Entropy inequalities for factors of iid

This paper is concerned with certain invariant random processes (called factors of IID) on infinite trees. Given such a process, one can assign entropies to different finite subgraphs of the tree. There are linear inequalities between these entropies that hold for any factor of IID process (e.g. "edge versus vertex" or "star versus edge"). These inequalities turned out to be very useful: they have several applications already, the most recent one is the Backhausz-Szegedy result on the eigenvectors of random regular graphs. We present new entropy inequalities in this paper. In fact, our approach provides a general "recipe" for how to find and prove such inequalities. Our key tool is a generalization of the edge-vertex inequality for a broader class of factor processes with fewer symmetries

Acute Sets of Exponentially Optimal Size

We present a simple construction of an acute set of size (Formula presented.) in (Formula presented.) for any dimension d. That is, we explicitly give (Formula presented.) points in the d-dimensional Euclidean space with the property that any three points form an acute triangle. It is known that the maximal number of such points is less than (Formula presented.). Our result significantly improves upon a recent construction, due to Dmitriy Zakharov, with size of order (Formula presented.) where (Formula presented.) is the golden ratio. © 2018 Springer Science+Business Media, LLC, part of Springer Natur

How large dimension guarantees a given angle?

We study the following two problems: (1) Given $n\ge 2$ and \al, how large Hausdorff dimension can a compact set A\su\Rn have if $A$ does not contain three points that form an angle \al? (2) Given \al and \de, how large Hausdorff dimension can a %compact subset $A$ of a Euclidean space have if $A$ does not contain three points that form an angle in the \de-neighborhood of \al? An interesting phenomenon is that different angles show different behaviour in the above problems. Apart from the clearly special extreme angles 0 and $180^\circ$, the angles $60^\circ,90^\circ$ and $120^\circ$ also play special role in problem (2): the maximal dimension is smaller for these special angles than for the other angles. In problem (1) the angle $90^\circ$ seems to behave differently from other angles

How large dimension guarantees a given angle

Abstract We study the following two problems: (1) Given n ≥ 2 and α, how large Hausdorff dimension can a compact set A ⊂ R n have if A does not contain three points that form an angle α? (2) Given α and δ, how large Hausdorff dimension can a compact subset A of a Euclidean space have if A does not contain three points that form an angle in the δ-neighborhood of α? Some angles (0, 60 • ) turn out to behave differently than other α ∈ [0, 180 • ]

Depictions of Thailand in Australian and Thai writings:Reflections of the Self and Other

This thesis offers both an examination of the depiction of Thailand in Australian novels, short stories and poems written in the 1980s and after, and an analysis of modern Thai novels and short stories that reflect similar themes to those covered in the Australian literature. One Australian film is also examined as the film provides an important framework for the analysis of some of the short stories and novels under consideration. The thesis establishes a dialogue between Thai and Australian literatures and demonstrates that the comparison of Australian representations of Thailand with Thai representations challenges constructively certain dominant political and social ideologies that enhance conservatism and the status quo in Thailand. The author acknowledges that the discussion of the representations of Thailand in contemporary Australian novels and short stories needs to take into account the colonial legacy and the discourse of Orientalism that tends to posit the ‘East’ as the ‘West’’s ‘Other’. Textual analysis is thus informed by post-colonial and cross-cultural theories, starting from Edward Said’s powerful and controversial critique of Western representation of the East in Orientalism. The first part of the thesis examines Australian crime stories and shows how certain Orientalist images and perceptions persist and help reinforce the image of the East and its people as the antithesis of the West. From Chapters Three through Six, however, more literary works by Australian authors are examined. The important finding is that most of the Australian authors under consideration attempt, though not always successfully, to resist and challenge the Eurocentric stereotypes of Asia and Asians that dominated Australian literature in earlier periods. This difference between contemporary Australian authors and their predecessors seems to reflect modern Australia’s endeavor to distinguish itself from the rest of the Western world and to redefine its relationship with Asia. As literary representations cannot be separated from socio-political contexts, the thesis also includes discussion of the Thai social and political history and, where appropriate, shows how colonialism and neo-colonialism exert their impact on modern Thailand

Deep Learning-based Approach for the Semantic Segmentation of Bright Retinal Damage

Regular screening for the development of diabetic retinopathy is imperative for an early diagnosis and a timely treatment, thus preventing further progression of the disease. The conventional screening techniques based on manual observation by qualified physicians can be very time consuming and prone to error. In this paper, a novel automated screening model based on deep learning for the semantic segmentation of exudates in color fundus images is proposed with the implementation of an end-to-end convolutional neural network built upon UNet architecture. This encoder-decoder network is characterized by the combination of a contracting path and a symmetrical expansive path to obtain precise localization with the use of context information. The proposed method was validated on E-OPHTHA and DIARETDB1 public databases achieving promising results compared to current state-of-theart methods.This paper was supported by the European Union’s Horizon 2020 research and innovation programme under the Project GALAHAD [H2020-ICT2016-2017, 732613]. The work of Adri´an Colomer has been supported by the Spanish Government under a FPI Grant [BES-2014-067889]. We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this research.Silva, C.; Colomer, A.; Naranjo Ornedo, V. (2018). Deep Learning-based Approach for the Semantic Segmentation of Bright Retinal Damage. En Intelligent Data Engineering and Automated Learning – IDEAL 2018. Springer. 164-173. https://doi.org/10.1007/978-3-030-03493-1_18S164173World Health Organization: Diabetes fact sheet. Sci. Total Environ. 20, 1–88 (2011)Verma, L., Prakash, G., Tewari, H.K.: Diabetic retinopathy: time for action. No complacency please! Bull. 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Subtended angles

The first is partially supported by NSF grant DMS 1301614. The second author is partially supported by NSF grant DMS 1301614 and MULTIPLEX no. 317532. The third author’s research supported in part by the Hungarian National Science Foundation OTKA 104343, by the Simons Foundation Collaboration Grant #317487, and by the European Research Council Advanced Investigators Grant 267195

Noble gas and carbon isotope systematics at the seemingly inactive Ciomadul volcano (Eastern‐Central Europe, Romania): evidence for volcanic degassing

Ciomadul is the youngest volcano in the Carpathian-Pannonian Region, Eastern-Central Europe, which last erupted 30 ka. This volcano is considered to be inactive, however, combined evidence from petrologic and magnetotelluric data, as well as seismic tomography studies suggest the existence of a subvolcanic crystal mush with variable melt content. The volcanic area is characterized by high CO2 gas output rate, with a minimum of 8.7 × 103 t yr-1. We investigated 31 gas emissions at Ciomadul to constrain the origin of the volatiles. The δ13C-CO2 and 3He/4He compositions suggest the outgassing of a significant component of mantle-derived fluids. The He isotope signature in the outgassing fluids (up to 3.10 Ra) is lower than the values in the peridotite xenoliths of the nearby alkaline basalt volcanic field (R/Ra 5.95Ra±0.01) which are representative of a continental lithospheric mantle and significantly lower than MORB values. Considering the chemical characteristics of the Ciomadul dacite, including trace element and Sr- Nd and O isotope compositions, an upper crustal contamination is less probable, whereas the primary magmas could have been derived from an enriched mantle source. The low He isotopic ratios could indicate a strongly metasomatized mantle lithosphere. This could be due to infiltration of subduction-related fluids and postmetasomatic ingrowth of radiogenic He. The metasomatic fluids are inferred to have contained subducted carbonate material resulting in a heavier carbon isotope composition (13C is in the range of -1.4 to -4.6 ‰) and an increase of CO2/3He ratio. Our study shows the magmatic contribution to the emitted gases

Familial hypercholesterolaemia in children and adolescents from 48 countries: a cross-sectional study

Background Approximately 450 000 children are born with familial hypercholesterolaemia worldwide every year, yet only 2·1% of adults with familial hypercholesterolaemia were diagnosed before age 18 years via current diagnostic approaches, which are derived from observations in adults. We aimed to characterise children and adolescents with heterozygous familial hypercholesterolaemia (HeFH) and understand current approaches to the identification and management of familial hypercholesterolaemia to inform future public health strategies. Methods For this cross-sectional study, we assessed children and adolescents younger than 18 years with a clinical or genetic diagnosis of HeFH at the time of entry into the Familial Hypercholesterolaemia Studies Collaboration (FHSC) registry between Oct 1, 2015, and Jan 31, 2021. Data in the registry were collected from 55 regional or national registries in 48 countries. Diagnoses relying on self-reported history of familial hypercholesterolaemia and suspected secondary hypercholesterolaemia were excluded from the registry; people with untreated LDL cholesterol (LDL-C) of at least 13·0 mmol/L were excluded from this study. Data were assessed overall and by WHO region, World Bank country income status, age, diagnostic criteria, and index-case status. The main outcome of this study was to assess current identification and management of children and adolescents with familial hypercholesterolaemia. Findings Of 63 093 individuals in the FHSC registry, 11 848 (18·8%) were children or adolescents younger than 18 years with HeFH and were included in this study; 5756 (50·2%) of 11 476 included individuals were female and 5720 (49·8%) were male. Sex data were missing for 372 (3·1%) of 11 848 individuals. Median age at registry entry was 9·6 years (IQR 5·8–13·2). 10 099 (89·9%) of 11 235 included individuals had a final genetically confirmed diagnosis of familial hypercholesterolaemia and 1136 (10·1%) had a clinical diagnosis. Genetically confirmed diagnosis data or clinical diagnosis data were missing for 613 (5·2%) of 11 848 individuals. Genetic diagnosis was more common in children and adolescents from high-income countries (9427 [92·4%] of 10 202) than in children and adolescents from non-high-income countries (199 [48·0%] of 415). 3414 (31·6%) of 10 804 children or adolescents were index cases. Familial-hypercholesterolaemia-related physical signs, cardiovascular risk factors, and cardiovascular disease were uncommon, but were more common in non-high-income countries. 7557 (72·4%) of 10 428 included children or adolescents were not taking lipid-lowering medication (LLM) and had a median LDL-C of 5·00 mmol/L (IQR 4·05–6·08). Compared with genetic diagnosis, the use of unadapted clinical criteria intended for use in adults and reliant on more extreme phenotypes could result in 50–75% of children and adolescents with familial hypercholesterolaemia not being identified. Interpretation Clinical characteristics observed in adults with familial hypercholesterolaemia are uncommon in children and adolescents with familial hypercholesterolaemia, hence detection in this age group relies on measurement of LDL-C and genetic confirmation. Where genetic testing is unavailable, increased availability and use of LDL-C measurements in the first few years of life could help reduce the current gap between prevalence and detection, enabling increased use of combination LLM to reach recommended LDL-C targets early in life. Funding Pfizer, Amgen, Merck Sharp & Dohme, Sanofi–Aventis, Daiichi Sankyo, and Regeneron