arXiv research

Computes fundamental groups of restricted configuration spaces.

We study the configuration space of equilateral and equiangular spatial hexagons for any bond angle by giving explicit expressions of all the possible shapes. We show that the chair configuration is isolated, whereas the boat configuration allows one-dimensional deformations which form a circle in the configuration spa…

Study shows configuration spaces' homological dimension increases monotonically.

Researchers create a model for surface point configurations.

Tripod configurations of plane curves, formed by certain triples of normal lines coinciding at a point, were introduced by Tabachnikov, who showed that $C^2$ closed convex curves possess at least two tripod configurations. Later, Kao and Wang established the existence of tripod configurations for $C^2$ closed locally c…

We study the Orchard relation for generic configurations of points in the plane (also called order types). We introduce infinitesimally-close points and analyse the relation of this notion with the Orchard relation. The second part of the paper deals with monochromatic configurations (for the Orchard relation). We give…

This paper extends homological stability results for configuration spaces of manifolds.

Quantum groups created from disk configuration space homologies.

We study configurations of immersed curves in surfaces and surfaces in 3-manifolds. Among other results, we show that primitive curves have only finitely many configurations which minimize the number of double points. We give examples of minimal configurations not realized by geodesics in any hyperbolic metric.

A machine learning configuration refers to a combination of preprocessor, learner, and hyperparameters. Given a set of configurations and a large dataset randomly split into training and testing set, we study how to efficiently select the best configuration with approximately the highest testing accuracy when trained f…

Study orders of canonical bundles over graph configuration spaces.

Solves Plateau-Douglas problem for singular configurations in general metric spaces.

Ensuring that all supposedly valid configurations of a software product line (SPL) lead to well-formed and acceptable products is challenging since it is most of the time impractical to enumerate and test all individual products of an SPL. Machine learning classifiers have been recently used to predict the acceptabilit…

Study on disk configurations in strips shows stability patterns.

Study maps surface configurations to Heisenberg homologies for mapping class groups.

Sharp upper bound for quasi polynomial degree of manifold configuration spaces.

We prove a conjecture of Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. We use this result in order to define an invariant, spindle-genus, for spindle-configurations. We also slightly simplify the exposition of some known invariants for configurations of skew lines an…

We consider the problem of configuring general-purpose solvers to run efficiently on problem instances drawn from an unknown distribution. The goal of the configurator is to find a configuration that runs fast on average on most instances, and do so with the least amount of total work. It can run a chosen solver on a r…

Optimizes glmnet configuration for better accuracy and efficiency.

The square-peg problem is solved using configuration spaces and multijet transversality.

We show that every negative definite configuration of symplectic surfaces in a symplectic 4--manifold has a strongly symplectically convex neighborhood. We use this to show that, if a negative definite configuration satisfies an additional negativity condition at each surface in the configuration, and if the complex si…

We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.

This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configuration spaces of graphs. These are lovely spaces: we show for example that the configuration space of two points on the complete graph of fi…

In this paper we determine the topological complexity of configuration spaces of graphs which are not necessarily trees, which is a crucial assumption in previous results. We do this for two very different classes of graphs: fully articulated graphs and banana graphs. We also complete the computation in the case of tre…

We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2 which 'admits a boundary', with labels in a path-connected space X, and with an …

We discuss Darboux-Staude type of thread configurations for the ellipsoid similar to Chasles-Graves type of thread configurations for the ellipse. These threads are formed by rectilinear segments, geodesic and line of curvature segments on the considered ellipsoid and with tangents tangent to the given ellipsoid and a …

Researchers calculate cohomological dimensions of manifold configuration spaces, proving arithmeticity and providing bounds.

The paper establishes a correspondence for projective bundles over curves using test configurations and extremal metrics.

Research connects Lie algebras to configuration space (co)homology.

Classifies graph configuration spaces homeomorphic to manifolds.

We complete the classification of supersymmetric configurations of two M5-branes, started by Ohta and Townsend. The novel configurations not considered before are those in which the two branes are moving relative to one another. These configurations are obtained by starting with two coincident branes and Lorentz-transf…

The study examines when a section exists for graph configuration spaces.

Using results on the topology of moduli space of polygons [Jaggi, 92; Kapovich and Millson, 94], it can be shown that for a planar robot arm with $n$ segments there are some values of the base-length, $z$, at which the configuration space of the constrained arm (arm with its end effector fixed) has two disconnected com…

Study smooth embeddings of line configurations in complex projective plane.

The paper classifies equivariant test configurations for spherical varieties.

Decouples homotopy quotients of generalised configuration spaces on surfaces.

This paper studies the configuration space of all possible positions of a linkage in R^n. For example, it shows that for every compact algebraic set, there is a linkage whose configuration space is analytically isomorphic to a finite number of copies of the algebraic set. If flexible edges are allowed, any compact set …

We show that the configuration space over a manifold M inherits many curvature properties of the manifold. For instance, we show that a lower Ricci curvature bound on M implies for the configuration space a lower Ricci curvature bound in the sense of Lott-Sturm-Villani, the Bochner inequality, gradient estimates and Wa…

The paper studies how points and lines can move while preserving incidences.

We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for the configuration spaces of three collinear and non-collinear points.

A pair of points in a riemannian manifold makes a secure configuration if the totality of geodesics connecting them can be blocked by a finite set. The manifold is secure if every configuration is secure. We investigate the security of compact, locally symmetric spaces.

We investigate local configuration controllability for mechanical control systems within the affine connection formalism. Extending the work by Lewis for the single-input case, we are able to characterize local configuration controllability for systems with $n$ degrees of freedom and $n-1$ input forces.

Study on tilings of the plane with two types of tiles of varying areas.

Exact universal interpolation property for landmark configurations in Euclidean space.

The paper addresses how to add points to existing configurations on surfaces without disrupting continuity.

We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be made transverse to any submanifold of the configuration space of points in Euclid…

For smooth test configurations, there always exist C^{1,1} geodesic rays in Kahler metric space parallel to the algebraic ray. The $\yen$ invariant agrees with Futaki invariant, at least under nice assumptions. Explicit examples in Toric cases are calculated. On simple test configurations, Donaldson's correspondence be…

Introduces non-Archimedean metrics for pseudoeffective classes on Kähler manifolds.