Flip Graphs of Degree-Bounded (Pseudo-)Triangulations

We study flip graphs of triangulations whose maximum vertex degree is bounded by a constant $k$. In particular, we consider triangulations of sets of $n$ points in convex position in the plane and prove that their flip graph is connected if and only if $k > 6$; the diameter of the flip graph is $O(n^2)$. We also show that, for general point sets, flip graphs of pointed pseudo-triangulations can be disconnected for $k \leq 9$, and flip graphs of triangulations can be disconnected for any $k$. Additionally, we consider a relaxed version of the original problem. We allow the violation of the degree bound $k$ by a small constant. Any two triangulations with maximum degree at most $k$ of a convex point set are connected in the flip graph by a path of length $O(n \log n)$, where every intermediate triangulation has maximum degree at most $k+4$.Comment: 13 pages, 12 figures, acknowledgments update

Structural Controls on Crustal Fluid Circulation and Hot Spring Geochemistry Above a Flat‐Slab Subduction Zone, Peru

Hot spring geochemistry from the Cordillera Blanca and Cordillera Huayhuash, Peru, reveal the influence of crustal‐scale structures on geothermal fluid circulation in an amagmatic region located above a flat‐slab subduction zone. To test the influence of contrasting modes of faulting in these regions, springs were targeted along the Cordillera Blanca detachment fault, within its hanging wall, in the footwall of the detachment, and in the Cordillera Huayhuash. Hot springs along the Cordillera Blanca detachment fault zone are associated with recent extension and normal faulting, and those in its footwall and the Cordillera Huayhuash are located in the Marañon fold and thrust belt where compressional structures dominate. Springs along and in the hanging wall of the Cordillera Blanca detachment fault yield brackish‐saline, alkaline‐chloride waters, with oxygen, hydrogen, carbon, and chlorine stable isotope values that suggest mixing between meteoric groundwater and saline brine affected by high water‐rock interaction. Geothermometry reservoir temperature estimates (RTEs) of 91–226°C indicate maximum flow path depths of 8.7 or 11 km, depending on geothermal gradient, associated with the Cordillera Blanca detachment fault. In contrast, springs in the footwall and in the Cordillera Huayhuash exhibit a wide range of water types with an isotopic affinity to meteoric water, suggesting a greater influence from shallow groundwater and less water‐rock interaction. For these springs, RTEs of 40–98°C correspond to much shallower circulation (1.6–4 km). Results indicate that the Cordillera Blanca detachment system accommodates significantly deeper circulation of crustal fluids compared to other regional compressional structures

A Sparse Stress Model

Force-directed layout methods constitute the most common approach to draw general graphs. Among them, stress minimization produces layouts of comparatively high quality but also imposes comparatively high computational demands. We propose a speed-up method based on the aggregation of terms in the objective function. It is akin to aggregate repulsion from far-away nodes during spring embedding but transfers the idea from the layout space into a preprocessing phase. An initial experimental study informs a method to select representatives, and subsequent more extensive experiments indicate that our method yields better approximations of minimum-stress layouts in less time than related methods.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

White matter structure and myelin-related gene expression alterations with experience in adult rats

White matter (WM) plasticity during adulthood is a recently described phenomenon by which experience can shape brain structure. It has been observed in humans using diffusion tensor imaging (DTI) and myelination has been suggested as a possible mechanism. Here, we set out to identify molecular and cellular changes associated with WM plasticity measured by DTI. We combined DTI, immunohistochemistry and mRNA expression analysis and examined the effects of somatosensory experience in adult rats. First, we observed experience-induced DTI differences in WM and in grey matter structure. C-Fos mRNA expression, a marker of cortical activity, in the barrel cortex correlated with the MRI WM metrics, indicating that molecular correlates of cortical activity relate to macroscale measures of WM structure. Analysis of myelin-related genes revealed higher myelin basic protein (MBP) mRNA expression. Higher MBP protein expression was also found via immunohistochemistry in WM. Finally, unbiased RNA sequencing analysis identified 134 differentially expressed genes encoding proteins in- volved in functions related to cell proliferation and differentiation, regulation of myelination and neuronal activity modulation. In conclusion, macroscale measures of WM plasticity are supported by both molecular and cellular evidence and confirm that myelination is one of the underlying mechanisms

Abel Symposia

Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics