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

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

Characteristics associated with quality of life among people with drug-resistant epilepsy

Quality of Life (QoL) is the preferred outcome in non-pharmacological trials, but there is little UK population evidence of QoL in epilepsy. In advance of evaluating an epilepsy self-management course we aimed to describe, among UK participants, what clinical and psycho-social characteristics are associated with QoL. We recruited 404 adults attending specialist clinics, with at least two seizures in the prior year and measured their self-reported seizure frequency, co-morbidity, psychological distress, social characteristics, including self-mastery and stigma, and epilepsy-specific QoL (QOLIE-31-P). Mean age was 42 years, 54% were female, and 75% white. Median time since diagnosis was 18 years, and 69% experienced ≥10 seizures in the prior year. Nearly half (46%) reported additional medical or psychiatric conditions, 54% reported current anxiety and 28% reported current depression symptoms at borderline or case level, with 63% reporting felt stigma. While a maximum QOLIE-31-P score is 100, participants’ mean score was 66, with a wide range (25–99). In order of large to small magnitude: depression, low self-mastery, anxiety, felt stigma, a history of medical and psychiatric comorbidity, low self-reported medication adherence, and greater seizure frequency were associated with low QOLIE-31-P scores. Despite specialist care, UK people with epilepsy and persistent seizures experience low QoL. If QoL is the main outcome in epilepsy trials, developing and evaluating ways to reduce psychological and social disadvantage are likely to be of primary importance. Educational courses may not change QoL, but be one component supporting self-management for people with long-term conditions, like epilepsy

Brain Rhythms Reveal a Hierarchical Network Organization

Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or “virtual brains”, whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease

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

Inhibition of APE1/Ref-1 redox signaling alleviates intestinal dysfunction and damage to myenteric neurons in a mouse model of spontaneous chronic colitis

Background:Inflammatory bowel disease (IBD) associates with damage to the enteric nervous system (ENS), leading to gastrointestinal (GI)dysfunction. Oxidative stress is important for the pathophysiology of inflammation-induced enteric neuropathy and GI dysfunction. Apurinic/apyrimidinic endonuclease 1/redox factor-1 (APE1/Ref-1) is a dual functioning protein that is an essential regulator of the cellular response tooxidative stress. In this study, we aimed to determine whether an APE1/Ref-1 redox domain inhibitor, APX3330, alleviates inflammation-inducedoxidative stress that leads to enteric neuropathy in the Winnie murine model of spontaneous chronic colitis.Methods: Winnie mice received APX3330 or vehicle via intraperitoneal injections over 2 weeks and were compared with C57BL/6 controls. Invivo disease activity and GI transit were evaluated. Ex vivo experiments were performed to assess functional parameters of colonic motility, immune cell infiltration, and changes to the ENS.Results: Targeting APE1/Ref-1 redox activity with APX3330 improved disease severity, reduced immune cell infiltration, restored GI function ,and provided neuroprotective effects to the enteric nervous system. Inhibition of APE1/Ref-1 redox signaling leading to reduced mitochondrial superoxide production, oxidative DNA damage, and translocation of high mobility group box 1 protein (HMGB1) was involved inneuroprotective effects of APX3330 in enteric neurons.Conclusions: This study is the first to investigate inhibition of APE1/Ref-1’s redox activity via APX3330 in an animal model of chronic intestinal inflammation. Inhibition of the redox function of APE1/Ref-1 is a novel strategy that might lead to a possible application of APX3330 forthe treatment of IBD

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

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