A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

One-Sided Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering Over Uniform and Non-Uniform Meshes

In this paper, we introduce a new position-dependent Smoothness-Increasing Accuracy-Conserving (SIAC) filter that retains the benefits of position dependence while ameliorating some of its shortcomings. As in the previous position-dependent filter, our new filter can be applied near domain boundaries, near a discontinuity in the solution, or at the interface of different mesh sizes; and as before, in general, it numerically enhances the accuracy and increases the smoothness of approximations obtained using the discontinuous Galerkin (dG) method. However, the previously proposed position-dependent one-sided filter had two significant disadvantages: (1) increased computational cost (in terms of function evaluations), brought about by the use of $4k+1$ central B-splines near a boundary (leading to increased kernel support) and (2) increased numerical conditioning issues that necessitated the use of quadruple precision for polynomial degrees of $k\ge 3$ for the reported accuracy benefits to be realizable numerically. Our new filter addresses both of these issues --- maintaining the same support size and with similar function evaluation characteristicsas the symmetric filter in a way that has better numerical conditioning --- making it, unlike its predecessor, amenable for GPU computing. Our new filter was conceived by revisiting the original error analysis for superconvergence of SIAC filters and by examining the role of the B-splines and their weights in the SIAC filtering kernel. We demonstrate, in the uniform mesh case, that our new filter is globally superconvergent for $k=1$ and superconvergent in the interior (e.g., region excluding the boundary) for $k\ge2$. Furthermore, we present the first theoretical proof of superconvergence for postprocessing over smoothly varying meshes, and explain the accuracy-order conserving nature of this new filter when applied to certain non-uniform meshes cases. We provide numerical examples supporting our theoretical results and demonstrating that our new filter, in general, enhances the smoothness and accuracy of the solution. Numerical results are presented for solutions of both linear and nonlinear equation solved on both uniform and non-uniform one- and two-dimensional meshes

Systematic review of factors influencing patient and practitioner delay in diagnosis of upper gastrointestinal cancer

As knowledge on the causation of cancers advances and new treatments are developed, early recognition and accurate diagnosis becomes increasingly important. This review focused on identifying factors influencing patient and primary care practitioner delay for upper gastrointestinal cancer. A systematic methodology was applied, including extensive searches of the literature published from 1970 to 2003, systematic data extraction, quality assessment and narrative data synthesis. Included studies were those evaluating factors associated with the time interval between a patient first noticing a cancer symptom and presenting to primary care, between a patient first presenting to primary care and being referred to secondary care, or describing an intervention designed to reduce those intervals. Twenty-five studies were included in the review. Studies reporting delay intervals demonstrated that the patient phase of delay was greater than the practitioner phase, whilst patient-related research suggests that recognition of symptom seriousness is more important than recognition of the presence of the symptom. The main factors related to practitioner delay were misdiagnosis, application and interpretation of tests, and the confounding effect of existing disease. Greater understanding of patient factors is required, along with evaluation of interventions to ensure appropriate diagnosis, examination and investigation

Incidental sounds of locomotion in animal cognition

The highly synchronized formations that characterize schooling in fish and the flight of certain bird groups have frequently been explained as reducing energy expenditure. I present an alternative, or complimentary, hypothesis that synchronization of group movements may improve hearing perception. Although incidental sounds produced as a by-product of locomotion (ISOL) will be an almost constant presence to most animals, the impact on perception and cognition has been little discussed. A consequence of ISOL may be masking of critical sound signals in the surroundings. Birds in flight may generate significant noise; some produce wing beats that are readily heard on the ground at some distance from the source. Synchronization of group movements might reduce auditory masking through periods of relative silence and facilitate auditory grouping processes. Respiratory locomotor coupling and intermittent flight may be other means of reducing masking and improving hearing perception. A distinct border between ISOL and communicative signals is difficult to delineate. ISOL seems to be used by schooling fish as an aid to staying in formation and avoiding collisions. Bird and bat flocks may use ISOL in an analogous way. ISOL and interaction with animal perception, cognition, and synchronized behavior provide an interesting area for future study

Agrarian diet and diseases of affluence – Do evolutionary novel dietary lectins cause leptin resistance?

