Synthesis of pH‐ and thermoresponsive poly(2‐n‐propyl‐2‐oxazoline) based copolymers

Polymers that possess lower critical solution temperature behavior such as poly(2‐alkyl‐2‐oxazoline)s (PAOx) are interesting for their application as stimulus‐responsive materials, for example in the biomedical field. In this work, we discuss the scalable and controlled synthesis of a library of pH‐ and temperature‐sensitive 2‐n‐propyl‐2‐oxazoline P(nPropOx) based copolymers containing amine and carboxylic acid functionalized side chains by cationic ring opening polymerization and postpolymerization functionalization strategies. Using turbidimetry, we found that the cloud point temperature (CP) is strongly dependent on both the polymer concentration and the polymer charge (as a function of pH). Furthermore, we observed that the CP decreased with increasing salt concentration, whereas the CP increased linearly with increasing amount of carboxylic acid groups. Finally, turbidimetry studies in PBS‐buffer indicate that CPs of these polymers are close to body temperature at biologically relevant polymer concentrations, which demonstrates the potential of P(nPropOx) as stimulus‐responsive polymeric systems in, for example, drug delivery applications. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1573–1582     

Morita invariants for semigroups with local units

In this paper we study Morita invariants for strongly Morita equivalent semigroups with local units of various kinds. Among others we prove that, under a certain condition of this kind, congruence lattices are preserved by strong Morita equivalence.     

Morita equivalence of finite semigroups

Semigroup Forum - Two semigroups are called Morita equivalent if the categories of firm right acts over them are equivalent. We prove that every semigroup is Morita equivalent to its subsemigroup...     

A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems there is some hierarchical ordering of the players. In this paper we consider a class of games with a permission structure describing situations in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. The corresponding restricted game takes account of the limited cooperation possibilities by assigning to every coalition the worth of its largest feasible subset. In this paper we provide a polynomial time algorithm for computing the nucleolus of the restricted games corresponding to a class of games with a permission structure which economic applications include auction games, dual airport games, dual polluted river games and information market games.     

Constrained core solutions for totally positive games with ordered players

In many applications of cooperative game theory to economic allocation problems, such as river-, polluted river- and sequencing games, the game is totally positive (i.e., all dividends are nonnegative), and there is some ordering on the set of the players. A totally positive game has a nonempty core. In this paper we introduce constrained core solutions for totally positive games with ordered players which assign to every such a game a subset of the core. These solutions are based on the distribution of dividends taking into account the hierarchical ordering of the players. The Harsanyi constrained core of a totally positive game with ordered players is a subset of the core of the game and contains the Shapley value. For special orderings it coincides with the core or the Shapley value. The selectope constrained core is defined for acyclic orderings and yields a subset of the Harsanyi constrained core. We provide a characterization for both solutions.     

Solving discrete zero point problems

In this paper we present two theorems on the existence of a discrete zero point of a function from the n-dimensional integer lattice ℤⁿ to the n-dimensional Euclidean space ℝⁿ. The theorems differ in their boundary conditions. For both theorems we give a proof using a combinatorial lemma and present a constructive proof based on a simplicial algorithm that finds a discrete zero point within a finite number of steps. This research was carried out when Gerard van der Laan and Zaifu Yang were visiting the CentER of Tilburg University in the summer of 2004. The visit of Zaifu Yang has been made possible by financial support of CentER and the Netherlands Organization for Scientific Research (NWO). The authors gratefully acknowledge the inspiring and helpful remarks of the referees.     

Tree-based multivariate regression and density estimation with right-censored data

We propose a unified strategy for estimator construction, selection, and performance assessment in the presence of censoring. This approach is entirely driven by the choice of a loss function for the full (uncensored) data structure and can be stated in terms of the following three main steps. (1) First, define the parameter of interest as the minimizer of the expected loss, or risk, for a full data loss function chosen to represent the desired measure of performance. Map the full data loss function into an observed (censored) data loss function having the same expected value and leading to an efficient estimator of this risk. (2) Next, construct candidate estimators based on the loss function for the observed data. (3) Then, apply cross-validation to estimate risk based on the observed data loss function and to select an optimal estimator among the candidates. A number of common estimation procedures follow this approach in the full data situation, but depart from it when faced with the obstacle of evaluating the loss function for censored observations. Here, we argue that one can, and should, also adhere to this estimation road map in censored data situations.Tree-based methods, where the candidate estimators in Step 2 are generated by recursive binary partitioning of a suitably defined covariate space, provide a striking example of the chasm between estimation procedures for full data and censored data (e.g., regression trees as in CART for uncensored data and adaptations to censored data). Common approaches for regression trees bypass the risk estimation problem for censored outcomes by altering the node splitting and tree pruning criteria in manners that are specific to right-censored data. This article describes an application of our unified methodology to tree-based estimation with censored data. The approach encompasses univariate outcome prediction, multivariate outcome prediction, and density estimation, simply by defining a suitable loss function for each of these problems. The proposed method for tree-based estimation with censoring is evaluated using a simulation study and the analysis of CGH copy number and survival data from breast cancer patients.     

On Descent Theory for Monoid Actions

We give some sufficient conditions for a monoid homomorphism to be an effective descent morphism.