On Convex Approximation by Quadratic Splines

AbstractIn a recent paper by Hu it is proved that for any convex functionfthere is aC1convex quadratic splineswithnknots that approximatesfat the rate ofω3(f, n−1). The knots of the spline are basically equally spaced. In this paper we give a simple construction of such a spline with equally spaced knots

Existence and multiplicity for elliptic problems with quadratic growth in the gradient

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.Comment: To appear in Comm. PD

Selective laser sintering of hydroxyapatite reinforced polyethylene composites for bioactive implants and tissue scaffold development

Selective laser sintering (SLS) has been investigated for the production of bioactive implants and tissue scaffolds using composites of high-density polyethylene (HDPE) reinforced with hydroxyapatite (HA) with the aim of achieving the rapid manufacturing of customized implants. Single-layer and multilayer block specimens made of HA-HDPE composites with 30 and 40 vol % HA were sintered successfully using a CO2 laser sintering system. Laser power and scanning speed had a significant effect on the sintering behaviour. The degree of particle fusion and porosity were influenced by the laser processing parameters, hence control can be attained by varying these parameters. Moreover, the SLS processing allowed exposure of HA particles on the surface of the composites and thereby should provide bioactive products. Pores existed in the SLS-fabricated composite parts and at certain processing parameters a significant fraction of the pores were within the optimal sizes for tissue regeneration. The results indicate that the SLS technique has the potential not only to fabricate HA-HDPE composite products but also to produce appropriate features for their application as bioactive implants and tissue scaffolds

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Anthropogenic Disturbance and Population Viability of Woodland Caribou in Ontario

One of the most challenging tasks in wildlife conservation and management is to clarify how spatial variation in land cover due to anthropogenic disturbance influences wildlife demography and long‐term viability. To evaluate this, we compared rates of survival and population growth by woodland caribou (Rangifer tarandus caribou) from 2 study sites in northern Ontario, Canada that differed in the degree of anthropogenic disturbance because of commercial logging and road development, resulting in differences in predation risk due to gray wolves (Canis lupus). We used an individual‐based model for population viability analysis (PVA) that incorporated adaptive patterns of caribou movement in relation to predation risk and food availability to predict stochastic variation in rates of caribou survival. Field estimates of annual survival rates for adult female caribou in the unlogged ( x̄ = 0.90) and logged ( x̄ = 0.76) study sites recorded during 2010–2014 did not differ significantly (P \u3e 0.05) from values predicted by the individual‐based PVA model (unlogged:  x̄ = 0.87; logged:  x̄ = 0.79). Outcomes from the individual‐based PVA model and a simpler stage‐structured matrix model suggest that substantial differences in adult survival largely due to wolf predation are likely to lead to long‐term decline of woodland caribou in the commercially logged landscape, whereas the unlogged landscape should be considerably more capable of sustaining caribou. Estimates of population growth rates (λ) for the 2010–2014 period differed little between the matrix model and the individual‐based PVA model for the unlogged (matrix model  x̄ = 1.01; individual‐based model x̄ = 0.98) and logged landscape (matrix model x̄ = 0.88; individual‐based model x̄ = 0.89). We applied the spatially explicit PVA model to assess the viability of woodland caribou across 14 woodland caribou ranges in Ontario. Outcomes of these simulations suggest that woodland caribou ranges that have experienced significant levels of commercial forestry activities in the past had annual growth rates 0.96. These differences were strongly related to regional variation in wolf densities. Our results suggest that increased wolf predation risk due to anthropogenic disturbance is of sufficient magnitude to cause appreciable risk of population decline in woodland caribou in Ontario. © 2020 The Authors. The Journal of Wildlife Management published by Wiley Periodicals, Inc. on behalf of The Wildlife Society

Improving dental epithelial junction on dental implants with bioengineered peptides

Introduction: The functionalization of titanium (Ti) and titanium alloys (Ti6Al4V) implant surfaces via material-specific peptides influence host/biomaterial interaction. The impact of using peptides as molecular linkers between cells and implant material to improve keratinocyte adhesion is reported.Results: The metal binding peptides (MBP-1, MBP-2) SVSVGMKPSPRP and WDPPTLKRPVSP were selected via phage display and combined with laminin-5 or E-cadherin epithelial cell specific peptides (CSP-1, CSP-2) to engineer four metal-cell specific peptides (MCSPs). Single-cell force spectroscopy and cell adhesion experiments were performed to select the most promising candidate. In vivo tests using the dental implant for rats showed that the selected bi functional peptide not only enabled stable cell adhesion on the trans-gingival part of the dental implant but also arrested the unwanted apical migration of epithelial cells.Conclusion: The results demonstrated the outstanding performance of the bioengineered peptide in improving epithelial adhesion to Ti based implants and pointed towards promising new opportunities for applications in clinical practice

