Simplicial blowups and discrete normal surfaces in simpcomp

simpcomp is an extension to GAP, the well known system for computational discrete algebra. It allows the user to work with simplicial complexes. In the latest version, support for simplicial blowups and discrete normal surfaces was added, both features unique to simpcomp. Furthermore, new functions for constructing certain infinite series of triangulations have been implemented and interfaces to other software packages have been improved to previous versions.Comment: 10 page

Stacked polytopes and tight triangulations of manifolds

Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplexwise linear embedding of the triangulation into euclidean space is "as convex as possible". It can thus be understood as a generalization of the concept of convexity. In even dimensions, super-neighborliness is known to be a purely combinatorial condition which implies the tightness of a triangulation. Here we present other sufficient and purely combinatorial conditions which can be applied to the odd-dimensional case as well. One of the conditions is that all vertex links are stacked spheres, which implies that the triangulation is in Walkup's class $\mathcal{K}(d)$. We show that in any dimension $d\geq 4$ \emph{tight-neighborly} triangulations as defined by Lutz, Sulanke and Swartz are tight. Furthermore, triangulations with $k$-stacked vertex links and the centrally symmetric case are discussed.Comment: 28 pages, 2 figure

simpcomp -- A GAP toolbox for simplicial complexes

simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct new complexes from existing ones and an extensive library of triangulations of manifolds.Comment: 4 page

A novel feature-scrambling approach reveals the capacity of convolutional neural networks to learn spatial relations

Convolutional neural networks (CNNs) are one of the most successful computer vision systems to solve object recognition. Furthermore, CNNs have major applications in understanding the nature of visual representations in the human brain. Yet it remains poorly understood how CNNs actually make their decisions, what the nature of their internal representations is, and how their recognition strategies differ from humans. Specifically, there is a major debate about the question of whether CNNs primarily rely on surface regularities of objects, or whether they are capable of exploiting the spatial arrangement of features, similar to humans. Here, we develop a novel feature-scrambling approach to explicitly test whether CNNs use the spatial arrangement of features (i.e. object parts) to classify objects. We combine this approach with a systematic manipulation of effective receptive field sizes of CNNs as well as minimal recognizable configurations (MIRCs) analysis. In contrast to much previous literature, we provide evidence that CNNs are in fact capable of using relatively long-range spatial relationships for object classification. Moreover, the extent to which CNNs use spatial relationships depends heavily on the dataset, e.g. texture vs. sketch. In fact, CNNs even use different strategies for different classes within heterogeneous datasets (ImageNet), suggesting CNNs have a continuous spectrum of classification strategies. Finally, we show that CNNs learn the spatial arrangement of features only up to an intermediate level of granularity, which suggests that intermediate rather than global shape features provide the optimal trade-off between sensitivity and specificity in object classification. These results provide novel insights into the nature of CNN representations and the extent to which they rely on the spatial arrangement of features for object classification

Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

A gut bacterial signature in blood and liver tissue characterizes cirrhosis and hepatocellular carcinoma

BackgroundHCC is the leading cause of cancer in chronic liver disease. A growing body of experimental mouse models supports the notion that gut-resident and liver-resident microbes control hepatic immune responses and, thereby, crucially contribute to liver tumorigenesis. However, a comprehensive characterization of the intestinal microbiome in fueling the transition from chronic liver disease to HCC in humans is currently missing.MethodsHere, we profiled the fecal, blood, and liver tissue microbiome of patients with HCC by 16S rRNA sequencing and compared profiles to nonmalignant cirrhotic and noncirrhotic NAFLD patients.ResultsWe report a distinct bacterial profile, defined from 16S rRNA gene sequences, with reduced α-and β-diversity in the feces of patients with HCC and cirrhosis compared to NAFLD. Patients with HCC and cirrhosis exhibited an increased proportion of fecal bacterial gene signatures in the blood and liver compared to NAFLD. Differential analysis of the relative abundance of bacterial genera identified an increased abundance of Ruminococcaceae and Bacteroidaceae in blood and liver tissue from both HCC and cirrhosis patients compared to NAFLD. Fecal samples from cirrhosis and HCC patients both showed a reduced abundance for several taxa, including short-chain fatty acid-producing genera, such as Blautia and Agathobacter. Using paired 16S rRNA and transcriptome sequencing, we identified a direct association between gut bacterial genus abundance and host transcriptome response within the liver tissue.ConclusionsOur study indicates perturbations of the intestinal and liver-resident microbiome as a critical determinant of patients with cirrhosis and HCC

Dietary lipids fuel GPX4-restricted enteritis resembling Crohn’s disease

Abstract: The increased incidence of inflammatory bowel disease (IBD) has become a global phenomenon that could be related to adoption of a Western life-style. Westernization of dietary habits is partly characterized by enrichment with the ω-6 polyunsaturated fatty acid (PUFA) arachidonic acid (AA), which entails risk for developing IBD. Glutathione peroxidase 4 (GPX4) protects against lipid peroxidation (LPO) and cell death termed ferroptosis. We report that small intestinal epithelial cells (IECs) in Crohn’s disease (CD) exhibit impaired GPX4 activity and signs of LPO. PUFAs and specifically AA trigger a cytokine response of IECs which is restricted by GPX4. While GPX4 does not control AA metabolism, cytokine production is governed by similar mechanisms as ferroptosis. A PUFA-enriched Western diet triggers focal granuloma-like neutrophilic enteritis in mice that lack one allele of Gpx4 in IECs. Our study identifies dietary PUFAs as a trigger of GPX4-restricted mucosal inflammation phenocopying aspects of human CD