The Relativistic Rotation

The classical rotation is not self-consistent in the framework of the special theory of relativity. the Relativistic rotation is obtained, which takes the relativistic effect into account. It is demonstrated that the angular frequency of classical rotation is only valid in local approximation. The properties of the relativistic rotation and the relativistic transverse Doppler shift are discussed in this work

The Structure on Invariant Measures of C1C^1 generic diffeomorphisms

Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism f\in\Diff(M). We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in $\Lambda$ (which implies the set of irregular$^+$ points is also residual in $\Lambda$). As an application, we show that the non-uniform hyperbolicity of irregular$^+$ points in $\Lambda$ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in $\Lambda$) determines the uniform hyperbolicity of $\Lambda$

Coupled clustering ensemble by exploring data interdependence

© 2018 ACM. Clustering ensembles combine multiple partitions of data into a single clustering solution. It is an effective technique for improving the quality of clustering results. Current clustering ensemble algorithms are usually built on the pairwise agreements between clusterings that focus on the similarity via consensus functions, between data objects that induce similarity measures from partitions and re-cluster objects, and between clusters that collapse groups of clusters into meta-clusters. In most of those models, there is a strong assumption on IIDness (i.e., independent and identical distribution), which states that base clusterings perform independently of one another and all objects are also independent. In the real world, however, objects are generally likely related to each other through features that are either explicit or even implicit. There is also latent but definite relationship among intermediate base clusterings because they are derived from the same set of data. All these demand a further investigation of clustering ensembles that explores the interdependence characteristics of data. To solve this problem, a new coupled clustering ensemble (CCE) framework that works on the interdependence nature of objects and intermediate base clusterings is proposed in this article. The main idea is to model the coupling relationship between objects by aggregating the similarity of base clusterings, and the interactive relationship among objects by addressing their neighborhood domains. Once these interdependence relationships are discovered, they will act as critical supplements to clustering ensembles. We verified our proposed framework by using three types of consensus function: clustering-based, object-based, and cluster-based. Substantial experiments on multiple synthetic and real-life benchmark datasets indicate that CCE can effectively capture the implicit interdependence relationships among base clusterings and among objects with higher clustering accuracy, stability, and robustness compared to 14 state-of-the-art techniques, supported by statistical analysis. In addition, we show that the final clustering quality is dependent on the data characteristics (e.g., quality and consistency) of base clusterings in terms of sensitivity analysis. Finally, the applications in document clustering, as well as on the datasets with much larger size and dimensionality, further demonstrate the effectiveness, efficiency, and scalability of our proposed models

Engineering a light-responsive, quorum quenching biofilm to mitigate biofouling on water purification membranes

Copyright © 2018 The Authors. Quorum quenching (QQ) has been reported to be a promising approach for membrane biofouling control. Entrapment of QQ bacteria in porous matrices is required to retain them in continuously operated membrane processes and to prevent uncontrollable biofilm formation by the QQ bacteria on membrane surfaces. It would be more desirable if the formation and dispersal of biofilms by QQ bacteria could be controlled so that the QQ bacterial cells are self-immobilized, but the QQ biofilm itself still does not compromise membrane performance. In this study, we engineered a QQ bacterial biofilm whose growth and dispersal can be modulated by light through a dichromatic, optogenetic c-di-GMP gene circuit in which the bacterial cells sense near-infrared (NIR) light and blue light to adjust its biofilm formation by regulating the c-di-GMP level. We also demonstrated the potential application of the engineered light-responsive QQ biofilm in mitigating biofouling of water purification forward osmosis membranes. The c-di-GMP–targeted optogenetic approach for controllable biofilm development we have demonstrated here should prove widely applicable for designing other controllable biofilm-enabled applications such as biofilm-based biocatalysis

Methods for biomimetic remineralization of human dentine: A systematic review

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Methods for Biomimetic Mineralisation of Human Enamel: A Systematic Review

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A novel self-assembled oligopeptide amphiphile for biomimetic mineralization of enamel

