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

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

Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

In Vitro Generation of Cartilage-Carrier-Constructs on Hydroxylapatite Ceramics with Different Surface Structures

Tissue engineering approaches for healing cartilage defects are partly limited by the inability to fix cartilage to bone during implantation. To overcome this problem, cartilage can be - already in vitro - generated on a ceramic carrier which serves as bone substitute. In this study, the influence of a hydroxylapatite carrier and its surface structure on the quality of tissue engineered cartilage was investigated. Application of the carrier reduced significantly biomechanical and biochemical properties of the generated tissue. In addition, slight changes in the quality of the formed matrix, in the adhesive strength between cartilage and biomaterial and in attachment and proliferation of a chondrocyte monolayer could be observed for commercial grade carriers, with respect to modified topographies obtained by smooth grinding/polishing. These first results demonstrated an influence of the carrier and its surface structure, but further research is needed for explaining the described effects and for optimization of cartilage-carrier-constructs

Surface modification of starch based blends using potassium permanganate-nitric acid system and its effect on the adherence and proliferation of osteoblastic-like cells

The surface modification of three starch based polymeric biomaterials, using a KMnO4/NHO3 oxidizing system, and the effect of that modification on the osteoblastic cell adhesion has been investigated. The rationale of this work is as follows—starch based polymers have been proposed for use as tissue engineering scaffolds in several publications. It is known that in biodegradable systems it is quite difficult to have both cell adhesion and proliferation. Starch based polymers have shown to perform better than poly-lactic acid based materials but there is still room for improvement. This particular work is aimed at enhancing cell adhesion and proliferation on the surface of several starch based polymer blends that are being proposed as tissue engineering scaffolds. The surface of the polymeric biomaterials was chemically modified using a KMnO4/HNO3 system. This treatment resulted in more hydrophilic surfaces, which was confirmed by contact angle measurements. The effect of the treatment on the bioactivity of the surface modified biomaterials was also studied. The bioactivity tests, performed in simulated body fluid after biomimetic coating, showed that a dense film of calcium phosphate was formed after 30 days. Finally, human osteoblast-like cells were cultured on unmodified (control) and modified materials in order to observe the effect of the presence of higher numbers of polar groups on the adhesion and proliferation of those cells. Two of the modified polymers presented changes in the adhesion behavior and a significant increase in the proliferation rate kinetics when compared to the unmodified controls.FCT (Portugal) for providing the postdoctoral grant (BPD/8491/2002)

An investigation of the potential application of chitosan/aloe-based membranes for regenerative medicine

A significant number of therapeutics derived from natural polymers and plants have been developed to replace or to be used in conjunction with existing dressing products. The use of the therapeutic properties of aloe vera could be very useful in the creation of active wound dressing materials. The present work was undertaken to examine issues concerning structural features, topography, enzymatic degradation behavior, antibacterial activity and cellular response of chitosan/aloe vera-based membranes. The chitosan/aloe vera-based membranes that were developed displayed satisfactory degradation, roughness, wettability and mechanical properties. A higher antibacterial potency was displayed by the blended membranes. Moreover, in vitro assays demonstrated that these blended membranes have good cell compatibility with primary human dermal fibroblasts. The chitosan/aloe vera-based membranes might be promising wound dressing materials.The authors acknowledge financial support from the Portuguese Foundation for Science and Technology (grants SFRH/BPD/45307/2008 and SFRH/BD/64601/2009), the "Fundo Social Europeu", and the "Programa Diferencial de Potencial Humano". This work was partially supported by the FEDER through POCTEP 0330_IBEROMARE_1_P

Approximate policy iteration: A survey and some new methods

We consider the classical policy iteration method of dynamic programming (DP), where approximations and simulation are used to deal with the curse of dimensionality. We survey a number of issues: convergence and rate of convergence of approximate policy evaluation methods, singularity and susceptibility to simulation noise of policy evaluation, exploration issues, constrained and enhanced policy iteration, policy oscillation and chattering, and optimistic and distributed policy iteration. Our discussion of policy evaluation is couched in general terms and aims to unify the available methods in the light of recent research developments and to compare the two main policy evaluation approaches: projected equations and temporal differences (TD), and aggregation. In the context of these approaches, we survey two different types of simulation-based algorithms: matrix inversion methods, such as least-squares temporal difference (LSTD), and iterative methods, such as least-squares policy evaluation (LSPE) and TD (λ), and their scaled variants. We discuss a recent method, based on regression and regularization, which rectifies the unreliability of LSTD for nearly singular projected Bellman equations. An iterative version of this method belongs to the LSPE class of methods and provides the connecting link between LSTD and LSPE. Our discussion of policy improvement focuses on the role of policy oscillation and its effect on performance guarantees. We illustrate that policy evaluation when done by the projected equation/TD approach may lead to policy oscillation, but when done by aggregation it does not. This implies better error bounds and more regular performance for aggregation, at the expense of some loss of generality in cost function representation capability. Hard aggregation provides the connecting link between projected equation/TD-based and aggregation-based policy evaluation, and is characterized by favorable error bounds.National Science Foundation (U.S.) (No.ECCS-0801549)Los Alamos National Laboratory. Information Science and Technology InstituteUnited States. Air Force (No.FA9550-10-1-0412

Redundant Mechanisms for Regulation of Midline Crossing in Drosophila

During development, all neurons have to decide on whether to cross the longitudinal midline to project on the contralateral side of the body. In vertebrates and invertebrates regulation of crossing is achieved by interfering with Robo signalling either through sorting and degradation of the receptor, in flies, or through silencing of its repulsive activity, in vertebrates. Here I show that in Drosophila a second mechanism of regulation exists that is independent from sorting. Using in vitro and in vivo assays I mapped the region of Robo that is sufficient and required for its interaction with Comm, its sorting receptor. By modifying that region, I generated new forms of Robo that are insensitive to Comm sorting in vitro and in vivo, yet still able to normally translate repulsive activity in vivo. Using gene targeting by homologous recombination I created new conditional alleles of robo that are sorting defective (roboSD). Surprisingly, expression of these modified proteins results in phenotypically normal flies, unveiling a sorting independent mechanism of regulation

FIB patterning of stainless steel for the development of nano-structured stent surfaces for cardiovascular applications

Stent implantation is a percutaneous interventional procedure that mitigates vessel stenosis, providing mechanical support within the artery and as such a very valuable tool in the fight against coronary artery disease. However, stenting causes physical damage to the arterial wall. It is well accepted that a valuable route to reduce in-stent re-stenosis can be based on promoting cell response to nano-structured stainless steel (SS) surfaces such as by patterning nano-pits in SS. In this regard patterning by focused ion beam (FIB) milling offers several advantages for flexible prototyping. On the other hand FIB patterning of polycrystalline metals is greatly influenced by channelling effects and redeposition. Correlative microscopy methods present an opportunity to study such effects comprehensively and derive structure–property understanding that is important for developing improved patterning. In this chapter we present a FIB patterning protocol for nano-structuring features (concaves) ordered in rectangular arrays on pre-polished 316L stainless steel surfaces. An investigation based on correlative microscopy approach of the size, shape and depth of the developed arrays in relation to the crystal orientation of the underlying SS domains is presented. The correlative microscopy protocol is based on cross-correlation of top-view scanning electron microscopy, electron backscattering diffraction, atomic force microscopy and cross-sectional (serial) sectioning. Various FIB tests were performed, aiming at improved productivity by preserving nano-size accuracy of the patterned process. The optimal FIB patterning conditions for achieving reasonably high throughput (patterned rate of about 0.03 mm2/h) and nano-size accuracy in dimensions and shapes of the features are discussed as well