The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Upper atmospheres and ionospheres of planets and satellites

The upper atmospheres of the planets and their satellites are more directly exposed to sunlight and solar wind particles than the surface or the deeper atmospheric layers. At the altitudes where the associated energy is deposited, the atmospheres may become ionized and are referred to as ionospheres. The details of the photon and particle interactions with the upper atmosphere depend strongly on whether the object has anintrinsic magnetic field that may channel the precipitating particles into the atmosphere or drive the atmospheric gas out to space. Important implications of these interactions include atmospheric loss over diverse timescales, photochemistry and the formation of aerosols, which affect the evolution, composition and remote sensing of the planets (satellites). The upper atmosphere connects the planet (satellite) bulk composition to the near-planet (-satellite) environment. Understanding the relevant physics and chemistry provides insight to the past and future conditions of these objects, which is critical for understanding their evolution. This chapter introduces the basic concepts of upper atmospheres and ionospheres in our solar system, and discusses aspects of their neutral and ion composition, wind dynamics and energy budget. This knowledge is key to putting in context the observations of upper atmospheres and haze on exoplanets, and to devise a theory that explains exoplanet demographics.Comment: Invited Revie

The nuclear receptors of Biomphalaria glabrata and Lottia gigantea: Implications for developing new model organisms

© 2015 Kaur et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedNuclear receptors (NRs) are transcription regulators involved in an array of diverse physiological functions including key roles in endocrine and metabolic function. The aim of this study was to identify nuclear receptors in the fully sequenced genome of the gastropod snail, Biomphalaria glabrata, intermediate host for Schistosoma mansoni and compare these to known vertebrate NRs, with a view to assessing the snail's potential as a invertebrate model organism for endocrine function, both as a prospective new test organism and to elucidate the fundamental genetic and mechanistic causes of disease. For comparative purposes, the genome of a second gastropod, the owl limpet, Lottia gigantea was also investigated for nuclear receptors. Thirty-nine and thirty-three putative NRs were identified from the B. glabrata and L. gigantea genomes respectively, based on the presence of a conserved DNA-binding domain and/or ligand-binding domain. Nuclear receptor transcript expression was confirmed and sequences were subjected to a comparative phylogenetic analysis, which demonstrated that these molluscs have representatives of all the major NR subfamilies (1-6). Many of the identified NRs are conserved between vertebrates and invertebrates, however differences exist, most notably, the absence of receptors of Group 3C, which includes some of the vertebrate endocrine hormone targets. The mollusc genomes also contain NR homologues that are present in insects and nematodes but not in vertebrates, such as Group 1J (HR48/DAF12/HR96). The identification of many shared receptors between humans and molluscs indicates the potential for molluscs as model organisms; however the absence of several steroid hormone receptors indicates snail endocrine systems are fundamentally different.The National Centre for the Replacement, Refinement and Reduction of Animals in Research, Grant Ref:G0900802 to CSJ, LRN, SJ & EJR [www.nc3rs.org.uk]

