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Two self-associating biopolymers, namely chitosan (Ch) and a high-molar-mass hyaluronan (HA), were used to prepare membranes with the aim to protect and to enhance the healing of injured skin. A mitochondrially-targeted antioxidant—MitoQ—was incorporated into the mixture of biopolymers prior to their self-association. These three-component membranes were evaluated in detail utilising surface roughness measurements, contact angle measurements, hemocompatibility, and thrombogenicity analyses. Furthermore, in vivo application of Ch/HA/MitoQ membranes was assessed on injured rabbit and rat skin utilizing histological methods. The results showed that the prepared thrombogenic Ch/HA/MitoQ membranes had higher roughness, which allowed for greater surface area for tissue membrane interaction during the healing processes, and lower cytotoxicity levels than controls. MitoQ-loaded composite membranes displayed superior healing properties in these animal models compared to control membranes.

A game starts with the empty graph on n vertices, and two player alternate adding edges to the graph. Only moves which do not create a triangle are valid. The game ends when a maximal triangle-free graph is reached. The goal of one player is to end the game as soon as possible, while the other player is trying to prolong the game. With optimal play, the length of the game (number of edges played) is called the K 3 game saturation number.In this paper we prove an upper bound for this number.

Joret, Micek, Milans, Trotter, Walczak, and Wang recently asked if there exists a constant d such that if P is a poset with cover graph of P of pathwidth at most 2, then dim(P ) ≤ d. We answer this question in the affirmative by showing that d = 17 is sufficient. We also show that if P is a poset containing the standard example S 5 as a subposet, then the cover graph of P has treewidth at least 3.

The dimension of a poset P , denoted dim(P ), is the least positive integer d for which P is the intersection of d linear extensions of P . The maximum dimension of a poset P with |P | ≤ 2n + 1 is n, provided n ≥ 2, and this inequality is tight when P contains the standard example Sn. However, there are posets with large dimension that do not contain the standard example S 2 . Moreover, for each fixed d ≥ 2, if P is a poset with |P | ≤ 2n+1 and P does not contain the standard example S d , then dim(P ) = o(n). Also, for large n, there is a poset P with |P | = 2n and dim(P ) ≥ (1 − o(1))n such that the largest d so that P contains the standard example S d is o(n). In this paper, we will show that for every integer c ≥ 1, there is an integer f (c) = O(c 2 ) so that for large enough n, if P is a poset with |P | ≤ 2n + 1 and dim(P ) ≥ n − c, then P contains a standard example S d with d ≥ n − f (c). From below, we show that f (c) = Ω(c 4/3 ). On the other hand, we also prove an analogous result for fractional dimension, and in this setting f (c) is linear in c. Here the result is best possible up to the value of the multiplicative constant.2010 Mathematics Subject Classification. 06A07, 05C35.

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In our previous papers, we investigated several aspects of applying Optimization Modulo Theories (OMT) solvers to Wireless Sensor Networks (WSNs). None of the solvers we used in our experiments scaled enough for WSNs of common size in practice. This is particularly true when investigating additional dependability and security constraints on WSNs of high density.In this paper, we propose an idea of speeding up the OMT solving process by taking into consideration some resources in the systems and by applying regression analysis on those resource values. For instance, in WSNs, the electrical charge in the batteries of sensor nodes can be considered to be a resource that is being consumed as approaching the maximal lifetime of the network. Another example is the knapsack problem where the remaining capacity of the knapsack can be used as such a resource. We show how to integrate this idea in search algorithms in the OMT framework and introduce a new OMT solver called Puli. We present experiments with Puli on WSN and knapsack benchmarks, which show remarkable improvements in the number of solved instances as well as computation time compared to existing solvers. Furthermore, we show that further signicant improvement can be realized on so-called monotonous problems, such as WSN optimization, for which Puli can generate more precise assertions. We present Puli as a work-in-progress prototype that we are planning to upgrade to an ocial release soon, which we want to make publicly available.