Balancing and model reduction for discrete-time nonlinear systems based on Hankel singular value analysis

This paper is concerned with balanced realization and model reduction for discrete-time nonlinear systems. Singular perturbation type balanced truncation method is proposed. In this procedure, the Hankel singular values and the related controllability and observability properties are preserved, which is a natural generalization of both the linear discrete-time case and the nonlinear continuous-time case.

Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces

We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with Q-Gorenstein deformation classes of del Pezzo surfaces

Strong Public Health Recommendations from Weak Evidence? Lessons Learned in Developing Guidance on the Public Health Management of Meningococcal Disease.

The evidence underpinning public health policy is often of low quality, leading to inconsistencies in recommended interventions. One example is the divergence in national policies across Europe for managing contacts of invasive meningococcal disease. Aiming to develop consistent guidance at the European level, a group of experts reviewed the literature and formulated recommendations. The group defined eight priority research questions, searched the literature, and formulated recommendations using GRADE methodology. Five of the research questions are discussed in this paper. After taking into account quality of evidence, benefit, harm, value, preference, burden on patient of the intervention, and resource implications, we made four strong recommendations and five weak recommendations for intervention. Strong recommendations related not only to one question with very low quality of evidence as well as to two questions with moderate to high quality of evidence. The weak recommendations related to two questions with low and very low quality of evidence but also to one question with moderate quality of evidence. GRADE methodology ensures a transparent process and explicit recognition of additional factors that should be considered when making recommendations for policy. This approach can be usefully applied to many areas of public health policy where evidence quality is often low

Impacted maxillary canines and root resorptions of neighbouring teeth: a radiographic analysis using cone-beam computed tomography

The study analyses the location of impacted maxillary canines and factors influencing root resorptions of adjacent teeth using cone-beam computed tomography (CBCT). In addition, the interrater reliability between observers of two different dental specialties for radiographic parameters will be evaluated. CBCT images of patients who were referred for radiographic localization of impacted maxillary canines and/or suspicion of root resorptions of adjacent teeth were included. The study analysed the exact three-dimensional location of the impacted canines in the anterior maxilla, frequency and extent of root resorptions, and potential influencing factors. To assess interrater agreement, Cohen's correlation parameters were calculated. This study comprises 113 patients with CBCT scans, and 134 impacted canines were analysed retrospectively. In the patients evaluated, 69 impacted canines were located palatally (51.49 per cent), 41 labially (30.60 per cent), and 24 (17.91 per cent) in the middle of the alveolar process. Root resorptions were found in 34 lateral incisors (25.37 per cent), 7 central incisors (5.22 per cent), 6 first premolars (4.48 per cent), and 1 second premolar (0.75 per cent). There was a significant correlation between root resorptions on adjacent teeth and localization of the impacted canine in relation to the bone, as well as vertical localization of the canine. Interrater agreement showed values of 0.546-0.877. CBCT provides accurate information about location of the impacted canine and prevalence and degree of root resorption of neighbouring teeth with high interrater correlation. This information is of great importance for surgeons and orthodontists for accurate diagnostics and interdisciplinary treatment plannin

Del Pezzo surfaces with 1/3(1,1) points

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface, minor corrections, minor changes to presentation, references adde

Tur\'an Graphs, Stability Number, and Fibonacci Index

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an graphs and a connected variant of them are also extremal for these particular problems.Comment: 11 pages, 3 figure

Transverse thermal depinning and nonlinear sliding friction of an adsorbed monolayer

We study the response of an adsorbed monolayer under a driving force as a model of sliding friction phenomena between two crystalline surfaces with a boundary lubrication layer. Using Langevin-dynamics simulation, we determine the nonlinear response in the direction transverse to a high symmetry direction along which the layer is already sliding. We find that below a finite transition temperature, there exist a critical depinning force and hysteresis effects in the transverse response in the dynamical state when the adlayer is sliding smoothly along the longitudinal direction.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Investigation of the Effect of a Diamine-Based Friction Modifier on Micropitting and the Properties of Tribofilms in Rolling-Sliding Contacts

The effect of N-Tallow-1,3-DiaminoPropane (TDP) on friction, rolling wear and micropitting has been investigated with the ultimate objective of developing lubricants with no or minimal environmental impact. A Mini Traction Machine (MTM-SLIM) has been utilised in order to generate tribofilms and observe the effect of TDP on anti-wear tribofilm formation and friction. Micropitting was induced on the surface of specimens using a MicroPitting Rig (MPR). The X-ray Photoelectron Spectroscopy (XPS) surface analytical technique has been employed to investigate the effect of TDP on the chemical composition of the tribofilm while Atomic Force Microscopy (AFM) was used to generate high resolution topographical images of the tribofilms formed on the MTM discs. Experimental and analytical results showed that TDP delays the Zinc DialkylDithioPhosphate (ZDDP) anti-wear tribofilm formation. TDP in combination with ZDDP induces a thinner and smoother anti-wear tribofilm with a modified chemical structure composed of mixed Fe/Zn (poly)phosphates. The sulphide contribution to the tribofilm and oxygen-to-phosphorous atomic concentration ratio are greater in the bulk of the tribofilm derived from a combination of TDP and ZDDP compared to a tribofilm derived from ZDDP alone. Surface analysis showed that utilising TDP effectively mitigates micropitting wear in the test conditions used in this study. Reduction of micropitting, relevant to rolling bearing applications, can be attributed to the improved running-in procedure, reduced friction, formation of a smoother tribofilm and modification of the tribofilm composition induced by TDP

'Worldmindedness' and Development Education: A Teacher Voice

This research demonstrates that a teacher’s ‘worldmindedness’ influences both the significance teachers give development education teaching in the classroom and the idea of the future they are preparing the children for. It also highlights the current challenges that worldmindedness brings to primary school teachers in an inner-city, multicultural setting. The changing relationship between the local and the global has implications for the realities of both the children’s and the teachers’ ideas of community and also for their personal ideas of the future. With no official guidance on how to address these complex issues in school, there is much inconsistency amongst teachers’ practice. This research suggests that guidance and training, through continued professional development, is necessary to amend this and to create a more consistent idea of what development education in the 21st century should look like

Anisotropic Local Stress and Particle Hopping in a Deeply Supercooled Liquid

The origin of the microscopic motions that lead to stress relaxation in deeply supercooled liquid remains unclear. We show that in such a liquid the stress relaxation is locally anisotropic which can serve as the driving force for the hopping of the system on its free energy surface. However, not all hopping are equally effective in relaxing the local stress, suggesting that diffusion can decouple from viscosity even at local level. On the other hand, orientational relaxation is found to be always coupled to stress relaxation.Comment: 4 pages, 3 figure