Mathematical results for some α\displaystyle{\alpha} models of turbulence with critical and subcritical regularizations

In this paper, we establish the existence of a unique "regular" weak solution to turbulent flows governed by a general family of $\alpha$ models with critical regularizations. In particular this family contains the simplified Bardina model and the modified Leray-$\alpha$ model. When the regularizations are subcritical, we prove the existence of weak solutions and we establish an upper bound on the Hausdorff dimension of the time singular set of those weak solutions. The result is an interpolation between the bound proved by Scheffer for the Navier-Stokes equations and the regularity result in the critical case

Encountering the Victims of Romanian Communism: Young People and Empathy in a Memorial Museum

Many states in post-communist East-Central Europe have established memorial museums which aim to tell the story of suffering under the communist regime. They also seek to encourage visitors to develop empathy for the victims of communist repression.This paper explores the responses of a group of young people to a memorial museum in Romania (Sighet Memorial Museum), focusing on how these visitors experienced empathy for the victims of communist-era violence. Data were collected using focus groups. Most participants showed a degree of empa- thy for the victims of suffering but this was usually shallow in nature. However some visitors displayed more“active” empathy (characterized by deeper imaginative and cogni- tive engagement). The paper explores how both the design and environment of the museum and the back- ground experiences of visitors influenced the develop- ment of empathy. It argues that empathy is not an automatic response to suffering and instead can be con- sidered as an interaction between the design of the museum and the background knowledge of visitors. The paper argues that empathy is an important means for young people to participate in remembering the commu- nist period, and is a means to make“prosthetic”memories of an authoritarian past which they have not experienced first-hand

Identifying and visualising multimorbidity and comorbidity patterns in patients in the English National Health Service: a population-based study

Summary. Background: Globally, there is a paucity of multimorbidity and comorbidity data, especially for minority ethnic groups and younger people. We estimated the frequency of common disease combinations and identified non-random disease associations for all ages in a multiethnic population. Methods In this population-based study, we examined multimorbidity and comorbidity patterns stratified by ethnicity or race, sex, and age for 308 health conditions using electronic health records from individuals included on the Clinical Practice Research Datalink linked with the Hospital Episode Statistics admitted patient care dataset in England. We included individuals who were older than 1 year and who had been registered for at least 1 year in a participating general practice during the study period (between April 1, 2010, and March 31, 2015). We identified the most common combinations of conditions and comorbidities for index conditions. We defined comorbidity as the accumulation of additional conditions to an index condition over an individual's lifetime. We used network analysis to identify conditions that co-occurred more often than expected by chance. We developed online interactive tools to explore multimorbidity and comorbidity patterns overall and by subgroup based on ethnicity, sex, and age. Findings: We collected data for 3 872 451 eligible patients, of whom 1 955 700 (50·5%) were women and girls, 1 916 751 (49·5%) were men and boys, 2 666 234 (68·9%) were White, 155 435 (4·0%) were south Asian, and 98 815 (2·6%) were Black. We found that a higher proportion of boys aged 1–9 years (132 506 [47·8%] of 277 158) had two or more diagnosed conditions than did girls in the same age group (106 982 [40·3%] of 265 179), but more women and girls were diagnosed with multimorbidity than were boys aged 10 years and older and men (1 361 232 [80·5%] of 1 690 521 vs 1 161 308 [70·8%] of 1 639 593). White individuals (2 097 536 [78·7%] of 2 666 234) were more likely to be diagnosed with two or more conditions than were Black (59 339 [60·1%] of 98 815) or south Asian individuals (93 617 [60·2%] of 155 435). Depression commonly co-occurred with anxiety, migraine, obesity, atopic conditions, deafness, soft-tissue disorders, and gastrointestinal disorders across all subgroups. Heart failure often co-occurred with hypertension, atrial fibrillation, osteoarthritis, stable angina, myocardial infarction, chronic kidney disease, type 2 diabetes, and chronic obstructive pulmonary disease. Spinal fractures were most strongly non-randomly associated with malignancy in Black individuals, but with osteoporosis in White individuals. Hypertension was most strongly associated with kidney disorders in those aged 20–29 years, but with dyslipidaemia, obesity, and type 2 diabetes in individuals aged 40 years and older. Breast cancer was associated with different comorbidities in individuals from different ethnic groups. Asthma was associated with different comorbidities between males and females. Bipolar disorder was associated with different comorbidities in younger age groups compared with older age groups. Interpretation: Our findings and interactive online tools are a resource for: patients and their clinicians, to prevent and detect comorbid conditions; research funders and policy makers, to redesign service provision, training priorities, and guideline development; and biomedical researchers and manufacturers of medicines, to provide leads for research into common or sequential pathways of disease and inform the design of clinical trials

Mutvei's solution: an ideal agent for resolving microgrowth structures of biogenic carbonates

Accretionary hard parts of many organisms provide excellent archives of past climate and environmental conditions or life history traits. Variable growth rates function as environmental and physiological proxies, and growth increments as calendars. Recognition of growth structures is thus a prime necessity for sclerochronological studies. Here we present a new, handy, easy-to-use and time-efficient technique that resolves annual and sub-annual growth structures in skeletons of a wide range of different organisms. Mutvei's solution simultaneously etches biogenic carbonates and calcium phosphates, fixates the soluble and insoluble organic matrices and fibers, and stains mucopolysaccharides. It produces a filigreed three-dimensional relief of etch-resistant ridges (growth lines) and etched depressions (growth increments) and stains skeletal growth structures in shadings of blue. Growth lines stand out as crisp, darker-blue stained lines. Reflected optical light microscopy (axial and oblique illumination) and scanning electron microscopy can be used to analyze the microgrowth structures. We demonstrate the use of the technique on hard tissues of various marine and freshwater bivalves, a coral, a sclerosponge, a barnacle, gastropods, a cephalopod, a fish otolith and a whale's ear bone. This technique may be of interest for paleoclimatologists, geochemists and biologists. It can significantly expand the use of biogenic hard parts as environmental and physiological indicators because it reveals microgrowth structures of biogenic skeletons that potentially form on a periodic basis and thus function as calendars

Metody analizy przestrzennej danych rastrowych stosowanych w systemach informacji geograficznej

The most important feature of a GIS is its ability to perform spatial analysis, ie to process spatial (geographical) data in order to obtain information (reports) regarding the studied area. Through this feature of spatial analysis the GIS software differs to other software, such as CAD. The spatial analysis is the process of modeling, examination and interpretation of model results. Following the spatial analysis it can be extracted or created new information about a set of geographic data. This paper aims to treat two methods of raster spatial analysis, namely the raster spatial analysis and map algebra functions and the spatial analysis based on some statistical analysis: local, neighborhood, regional and global.Najważniejszą cechą GIS jest jego zdolność do wykonywania analiz przestrzennych, tj. do przetwarzania danych przestrzennych (geograficznych) w celu uzyskania informacji (raportów) dotyczących badanego obszaru. Dzięki funkcji analizy przestrzennej oprogramowanie GIS różni się od innych oprogramowań takich jak CAD. Analiza przestrzenna jest procesem modelowania, badania i interpretacji wyników modelu. Dzięki analizie przestrzennej można wyodrębnić lub utworzyć nową informację o zbiorze danych geograficznych. Artykuł ma na celu przedstawienie dwóch metod analizy przestrzennej rastrowej, a mianowicie przestrzennej analizy rastrowej i funkcji algebry mapy oraz analizy przestrzenne na podstawie analizy statystycznej: lokalne, sąsiedzkie, regionalne i globalne