Some approximation properties of Szasz–Mirakyan–Bernstein operators of the Chlodovsky type

We motivate a new sequence of positive linear operators by means of the Chlodovsky-type Szasz–Mirakyan–Bernstein operators and investigate some approximation properties of these operators in the space of continuous functions defined on the right semiaxis. We also find the order of this approximation by using the modulus of continuity and present the Voronovskaya-type theorem.Метою даної статті є обґрунтування нової послідовності додатних лінійних onepaTopiB за допомогою onepaTopiB Сaсa-Мiрaкянa-Бернштейнa типу Хлодовського та дослідження деяких апроксимаційних властивостей цих операторів у просторі неперервних функцій, заданих на правій півосі. Крім того, встановлено порядок таких наближень за допомогою модуля неперервності та наведено теорему типу Вороновської

On Hermite-Hadamard type inequalities for F-convex function

WOS: 000471249600014In this study, we firstly give some properties the family F and F-convex function which are defined by B. Samet. Then, we obtain some midpoint inequalities for differentiable function. Moreover, we establish some midpoint and trapezoid type inequalities for function whose second derivatives in absolute value are F-convex

Distance-Based Analysis of Variance for Brain Connectivity

The field of neuroimaging dedicated to mapping connections in the brain is increasingly being recognized as key for understanding neurodevelopment and pathology. Networks of these connections are quantitatively represented using complex structures including matrices, functions, and graphs, which require specialized statistical techniques for estimation and inference about developmental and disorder-related changes. Unfortunately, classical statistical testing procedures are not well suited to high-dimensional testing problems. In the context of global or regional tests for differences in neuroimaging data, traditional analysis of variance (ANOVA) is not directly applicable without first summarizing the data into univariate or low-dimensional features, a process that may mask salient features of the high-dimensional distributions. In this work, we consider a general framework for two-sample testing of complex structures by studying generalized within- and between-group variances based on distances between complex and potentially high-dimensional observations. We derive an asymptotic approximation to the null distribution of the ANOVA test statistic, and conduct simulation studies with scalar and graph outcomes to study finite sample properties of the test. Finally, we apply our test to our motivating study of structural connectivity in autism spectrum disorder

Label-free nanometer-resolution imaging of biological architectures through surface enhanced raman scattering

Label free imaging of the chemical environment of biological specimens would readily bridge the supramolecular and the cellular scales, if a chemical fingerprint technique such as Raman scattering can be coupled with super resolution imaging. We demonstrate the possibility of label-free super-resolution Raman imaging, by applying stochastic reconstruction to temporal fluctuations of the surface enhanced Raman scattering (SERS) signal which originate from biomolecular layers on large-area plasmonic surfaces with a high and uniform hot-spot density (>1011/cm2, 20 to 35 nm spacing). A resolution of 20 nm is demonstrated in reconstructed images of self-assembled peptide network and fibrilated lamellipodia of cardiomyocytes. Blink rate density is observed to be proportional to the excitation intensity and at high excitation densities (>10 kW/cm2) blinking is accompanied by molecular breakdown. However, at low powers, simultaneous Raman measurements show that SERS can provide sufficient blink rates required for image reconstruction without completely damaging the chemical structure

Label-Free Nanometer-Resolution Imaging of Biological Architectures through Surface Enhanced Raman Scattering

Label free imaging of the chemical environment of biological specimens would readily bridge the supramolecular and the cellular scales, if a chemical fingerprint technique such as Raman scattering can be coupled with super resolution imaging. We demonst

A cyclic nucleotide-gated channel (CNGC16) in pollen is critical for stress tolerance in pollen reproductive development

