Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.Comment: 5 pages Late

The plastic number and its generalized polynomial

The polynomial $X^{3}-X-1$ has a unique positive root known as plastic number, which is denoted by $\rho$ and is approximately equal to $1.32471795$. In this note we study the zeroes of the generalized polynomial $X^{k}-\sum_{j=0}^{k-2}X^{j}$ for $k\geq 3$ and prove that its unique positive root $\lambda_{k}$ tends to the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ as $k \to \infty$. We also derive bounds on $\lambda_{k}$ in terms of Fibonacci numbers.Comment: Publisher's pdf versio

A birational mapping with a strange attractor: Post critical set and covariant curves

We consider some two-dimensional birational transformations. One of them is a birational deformation of the H\'enon map. For some of these birational mappings, the post critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These covariant curves are used to build the preserved meromorphic two-form. One may have also an infinite post critical set yielding a covariant curve which is not algebraic (transcendent). For two of the birational mappings considered, the post critical set is not infinite and we claim that there is no algebraic covariant curve and no preserved meromorphic two-form. For these two mappings with non infinite post critical sets, attracting sets occur and we show that they pass the usual tests (Lyapunov exponents and the fractal dimension) for being strange attractors. The strange attractor of one of these two mappings is unbounded.Comment: 26 pages, 11 figure

Irisin Attenuates Muscle Impairment during Bed Rest through Muscle-Adipose Tissue Crosstalk

The detrimental effect of physical inactivity on muscle characteristics are well known. Irisin, an exercise-induced myokine cleaved from membrane protein fibronectin type III domain-containing protein-5 (FNDC5), mediates at least partially the metabolic benefits of exercise. This study aimed to assess the interplay between prolonged inactivity, circulating irisin, muscle performance, muscle fibers characteristics, as well as the FNDC5 gene expression (FNDC5ge) in muscle and adipose tissue among healthy subjects. Twenty-three healthy volunteers were tested before and after 14 days of Bed Rest, (BR). Post-BR circulating levels of irisin significantly increased, whereas body composition, muscle performance, and muscle fiber characteristics deteriorated. Among the subjects achieving the highest post-BR increase of irisin, the lowest reduction in maximal voluntary contraction and specific force of Fiber Slow/1, the highest increase of FNDC5ge in adipose tissue, and no variation of FNDC5ge in skeletal muscle were recorded. Subjects who had the highest FNDC5ge in adipose tissue but not in muscle tissue showed the highest circulating irisin levels and could better withstand the harmful effect of BR

Sarcopenia parameters in active older adults - an eight-year longitudinal study

BACKGROUD: Sarcopenia is a common skeletal muscle syndrome that is common in older adults but can be mitigated by adequate and regular physical activity. The development and severity of sarcopenia is favored by several factors, the most influential of which are a sedentary lifestyle and physical inactivity. The aim of this observational longitudinal cohort study was to evaluate changes in sarcopenia parameters, based on the EWGSOP2 definition in a population of active older adults after eight years. It was hypothesized that selected active older adults would perform better on sarcopenia tests than the average population. METHODS: The 52 active older adults (22 men and 30 women, mean age: 68.4 ± 5.6 years at the time of their first evaluation) participated in the study at two time points eight-years apart. Three sarcopenia parameters were assessed at both time points: Muscle strength (handgrip test), skeletal muscle mass index, and physical performance (gait speed), these parameters were used to diagnose sarcop0enia according to the EWGSOP2 definition. Additional motor tests were also performed at follow-up measurements to assess participants' overall fitness. Participants self-reported physical activity and sedentary behavior using General Physical Activity Questionnaire at baseline and at follow-up measurements. RESULTS: In the first measurements we did not detect signs of sarcopenia in any individual, but after 8 years, we detected signs of sarcopenia in 7 participants. After eight years, we detected decline in ; muscle strength (-10.2%; p < .001), muscle mass index (-5.4%; p < .001), and physical performance measured with gait speed (-28.6%; p < .001). Similarly, self-reported physical activity and sedentary behavior declined, too (-25.0%; p = .030 and - 48.5%; p < .001, respectively). CONCLUSIONS: Despite expected lower scores on tests of sarcopenia parameters due to age-related decline, participants performed better on motor tests than reported in similar studies. Nevertheless, the prevalence of sarcopenia was consistent with most of the published literature. TRIAL REGISTRATION: The clinical trial protocol was registered on ClinicalTrials.gov, identifier: NCT04899531