Apraxia and motor dysfunction in corticobasal syndrome

Background: Corticobasal syndrome (CBS) is characterized by multifaceted motor system dysfunction and cognitive disturbance; distinctive clinical features include limb apraxia and visuospatial dysfunction. Transcranial magnetic stimulation (TMS) has been used to study motor system dysfunction in CBS, but the relationship of TMS parameters to clinical features has not been studied. The present study explored several hypotheses; firstly, that limb apraxia may be partly due to visuospatial impairment in CBS. Secondly, that motor system dysfunction can be demonstrated in CBS, using threshold-tracking TMS, and is linked to limb apraxia. Finally, that atrophy of the primary motor cortex, studied using voxel-based morphometry analysis (VBM), is associated with motor system dysfunction and limb apraxia in CBS.   Methods: Imitation of meaningful and meaningless hand gestures was graded to assess limb apraxia, while cognitive performance was assessed using the Addenbrooke's Cognitive Examination - Revised (ACE-R), with particular emphasis placed on the visuospatial subtask. Patients underwent TMS, to assess cortical function, and VBM.   Results: In total, 17 patients with CBS (7 male, 10 female; mean age 64.4+/2 6.6 years) were studied and compared to 17 matched control subjects. Of the CBS patients, 23.5% had a relatively inexcitable motor cortex, with evidence of cortical dysfunction in the remaining 76.5% patients. Reduced resting motor threshold, and visuospatial performance, correlated with limb apraxia. Patients with a resting motor threshold <50% performed significantly worse on the visuospatial sub-task of the ACE-R than other CBS patients. Cortical function correlated with atrophy of the primary and pre-motor cortices, and the thalamus, while apraxia correlated with atrophy of the pre-motor and parietal cortices.   Conclusions: Cortical dysfunction appears to underlie the core clinical features of CBS, and is associated with atrophy of the primary motor and pre-motor cortices, as well as the thalamus, while apraxia correlates with pre-motor and parietal atrophy

Transcriptomics reveal an integrative role for maternal thyroid hormones during zebrafish embryogenesis

Thyroid hormones (THs) are essential for embryonic brain development but the genetic mechanisms involved in the action of maternal THs (MTHs) are still largely unknown. As the basis for understanding the underlying genetic mechanisms of MTHs regulation we used an established zebrafish monocarboxylic acid transporter 8 (MCT8) knock-down model and characterised the transcriptome in 25hpf zebrafish embryos. Subsequent mapping of differentially expressed genes using Reactome pathway analysis together with in situ expression analysis and immunohistochemistry revealed the genetic networks and cells under MTHs regulation during zebrafish embryogenesis. We found 4,343 differentially expressed genes and the Reactome pathway analysis revealed that TH is involved in 1681 of these pathways. MTHs regulated the expression of core developmental pathways, such as NOTCH and WNT in a cell specific context. The cellular distribution of neural MTH-target genes demonstrated their cell specific action on neural stem cells and differentiated neuron classes. Taken together our data show that MTHs have a role in zebrafish neurogenesis and suggest they may be involved in cross talk between key pathways in neural development. Given that the observed MCT8 zebrafish knockdown phenotype resembles the symptoms in human patients with Allan-Herndon-Dudley syndrome our data open a window into understanding the genetics of this human congenital condition.Portuguese Fundacao para Ciencia e Tecnologia (FCT) [PTDC/EXPL/MARBIO/0430/2013]; CCMAR FCT Plurianual financing [UID/Multi/04326/2013]; FCT [SFRH/BD/111226/2015, SFRH/BD/108842/2015, SFRH/BPD/89889/2012]; FCT-IF Starting Grant [IF/01274/2014]info:eu-repo/semantics/publishedVersio

Quantitative Histomorphometry of the Healthy Peritoneum

The peritoneum plays an essential role in preventing abdominal frictions and adhesions and can be utilized as a dialysis membrane. Its physiological ultrastructure, however, has not yet been studied systematically. 106 standardized peritoneal and 69 omental specimens were obtained from 107 patients (0.1-60 years) undergoing surgery for disease not affecting the peritoneum for automated quantitative histomorphometry and immunohistochemistry. The mesothelial cell layer morphology and protein expression pattern is similar across all age groups. Infants below one year have a thinner submesothelium; inflammation, profibrotic activity and mesothelial cell translocation is largely absent in all age groups. Peritoneal blood capillaries, lymphatics and nerve fibers locate in three distinct submesothelial layers. Blood vessel density and endothelial surface area follow a U-shaped curve with highest values in infants below one year and lowest values in children aged 7-12 years. Lymphatic vessel density is much lower, and again highest in infants. Omental blood capillary density correlates with parietal peritoneal findings, whereas only few lymphatic vessels are present. The healthy peritoneum exhibits major thus far unknown particularities, pertaining to functionally relevant structures, and subject to substantial changes with age. The reference ranges established here provide a framework for future histomorphometric analyses and peritoneal transport modeling approaches. © 2016, EDP Science. All rights reserved