Cyclic nucleotide-gated channels (CNGCs) have been implicated in diverse aspects of plant growth and development, including responses to biotic and abiotic stress, as well as pollen tube growth and fertility. Here, genetic evidence identifies CNGC16 in Arabidopsis (Arabidopsis thaliana) as critical for pollen fertility under conditions of heat stress and drought. Two independent transfer DNA disruptions of cngc16 resulted in a greater than 10-fold stress-dependent reduction in pollen fitness and seed set. This phenotype was fully rescued through pollen expression of a CNGC16 transgene, indicating that cngc16-1 and 16-2 were both loss-of-function null alleles. The most stress-sensitive period for cngc16 pollen was during germination and the initiation of pollen tube tip growth. Pollen viability assays indicate that mutant pollen are also hypersensitive to external calcium chloride, a phenomenon analogous to calcium chloride hypersensitivities observed in other cngc mutants. A heat stress was found to increase concentrations of 3′,5′-cyclic guanyl monophosphate in both pollen and leaves, as detected using an antibody-binding assay. A quantitative PCR analysis indicates that cngc16 mutant pollen have attenuated expression of several heat-stress response genes, including two heat shock transcription factor genes, HsfA2 and HsfB1. Together, these results provide evidence for a heat stress response pathway in pollen that connects a cyclic nucleotide signal, a Ca(2+)-permeable ion channel, and a signaling network that activates a downstream transcriptional heat shock response

Epidemics in Adaptive Social Networks with Temporary Link Deactivation

Disease spread in a society depends on the topology of the network of social contacts. Moreover, individuals may respond to the epidemic by adapting their contacts to reduce the risk of infection, thus changing the network structure and affecting future disease spread. We propose an adaptation mechanism where healthy individuals may choose to temporarily deactivate their contacts with sick individuals, allowing reactivation once both individuals are healthy. We develop a mean-field description of this system and find two distinct regimes: slow network dynamics, where the adaptation mechanism simply reduces the effective number of contacts per individual, and fast network dynamics, where more efficient adaptation reduces the spread of disease by targeting dangerous connections. Analysis of the bifurcation structure is supported by numerical simulations of disease spread on an adaptive network. The system displays a single parameter-dependent stable steady state and non-monotonic dependence of connectivity on link deactivation rate

The burden attributable to headache disorders in children and adolescents in Lithuania: estimates from a national schools-based study

Background We recently showed headache to be common in children (aged 7–11 years) and adolescents (aged 12–17) in Lithuania. Here we provide evidence from the same study of the headache-attributable burden. Methods Following the generic protocol for Lifting The Burden’s global schools-based study, this cross-sectional survey administered self-completed structured questionnaires to pupils within classes in 24 nationally representative schools selected from seven regions of the country. Headache diagnostic questions were based on ICHD-3 beta criteria but for the inclusion of undifferentiated headache (UdH; defined as mild headache with usual duration < 1 h). Burden enquiry was conducted in multiple domains. Results Questionnaires were completed by 2505 pupils (1382 children, 1123 adolescents; participating proportion 67.4%), of whom 1858 reported headache in the preceding year, with mean frequency (±SD) of 3.7 ± 4.5 days/4 weeks and mean duration of 1.6 ± 1.9 h. Mean proportion of time in ictal state, estimated from these, was 0.9% (migraine 1.5%, probable medication-overuse headache [pMOH] 10.9%). Mean intensity on a scale of 1–3 was 1.6 ± 0.6 (mild-to-moderate). Symptomatic medication was consumed on 1.5 ± 2.8 days/4 weeks. Lost school time was 0.5 ± 1.5 days/4 weeks (migraine 0.7 ± 1.5, pMOH 5.0 ± 7.8) based on recall, but about 50% higher for migraine according to actual absences recorded in association with reported headache on the preceding day. More days were reported with limited activity (overall 1.2 ± 2.4, migraine 1.5 ± 2.2, pMOH 8.4 ± 8.5) than lost from school. One in 30 parents (3.3%) missed work at least once in 4 weeks because of their son’s or daughter’s headache. Emotional impact and quality-of-life scores generally reflected other measures of burden, with pMOH causing greatest detriments, followed by migraine and tension-type headache, and UdH least. Burdens were greater in adolescents than children as UdH differentiated into adult headache types. Conclusions Headache in children and adolescents in Lithuania is mostly associated with modest symptom burden. However, the consequential burdens, in particular lost school days, are far from negligible for migraine (which is prevalent) and very heavy for pMOH (which, while uncommon in children, becomes four-fold more prevalent in adolescents). These findings are of importance to both health and educational policies in Lithuania