On Kedlaya type inequalities for weighted means

In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean $\mathscr{M}$ the Kedlaya-type inequality $$\mathscr{A}\big(x_1,\mathscr{M}(x_1,x_2),\ldots,\mathscr{M}(x_1,\ldots,x_n)\big)\le \mathscr{M} \big(x_1, \mathscr{A}(x_1,x_2),\ldots,\mathscr{A}(x_1,\ldots,x_n)\big)$$ holds for an arbitrary $(x_n)$ ($\mathscr{A}$ stands for the arithmetic mean). We are going to prove the weighted counterpart of this inequality. More precisely, if $(x_n)$ is a vector with corresponding (non-normalized) weights $(\lambda_n)$ and $\mathscr{M}_{i=1}^n(x_i,\lambda_i)$ denotes the weighted mean then, under analogous conditions on $\mathscr{M}$, the inequality $$\mathscr{A}_{i=1}^n \big(\mathscr{M}_{j=1}^i (x_j,\lambda_j),\:\lambda_i\big) \le \mathscr{M}_{i=1}^n \big(\mathscr{A}_{j=1}^i (x_j,\lambda_j),\:\lambda_i\big)$$ holds for every $(x_n)$ and $(\lambda_n)$ such that the sequence $(\frac{\lambda_k}{\lambda_1+\cdots+\lambda_k})$ is decreasing.Comment: J. Inequal. Appl. (2018

Upregulated expression of oncomodulin, the beta isoform of parvalbumin, in perikarya and axons in the diencephalon of parvalbumin knockout mice

The calcium-binding proteins parvalbumin, calbindin D-28k, calretinin and calcineurin are present in subsets of GABAergic gigantic calyciform presynaptic terminals of the reticular thalamic nucleus (RTN). Previously it was hypothesized that GABA and calcium-binding proteins including parvalbumin are not only colocalized in the same neuron subpopulation, but that GABA synthesis and parvalbumin expression could be also genetically regulated by a common mechanism. Moreover, parvalbumin expression levels could influence GABA synthesis. For this, we analyzed GABA immunoreactivity in RTN gigantic calyciform presynaptic terminals of parvalbumin–deficient (PV−/−) mice. With respect to GABA immunoreactivity we found no differences compared to wild–type animals. However, using a polyclonal parvalbumin antibody raised against full-length rat muscle parvalbumin on brain sections of PV−/− mice, we observed paradoxical parvalbumin immunoreactivity in partly varicose axons in the diencephalon, mainly in the lamina medullaris externa surrounding the thalamus. A detailed immunohistochemical, biochemical and molecular biological analysis revealed this immunoreactivity to be the result of an upregulation of oncomodulin (OM), the mammalian beta isoform of parvalbumin in PV−/− mice. In addition, OM was present in a sparse subpopulation of neurons in the thalamus and in the dentate gyrus. OM expression has not been observed before in neurons of the mammalian brain; its expression was restricted to outer hair cells in the organ of Corti. Our results indicate that the absence of parvalbumin has no major effect on the GABA-synthesizing system in RTN presynaptic terminals excluding a direct effect of parvalbumin on this regulation. However, a likely homeostatic mechanism is induced resulting in the upregulation of OM in selected axons and neuronal perikarya. Our results warrant further detailed investigations on the putative role of OM in the brain

Asymptotic stability of the Cauchy and Jensen functional equations

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of the original error term. As consequences, we also obtain results of hyperstability character for these two functional equations

Some functional equations related to the characterizations of information measures and their stability

The main purpose of this paper is to investigate the stability problem of some functional equations that appear in the characterization problem of information measures.Comment: 36 pages. arXiv admin note: text overlap with arXiv:1307.0657, arXiv:1307.0631, arXiv:1307.0664, arXiv:1307.065

Investigation of the Antiremodeling Effects of Losartan, Mirabegron and Their Combination on the Development of Doxorubicin-Induced Chronic Cardiotoxicity in a Rat Model

Despite the effectiveness of doxorubicin (DOXO) as a chemotherapeutic agent, dose-dependent development of chronic cardiotoxicity limits its application. The angiotensin-II receptor blocker losartan is commonly used to treat cardiac remodeling of various etiologies. The beta-3 adrenergic receptor agonist mirabegron was reported to improve chronic heart failure. Here we investigated the effects of losartan, mirabegron and their combination on the development of DOXO-induced chronic cardiotoxicity. Male Wistar rats were divided into five groups: (i) control; (ii) DOXO-only; (iii) losartan-treated DOXO; (iv) mirabegron-treated DOXO; (v) losartan plus mirabegron-treated DOXO groups. The treatments started 5 weeks after DOXO administration. At week 8, echocardiography was performed. At week 9, left ventricles were prepared for histology, qRT-PCR, and Western blot measurements. Losartan improved diastolic but not systolic dysfunction and ameliorated SERCA2a repression in our DOXO-induced cardiotoxicity model. The DOXO-induced overexpression of Il1 and Il6 was markedly decreased by losartan and mirabegron. Mirabegron and the combination treatment improved systolic and diastolic dysfunction and significantly decreased overexpression of Smad2 and Smad3 in our DOXO-induced cardiotoxicity model. Only mirabegron reduced DOXO-induced cardiac fibrosis significantly. Mirabegron and its combination with losartan seem to be promising therapeutic tools against DOXO-induced chronic cardiotoxicity.Peer reviewe

