Parallel cleaning of a network with brushes

AbstractWe consider the process of cleaning a network where at each time step, all vertices that have at least as many brushes as incident, contaminated edges, send brushes down these edges and remove them from the network. An added condition is that, because of the contamination model used, the final configuration must be the initial configuration of another cleaning of the network. We find the minimum number of brushes required for trees, cycles, complete bipartite networks; and for all networks when all edges must be cleaned on each step. Finally, we give bounds on the number of brushes required for complete networks

Game Brush Number

We study a two-person game based on the well-studied brushing process on graphs. Players Min and Max alternately place brushes on the vertices of a graph. When a vertex accumulates at least as many brushes as its degree, it sends one brush to each neighbor and is removed from the graph; this may in turn induce the removal of other vertices. The game ends once all vertices have been removed. Min seeks to minimize the number of brushes played during the game, while Max seeks to maximize it. When both players play optimally, the length of the game is the game brush number of the graph $G$, denoted $b_g(G)$. By considering strategies for both players and modelling the evolution of the game with differential equations, we provide an asymptotic value for the game brush number of the complete graph; namely, we show that $b_g(K_n) = (1+o(1))n^2/e$. Using a fractional version of the game, we couple the game brush numbers of complete graphs and the binomial random graph $\mathcal{G}(n,p)$. It is shown that for $pn \gg \ln n$ asymptotically almost surely $b_g(\mathcal{G}(n,p)) = (1 + o(1))p b_g(K_n) = (1 + o(1))pn^2/e$. Finally, we study the relationship between the game brush number and the (original) brush number.Comment: 20 pages, 3 figure

Functionalised Polymer Fibres for Orthopaedic Interfacial Tissue Engineering and Other Biomedical Applications

Tissue engineering is a promising approach for the regeneration of a variety of human tissues, where traditional surgical repairs produce inadequate results or appropriate transplant material is in scarce supply. In orthopaedic tissue engineering, the regeneration of the bone/soft tissue interface is of special interest. However, this requires the creation of biomaterial scaffolds with controlled gradients of biochemical cues, in addition to mimicking the microstructure of the natural tissue. For this purpose, a scheme for the covalent immobilisation of biomolecule gradients on aligned synthetic nanofibre scaffolds created via electrospinning was devised. Surface-initiated atom transfer radical polymerisation allows for the controlled growth of a polymer brush containing reactive functional groups on the scaffold surface, specifically poly (glycidyl methacrylate) (PGMA), which contains epoxy groups that can conjugate to biomolecules via nucleophiles such as amines or thiols. A PGMA-based biomolecule attachment scheme in a 2D model system was optimised. Creating a brush with a larger inter-chain spacing (by the replacement of a fraction of the ATRP initiator with an inactive molecule), as well as improving its water-swellability by incorporation of a water-soluble monomer (hydroxyethyl methacrylate, HEMA), were shown to increase the amount of peptide that could be bound to the polymer surface. Initial results indicate that this system can be used to create covalently immobilised gradients of biomolecules on aligned electrospun scaffolds. The versatility of the ATRP-based functionalistion approach was further demonstrated by creation of brushes of Poly (2-Methacryloyloxyethyl phosphorylcholine) (PMPC) on electrospun polymer fibres. Due to PMPC’s excellent haemocompatibility, these materials show great promise in vascular tissue engineering.Open Acces

Randomized multicenter study on the plaque removal efficacy of 2 interdental brushes around the base of orthodontic brackets.

