Local generalized (α,β)-derivations.
Ontology highlight
ABSTRACT:
SUBMITTER: Fosner A
PROVIDER: S-EPMC3947900 | biostudies-other | 2014
REPOSITORIES: biostudies-other
Similar Datasets
Project description:We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.
| S-EPMC4034443 | biostudies-other
Project description:Any given area in human cortex may receive input from multiple, functionally heterogeneous areas, potentially representing different processing threads. Alpha (8-13 Hz) and beta oscillations (13-20 Hz) have been hypothesized by other investigators to gate local cortical processing, but their influence on cortical responses to input from other cortical areas is unknown. To study this, we measured the effect of local oscillatory power and phase on cortical responses elicited by single-pulse electrical stimulation (SPES) at distant cortical sites, in awake human subjects implanted with intracranial electrodes for epilepsy surgery. In 4 out of 5 subjects, the amplitudes of corticocortical evoked potentials (CCEPs) elicited by distant SPES were reproducibly modulated by the power, but not the phase, of local oscillations in alpha and beta frequencies. Specifically, CCEP amplitudes were higher when average oscillatory power just before distant SPES (-110 to -10 ms) was high. This effect was observed in only a subset (0-33%) of sites with CCEPs and, like the CCEPs themselves, varied with stimulation at different distant sites. Our results suggest that although alpha and beta oscillations may gate local processing, they may also enhance the responsiveness of cortex to input from distant cortical sites.
| S-EPMC6319171 | biostudies-literature
Project description:Predictions of protein local structure, derived from sequence alignment information alone, provide visualization tools for biologists to evaluate the importance of amino acid residue positions of interest in the absence of X-ray crystal/NMR structures or homology models. They are also useful as inputs to sequence analysis and modeling tools, such as hidden Markov models (HMMs), which can be used to search for homology in databases of known protein structure. In addition, local structure predictions can be used as a component of cost functions in genetic algorithms that predict protein tertiary structure. We have developed a program (predict-2nd) that trains multilayer neural networks and have applied it to numerous local structure alphabets, tuning network parameters such as the number of layers, the number of units in each layer and the window sizes of each layer. We have had the most success with four-layer networks, with gradually increasing window sizes at each layer.Because the four-layer neural nets occasionally get trapped in poor local optima, our training protocol now uses many different random starts, with short training runs, followed by more training on the best performing networks from the short runs. One recent addition to the program is the option to add a guide sequence to the profile inputs, increasing the number of inputs per position by 20. We find that use of a guide sequence provides a small but consistent improvement in the predictions for several different local-structure alphabets.Local structure prediction with the methods described here is available for use online at http://www.soe.ucsc.edu/compbio/SAM_T08/T08-query.html. The source code and example networks for PREDICT-2ND are available at http://www.soe.ucsc.edu/~karplus/predict-2nd/ A required C++ library is available at http://www.soe.ucsc.edu/~karplus/ultimate/
| S-EPMC2732275 | biostudies-literature
Project description:This study presents a generalized elastodynamic theory, based on fractional-order operators, capable of modelling the propagation of elastic waves in non-local attenuating solids and across complex non-local interfaces. Classical elastodynamics cannot capture hybrid field transport processes that are characterized by simultaneous propagation and diffusion. The proposed continuum mechanics formulation, which combines fractional operators in both time and space, offers unparalleled capabilities to predict the most diverse combinations of multiscale, non-local, dissipative and attenuating elastic energy transport mechanisms. Despite the many features of this theory and the broad range of applications, this work focuses on the behaviour and modelling capabilities of the space-fractional term and on its effect on the elastodynamics of solids. We also derive a generalized fractional-order version of Snell's Law of refraction and of the corresponding Fresnel's coefficients. This formulation allows predicting the behaviour of fully coupled elastic waves interacting with non-local interfaces. The theoretical results are validated via direct numerical simulations.
| S-EPMC7428027 | biostudies-literature
Project description:We describe a general strategy for creating peptidic oligomers that have unnatural backbones but nevertheless adopt a conformation very similar to the α-helix. These oligomers contain both α- and β-amino acid residues (α/β-peptides). If the β content reaches 25-30% of the residue total, and the β residues are evenly distributed along the backbone, then substantial resistance to proteolytic degradation is often observed. These α/β-peptides can mimic the informational properties of α-helices involved in protein-protein recognition events, as documented in numerous crystal structures. Thus, these unnatural oligomers can be a source of antagonists of undesirable protein-protein interactions that are mediated by natural α-helices, or agonists of receptors for which the natural polypeptide ligands are α-helical. Successes include mimicry of BH3 domains found in proapoptotic proteins, which leads to ligands for antiapoptotic Bcl-2 family proteins, and mimicry of the gp41 CHR domain, which leads to inhibition of HIV infection in cell-based assays.
| S-EPMC3928965 | biostudies-literature
Project description:Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data.
