arXiv research

Describes geometry of positive configurations in limiting buildings.

Geodesic rays and chordal distances link algebraic and geometric properties of positive metrics.

Positive scalar curvature metrics on cobordisms yield only reducible Seiberg-Witten solutions.

Geodesic rays of class C^{1,1} are constructed for any test configuration of a positive line bundle L on X using resolution of singularities. The construction reduces to finding a subsolution of the corresponding Monge-Ampere equation. Geometrically, this is accomplished by the use a positive line bundle on the resolut…

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 …

This paper is an updated version of a survey on projective configurations of subspaces in general position. The preceding version was published in Russian in 1989 and in English in 1990 (in Leningrad Math. J.) opening a new section ``Light reading for the professional''. The paper is written in the form of introduction…

Positive configurations of points in the affine building were introduced in \cite{Le} as the basic object needed to define higher laminations. We start by giving a self-contained, elementary definition of positive configurations of points in the affine building and their basic properties. Then we study the geometry of …

Adversarial configurations improve SPL classifier and implementation.

Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in Kähler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as…

We consider a generic configuration of regions, consisting of a collection of distinct compact regions $\{Ω_i\}$ in $\mathbb{R}^{n+1}$ which may be either smooth regions disjoint from the others or regions which meet on their piecewise smooth boundaries $\mathcal{B}_i$ in a generic way. We introduce a skeletal linking …

Paper learns robot's end-effector position without prior info.

The study identifies conjugate and cut points in ideal fluid motion configurations.

A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a subset of the vertices. We characterize the possible partial configuration spaces of…

Classifies low energy maps from curved surfaces into spheres.

For any tangle $T$ (up to isotopy) and integer $k\geq 1$ we construct a group $F(T)$ (up to isomorphism). It is the fundamental group of the configuration space of $k$ points in a horizontal plane avoiding the tangle, provided the tangle is in what we call Heegaard position. This is analogous to the first half of Lawre…

In this paper, we study continuous Kakeya line and needle configurations, of both the oriented and unoriented varieties, in connected Lie groups and some associated homogenous spaces. These are the analogs of Kakeya line (needle) sets (subsets of $\mathbb{R}^n$ where it is possible to turn a line (respectively an inter…

In this note we show that the configuration spaces of the kinematic system constructed in [4] and [12] gives rise to a natural tower of sphere bundles. Moreover, we prove that, each tower of projective bundles associated to special multi- flags (cf [1], [13], [2], [3]), we can associate such a tower of sphere bundles w…

In this paper we present a geometric control law for position and line-of-sight stabilization of the nonholonomic spherical robot actuated by three independent actuators. A simple configuration error function with an appropriately defined transport map is proposed to extract feedforward and proportional-derivative cont…

We show that the topological charge of the n-soliton solution of the sine-Gordon equation n is related to the genus g > 1 of a constant negative curvature compact surface described by this configuration. The relation is n=2(g-1), where n is even. The moduli space of complex dimension B(g)=3(g-1) corresponds precisely t…

Paper proposes a method to recover point configurations from noisy distance data.

Adaptive tuning of portfolio selection parameters improves performance in volatile markets.

A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a subset of the vertices. We characterize the possible partial configuration spaces of…

We study neighborhoods of configurations of symplectic surfaces in symplectic 4-manifolds. We show that suitably `positive' configurations have neighborhoods with concave boundaries and we explicitly describe open book decompositions of the boundaries supporting the associated negative contact structures. This is used …

This paper characterizes which subsets of C^n can be the set of positions of n points on a linkage in the complex plane C. For example, assuming compactness they are just compact semialgebraic sets. Noncompact configuration spaces are semialgebraics sets invariant under the Euclidean group, with compact quotient.

Let $X$ be a compact complex manifold, $L\to X$ an ample line bundle over $X$, and ${\cal H}$ the space of all positively curved metrics on $L$. We show that a pair $(h_0,T)$ consisting of a point $h_0\in {\cal H}$ and a test configuration $T=({\cal L}\to {\cal X}\to {\bf C})$, canonically determines a weak geodesic ra…

Two surfaces minimize variance of Gaussian curvature.

New proof of trapezoidal property for Alexander polynomials of special alternating links.

Study proves Yau-Tian-Donaldson conjecture for generalized Kähler-Ricci solitons.

Researchers prove long-time existence for two landmark Brownian motion.

Deep RL learns grasping from 2.5D images.

New approach treats coordination as an architectural layer to improve LLM-based multi-agent systems.

Combines conformal prediction intervals with Kelly strategy to optimize portfolio growth.

Study of separatrix configurations in holomorphic flows with real time.

We give a formula of the Donaldson-Futaki invariants for certain type of semi test configurations, which essentially generalizes Ross-Thomas' slope theory. The positivity (resp. non-negativity) of those "a priori special" Donaldson-Futaki invariants implies K-stability (resp. K-semistability). We show its applicability…

We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various configurations of correlation coefficients ($r$), size of the parameter vector ($β$), …

Study configuration spaces of punctured spaces, focusing on homology and group actions.

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (in…

This paper presents a spermwhale' localization architecture using jointly a bag-of-features (BoF) approach and machine learning framework. BoF methods are known, especially in computer vision, to produce from a collection of local features a global representation invariant to principal signal transformations. Our idea …

New constraints on embedded spheres and projective planes in 4-manifolds from Seiberg-Witten theory.

We study open books on three manifolds which are compatible with an overtwisted contact structure. We show that the existence of certain arcs, called sobering arcs, is a sufficient condition for an open book to be overtwisted, and is necessary up to stabilization by positive Hopf-bands. Using these techniques we prove …

Computes fundamental groups of restricted configuration spaces.

New groups derived from square configurations have right-angled and HNN structures.

It is well-known by the work of Hsiang and Kleiner that every closed oriented positively curved 4-dimensional manifold with an effective isometric S^1-action is homeomorphic to S^4 or CP^2. As stated, it is a topological classification. The primary goal of this paper is to show that it is indeed a diffeomorphism classi…

We discuss a connection between the lantern relation in mapping class groups and the rational blowing down process for 4-manifolds. More precisely, if we change a positive relator in Dehn twist generators of the mapping class group by using a lantern relation, the corresponding Lefschetz fibration changes into its rati…

This paper improves indoor positioning accuracy by deploying reference nodes to ensure Line-of-Sight.

Software finds ideal polyhedra with rational dihedral angles and volume maxima.

We found a 'Goldilocks zone' in neural network loss landscapes that correlates with good initialization.

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…