BACKGROUND: The global pattern of varying prevalence of diseases of affluence, such as obesity, cardiovascular disease and diabetes, suggests that some environmental factor specific to agrarian societies could initiate these diseases. PRESENTATION OF THE HYPOTHESIS: We propose that a cereal-based diet could be such an environmental factor. Through previous studies in archaeology and molecular evolution we conclude that humans and the human leptin system are not specifically adapted to a cereal-based diet, and that leptin resistance associated with diseases of affluence could be a sign of insufficient adaptation to such a diet. We further propose lectins as a cereal constituent with sufficient properties to cause leptin resistance, either through effects on metabolism central to the proper functions of the leptin system, and/or directly through binding to human leptin or human leptin receptor, thereby affecting the function. TESTING THE HYPOTHESIS: Dietary interventions should compare effects of agrarian and non-agrarian diets on incidence of diseases of affluence, related risk factors and leptin resistance. A non-significant (p = 0.10) increase of cardiovascular mortality was noted in patients advised to eat more whole-grain cereals. Our lab conducted a study on 24 domestic pigs in which a cereal-free hunter-gatherer diet promoted significantly higher insulin sensitivity, lower diastolic blood pressure and lower C-reactive protein as compared to a cereal-based swine feed. Testing should also evaluate the effects of grass lectins on the leptin system in vivo by diet interventions, and in vitro in various leptin and leptin receptor models. Our group currently conducts such studies. IMPLICATIONS OF THE HYPOTHESIS: If an agrarian diet initiates diseases of affluence it should be possible to identify the responsible constituents and modify or remove them so as to make an agrarian diet healthier

Pathogenesis of adolescent idiopathic scoliosis in girls - a double neuro-osseous theory involving disharmony between two nervous systems, somatic and autonomic expressed in the spine and trunk: possible dependency on sympathetic nervous system and hormones with implications for medical therapy

Anthropometric data from three groups of adolescent girls - preoperative adolescent idiopathic scoliosis (AIS), screened for scoliosis and normals were analysed by comparing skeletal data between higher and lower body mass index subsets. Unexpected findings for each of skeletal maturation, asymmetries and overgrowth are not explained by prevailing theories of AIS pathogenesis. A speculative pathogenetic theory for girls is formulated after surveying evidence including: (1) the thoracospinal concept for right thoracic AIS in girls; (2) the new neuroskeletal biology relating the sympathetic nervous system to bone formation/resorption and bone growth; (3) white adipose tissue storing triglycerides and the adiposity hormone leptin which functions as satiety hormone and sentinel of energy balance to the hypothalamus for long-term adiposity; and (4) central leptin resistance in obesity and possibly in healthy females. The new theory states that AIS in girls results from developmental disharmony expressed in spine and trunk between autonomic and somatic nervous systems. The autonomic component of this double neuro-osseous theory for AIS pathogenesis in girls involves selectively increased sensitivity of the hypothalamus to circulating leptin (genetically-determined up-regulation possibly involving inhibitory or sensitizing intracellular molecules, such as SOC3, PTP-1B and SH2B1 respectively), with asymmetry as an adverse response (hormesis); this asymmetry is routed bilaterally via the sympathetic nervous system to the growing axial skeleton where it may initiate the scoliosis deformity (leptin-hypothalamic-sympathetic nervous system concept = LHS concept). In some younger preoperative AIS girls, the hypothalamic up-regulation to circulating leptin also involves the somatotropic (growth hormone/IGF) axis which exaggerates the sympathetically-induced asymmetric skeletal effects and contributes to curve progression, a concept with therapeutic implications. In the somatic nervous system, dysfunction of a postural mechanism involving the CNS body schema fails to control, or may induce, the spinal deformity of AIS in girls (escalator concept). Biomechanical factors affecting ribs and/or vertebrae and spinal cord during growth may localize AIS to the thoracic spine and contribute to sagittal spinal shape alterations. The developmental disharmony in spine and trunk is compounded by any osteopenia, biomechanical spinal growth modulation, disc degeneration and platelet calmodulin dysfunction. Methods for testing the theory are outlined. Implications are discussed for neuroendocrine dysfunctions, osteopontin, sympathoactivation, medical therapy, Rett and Prader-Willi syndromes, infantile idiopathic scoliosis, and human evolution. AIS pathogenesis in girls is predicated on two putative normal mechanisms involved in trunk growth, each acquired in evolution and unique to humans

