Felix Effenberger

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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(More)
Structural inhomogeneities in synaptic efficacies have a strong impact on population response dynamics of cortical networks and are believed to play an important role in their functioning. However, little is known about how such inhomogeneities could evolve by means of synaptic plasticity. Here we present an adaptive model of a balanced neuronal network(More)
simpcomp [4] is an extension (a so called package) to GAP [6], 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. For an introduction(More)
We present a novel approach to finding critical points in cell-wise barycentrically or bilinearly interpolated vector fields on surfaces. The Poincaré index of the critical points is determined by investigating the qualitative behavior of 0-level sets of the interpolants of the vector field components in parameter space using precomputed combinatorial(More)
This work is set in the field of combinatorial topology, a mathematical field of research in the intersection of the fields of topology, geometry, polytope theory and combinatorics. This work investigates polyhedral manifolds as subcomplexes of the boundary complex of a regular polytope. Such a subcomplex is called k-Hamiltonian, if it contains the full(More)
simpcomp is a GAP package for working with simplicial complexes. It allows the computation of many properties of simplicial complexes (such as the f -, gand h-vectors, the face lattice, the automorphism group, (co-)homology with explicit basis computation, intersection form, etc.) and provides the user with functions to compute new complexes from old(More)
We present here a novel method for the classical task of extracting reoccurring spatiotemporal patterns from spiking activity of large populations of neurons. In contrast to previous studies that mainly focus on synchrony detection or exactly recurring binary patterns, we perform the search in an approximate way that clusters together nearby, noisy network(More)
simpcomp is a GAP package for working with simplicial complexes. It allows the computation of many properties of simplicial complexes (such as the f -, gand h-vectors, the face lattice, the automorphism group, (co-)homology with explicit basis computation, intersection form, etc.) and provides the user with functions to compute new complexes from old(More)
Felix E↵enberger, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany Christopher Hillar, Redwood Center for Theoretical Neuroscience, Berkeley, CA 94720, USA Summary. We present here a novel method for finding and extracting salient low-dimensional representations of the dynamics of populations of spiking neurons. This is a classical(More)