Related papers: Local cohomology and stratification
We find canonical decompositions for finitely presented groups which specialize to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The decompositions that we obtain are invariant under…
Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
We extend the class of SQP methods for equality constrained optimization to the setting of differentiable manifolds. The use of retractions and stratifications allows us to pull back the involved mappings to linear spaces. We study local…
We extend the persistence algorithm, viewed as an algorithm computing the homology of a complex of free persistence or graded modules, to complexes of modules that are not free. We replace persistence modules by their presentations and…
We study sharply localized sectors, known as sectors of DHR-type, of a net of local observables, in arbitrary globally hyperbolic spacetimes with dimension $\geq 3$. We show that these sectors define, has it happens in Minkowski space, a…
We prove a new kind of stabilisation result, "secondary homological stability", for the homology of mapping class groups of orientable surfaces with one boundary component. These results are obtained by constructing CW approximations to the…
We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by…
Recent empirical work has shown that hierarchical convolutional kernels inspired by convolutional neural networks (CNNs) significantly improve the performance of kernel methods in image classification tasks. A widely accepted explanation…
We investigate one-point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h-regular…
We present an algorithm to recover a minimal local apolar scheme to a homogeneous polynomial $F$. The socle degree of the scheme determines whether it is evinced by a Generalized Additive Decomposition (GAD) of $F$ or of an extension. We…
The most successful unfolding rules used nowadays in the partial evaluation of logic programs are based on well quasi orders (wqo) applied over (covering) ancestors, i.e., a subsequence of the atoms selected during a derivation. Ancestor…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of "parity sheaves", which are objects in the constructible derived category of sheaves with coefficients in…
This paper presents a method that improve state-of-the-art of the concave point detection methods as a first step to segment overlapping objects on images. It is based on the analysis of the curvature of the objects contour. The method has…
After 1-point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative…
For each subcomplex of the standard CW-structure on any torus, we compute the homology of a certain infinite cyclic regular covering space. In all cases when the homology is finitely generated, we also compute the cohomology ring. For…