Related papers: Computing global Ext for complexes
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. Based on the results of math.AG/0510670, we then show that the derived…
We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give…
Clustering ensemble has emerged as an important research topic in the field of machine learning. Although numerous methods have been proposed to improve clustering quality, most existing approaches overlook the need for interpretability in…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
The space of global sections of the chiral de Rham complex on any closed complex curve with genus $g \ge2$ is calculated.
We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
We describe an algorithm for finding sharp upper bounds for the total Betti numbers of a saturated ideal given certain constraints on its Hilbert function. This algorithm is implemented in the Macaulay2 package, MaxBettiNumbers, along with…
Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none…
We exhibit an explicit algorithm to compute three-point branched covers of the complex projective line when the uniformizing triangle group is Euclidean.
We show that the derived category of coherent sheaves on the quotient stack of the affine plane by a finite small subgroup of the general linear group is obtained from the derived category of coherent sheaves on the minimal resolution by…
We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility…
We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or…
We show how derived categories build bridges across the current mathematical mainstream, linking geometric and algebraic, commutative and noncommutative, local and global banks. Arches in these bridges are pieces of semiorthogonal…
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…
In recent years, there has been considerable success in computing Ext-groups of modular representations associated to the general linear group by relating this problem to one of computing Ext-groups in functor categories. In this paper, we…
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 explicitly compute examples of sheaves over the projectivization of the spectrum of the cohomology of sl_2. In particular, we compute \ker\Theta_M for every indecomposable M and we compute F_i(M) when M is an indecomposable Weyl module…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…