Prevention and contrast of child abuse and neglect in the practice of European paediatricians: a multi-national pilot study

Background: Child abuse and neglect, or maltreatment, is a serious public health problem, which may cause long-term effects on children's health and wellbeing and expose them to further adulthood vulnerabilities. Studies on child maltreatment performed in Europe are scarce, and the number of participants enrolled relatively small. The aim of this multi-national European pilot study, was to evaluate the level of understanding and perception of the concepts of child abuse and neglect by European paediatricians working in different medical settings, and the attitude toward these forms of maltreatment in their practice. Methods: The study was performed by a cross-sectional, descriptive, online survey, made available online to European paediatricians members of 50 national paediatric, who belonged to four different medical settings: hospital, family care, university centres and private practice. The questionnaire, designed as a multiple choice questions survey, with a single answer option consisted of 22 questions/statements. Frequency analyses were applied. Most of the data were described using univariate analysis and Chi-squared tests were used to compare the respondents and answers and a significance level of p ≤ 0.05 applied. Results: Findings show that European paediatricians consider the training on child maltreatment currently provided by medical school curricula and paediatric residency courses to be largely insufficient and continuing education courses were considered of great importance to cover educational gaps. Physical violence was recognized by paediatricians mostly during occasional visits with a significant correlation between detecting abuse during an occasional visit and being a primary care paediatrician. Results also showed a reluctance by paediatricians to report cases of maltreatment to the competent judicial authorities. Conclusions: Data of this study may provide useful contribution to the current limited knowledge about the familiarity of European paediatricians with child maltreatment and their skills to recognize, manage and contrast abusive childhood experiences in their practice. Finally, they could provide local legislators and health authorities with information useful to further improve public health approaches and rules able to effectively address shared risk and protective factors, which could prevent child abuse and neglect from ever occurring

Estimation of interdomain flexibility of N-terminus of factor H using residual dipolar couplings

Characterization of segmental flexibility is needed to understand the biological mechanisms of the very large category of functionally diverse proteins, exemplified by the regulators of complement activation, that consist of numerous compact modules or domains linked by short, potentially flexible, sequences of amino acid residues. The use of NMR-derived residual dipolar couplings (RDCs), in magnetically aligned media, to evaluate interdomain motion is established but only for two-domain proteins. We focused on the three N-terminal domains (called CCPs or SCRs) of the important complement regulator, human factor H (i.e. FH1-3). These domains cooperate to facilitate cleavage of the key complement activation-specific protein fragment, C3b, forming iC3b that no longer participates in the complement cascade. We refined a three-dimensional solution structure of recombinant FH1-3 based on nuclear Overhauser effects and RDCs. We then employed a rudimentary series of RDC datasets, collected in media containing magnetically aligned bicelles (disk-like particles formed from phospholipids) under three different conditions, to estimate interdomain motions. This circumvents a requirement of previous approaches for technically difficult collection of five independent RDC datasets. More than 80% of conformers of this predominantly extended three-domain molecule exhibit flexions of < 40 °. Such segmental flexibility (together with the local dynamics of the hypervariable loop within domain 3), could facilitate recognition of C3b via initial anchoring and eventual reorganization of modules to the conformation captured in the previously solved crystal structure of a C3b:FH1-4 complex

Residual dipolar coupling investigation of a heparin tetrasaccharide confirms the limited effect of flexibility of the iduronic acid on the molecular shape of heparin

The solution conformation of a fully sulfated heparin-derived tetrasaccharide, I, was studied in the presence of a 4-fold excess of Ca2+. Proton–proton and proton–carbon residual dipolar couplings (RDCs) were measured in a neutral aligning medium. The order parameters of two rigid hexosamine rings of I were determined separately using singular value decomposition and ab initio structures of disaccharide fragments of I. The order parameters were very similar implying that a common order tensor can be used to analyze the structure of I. Using one order tensor, RDCs of both hexosamine rings were used as restraints in molecular dynamics simulations. RDCs of the inner iduronic acid were calculated for every point of the molecular dynamics trajectory. The fitting of the calculated RDCs of the two forms of the iduronic acid to the experimental values yielded a population of 1C4 and 2So conformers of iduronic acid that agreed well with the analysis based on proton–proton scalar coupling constants. The glycosidic linkage torsion angles in RDC-restrained molecular dynamics (MD) structures of I are consistent with the interglycosidic three-bond proton–carbon coupling constants. These structures also show that the shape of heparin is not affected dramatically by the conformational flexibility of the iduronic acid ring. This is in line with conclusions of previous studies based on MD simulations and the analysis of 1H-1H NOEs. Our work therefore demonstrates the effectiveness of RDCs in the conformational analysis of glycosaminoglycans

A unifying probabilistic framework for analyzing residual dipolar couplings

Residual dipolar couplings provide complementary information to the nuclear Overhauser effect measurements that are traditionally used in biomolecular structure determination by NMR. In a de novo structure determination, however, lack of knowledge about the degree and orientation of molecular alignment complicates the analysis of dipolar coupling data. We present a probabilistic framework for analyzing residual dipolar couplings and demonstrate that it is possible to estimate the atomic coordinates, the complete molecular alignment tensor, and the error of the couplings simultaneously. As a by-product, we also obtain estimates of the uncertainty in the coordinates and the alignment tensor. We show that our approach encompasses existing methods for determining the alignment tensor as special cases, including least squares estimation, histogram fitting, and elimination of an explicit alignment tensor in the restraint energy