Morse set classification and hierarchical refinement using Conley index

Morse decomposition provides a numerically stable topological representation of vector fields that is crucial for their rigorous interpretation. However, Morse decomposition is not unique, and its granularity directly impacts its computational cost. In this paper, we propose an automatic refinement scheme to construct the Morse Connection Graph (MCG) of a given vector field in a hierarchical fashion. Our framework allows a Morse set to be refined through a local update of the flow combinatorialization graph, as well as the connection regions between Morse sets. The computation is fast because the most expensive computation is concentrated on a small portion of the domain. Furthermore, the present work allows the generation of a topologically consistent hierarchy of MCGs, which cannot be obtained using a global method. The classification of the extracted Morse sets is a crucial step for the construction of the MCG, for which the Poincare′ index is inadequate. We make use of an upper bound for the Conley index, provided by the Betti numbers of an index pair for a translation along the flow, to classify the Morse sets. This upper bound is sufficiently accurate for Morse set classification and provides supportive information for the automatic refinement process. An improved visualization technique for MCG is developed to incorporate the Conley indices. Finally, we apply the proposed techniques to a number of synthetic and realworld simulation data to demonstrate their utility.     

An optimization of allocation of information granularity in the interpretation of data structures: toward granular fuzzy clustering

Clustering forms one of the most visible conceptual and algorithmic framework of developing information granules. In spite of the algorithm being used, the representation of information granules-clusters is predominantly numeric (coming in the form of prototypes, partition matrices, dendrograms, etc.). In this paper, we consider a concept of granular prototypes that generalizes the numeric representation of the clusters and, in this way, helps capture more details about the data structure. By invoking the granulation-degranulation scheme, we design granular prototypes being reflective of the structure of data to a higher extent than the representation that is provided by their numeric counterparts (prototypes). The design is formulated as an optimization problem, which is guided by the coverage criterion, meaning that we maximize the number of data for which their granular realization includes the original data. The granularity of the prototypes themselves is treated as an important design asset; hence, its allocation to the individual prototypes is optimized so that the coverage criterion becomes maximized. With this regard, several schemes of optimal allocation of information granularity are investigated, where interval-valued prototypes are formed around the already produced numeric representatives. Experimental studies are provided in which the design of granular prototypes of interval format is discussed and characterized.     

Modified calcium silicates as active rubber fillers

The physicochemical characteristics of calcium silicates obtained from the reaction of sodium metasilicate solution with calcium nitrate are given. Further, studies of the modification of the silicate surface with silane and titanate coupling agents are presented. By wettability measurements and an analysis of the chemically adsorbed carbon arising from the coupling agents, the degree of modification of these surfaces was estimated. The modification of the surface of the silicates with the same agents, but in the presence of acid protons, was also performed with a positive effect. The usefulness of modifications is justified by the results of strength studies of vulcanizates filled with the modified silicates.     

Complement-Opsonized Nano-Carriers Are Bound by Dendritic Cells (DC) via Complement Receptor (CR)3, and by B Cell Subpopulations via CR-1/2, and Affect the Activation of DC and B-1 Cells

The development of nanocarriers (NC) for biomedical applications has gained large interest due to their potential to co-deliver drugs in a cell-type-targeting manner. However, depending on their surface characteristics, NC accumulate serum factors, termed protein corona, which may affect their cellular binding. We have previously shown that NC coated with carbohydrates to enable biocompatibility triggered the lectin-dependent complement pathway, resulting in enhanced binding to B cells via complement receptor (CR)1/2. Here we show that such NC also engaged all types of splenic leukocytes known to express CR3 at a high rate when NC were pre-incubated with native mouse serum resulting in complement opsonization. By focusing on dendritic cells (DC) as an important antigen-presenting cell type, we show that CR3 was essential for binding/uptake of complement-opsonized NC, whereas CR4, which in mouse is specifically expressed by DC, played no role. Further, a minor B cell subpopulation (B-1), which is important for first-line pathogen responses, and co-expressed CR1/2 and CR3, in general, engaged NC to a much higher extent than normal B cells. Here, we identified CR-1/2 as necessary for binding of complement-opsonized NC, whereas CR3 was dispensable. Interestingly, the binding of complement-opsonized NC to both DC and B-1 cells affected the expression of activation markers. Our findings may have important implications for the design of nano-vaccines against infectious diseases, which codeliver pathogen-specific protein antigen and adjuvant, aimed to induce a broad adaptive cellular and humoral immune response by inducing cytotoxic T lymphocytes that kill infected cells and pathogen-neutralizing antibodies, respectively. Decoration of nano-vaccines either with carbohydrates to trigger complement activation in vivo or with active complement may result in concomitant targeting of DC and B cells and thereby may strongly enhance the extent of dual cellular/humoral immune responses.     

