Related papers: The directed landscape seen from its trees
Trajectory inference investigates how to interpolate paths between observed timepoints of dynamical systems, such as temporally resolved population distributions, with the goal of inferring trajectories at unseen times and better…
In distance query reconstruction, we wish to reconstruct the edge set of a hidden graph by asking as few distance queries as possible to an oracle. Given two vertices $u$ and $v$, the oracle returns the shortest path distance between $u$…
In evolutionary biology, phylogenetic networks are now widely used to represent the historical relationships between species and population, when this history includes reticulation events such as hybridization, gene flow and admixture…
Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…
Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with binary coplanarity relation, as well as with binary relation of being in one pencil of lines, is a sufficient…
How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…
This work introduces a systematic algorithm for generating directed networks with prescribed symmetries by constructing expansions from a given quotient network. The method enables researchers to synthesize realistic network models with…
This paper sheds light on the essential characteristics of geodesics, which frequently occur in considerations from motion in Euclidean space. Focus is mainly on a method of obtaining them from the calculus of variations, and an explicit…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
We present an end-to-end 3D reconstruction method for a scene by directly regressing a truncated signed distance function (TSDF) from a set of posed RGB images. Traditional approaches to 3D reconstruction rely on an intermediate…
There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High…
Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape near the local minima to which they converge. This suggests that qualitative and quantitative…
We present a physics-based inverse rendering method that learns the illumination, geometry, and materials of a scene from posed multi-view RGB images. To model the illumination of a scene, existing inverse rendering works either completely…
The Euclidean Directed Spanning Forest is a random forest in $\mathbb{R}^d$ introduced by Baccelli and Bordenave in 2007 and we introduce and study here the analogous tree in the hyperbolic space. The topological properties of the Euclidean…
We study the growth of networks from a set of isolated ground nodes by the addition of one new node per time step and also of a fixed number of directed edges leading from the new node to randomly selected nodes already in the network. A…
In a projective space we fix some set of points, a horizon, and investigate the complement of that horizon. We prove, under some assumptions on the size of lines, that the ambient projective space, together with its horizon, both can be…
In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain…
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…
In this paper we analyze the problem of the geodesic connectedness of subsets of Riemannian manifolds. By using variational methods, the geodesic connectedness of open domains (whose boundaries can be not differentiable and not convex) of a…