Estrogen-dependent dynamic profile of eNOS-DNA associations in prostate cancer

In previous work we have documented the nuclear translocation of endothelial NOS (eNOS) and its participation in combinatorial complexes with Estrogen Receptor Beta (ERβ) and Hypoxia Inducible Factors (HIFs) that determine localized chromatin remodeling in response to estrogen (E2) and hypoxia stimuli, resulting in transcriptional regulation of genes associated with adverse prognosis in prostate cancer (PCa). To explore the role of nuclear eNOS in the acquisition of aggressive phenotype in PCa, we performed ChIP-Sequencing on chromatin-associated eNOS from cells from a primary tumor with poor outcome and from metastatic LNCaP cells. We found that: 1. the eNOS-bound regions (peaks) are widely distributed across the genome encompassing multiple transcription factors binding sites, including Estrogen Response Elements. 2. E2 increased the number of peaks, indicating hormone-dependent eNOS re-localization. 3. Peak distribution was similar with/without E2 with ≈ 55% of them in extragenic DNA regions and an intriguing involvement of the 5′ domain of several miRs deregulated in PCa. Numerous potentially novel eNOS-targeted genes have been identified suggesting that eNOS participates in the regulation of large gene sets. The parallel finding of downregulation of a cluster of miRs, including miR-34a, in PCa cells associated with poor outcome led us to unveil a molecular link between eNOS and SIRT1, an epigenetic regulator of aging and tumorigenicity, negatively regulated by miR-34a and in turn activating eNOS. E2 potentiates miR-34a downregulation thus enhancing SIRT1 expression, depicting a novel eNOS/SIRT1 interplay fine-tuned by E2-activated ER signaling, and suggesting that eNOS may play an important role in aggressive PCa

Therapeutic DNA vaccine induces broad T cell responses in the gut and sustained protection from viral rebound and AIDS in SIV-infected rhesus macaques.

Immunotherapies that induce durable immune control of chronic HIV infection may eliminate the need for life-long dependence on drugs. We investigated a DNA vaccine formulated with a novel genetic adjuvant that stimulates immune responses in the blood and gut for the ability to improve therapy in rhesus macaques chronically infected with SIV. Using the SIV-macaque model for AIDS, we show that epidermal co-delivery of plasmids expressing SIV Gag, RT, Nef and Env, and the mucosal adjuvant, heat-labile E. coli enterotoxin (LT), during antiretroviral therapy (ART) induced a substantial 2-4-log fold reduction in mean virus burden in both the gut and blood when compared to unvaccinated controls and provided durable protection from viral rebound and disease progression after the drug was discontinued. This effect was associated with significant increases in IFN-γ T cell responses in both the blood and gut and SIV-specific CD8+ T cells with dual TNF-α and cytolytic effector functions in the blood. Importantly, a broader specificity in the T cell response seen in the gut, but not the blood, significantly correlated with a reduction in virus production in mucosal tissues and a lower virus burden in plasma. We conclude that immunizing with vaccines that induce immune responses in mucosal gut tissue could reduce residual viral reservoirs during drug therapy and improve long-term treatment of HIV infection in humans

Observation of associated near-side and away-side long-range correlations in √sNN=5.02 TeV proton-lead collisions with the ATLAS detector

Two-particle correlations in relative azimuthal angle (Δϕ) and pseudorapidity (Δη) are measured in √sNN=5.02  TeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1  μb-1 of data as a function of transverse momentum (pT) and the transverse energy (ΣETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Δη|<5) “near-side” (Δϕ∼0) correlation that grows rapidly with increasing ΣETPb. A long-range “away-side” (Δϕ∼π) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ΣETPb, is found to match the near-side correlation in magnitude, shape (in Δη and Δϕ) and ΣETPb dependence. The resultant Δϕ correlation is approximately symmetric about π/2, and is consistent with a dominant cos⁡2Δϕ modulation for all ΣETPb ranges and particle pT