Maintaining everyday life praxis in the time of COVID-19 pandemic measures (ELP-COVID-19 survey)

Background: The extreme social circumstances caused by declared COVID-19 pandemic deeply intervene people's everyday life and should not be neglected but seen through the view of social reality pinpointing the 'ordinary' people. In this article, authors explored basic segments of everyday and their subjective perception to what extent sleeping habits, physical inactivity, physical activity, nutritional habits and smoking have changed. Methods: The online survey was conducted in nine European countries (Bosnia and Herzegovina, Croatia, Greece, Kosovo*, Italy, Serbia, Slovakia, Slovenia and Spain) in 4108 participants, aged 15-82 years. The survey took place 30-40 days after World Health Organization declared COVID-19 pandemic state, from 15 April to 3 May 2020. Results: The results have shown 30 min longer sleeping time, 50% longer physical inactivity time, 65% longer screen time, 43% shorter walking time, 24% shorter sport time and 37% longer physical work time. Additionally, body mass gains (0.3 kg) could be explained in 20.6% with meals sizes, unhealthy food consumption, screen time and sport time. Further, respondents reported more regular meals (44%) and healthier meals with less alcohol consumption and less smoking, which have been positive outcomes of home confinement. Conclusion: The findings draw attention to negative changes in everyday praxis (inactivity, body mass gain) after such a short period. Because of possible risk to population's health (especially of countries such as Italy and Spain with serious threat and more stringent measures), findings enable development of recommendations for maintaining healthy lifestyle habits with minimal negative health consequences in similar pandemic circumstances

Myalgic encephalomyelitis/chronic fatigue Syndrome (ME/CFS) : Investigating care practices pointed out to disparities in diagnosis and treatment across European Union

ME/CFS is a chronic, complex, multisystem disease that often limits the health and functioning of the affected patients. Diagnosing patients with ME/CFS is a challenge, and many different case definitions exist and are used in clinical practice and research. Even after diagnosis, medical treatment is very challenging. Symptom relief and coping may affect how patients live with their disease and their quality of life. There is no consensus on which diagnostic criteria should be used and which treatment strategies can be recommended for patients. The purpose of the current project was to map the landscape of the Euromene countries in respect of national guidelines and recommendations for case definition, diagnosis and clinical approaches for ME/CFS patients. A 23 items questionnaire was sent out by email to the members of Euromene. The form contained questions on existing guidelines for case definitions, treatment/management of the disease, tests and questionnaires applied, and the prioritization of information for data sampling in research. We obtained information from 17 countries. Five countries reported having national guidelines for diagnosis, and five countries reported having guidelines for clinical approaches. For diagnostic purposes, the Fukuda criteria were most often recommended, and also the Canadian Consensus criteria, the International Consensus Criteria and the Oxford criteria were used. A mix of diagnostic criteria was applied within those countries having no guidelines. Many different questionnaires and tests were used for symptom registration and diagnostic investigation. For symptom relief, pain and anti-depressive medication were most often recommended. Cognitive Behavioral Therapy and Graded Exercise treatment were often recommended as disease management and rehabilitative/palliative strategies. The lack of consistency in recommendations across European countries urges the development of regulations, guidance and standards. The results of this study will contribute to the harmonization of diagnostic criteria and treatment for ME/CFS in Europe

Remarks on the Cauchy functional equation and variations of it

This paper examines various aspects related to the Cauchy functional equation $f(x+y)=f(x)+f(y)$, a fundamental equation in the theory of functional equations. In particular, it considers its solvability and its stability relative to subsets of multi-dimensional Euclidean spaces and tori. Several new types of regularity conditions are introduced, such as a one in which a complex exponent of the unknown function is locally measurable. An initial value approach to analyzing this equation is considered too and it yields a few by-products, such as the existence of a non-constant real function having an uncountable set of periods which are linearly independent over the rationals. The analysis is extended to related equations such as the Jensen equation, the multiplicative Cauchy equation, and the Pexider equation. The paper also includes a rather comprehensive survey of the history of the Cauchy equation.Comment: To appear in Aequationes Mathematicae (important remark: the acknowledgments section in the official paper exists, but it appears before the appendix and not before the references as in the arXiv version); correction of a minor inaccuracy in Lemma 3.2 and the initial value proof of Theorem 2.1; a few small improvements in various sections; added thank