Inhibition of focal adhesion kinase suppresses the adverse phenotype of endocrine-resistant breast cancer cells and improves endocrine response in endocrine-sensitive cells

International audienceAcquired resistance to endocrine therapy in breast cancer is a major clinical problem. Previous reports have demonstrated that cell models of acquired endocrine resistance have altered cell–matrix adhesion and a highly migratory phenotype, features which may impact on tumour spread in vivo. Focal adhesion kinase (FAK) is an intracellular kinase that regulates signalling pathways central to cell adhesion, migration and survival and its expression is frequently deregulated in breast cancer. In this study, we have used the novel FAK inhibitor PF573228 to address the role of FAK in the development of endocrine resistance. Whilst total-FAK expression was similar between endocrine-sensitive and endocrine-resistant MCF7 cells, FAK phosphorylation status (Y397 or Y861) was altered in resistance. PF573228 promoted a dose-dependent inhibition of FAK phosphorylation at Y397 but did not affect other FAK activation sites (pY407, pY576 and pY861). Endocrine-resistant cells were more sensitive to these inhibitory effects versus MCF7 (mean IC for FAK pY397 inhibition: 0.43 μM, 0.05 μM and 0.13 μM for MCF7, TamR and FasR cells, respectively). Inhibition of FAK pY397 was associated with a reduction in TamR and FasR adhesion to, and migration over, matrix components. PF573228 as a single agent (0–1 μM) did not affect the growth of MCF7 cells or their endocrine-resistant counterparts. However, treatment of endocrine-sensitive cells with PF573228 and tamoxifen combined resulted in greater suppression of proliferation versus single agent treatment. Together these data suggest the importance of FAK in the process of endocrine resistance, particularly in the development of an aggressive, migratory cell phenotype and demonstrate the potential to improve endocrine response through combination treatment

Pharmacoperones for misfolded gonadotropin receptors

The gonadotropin receptors (luteinising hormone receptor; LHR and follicle-stimulating hormone receptor; FSHR) are G protein-coupled receptors (GPCRs) that play an important role in the endocrine control of reproduction. Thus genetic mutations that cause impaired function of these receptors have been implicated in a number of reproductive disorders. Disease-causing genetic mutations in GPCRs frequently result in intracellular retention and degradation of the nascent protein through misfolding and subsequent recognition by cellular quality control machinery. The discovery and development of novel compounds termed pharmacological chaperones (pharmacoperones) that can stabilise misfolded receptors and restore trafficking and plasma membrane expression are therefore of great interest clinically, and promising in vitro data describing the pharmacoperone rescue of a number of intracellularly retained mutant GPCRs has provided a platform for taking these compounds into in vivo trials. Thienopyrimidine small molecule allosteric gonadotropin receptor agonists (Org 42599 and Org 41841) have been demonstrated to have pharmacoperone activity. These compounds can rescue cell surface expression and in many cases, hormone responsiveness, of a range of retained mutant gonadotropin receptors. Should gonadotropin receptor selectivity of these compounds be improved, they could offer therapeutic benefit to subsets of patients suffering from reproductive disorders attributed to defective gonadotropin receptor trafficking.https://www.springer.com/series/1642018-12-01hj2018Immunolog