setting

This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [http://www.who.int/mediacentre/factsheets/fs387/en/ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time. This paper incorporates the diffusion of the mosquitoes into the controlled model and presents a number of numerical simulations

Neuroanatomical substrates for the volitional regulation of heart rate

The control of physiological arousal can assist in the regulation of emotional state. A subset cortical and subcortical brain regions are implicated in autonomic control of bodily arousal during emotional behaviors. Here, we combined human functional neuroimaging with autonomic monitoring to identify neural mechanisms that support the volitional regulation of heart rate, a process that may be assisted by visual feedback. During functional magnetic resonance imaging (fMRI), 15 healthy adults performed an experimental task in which they were prompted voluntarily to increase or decrease cardiovascular arousal (heart rate) during true, false, or absent visual feedback. Participants achieved appropriate changes in heart rate, without significant modulation of respiratory rate, and were overall not influenced by the presence of visual feedback. Increased activity in right amygdala, striatum and brainstem occurred when participants attempted to increase heart rate. In contrast, activation of ventrolateral prefrontal and parietal cortices occurred when attempting to decrease heart rate. Biofeedback enhanced activity within occipito-temporal cortices, but there was no significant interaction with task conditions. Activity in regions including pregenual anterior cingulate and ventral striatum reflected the magnitude of successful task performance, which was negatively related to subclinical anxiety symptoms. Measured changes in respiration correlated with posterior insula activation and heart rate, at a more lenient threshold, change correlated with insula, caudate, and midbrain activity. Our findings highlight a set of brain regions, notably ventrolateral prefrontal cortex, supporting volitional control of cardiovascular arousal. These data are relevant to understanding neural substrates supporting interaction between intentional and interoceptive states related to anxiety, with implications for biofeedback interventions, e.g., real-time fMRI, that target emotional regulation

Interoception and mental health: a roadmap

Interoception refers to the process by which the nervous system senses, interprets, and integrates signals originating from within the body, providing a moment-by moment mapping of the body’s internal landscape across conscious and unconscious levels. Interoceptive signaling has been considered a component process of reflexes, urges, feelings, drives, adaptive responses, and cognitive and emotional experiences, highlighting its contributions to the maintenance of homeostatic functioning, body regulation, and survival. Dysfunction of interoception is increasingly recognized as an important component of different mental health conditions, including anxiety disorders, mood disorders, eating disorders, addictive disorders, and somatic symptom disorders. However, a number of conceptual and methodological challenges have made it difficult for interoceptive constructs to be broadly applied in mental health research and treatment settings. In November 2016, the Laureate Institute for Brain Research organized the first Interoception Summit, a gathering of interoception experts from around the world, with the goal of accelerating progress in understanding the role of interoception in mental health. The discussions at the meeting were organized around four themes: interoceptive assessment, interoceptive integration, interoceptive psychopathology, and the generation of a roadmap that could serve as a guide for future endeavors. This review article presents an overview of the emerging consensus generated by the meeting

Interactions of malnutrition and immune impairment, with specific reference to immunity against parasites

KEY POINTS: 1. Clinical malnutrition is a heterogenous group of disorders including macronutrient deficiencies leading to body cell mass depletion and micronutrient deficiencies, and these often coexist with infectious and inflammatory processes and environmental problems. 2. There is good evidence that specific micronutrients influence immunity, particularly zinc and vitamin A. Iron may have both beneficial and deleterious effects depending on circumstances. 3. There is surprisingly slender good evidence that immunity to parasites is dependent on macronutrient intake or body composition

Optic chiasm in the species of order Clupeiformes, family Clupeidae: Optic chiasm of Spratelloides gracilis shows an opposite laterality to that of Etrumeus teres

In most teleost fishes, the optic nerves decussate completely as they project to the mesencephalic region. Examination of the decussation pattern of 25 species from 11 different orders in Pisces revealed that each species shows a specific chiasmic type. In 11 species out of the 25, laterality of the chiasmic pattern was not determined; in half of the individuals examined, the left optic nerve ran dorsally to the right optic nerve, while in the other half, the right optic nerve was dorsal. In eight other species the optic nerves from both eyes branched into several bundles at the chiasmic point, and intercalated to form a complicated decussation pattern. In the present study we report our findings that Spratelloides gracilis, of the order Clupeiformes, family Clupeidae, shows a particular laterality of decussation: the left optic nerve ran dorsally to the right (n = 200/202). In contrast, Etrumeus teres, of the same order and family, had a strong preference of the opposite (complementary) chiasmic pattern to that of S. gracilis (n = 59/59), revealing that these two species display opposite left–right optic chiasm patterning. As far as we investigated, other species of Clupeiformes have not shown left–right preference in the decussation pattern. We conclude that the opposite laterality of the optic chiasms of these two closely related species, S. gracilis and E. teres, enables investigation of species-specific laterality in fishes of symmetric shapes

Galaxy bulges and their massive black holes: a review

With references to both key and oft-forgotten pioneering works, this article starts by presenting a review into how we came to believe in the existence of massive black holes at the centres of galaxies. It then presents the historical development of the near-linear (black hole)-(host spheroid) mass relation, before explaining why this has recently been dramatically revised. Past disagreement over the slope of the (black hole)-(velocity dispersion) relation is also explained, and the discovery of sub-structure within the (black hole)-(velocity dispersion) diagram is discussed. As the search for the fundamental connection between massive black holes and their host galaxies continues, the competing array of additional black hole mass scaling relations for samples of predominantly inactive galaxies are presented.Comment: Invited (15 Feb. 2014) review article (submitted 16 Nov. 2014). 590 references, 9 figures, 25 pages in emulateApJ format. To appear in "Galactic Bulges", E. Laurikainen, R.F. Peletier, and D.A. Gadotti (eds.), Springer Publishin

Adsorption in ℝ\u3csup\u3en\u3c/sup\u3e

The mathematical description of adsorption of a gas flowing along a given velocity field ∀H through a bounded C1-domain G in Rn filled by an adsorbing material leads to the system of PDE’s for the unknown functions where the gradient is with respect to x, ε is a given positive parameter, the values of a are specified at t = 0, and certain boundary conditions are fixed for u on the boundary of G. It is shown that the Cauchy-boundary-value problem is well posed in the Lp spaces, and the regularity properties of a solution are studied. We also show that the solution of (*) converges to the solution of at+ ∀H · ∀(g(a)) = 0 as ε ↓ 0. © 1994, Khayyam Publishing

A river water quality model for time varying BOD discharge concentration

<p>We consider a model for biochemical oxygen demand (BOD) in a semi-infinite river where the BOD is prescribed by a time varying function at the left endpoint. That is, we study the problem with a time varying boundary loading. We obtain the well-posedness for the model when the boundary loading is smooth in time. We also obtain various qualitative results such as ordering, positivity, and boundedness. Of greatest interest, we show that a periodic loading function admits a unique asymptotically attracting periodic solution. For non-smooth loading functions, we obtain weak solutions. Finally, for certain special cases, we show how to obtain explicit solutions in the form of infinite series.</p