Predicting the bioactivity of glasses using the network connectivity or split network models

Bioactive glasses (BG) are used as bone substitutes and re-mineralising additives in toothpastes. They work by precipitating apatite on their surface, and the network connectivity (NC) and split network models can be used to predict their bioactivity, i.e. their ability to form apatite.While NC predicts glass degradation and has been used successfully to predict the bioactivity of BG, it does not take into account their phosphate content. Our experimental data confirm predictions using the split network model by Edén [Journal of Non-Crystalline Solids 357 (2011) 1595–1602], that “as long as P remains predominantly as Q_P⁰ tetrahedra and the average silicate network-polymerisation is ‘favourable’, the bioactivity enhances monotonically for increasing phosphorus content of the BG”. Results show that phosphate plays a key role in bioactivity and apatite formation of BG. This can be explained by the fact that phosphorus does not form part of the silicate network, but instead forms a separate orthophosphate phase. However, NC and split network models are still useful approaches for predicting BG bioactivity and apatite formation, if care is exercised when applying the models to glasses that contain more components than simple SiO₂–P₂O₅–CaO–Na₂O systems.     

Teil II: Ergebnisse bei der Bestrahlung einzelner Nahrungsmittelgruppen (Zusammenfassender Bericht)

Nachdem im ersten Teil dieser Arbeit [170] einige Grundprobleme der Nahrungsmittelbestrahlung behandelt wurden, sollen nun die bei der Bestrahlung wichtiger Nahrungsmittelgruppen erzielten Ergebnisse dargelet und eine Einschätzung der Entwicklungstendenzen versucht werden.     

Economic Characterization of Reciprocal Isoperimetric Control Problems Revisited

Theorem 2.1 of Caputo (Ref. 1) linking the optimal solution functions and optimal value functions of reciprocal pairs of isoperimetric control problems is correct, but requires stronger assumptions than those used explicitly to establish its veracity. One such set of stronger assumptions is provided in this note.     

THE MEASUREMENT OF WELFARE GAINS FROM GENETIC PROGRESS IN FORESTRY: GENERAL EQUILIBRIUM AND DISEQUILIBRIUM RESULTS

The paper contains an extension of existing results on the economics of tree improvement programs. The properties of the indirect utility function and the present value function are used to derive general equilibrium and disequilibrium cost–benefit rules for marginal projects resulting in an improved production function. Corresponding results for projects resulting in large second order effects in both prices and quantities are also provided, and indirect methods to estimate the net benefits are suggested. It is also briefly discussed how recreational and option values can be dealt with.     

Fast deterministic approximation for the multicommodity flow problem

In this paper we consider an optimization version of the multicommodity flow problem which is known as the maximum concurrent flow problem. We show that an approximate solution to this problem can be computed deterministically using O(k(ε ⁻² + logk) logn) 1-commodity minimum-cost flow computations, wherek is the number of commodities,n is the number of nodes, andε is the desired precision. We obtain this bound by proving that in the randomized algorithm developed by Leighton et al. (1995) the random selection of commodities can be replaced by the deterministic round-robin without increasing the total running time. Our bound significantly improves the previously known deterministic upper bounds and matches the best known randomized upper bound for the approximation concurrent flow problem. A preliminary version of this paper appeared inProceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, San Francisco CA, 1995, pp. 486–492.     

Wireless network capacity management: A real options approach

This paper applies financial option valuation methods to new wireless network capacity investment decision timing. In particular, we consider the case of network capacity for cellular telephone service. Given a cluster of base stations (with a certain traffic capacity per base station), we determine when it is optimal to increase capacity for each of the base stations contained in the cluster. We express this in terms of the fraction of total cluster capacity in use, i.e. we calculate the optimal time to upgrade in terms of the ratio of observed usage to existing capacity. We study the optimal decision problem of adding new capacity in the presence of stochastic wireless demand for services. A four factor algorithm is developed, based on a real options formulation. Numerical examples are provided to illustrate various aspects of the model.     

Optimal infrastructure design and expansion of broadband wireless access networks

This paper investigates the important infrastructure design and expansion problem for broadband wireless access networks subject to user demand constraints and system capacity constraints. For the problem, an integer program is derived and a heuristic solution procedure is proposed based on Lagrangean relaxation. In the computational experiments, our Lagrangean relaxation based algorithm can solve this complex design and expansion problem quickly and near optimally. Based on the test results, it is suggested that the proposed algorithm may be practically used for the infrastructure design and expansion problem for broadband wireless access networks.     

Improving multicut in directed trees by upgrading nodes

In this paper, we consider the network improvement problem for multicut by upgrading nodes in a directed tree T = (V, E) with multiple sources and multiple terminals. In a node based upgrading model, a node v can be upgraded at the expense of c(v) and such an upgrade reduces weights on all edges incident to v. The objective is to upgrade a minimum cost subset S ⊆ V of nodes such that the resulting network has a multicut in which no edge has weight larger than a given value D. We first obtain a minimum cardinality node multicut V_c for tree T, then find the minimum cost upgrading set based on the upgrading sets for the subtrees rooted at the nodes in V_c. We show that our algorithm is polynomial when the number of source–terminal pairs is upper bounded by a given value.