Orientation-Dispersed Apparent Axon Diameter via Multi-Stage Spherical Mean Optimization

The estimation of the apparent axon diameter (AAD) via diffusion MRI is affected by the incoherent alignment of single axons around its axon bundle direction, also known as orientational dispersion. The simultaneous estimation of AAD and dispersion is challenging and requires the optimization of many parameters at the same time. We propose to reduce the complexity of the estimation with an multi-stage approach, inspired to alternate convex search, that separates the estimation problem into simpler ones, thus avoiding the estimation of all the relevant model parameters at once. The method is composed of three optimization stages that are iterated, where we separately estimate the volume fractions, diffusivities, dispersion, and mean AAD, using a Cylinder and Zeppelin model. First, we use multi-shell data to estimate the undispersed axon micro-environment’s signal fractions and diffusivities using the spherical mean technique; then, to account for dispersion, we use the obtained micro-environment parameters to estimate a Watson axon orientation distribution; finally, we use data acquired perpendicularly to the axon bundle direction to estimate the mean AAD and updated signal fractions, while fixing the previously estimated diffusivity and dispersion parameters. We use the estimated mean AAD to initiate the following iteration. We show that our approach converges to good estimates while being more efficient than optimizing all model parameters at once. We apply our method to ex-vivo spinal cord data, showing that including dispersion effects results in mean apparent axon diameter estimates that are closer to their measured histological values

Generalized Multiple Objective Bottleneck Problems

We consider multiple objective combinatiorial optimization problems in which the first objective is of arbitrary type and the remaining objectives are either bottleneck or k-max objective functions. While the objective value of a bottleneck objective is determined by the largest cost value of any element in a feasible solution, the kth-largest element defines the objective value of the k-max objective. An efficient solution approach for the generation of the complete nondominated set is developed which is independent of the specific combinatiorial problem at hand. This implies a polynomial time algorithm for several important problem classes like shortest paths, spanning tree, and assignment problems with bottleneck objectives which are known to be NP-hard in the general multiple objective case

Connectedness of Efficient Solutions in Multiple Objective Combinatorial Optimization

Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. In this paper we show that, however, most of the classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among others, knapsack problems (and even several special cases of knapsack problems) and linear assignment problems. We also extend already known non-connectedness results for several optimization problems on graphs like shortest path, spanning tree and minimum cost flow problems. Different concepts of connectedness are discussed in a formal setting, and numerical tests are performed for different variants of the knapsack problem to analyze the likelihood with which non-connected adjacency graphs occur in randomly generated problem instances

Generalized Multiple Objective Bottleneck Problems

We consider multiple objective combinatiorial optimization problems in which the first objective is of arbitrary type and the remaining objectives are either bottleneck or k-max objective functions. While the objective value of a bottleneck objective is determined by the largest cost value of any element in a feasible solution, the kth-largest element defines the objective value of the k-max objective. An efficient solution approach for the generation of the complete nondominated set is developed which is independent of the specific combinatiorial problem at hand. This implies a polynomial time algorithm for several important problem classes like shortest paths, spanning tree, and assignment problems with bottleneck objectives which are known to be NP-hard in the general multiple objective case

Connectedness of Efficient Solutions in Multiple Objective Combinatorial Optimization

Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. In this paper we show that, however, most of the classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among others, knapsack problems (and even several special cases of knapsack problems) and linear assignment problems. We also extend already known non-connectedness results for several optimization problems on graphs like shortest path, spanning tree and minimum cost flow problems. Different concepts of connectedness are discussed in a formal setting, and numerical tests are performed for different variants of the knapsack problem to analyze the likelihood with which non-connected adjacency graphs occur in randomly generated problem instances

Connectedness of Efficient Solutions in Multiple Abstract Objective Combinatorial Optimization

Connectedness of efficient solutions is a powerful property in multiple objective com-binatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. In this paper we show that, however, most of the classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among others, knapsack problems (and even several special cases of knapsack problems) and linear assignment problems. We also extend already known non-connectedness results for several optimization problems on graphs like shortest path, spanning tree and minimum cost flow problems. Different concepts of connectedness are discussed in a formal setting, and numerical tests are performed for different variants of the knapsack problem to analyze the likelihood with which non-connected adjacency graphs occur in randomly generated problem instances

Poor risk factor control in outpatients with diabetes mellitus type 2 in Germany: The DIAbetes COhoRtE (DIACORE) study

Introduction Patients with diabetes mellitus type 2 (DM2) are at high risk for micro-and macrovascular disease. Here, we explore the degree of traditional risk factor control in the baseline visit of a cohort of DM2 outpatients. Methods DIACORE (DIAbetes COhoRtE) is a prospective cohort study of 3000 adult DM2 outpatients. Here, we present results from the baseline visit. Sociodemographic and anthropometric variables, cardiovascular risk factors, comorbidities and medication were assessed by interview and medical exams. Serum-creatinine based estimated glomerular filtration rate (eGFRcrea) and urinary albumin-creatinine ratio (UACR) were determined for classification of chronic kidney disease (CKD). The proportion of patients with adequate control of traditional risk factors (blood pressure= 30mg/g. Adequate blood pressure, HbA1c and LDL control was achieved in 55.7%, 78.5% and 34.4%, respectively. In 16.4% of patients (473), all three risk factors were below recommended targets. The proportion of adequate risk factor control was similar across KDIGO eGFRcrea classes. Adequate blood pressure and HbA1c control were significantly associated with lower UACR category without and with controlling for other risk factors (p<0.0001, p = 0.0002, respectively). Conclusion In our study of patients with diabetes mellitus type 2, we observed a low level of risk factor control indicating potential for risk reduction