Variable Exponent Sobolev Spaces and Regularity of Domains

Indexación: Scopus.We study the embeddings of variable exponent Sobolev and Hölder function spaces over Euclidean domains, providing necessary and/or sufficient conditions on the regularity of the exponent and/or the domain in various contexts. Concerning the exponent, the relevant condition is log-Hölder continuity; concerning the domain, the relevant condition is the measure density condition.https://link.springer.com/article/10.1007%2Fs12220-020-00499-

Thermodynamics of String Field Theory Motivated Nonlocal Models

We investigate the thermodynamic properties of the nonlocal tachyon motivated by their nonlocal structure in string field theory. We use previously developed perturbative methods for nonlocal fields to calculate the partition function and the equation of state in the high temperature limit. We find that in these models the tachyons undergo a second order phase transition. We compare our results with those of ordinary scalar field theory. We also calculate the one loop finite temperature effective potential.Comment: 31 pages, 9 figure

NrCAM, a neuronal system cell-adhesion molecule, is induced in papillary thyroid carcinomas

NrCAM (neuron-glia-related cell-adhesion molecule) is primarily, although not solely, expressed in the nervous system. In the present study, NrCAM expression was analysed in a series (46) of papillary thyroid carcinomas (PTCs) and paired normal tissues (NT). Quantitative reverse transcriptase (QRT)-PCR revealed that NrCAM expression was upregulated in all PTCs compared to normal thyroid, whatever the stage or size of the primary tumour. NrCAM transcript levels were 1.3- to 30.7-fold higher in PTCs than in NT. Immunohistochemistry (IHC) confirmed that the expression of NrCAM was considerably higher in tumours (score 2+/3+) than in adjacent normal paratumoural thyroid tissue. The NrCAM protein was detected in all but three (93.3%) PTC samples, and it was mainly cytoplasmic; in some cases there was additional membranous localisation – basolateral and partly apical. In the normal thyroid and tissues surrounding tumours, focal NrCAM immunolabelling was seen only in follicles containing tall cells, where staining was restricted to the apical pole of thyrocytes. Western blot analysis corroborated the QRT–PCR and IHC results, showing higher NrCAM protein levels in PTCs than in paired NT. The level of overexpression of the NrCAM mRNA in tumourous tissue appeared to be independent of the primary tumour stage (pT) or the size of the PTC. These data provide the first evidence that NrCAM is overexpressed in human PTCs at the mRNA and protein levels, whatever the tumour stage. Thus, the induction and upregulation of NrCAM expression could be implicated in the pathogenesis and behaviour of papillary thyroid cancers

Relationship between the Clinical Frailty Scale and short-term mortality in patients ≥ 80 years old acutely admitted to the ICU: a prospective cohort study.

BACKGROUND: The Clinical Frailty Scale (CFS) is frequently used to measure frailty in critically ill adults. There is wide variation in the approach to analysing the relationship between the CFS score and mortality after admission to the ICU. This study aimed to evaluate the influence of modelling approach on the association between the CFS score and short-term mortality and quantify the prognostic value of frailty in this context. METHODS: We analysed data from two multicentre prospective cohort studies which enrolled intensive care unit patients ≥ 80 years old in 26 countries. The primary outcome was mortality within 30-days from admission to the ICU. Logistic regression models for both ICU and 30-day mortality included the CFS score as either a categorical, continuous or dichotomous variable and were adjusted for patient's age, sex, reason for admission to the ICU, and admission Sequential Organ Failure Assessment score. RESULTS: The median age in the sample of 7487 consecutive patients was 84 years (IQR 81-87). The highest fraction of new prognostic information from frailty in the context of 30-day mortality was observed when the CFS score was treated as either a categorical variable using all original levels of frailty or a nonlinear continuous variable and was equal to 9% using these modelling approaches (p < 0.001). The relationship between the CFS score and mortality was nonlinear (p < 0.01). CONCLUSION: Knowledge about a patient's frailty status adds a substantial amount of new prognostic information at the moment of admission to the ICU. Arbitrary simplification of the CFS score into fewer groups than originally intended leads to a loss of information and should be avoided. Trial registration NCT03134807 (VIP1), NCT03370692 (VIP2)

Functional annotation of the cattle genome through systematic discovery and characterization of chromatin states and butyrate-induced variations

The functional annotation of genomes, including chromatin accessibility and modifications, is important for understanding and effectively utilizing the increased amount of genome sequences reported. However, while such annotation has been well explored in a diverse set of tissues and cell types in human and model organisms, relatively little data are available for livestock genomes, hindering our understanding of complex trait variation, domestication, and adaptive evolution. Here, we present the first complete global landscape of regulatory elements in cattle and explore the dynamics of chromatin states in rumen epithelial cells induced by the rumen developmental regulator—butyrate.https://doi.org/10.1186/s12915-019-0687-

Calculation accuracy check in computer processing of measurement data

W artykule przedstawiono wybrane metody automatycznej kontroli dokładności obliczeń w procesie przetwarzania danych pomiarowych. Metody te powinny - w założeniu - uwzględniać dokładność wyników pomiarów, jak i błędy numeryczne. Najwięcej uwagi poświęcono omówieniu możliwości zastosowania arytmetyki przedziałowej jako najbardziej uniwersalnej metody kontroli dokładności obliczeń. Przedstawiono zasady jej stosowania, zalety jak i uwagi dotyczące ominięcia jej mankamentów.The paper presents some methods of the automatic accuracy check of calculations performed during computer processing of measurement data. The mentioned methods should take into account the measurement data accuracy and numerical errors. The paper discusses mainly the interval arithmetic method which appears as the most universal one. The basis of the method, its advantages and possibility to avoid some problems which can be connected with the use of interval arithmetic are presented as well

Rekonstrukcja kształtu stykowej końcówki pomiarowej

Two existing methods of stylus tip geometry reconstruction were studied. Computer generated and measured random surfaces were the objects of the investigations. The benefits of creating connected profiles for tip reconstruction was discussed. The effect of quantisation error on tip reconstruction accuracy was analysed.Istnieją dwie najczęściej stosowane metody rekonstrukcji kształtu końcówki pomiarowej stosowanej podczas pomiarów stykowych struktury geometrycznej powierzchni. Zasadą pierwszej z nich jest znajdowanie części wspólnej kolejnych wierzchołków. Metoda druga polega na stosowaniu obwiedni dolnej, a następnie górnej mierzonego profilu, przy stale wzrastającym promieniu obwiedni, co prowadzi do określenia promienia końcówki pomiarowej. Metody te były analizowane w niniejszej pracy. Przedmiotem analizy były powierzchnie mierzone oraz generowane komputerowo o zróżnicowanym rozkładzie rzędnych. Zastosowano bezwymiarowe ilościowe i jakościowe wskaźniki dokładności rekonstrukcji. Oryginalną propozycją autorów jest łączenie kolejnych profili ułatwiające szacowanie kształtu końcówki pomiarowej. Przeanalizowano również wpływ błędu kwantyzacji na dokładność rekonstrukcji. Stwierdzono przydatność obu analizowanych metod. Metoda polegająca na estymacji promienia końcówki pomiarowej jest mniej wrażliwa na błędy pomiaru

Hausdorff operator in Lebesgue spaces

We study the boundedness of the Hausdorff operator in various types of Lebesgue spaces, e.g. weighted spaces, variable exponent and grand Lebesgue spaces. The results are illustrated by a number of examples. © 2019 Element D.O.O.. All rights reserved