Improving dental epithelial junction on dental implants with bioengineered peptides

Introduction: The functionalization of titanium (Ti) and titanium alloys (Ti6Al4V) implant surfaces via material-specific peptides influence host/biomaterial interaction. The impact of using peptides as molecular linkers between cells and implant material to improve keratinocyte adhesion is reported.Results: The metal binding peptides (MBP-1, MBP-2) SVSVGMKPSPRP and WDPPTLKRPVSP were selected via phage display and combined with laminin-5 or E-cadherin epithelial cell specific peptides (CSP-1, CSP-2) to engineer four metal-cell specific peptides (MCSPs). Single-cell force spectroscopy and cell adhesion experiments were performed to select the most promising candidate. In vivo tests using the dental implant for rats showed that the selected bi functional peptide not only enabled stable cell adhesion on the trans-gingival part of the dental implant but also arrested the unwanted apical migration of epithelial cells.Conclusion: The results demonstrated the outstanding performance of the bioengineered peptide in improving epithelial adhesion to Ti based implants and pointed towards promising new opportunities for applications in clinical practice

The Cercal Organ May Provide Singing Tettigoniids a Backup Sensory System for the Detection of Eavesdropping Bats

Conspicuous signals, such as the calling songs of tettigoniids, are intended to attract mates but may also unintentionally attract predators. Among them bats that listen to prey-generated sounds constitute a predation pressure for many acoustically communicating insects as well as frogs. As an adaptation to protect against bat predation many insect species evolved auditory sensitivity to bat-emitted echolocation signals. Recently, the European mouse-eared bat species Myotis myotis and M. blythii oxygnathus were found to eavesdrop on calling songs of the tettigoniid Tettigonia cantans. These gleaning bats emit rather faint echolocation signals when approaching prey and singing insects may have difficulty detecting acoustic predator-related signals. The aim of this study was to determine (1) if loud self-generated sound produced by European tettigoniids impairs the detection of pulsed ultrasound and (2) if wind-sensors on the cercal organ function as a sensory backup system for bat detection in tettigoniids. We addressed these questions by combining a behavioral approach to study the response of two European tettigoniid species to pulsed ultrasound, together with an electrophysiological approach to record the activity of wind-sensitive interneurons during real attacks of the European mouse-eared bat species Myotis myotis. Results showed that singing T. cantans males did not respond to sequences of ultrasound pulses, whereas singing T. viridissima did respond with predominantly brief song pauses when ultrasound pulses fell into silent intervals or were coincident with the production of soft hemi-syllables. This result, however, strongly depended on ambient temperature with a lower probability for song interruption observable at 21°C compared to 28°C. Using extracellular recordings, dorsal giant interneurons of tettigoniids were shown to fire regular bursts in response to attacking bats. Between the first response of wind-sensitive interneurons and contact, a mean time lag of 860 ms was found. This time interval corresponds to a bat-to-prey distance of ca. 72 cm. This result demonstrates the efficiency of the cercal system of tettigoniids in detecting attacking bats and suggests this sensory system to be particularly valuable for singing insects that are targeted by eavesdropping bats

DNA methylation-based classification of central nervous system tumours.

Accurate pathological diagnosis is crucial for optimal management of patients with cancer. For the approximately 100 known tumour types of the central nervous system, standardization of the diagnostic process has been shown to be particularly challenging-with substantial inter-observer variability in the histopathological diagnosis of many tumour types. Here we present a comprehensive approach for the DNA methylation-based classification of central nervous system tumours across all entities and age groups, and demonstrate its application in a routine diagnostic setting. We show that the availability of this method may have a substantial impact on diagnostic precision compared to standard methods, resulting in a change of diagnosis in up to 12% of prospective cases. For broader accessibility, we have designed a free online classifier tool, the use of which does not require any additional onsite data processing. Our results provide a blueprint for the generation of machine-learning-based tumour classifiers across other cancer entities, with the potential to fundamentally transform tumour pathology