| S-EPMC4392726 | biostudies-other
Project description:We consider the problem of calculating power and sample size for tests based on generalized estimating equations (GEE), that arise in studies involving clustered or correlated data (e.g., longitudinal studies and sibling studies). Previous approaches approximate the power of such tests using the asymptotic behavior of the test statistics under fixed alternatives. We develop a more accurate approach in which the asymptotic behavior is studied under a sequence of local alternatives that converge to the null hypothesis at root-m rate, where m is the number of clusters. Based on this approach, explicit sample size formulae are derived for Wald and quasi-score test statistics in a variety of GEE settings. Simulation results show that in the important special case of logistic regression with exchangeable correlation structure, previous approaches can inflate the projected sample size (to obtain nominal 90% power using the Wald statistic) by over 10%, whereas the proposed approach provides an accuracy of around 2%.
| S-EPMC3903421 | biostudies-literature
Project description:Identifying local structure in molecular simulations is of utmost importance. The most common existing approach to identify local structure is to calculate some geometrical quantity referred to as an order parameter. In simple cases order parameters are physically intuitive and trivial to develop (e.g., ion-pair distance), however in most cases, order parameter development becomes a much more difficult endeavor (e.g., crystal structure identification). Using ideas from computer vision, we adapt a specific type of neural network called a PointNet to identify local structural environments in molecular simulations. A primary challenge in applying machine learning techniques to simulation is selecting the appropriate input features. This challenge is system-specific and requires significant human input and intuition. In contrast, our approach is a generic framework that requires no system-specific feature engineering and operates on the raw output of the simulations, i.e., atomic positions. We demonstrate the method on crystal structure identification in Lennard-Jones (four different phases), water (eight different phases), and mesophase (six different phases) systems. The method achieves as high as 99.5% accuracy in crystal structure identification. The method is applicable to heterogeneous nucleation and it can even predict the crystal phases of atoms near external interfaces. We demonstrate the versatility of our approach by using our method to identify surface hydrophobicity based solely upon positions and orientations of surrounding water molecules. Our results suggest the approach will be broadly applicable to many types of local structure in simulations.
| S-EPMC6839808 | biostudies-literature
Project description:Several human studies have demonstrated that the amplitudes of cortical oscillations are altered by various sensorimotor and cognitive tasks. Event-related augmentation of gamma oscillations and attenuation of alpha and beta oscillations have been often used as surrogate markers of cortical activation elicited by tasks especially in presurgical identification of eloquent cortices. In the present study, we addressed a question whether somatosensory-related gamma augmentation 'precedes' or 'co-occurs with' somatosensory-related attenuation of alpha-beta oscillations.We studied 10 patients who underwent intracranial electrocorticography for epilepsy surgery, and determined the temporal and spatial characteristics of median-nerve somatosensory-related amplitude changes at gamma- (30-100Hz), beta- (14-28Hz) and alpha-band (8-12Hz) oscillations.We found that somatosensory-related gamma augmentation involving the post- and pre-central gyri evolved into beta and alpha augmentation, which was subsequently followed by beta and alpha attenuation involving the post- and pre-central gyri.These observations support the hypothesis that somatosensory-related gamma augmentation but not alpha-beta attenuation represents the initial cortical processing for external somatosensory stimuli. Somatosensory-related alpha-beta attenuation appears to represent a temporally distinct stage of somatosensory processing.The present study has increased our understanding of event-related gamma augmentation and alpha-beta attenuation seen on electrocorticography.
| S-EPMC2822081 | biostudies-literature
Project description:Mammalian brain expresses multiple nicotinic acetylcholine receptor (nAChR) subtypes that differ in subunit composition, sites of expression and pharmacological and functional properties. Among known subtypes of receptors, alpha 4 beta 2* and alpha 6 beta 2*-nAChR have the highest affinity for nicotine (where * indicates possibility of other subunits). The alpha 4 beta 2*-nAChRs are widely distributed, while alpha 6 beta 2*-nAChR are restricted to a few regions. Both subtypes modulate release of dopamine from the dopaminergic neurons of the mesoaccumbens pathway thought to be essential for reward and addiction. alpha 4 beta 2*-nAChR also modulate GABA release in these areas. Identification of selective compounds would facilitate study of nAChR subtypes. An improved understanding of the role of nAChR subtypes may help in developing more effective smoking cessation aids with fewer side effects than current therapeutics. We have screened a series of nicotinic compounds that vary in the distance between the pyridine and the cationic center, in steric bulk, and in flexibility of the molecule. These compounds were screened using membrane binding and synaptosomal function assays, or recordings from GH4C1 cells expressing h alpha 7, to determine affinity, potency and efficacy at four subtypes of nAChRs found in brain, alpha 4 beta 2*, alpha 6 beta 2*, alpha 7 and alpha 3 beta 4*. In addition, physiological assays in gain-of-function mutant mice were used to assess in vivo activity at alpha 4 beta 2* and alpha 6 beta 2*-nAChRs. This approach has identified several compounds with agonist or partial agonist activity that display improved selectivity for alpha 6 beta 2*-nAChR.
| S-EPMC2849849 | biostudies-literature