A Finite Model Property for Gödel Modal Logics

A new semantics with the finite model property is provided and used to establish decidability for Gödel modal logics based on (crisp or fuzzy) Kripke frames combined locally with Gödel logic. A similar methodology is also used to establish decidability, and indeed co-NP-completeness for a Gödel S5 logic that coincides with the one-variable fragment of first-order Gödel logic.

Multi-modal glioblastoma segmentation: man versus machine

BACKGROUND AND PURPOSE Reproducible segmentation of brain tumors on magnetic resonance images is an important clinical need. This study was designed to evaluate the reliability of a novel fully automated segmentation tool for brain tumor image analysis in comparison to manually defined tumor segmentations. METHODS We prospectively evaluated preoperative MR Images from 25 glioblastoma patients. Two independent expert raters performed manual segmentations. Automatic segmentations were performed using the Brain Tumor Image Analysis software (BraTumIA). In order to study the different tumor compartments, the complete tumor volume TV (enhancing part plus non-enhancing part plus necrotic core of the tumor), the TV+ (TV plus edema) and the contrast enhancing tumor volume CETV were identified. We quantified the overlap between manual and automated segmentation by calculation of diameter measurements as well as the Dice coefficients, the positive predictive values, sensitivity, relative volume error and absolute volume error. RESULTS Comparison of automated versus manual extraction of 2-dimensional diameter measurements showed no significant difference (p = 0.29). Comparison of automated versus manual segmentation of volumetric segmentations showed significant differences for TV+ and TV (p<0.05) but no significant differences for CETV (p>0.05) with regard to the Dice overlap coefficients. Spearman's rank correlation coefficients (ρ) of TV+, TV and CETV showed highly significant correlations between automatic and manual segmentations. Tumor localization did not influence the accuracy of segmentation. CONCLUSIONS In summary, we demonstrated that BraTumIA supports radiologists and clinicians by providing accurate measures of cross-sectional diameter-based tumor extensions. The automated volume measurements were comparable to manual tumor delineation for CETV tumor volumes, and outperformed inter-rater variability for overlap and sensitivity.

Factors controlling decomposition rates of fine root litter in temperate forests and grasslands

Background and aims Fine root decomposition contributes significantly to element cycling in terrestrial ecosystems. However, studies on root decomposition rates and on the factors that potentially influence them are fewer than those on leaf litter decomposition. To study the effects of region and land use intensity on fine root decomposition, we established a large scale study in three German regions with different climate regimes and soil properties. Methods In 150 forest and 150 grassland sites we deployed litterbags (100 μm mesh size) with standardized litter consisting of fine roots from European beech in forests and from a lowland mesophilous hay meadow in grasslands. In the central study region, we compared decomposition rates of this standardized litter with root litter collected on-site to separate the effect of litter quality from environmental factors. Results Standardized herbaceous roots in grassland soils decomposed on average significantly faster (24 ± 6 % mass loss after 12 months, mean ± SD) than beech roots in forest soils (12 ± 4 %; p < 0.001). Fine root decomposition varied among the three study regions. Land use intensity, in particular N addition, decreased fine root decomposition in grasslands. The initial lignin:N ratio explained 15 % of the variance in grasslands and 11 % in forests. Soil moisture, soil temperature, and C:N ratios of soils together explained 34 % of the variance of the fine root mass loss in grasslands, and 24 % in forests. Conclusions Grasslands, which have higher fine root biomass and root turnover compared to forests, also have higher rates of root decomposition. Our results further show that at the regional scale fine root decomposition is influenced by environmental variables such as soil moisture, soil temperature and soil nutrient content. Additional variation is explained by root litter quality.

A Hennessy-Milner Property for Many-Valued Modal Logics

A Hennessy-Milner property, relating modal equivalence and bisimulations, is defined for many-valued modal logics that combine a local semantics based on a complete MTL-chain (a linearly ordered commutative integral residuated lattice) with crisp Kripke frames. A necessary and sufficient algebraic condition is then provided for the class of image-finite models of these logics to admit the Hennessy-Milner property. Complete characterizations are obtained in the case of many-valued modal logics based on BL-chains (divisible MTL-chains) that are finite or have universe [0,1], including crisp Lukasiewicz, Gödel, and product modal logics.

Heuristic decomposition and LP-based scheduling in make-and-pack production

In this paper, we are concerned about the short-term scheduling of industrial make-and-pack production processes. The planning problem consists in minimizing the production makespan while meeting given end-product demands. Sequence-dependent changeover times, multi-purpose storage units with finite capacities, quarantine times, batch splitting, partial equipment connectivity, material transfer times, and a large number of operations contribute to the complexity of the problem. Known MILP formulations cover all technological constraints of such production processes, but only small problem instances can be solved in reasonable CPU times. In this paper, we develop a heuristic in order to tackle large instances. Under this heuristic, groups of batches are scheduled iteratively using a novel MILP formulation; the assignment of the batches to the groups and the scheduling sequence of the groups are determined using a priority rule. We demonstrate the applicability by means of a real-world production process.

Landmark Detection for Fusion of Fundus and MRI Towards a Patient-Specific Multi-Modal Eye Model

Ophthalmologists typically acquire different image modalities to diagnose eye pathologies. They comprise e.g., Fundus photography, Optical Coherence Tomography (OCT), Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Yet, these images are often complementary and do express the same pathologies in a different way. Some pathologies are only visible in a particular modality. Thus, it is beneficial for the ophthalmologist to have these modalities fused into a single patient-specific model. The presented article’s goal is a fusion of Fundus photography with segmented MRI volumes. This adds information to MRI which was not visible before like vessels and the macula. This article’s contributions include automatic detection of the optic disc, the fovea, the optic axis and an automatic segmentation of the vitreous humor of the eye.

Justifying induction on modal μ-formulae

We define a rank function for formulae of the propositional modal μ-calculus such that the rank of a fixed point is strictly bigger than the rank of any of its finite approximations. A rank function of this kind is needed, for instance, to establish the collapse of the modal μ-hierarchy over transitive transition systems. We show that the range of the rank function is ωω. Further we establish that the rank is computable by primitive recursion, which gives us a uniform method to generate formulae of arbitrary rank below ωω.