ELLIPTIC EQUATIONS AND SYSTEMS WITH CRITICAL TRUDINGER-MOSER NONLINEARITIES

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)In this article we give first a survey on recent results on some Trudinger-Moser type inequalities, and their importance in the study of nonlinear elliptic equations with nonlinearities which have critical growth in the sense of Trudinger-Moser. Furthermore, recent results concerning systems of such equations will be discussed.302SI455476INCTMatCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Inherited germline TP53 mutation encodes a protein with an aberrant C-terminal motif in a case of pediatric adrenocortical tumor

Childhood adrenocortical tumor (ACT), a very rare malignancy, has an annual worldwide incidence of about 0.3 per million children younger than 15 years. The association between inherited germline mutations of the TP53 gene and an increased predisposition to ACT was described in the context of the Li-Fraumeni syndrome. In fact, about two-thirds of children with ACT have a TP53 mutation. However, less than 10% of pediatric ACT cases occur in Li-Fraumeni syndrome, suggesting that inherited low-penetrance TP53 mutations play an important role in pediatric adrenal cortex tumorigenesis. We identified a novel inherited germline TP53 mutation affecting the acceptor splice site at intron 10 in a child with an ACT and no family history of cancer. The lack of family history of cancer and previous information about the carcinogenic potential of the mutation led us to further characterize it. Bioinformatics analysis showed that the non-natural and highly hydrophobic C-terminal segment of the frame-shifted mutant p53 protein may disrupt its tumor suppressor function by causing misfolding and aggregation. Our findings highlight the clinical and genetic counseling dilemmas that arise when an inherited TP53 mutation is found in a child with ACT without relatives with Li-Fraumeni-component tumors

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincare symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newton's law in the thin brane limit. In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the (thin) Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved as in the Lykken-Randall model and the model is completely free of naked singularities.Comment: 25 pages in latex, no figures, content changed, corrections to Newton's law included for smooth version of RS model and an author adde

Single-shot compressed ultrafast photography at one hundred billion frames per second

The capture of transient scenes at high imaging speed has been long sought by photographers, with early examples being the well known recording in 1878 of a horse in motion and the 1887 photograph of a supersonic bullet. However, not until the late twentieth century were breakthroughs achieved in demonstrating ultrahigh-speed imaging (more than 10^5 frames per second). In particular, the introduction of electronic imaging sensors based on the charge-coupled device (CCD) or complementary metal–oxide–semiconductor (CMOS) technology revolutionized high-speed photography, enabling acquisition rates of up to 10^7 frames per second. Despite these sensors’ widespread impact, further increasing frame rates using CCD or CMOS technology is fundamentally limited by their on-chip storage and electronic readout speed. Here we demonstrate a two-dimensional dynamic imaging technique, compressed ultrafast photography (CUP), which can capture non-repetitive time-evolving events at up to 10^(11) frames per second. Compared with existing ultrafast imaging techniques, CUP has the prominent advantage of measuring an x–y–t (x, y, spatial coordinates; t, time) scene with a single camera snapshot, thereby allowing observation of transient events with temporal resolution as tens of picoseconds. Furthermore, akin to traditional photography, CUP is receive-only, and so does not need the specialized active illumination required by other single-shot ultrafast imagers. As a result, CUP can image a variety of luminescent—such as fluorescent or bioluminescent—objects. Using CUP, we visualize four fundamental physical phenomena with single laser shots only: laser pulse reflection and refraction, photon racing in two media, and faster-than-light propagation of non-information (that is, motion that appears faster than the speed of light but cannot convey information). Given CUP’s capability, we expect it to find widespread applications in both fundamental and applied sciences, including biomedical research

