Commutators of singular integral operators satisfying a variant of a Lipschitz condition.
Ontology highlight
ABSTRACT:
SUBMITTER: Zhang P
PROVIDER: S-EPMC4032734 | biostudies-other | 2014
REPOSITORIES: biostudies-other
Similar Datasets
Project description:In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral.
| S-EPMC5517584 | biostudies-other
Project description:In the present paper, we introduce the Chlodowsky variant of [Formula: see text] Bernstein-Stancu-Schurer operators which is a generalization of [Formula: see text] Bernstein-Stancu-Schurer operators. We also discuss its Korovkin-type approximation properties and rate of convergence.
| S-EPMC5539272 | biostudies-other
Project description:Emerging SARS-CoV-2 variants raise concerns about our ability to withstand the Covid-19 pandemic, and therefore, understanding mechanistic differences of those variants is crucial. In this study, we investigate disparities between the SARS-CoV-2 wild type and five variants that emerged in late 2020, focusing on the structure and dynamics of the spike protein interface with the human angiotensin-converting enzyme 2 (ACE2) receptor, by using crystallographic structures and extended analysis of microsecond molecular dynamics simulations. Dihedral angle principal component analysis (PCA) showed the strong similarities in the spike receptor binding domain (RBD) dynamics of the Alpha, Beta, Gamma, and Delta variants, in contrast with those of WT and Epsilon. Dynamical perturbation networks and contact PCA identified the peculiar interface dynamics of the Delta variant, which cannot be directly imputable to its specific L452R and T478K mutations since those residues are not in direct contact with the human ACE2 receptor. Our outcome shows that in the Delta variant the L452R and T478K mutations act synergistically on neighboring residues to provoke drastic changes in the spike/ACE2 interface; thus a singular mechanism of action eventually explains why it dominated over preceding variants.
| S-EPMC9199437 | biostudies-literature
Project description:Due to the introduction of highly automated vehicles and systems, the tasks of operators (drivers, pilots, air traffic controllers, production process managers) are in transition from "active control" to "passive monitoring" and "supervising". As a result of this transition, the roles of task load and workload are decreasing while the role of the mental load is increasing, thereby the new type of loads might be defined as information load and communication load. This paper deals with operators' load monitoring and management in highly automated systems. This research (i) introduces the changes in the role of operators and requirements in load management, (ii) defines the operators' models, (iii) describes the possible application of sensors and their integration into the working environment of operators, and (iv) develops the load observation and management concept. There are some examples of analyses of measurements and the concept of validation is discussed. This paper mainly deals with operators, particularly pilots and air traffic controllers (ATCOs).
| S-EPMC7506982 | biostudies-literature
Project description:A manual search paradigm explored the development of English singular-plural comprehension. After being shown a box into which they could reach but not see, infants heard verbal descriptions about the contents of the box (e.g., "There are some cars in the box" vs. "There is a car in the box)" and were then allowed to reach into the box. At 24 months of age, but not at 20 months, infants' search patterns were influenced by verbal number markings. However, verbal number marking did not influence search behavior when plurality was signaled by noun morphology alone. These data converge with parental reports and preferential looking studies concerning the developmental course of mastery of English plural marking and show that infants can create a mental model of the number of objects on the basis of singular-plural morphology alone.
| S-EPMC2857978 | biostudies-literature
Project description:The bacterial flagellar motor is an intricate nanomachine powered by a transmembrane electrochemical gradient. Rotation is driven by the cumulative action of several peptidoglycan-anchored stator complexes on the rotor. In proton-motive force-driven motors, the stator complex is composed of a motility protein B (MotB) dimer surrounded by four copies of MotA, where both MotA and MotB are integral membrane proteins. The lack of full-length MotA and MotB structures hinders understanding of the mechanism of torque generation. Given the low levels of expression and low stability of detergent-solubilized MotB, a soluble chimaeric variant was engineered, where the two transmembrane helices of the MotB dimer were replaced by a leucine zipper. The biochemical and biophysical analysis of the resultant protein showed that it was properly folded, stable, behaved as a monodisperse dimer at low pH, had molecular dimensions close to those expected for native MotB and yielded reproducible crystals. The chimaeric protein is, therefore, a good candidate for structural studies. This 'solubilization by design' approach may be generally applicable to the production of soluble forms of other dimeric, trimeric and tetrameric single-span membrane proteins for functional and structural studies.