Myopathy-Sensitive G-Actin Segment 227-235 Is Involved in Salt-Induced Stabilization of Contacts within the Actin Filament

Formation of stable actin filaments, critically important for actin functions, is determined by the ionic strength of the solution. However, not much is known about the elements of the actin fold involved in ionic-strength-dependent filament stabilization. In this work, F-actin was destabilized by Cu²⁺ binding to Cys374, and the effects of solvent conditions on the dynamic properties of F-actin were correlated with the involvement of Segment 227-235 in filament stabilization. The results of our work show that the presence of Mg²⁺ at the high-affinity cation binding site of Cu-modified actin polymerized with MgCl₂ strongly enhances the rate of filament subunit exchange and promotes the filament instability. In the presence of 0.1 M KCl, the filament subunit exchange was 2–3-fold lower than that in the MgCl₂-polymerized F-actin. This effect correlates with the reduced accessibility of the D-loop and Segment 227-235 on opposite filament strands, consistent with an ionic-strength-dependent conformational change that modulates involvement of Segment 227-235 in stabilization of the intermonomer interface. KCl may restrict the mobility of the α-helix encompassing part of Segment 227-235 and/or be bound to Asp236 at the boundary of Segment 227-235. These results provide experimental evidence for the involvement of Segment 227-235 in salt-induced stabilization of contacts within the actin filament and suggest that they can be weakened by mutations characteristic of actin-associated myopathies.     

The Co-Culture of Staphylococcal Biofilm and Fibroblast Cell Line: The Correlation of Biological Phenomena with Metabolic NMR1 Footprint

Staphylococcus aureus is one of the most prevalent pathogens associated with several types of biofilm-based infections, including infections of chronic wounds. Mature staphylococcal biofilm is extremely hard to eradicate from a wound and displays a high tendency to induce recurring infections. Therefore, in the present study, we aimed to investigate in vitro the interaction between S. aureus biofilm and fibroblast cells searching for metabolites that could be considered as potential biomarkers of critical colonization and infection. Utilizing advanced microscopy and microbiological methods to examine biofilm formation and the staphylococcal infection process, we were able to distinguish 4 phases of biofilm development. The analysis of staphylococcal biofilm influence on the viability of fibroblasts allowed us to pinpoint the moment of critical colonization—12 h post contamination. Based on the obtained model we performed a metabolomics analysis by ¹H NMR spectroscopy to provide new insights into the pathophysiology of infection. We identified a set of metabolites related to the switch to anaerobic metabolism that was characteristic for staphylococcal biofilm co-cultured with fibroblast cells. The data presented in this study may be thus considered a noteworthy but preliminary step in the direction of developing a new, NMR-based tool for rapid diagnosing of infection in a chronic wound.     

Bubble Formation at a Rotating Cylindrical Surface in Cross‐Flowing Liquid

A novel method of gas sparging from a rotating cylinder is proposed, which prevents against formation of large attached gas cavities in cross‐flowing liquids including those flowing downwards. Experimental and theoretical results regarding critical rotation speed necessary to remove the attached cavity, bubble formation process and size distribution of the produced bubbles in a low viscosity system (air‐water) are presented in this study.     

Emission of excited potassium species from an industrial iron catalyst for ammonia synthesis

The angular dependence of potassium emission-desorption is studied from a fused iron catalyst of the type used for ammonia synthesis. The excited species (K^*, K _n ^* , etc.) and positive ions K⁺ have strongly different angular distributions. The bilobular distribution measured for ion desorption is concluded to be either due to excited atoms, so-called Rydberg atoms, or excited clusters. Both types of species have to desorb from the edges of the sample and become field ionized and deexcited just outside the sample, as reported in previous studies on an iron oxide catalyst. The peak in the normal direction measured for excited species is due to excited cluster formation outside the catalyst surface. Similarities with previous results for other catalysts are observed. The possibility that the promoter function of potassium in the ammonia synthesis is due to excited species is pointed out.On leave from Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Cracow, Poland.     

Asphalts as inhibitors of radical polymerization

The results of investigations concerning the effect of asphalts on radical polymerization of a monomer for model systems composed of styrene and two petroleum asphalts originated from two different crude oils: low sulphur nonparaffinic crude oil and medium sulphur paraffinic crude oil. Based on determination of styrene conversion in the radical polymerization process in the presence of asphalts, it was found that both asphalts act as inhibitors of this reaction. The inhibiting effect of asphalts is weakened by using higher temperatures and prolongation of polymerization time or application of greater initiator rates. On the basis of the analysis of group and elementary chemical composition of both asphalts as well as electron paramagnetic resonance, it was found that the inhibiting effect to radical polymerization is caused mainly by the presence of structures which are stable free radicals in character. The probability of inhibiting effect by sulphur compounds present in asphalts is also discussed.