Background Researchers are looking for biomimetic mineralization of ena/mel to manage dental erosion. This study evaluated biomimetic mineralization of demineralized enamel induced by a synthetic and self-assembled oligopeptide amphiphile (OPA). Results The results showed that the OPA self-assembled into nano-fibres in the presence of calcium ions and in neutral acidity. The OPA was alternately immersed in calcium chloride and sodium hypophosphate solutions to evaluate its property of mineralization. Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) showed nucleation and growth of amorphous calcium phosphate along the self-assembled OPA nano-fibres when it was repetitively exposed to solutions with calcium and phosphate ions. Energy dispersive spectrometry (EDS) confirmed that these nano-particles contained calcium and phosphate. Furthermore, electron diffraction pattern suggested that the nano-particles precipitated on OPA nano-fibres were comparable to amorphous calcium phosphate. Acid-etched human enamel slices were incubated at 37°C in metastable calcium phosphate solution with the OPA for biomimetic mineralization. SEM and X-ray diffraction indicated that the OPA induced the formation of hydroxyapatite crystals in organized bundles on etched enamel. TEM micrographs revealed there were 20–30 nm nano-amorphous calcium phosphate precipitates in the biomimetic mineralizing solution. The particles were found separately bound to the oligopeptide fibres. Biomimetic mineralization with or without the oligopeptide increased demineralized enamel microhardness. Conclusions A novel OPA was successfully fabricated, which fostered the biomimetic mineralization of demineralized enamel. It is one of the primary steps towards the design and construction of novel biomaterial for future clinical therapy of dental erosion.published_or_final_versio

Inhibitory effect of silver diamine fluoride on dentine demineralisation and collagen degradation

Objective To investigate the inhibitory effects of 38% silver diamine fluoride (SDF) on demineralised dentine. Methods Human dentine blocks were demineralised and allocated to four groups: SF, F, S and W. The blocks in group SF received a topical application of 38% SDF solution (253,900 ppm Ag, 44,800 ppm F), group F received a 10% sodium fluoride solution (44,800 ppm F), group S received a 42% silver nitrate solution (253,900 ppm Ag) and group W received deionised water (control). They were subjected to pH cycling using demineralisation solution (pH 5) and remineralisation solution (pH 7) for 8 days. The surface morphology, crystal characteristics, lesion depth and collagen matrix degradation of the specimens were investigated by scanning electron microscopy (SEM), X-ray diffraction (XRD), micro-CT testing and spectrophotometry with a hydroxyproline assay. Results The surface morphology under SEM showed evident demineralisation with exposed collagen in groups S and W, but not in group SF. Clusters of granular spherical grains were observed in the cross-sections of specimens in groups SF and F. XRD revealed precipitates of silver chloride in groups SF and S. The mean lesion depths (±SD) of groups SF, F, S and W were 182 ± 32 μm, 204 ± 26 μm, 259 ± 42 μm and 265 ± 40 μm, respectively (SDF, F < S, W; p < 0.01). Groups SF and S had significantly less hydroxyproline liberated from the dentine matrix than groups F and W (p < 0.01). Conclusion The use of 38% SDF inhibited demineralisation and preserved collagen from degradation in demineralised dentine. Clinical significance SDF application positively influences dentine remineralization

Resting-state EEG power and coherence vary between migraine phases

© 2016, The Author(s). Background: Migraine is characterized by a series of phases (inter-ictal, pre-ictal, ictal, and post-ictal). It is of great interest whether resting-state electroencephalography (EEG) is differentiable between these phases. Methods: We compared resting-state EEG energy intensity and effective connectivity in different migraine phases using EEG power and coherence analyses in patients with migraine without aura as compared with healthy controls (HCs). EEG power and isolated effective coherence of delta (1–3.5 Hz), theta (4–7.5 Hz), alpha (8–12.5 Hz), and beta (13–30 Hz) bands were calculated in the frontal, central, temporal, parietal, and occipital regions. Results: Fifty patients with episodic migraine (1–5 headache days/month) and 20 HCs completed the study. Patients were classified into inter-ictal, pre-ictal, ictal, and post-ictal phases (n = 22, 12, 8, 8, respectively), using 36-h criteria. Compared to HCs, inter-ictal and ictal patients, but not pre- or post-ictal patients, had lower EEG power and coherence, except for a higher effective connectivity in fronto-occipital network in inter-ictal patients (p <.05). Compared to data obtained from the inter-ictal group, EEG power and coherence were increased in the pre-ictal group, with the exception of a lower effective connectivity in fronto-occipital network (p <.05). Inter-ictal and ictal patients had decreased EEG power and coherence relative to HCs, which were “normalized” in the pre-ictal or post-ictal groups. Conclusion: Resting-state EEG power density and effective connectivity differ between migraine phases and provide an insight into the complex neurophysiology of migraine

A note on anti-coordination and social interactions

This note confirms a conjecture of [Bramoull\'{e}, Anti-coordination and social interactions, Games and Economic Behavior, 58, 2007: 30-49]. The problem, which we name the maximum independent cut problem, is a restricted version of the MAX-CUT problem, requiring one side of the cut to be an independent set. We show that the maximum independent cut problem does not admit any polynomial time algorithm with approximation ratio better than $n^{1-\epsilon}$, where $n$ is the number of nodes, and $\epsilon$ arbitrarily small, unless P=NP. For the rather special case where each node has a degree of at most four, the problem is still MAXSNP-hard.Comment: 7 page