| S-EPMC3565690 | biostudies-literature
Project description:Poor solubility and low expression levels often make membrane proteins difficult to study. An alternative to the use of detergents to solubilize these aggregation-prone proteins is the partial redesign of the sequence so as to confer water solubility. Recently, computationally assisted membrane protein solubilization (CAMPS) has been reported, where exposed hydrophobic residues on a protein's surface are computationally redesigned. Herein, the structure and fluctuations of a designed, water-soluble variant of KcsA (WSK-3) were studied using molecular dynamics simulations. The root mean square deviation of the protein from its starting structure, where the backbone coordinates are those of KcsA, was 1.8 angstroms. The structure of salt bridges involved in structural specificity and solubility were examined. The preferred configuration of ions and water in the selectivity filter of WSK-3 was consistent with the reported preferences for KcsA. The structure of the selectivity filter was maintained, which is consistent with WSK-3 having an affinity for agitoxin2 comparable to that of wild-type KcsA. In contrast to KcsA, the central cavity's side chains were observed to reorient, allowing water diffusion through the side of the cavity wall. These simulations provide an atomistic analysis of the CAMPS strategy and its implications for further investigations of membrane proteins.
| S-EPMC1367267 | biostudies-literature
Project description:Variable-order fractional operators were conceived and mathematically formalized only in recent years. The possibility of formulating evolutionary governing equations has led to the successful application of these operators to the modelling of complex real-world problems ranging from mechanics, to transport processes, to control theory, to biology. Variable-order fractional calculus (VO-FC) is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes. Recognizing this untapped potential, the scientific community has been intensively exploring applications of VO-FC to the modelling of engineering and physical systems. This review is intended to serve as a starting point for the reader interested in approaching this fascinating field. We provide a concise and comprehensive summary of the progress made in the development of VO-FC analytical and computational methods with application to the simulation of complex physical systems. More specifically, following a short introduction of the fundamental mathematical concepts, we present the topic of VO-FC from the point of view of practical applications in the context of scientific modelling.
| S-EPMC7069480 | biostudies-literature
Project description:We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics.
| S-EPMC6070579 | biostudies-literature
Project description:MotivationHigh throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data analysis. Existing methods, aimed at signal reconstruction and deconvolution, in general, are either supervised, contain parameters that need to be estimated or present other types of ad hoc features. We here introduce SubMatrix Selection Singular Value Decomposition (SMSSVD), a parameter-free unsupervised signal decomposition and dimension reduction method, designed to reduce noise, adaptively for each low-rank-signal in a given data matrix, and represent the signals in the data in a way that enable unbiased exploratory analysis and reconstruction of multiple overlaid signals, including identifying groups of variables that drive different signals.ResultsThe SMSSVD method produces a denoised signal decomposition from a given data matrix. It also guarantees orthogonality between signal components in a straightforward manner and it is designed to make automation possible. We illustrate SMSSVD by applying it to several real and synthetic datasets and compare its performance to golden standard methods like PCA (Principal Component Analysis) and SPC (Sparse Principal Components, using Lasso constraints). The SMSSVD is computationally efficient and despite being a parameter-free method, in general, outperforms existing statistical learning methods.Availability and implementationA Julia implementation of SMSSVD is openly available on GitHub (https://github.com/rasmushenningsson/SubMatrixSelectionSVD.jl).Supplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC6361234 | biostudies-literature