Which bills are lobbied? Predicting and interpreting lobbying activity in the US

Using lobbying data from OpenSecrets.org, we offer several experiments applying machine learning techniques to predict if a piece of legislation (US bill) has been subjected to lobbying activities or not. We also investigate the influence of the intensity of the lobbying activity on how discernible a lobbied bill is from one that was not subject to lobbying. We compare the performance of a number of different models (logistic regression, random forest, CNN and LSTM) and text embedding representations (BOW, TF-IDF, GloVe, Law2Vec). We report results of above 0.85\% ROC AUC scores, and 78\% accuracy. Model performance significantly improves (95\% ROC AUC, and 88\% accuracy) when bills with higher lobbying intensity are looked at. We also propose a method that could be used for unlabelled data. Through this we show that there is a considerably large number of previously unlabelled US bills where our predictions suggest that some lobbying activity took place. We believe our method could potentially contribute to the enforcement of the US Lobbying Disclosure Act (LDA) by indicating the bills that were likely to have been affected by lobbying but were not filed as such

Anatomical characteristics of the styloid process in internal carotid artery dissection: Case-control study

Introduction Pathophysiology of cervical artery dissection is complex and poorly understood. In addition to well-known causative and predisposing factors, including major trauma and monogenic connective tissue disorders, morphological characteristics of the styloid process have been recently recognized as a possible risk factor for cervical internal carotid artery dissection. Aims To study the association of the anatomical characteristics of styloid process with internal carotid artery dissection. Methods Retrospective, multicenter, case-control study of patients with internal carotid artery dissection and age- and sex-matched controls. Consecutive patients with internal carotid artery dissection and controls with ischemic stroke or transient ischemic attack of any etiology excluding internal carotid artery dissection, who had performed computed tomography angiography, diagnosed between January 2010 and September 2016. Two independent observers measured styloid process length and styloid process distance to internal carotid artery. Results Sixty-two patients with internal carotid artery dissection and 70 controls were included. Interobserver agreement was good for styloid process length and styloid process-internal carotid artery distance (interclass correlation coefficient = 0.89 and 0.76, respectively). Styloid process ipsilateral to dissection was longer than left and right styloid process in controls (35.8 ± 14.4 mm versus 30.4 ± 8.9 mm and 30.3 ± 8.2 mm, p = 0.011 and p = 0.008, respectively). Styloid process-internal carotid artery distance ipsilateral to dissection was shorter than left and right distance in controls (6.3 ± 1.9 mm versus 7.2 ± 2.1 mm and 7.0 ± 2.3 mm, p = 0.003 and p = 0.026, respectively). Internal carotid artery dissection was associated with styloid process length (odds ratio = 1.04 mm-1, 95% confidence interval = 1.01-1.08, p = 0.015) and styloid process-internal carotid artery distance (OR = 0.77 mm-1, 95% confidence interval = 0.64-0.92, p = 0.004). Conclusion Longer styloid process and shorter distance between styloid process and cervical internal carotid artery are associated with cervical internal carotid artery dissection.info:eu-repo/semantics/publishedVersio

Pathophysiology of aniridia-associated keratopathy: Developmental aspects and unanswered questions

Aniridia, a rare congenital disease, is often characterized by a progressive, pronounced limbal insufficiency and ocular surface pathology termed aniridia-associated keratopathy (AAK). Due to the characteristics of AAK and its bilateral nature, clinical management is challenging and complicated by the multiple coexisting ocular and systemic morbidities in aniridia. Although it is primarily assumed that AAK originates from a congenital limbal stem cell deficiency, in recent years AAK and its pathogenesis has been questioned in the light of new evidence and a refined understanding of ocular development and the biology of limbal stem cells (LSCs) and their niche. Here, by consolidating and comparing the latest clinical and preclinical evidence, we discuss key unanswered questions regarding ocular developmental aspects crucial to AAK. We also highlight hypotheses on the potential role of LSCs and the ocular surface microenvironment in AAK. The insights thus gained lead to a greater appreciation for the role of developmental and cellular processes in the emergence of AAK. They also highlight areas for future research to enable a deeper understanding of aniridia, and thereby the potential to develop new treatments for this rare but blinding ocular surface disease