INTRODUCTION The objective of this multicenter study was to analyze the efficacy of cleaning 2 interdental brushes (IDBs) around brackets in patients with fixed orthodontic appliances. METHODS The study design was a multicenter, randomized, examiner-blinded crossover study with 3 interventions, the first of which was a baseline intervention. This study included 20 patients (12 females, 8 males) aged 12-18 years with fixed orthodontic devices examined at the Department of Orthodontics, University Medical Center of the Johannes Gutenberg University Mainz, and the Children's Dental Clinic St. Gallen. The outcome was a conventional, cylindrically shaped IDB (IDBG-S [IB]; Top Caredent GmbH, Schönau, Germany) was examined in comparison with an innovative waist-shaped IDB (Circum, CDB-8 [CB]; Top Caredent GmbH). The participants did not use the IDB themselves. The brushing procedure was performed professionally by 1 operator (C.E.). Each buccal tooth surface with a bracket was split into 8 areas, the main areas being 1 and 8. These main areas, which were difficult for toothbrushes to reach, were mesial (area 1) and distal (area 8) of the bracket edges in the gingival direction. Plaque index (PI) scores were assessed at 2 examinations before and after the cleaning procedure on 8 tooth surfaces in the area with orthodontic brackets. A computer-generated program randomly allocated the IDB sequence to the participants. Examiners (L.Z.-G. and Y.W.) assessing the outcomes were blinded to the intervention and the randomized allocation of participants to the different IDBs. RESULTS Both IDBs showed a plaque removal effect (CB, 0.68 [interquartile range, 0.63-0.77]; IB, 0.43 [interquartile range, 0.33-0.55]). The difference between the 2 IDB was statistically significant (P = 0.002). In particular, the CB yielded a higher plaque removal efficacy (CB effect, 0.68; IB effect, 0.21) at the main areas 1 and 8, which were difficult to reach. Ten participants were randomized to each sequence, and all 20 completed the study. No side effects or adverse events were reported or observed. CONCLUSION The waist-shaped brush head of the CB significantly enhanced plaque reduction in total and particularly in problem areas. REGISTRATION This trial was registered at the German Clinical Trials Registry (no. DRKS00014088; https://www.drks.de/drks_web/navigate.xxdo?navigationId=trial.HTML&TRIAL_ID=DRKS00014088) PROTOCOL: The protocol was not published before trial commencement. FUNDING This study was supported by the manufacturer Top Caredent GmbH, Schönau, Germany, which provided all interdental brushes used in this study

Toppling Numbers of Complete and Random Graphs

We study a two-person game played on graphs based on the widely studied chip-firing game. Players Max and Min alternately place chips on the vertices of a graph. When a vertex accumulates as many chips as its degree, it fires, sending one chip to each neighbour; this may in turn cause other vertices to fire. The game ends when vertices continue firing forever. Min seeks to minimize the number of chips played during the game, while Max seeks to maximize it. When both players play optimally, the length of the game is the toppling number of a graph G, and is denoted by t(G). By considering strategies for both players and investigating the evolution of the game with differential equations, we provide asymptotic bounds on the toppling number of the complete graph. In particular, we prove that for sufficiently large n 0.596400n2 \u3c t(Kn) \u3c 0.637152n2. Using a fractional version of the game, we couple the toppling numbers of complete graphs and the binomial random graph G(n,p). It is shown that for pn ≥ n2 / √ log n asymptotically almost surely t(G(n,p)) = (1+o(1))pt(Kn)

Design of Autonomous Cleaning Robot

Today, the research is concentrated on designing and developing robots to address the challenges of human life in their everyday activities. The cleaning robots are the class of service robots whose demands are increasing exponentially. Nevertheless, the application of cleaning robots is confined to smaller areas such as homes. Not much autonomous cleaning products are commercialized for big areas such as schools, hospitals, malls, etc. In this thesis, the proof of concept is designed for the autonomous floor-cleaning robot and autonomous board-cleaning robot for schools. A thorough background study is conducted on domestic service robots to understand the technologies involved in these robots. The components of the vacuum cleaner are assembled on a commercial robotic platform. The principles of vacuum cleaning technology and airflow equations are employed for the component selection of the vacuum cleaner. As the autonomous board-cleaning robot acts against gravity, a magnetic adhesion is used to adhere the robot to the classroom board. This system uses a belt drive mechanism to manoeurve. The use of belt drive increases the area of magnetic attraction while the robot is in motion. A semi-systematic approach using patterned path planning techniques for the complete coverage of the working environment is discussed in this thesis. The outcome of this thesis depicts a new and conceptual mechanical design of an autonomous floor-cleaning robot and an autonomous board-cleaning robot. This evidence creates a preliminary design for proof-of-concept for these robots. This proof of concept design is developed from the basic equations of vacuum cleaning technology, airflow and magnetic adhesion. A general overview is discussed for collaborating the two robots. This research provides an extensive initial step to illustrate the development of an autonomous cleaning robot and further validates with quantitative data discussed in the thesis