Related papers: The directed landscape seen from its trees
We consider the Directed Spanning Forest (DSF) constructed as follows: given a Poisson point process N on the plane, the ancestor of each point is the nearest vertex of N having a strictly larger abscissa. We prove that the DSF is actually…
3D geometry is a very informative cue when interacting with and navigating an environment. This writing proposes a new approach to 3D reconstruction and scene understanding, which implicitly learns 3D geometry from depth maps pairing a deep…
We study an ill-posed problem of geological field reconstruction under limited observations. Engineers often have to deal with the problem of reconstructing the subsurface geological field from sparse measurements such as exploration well…
For the exactly solvable model of exponential last passage percolation on $\mathbb{Z}^2$, it is known that given any non-axial direction, all the semi-infinite geodesics starting from points in $\mathbb{Z}^2$ in that direction almost surely…
By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
A common metaphor for describing development is a rugged "epigenetic landscape" where cell fates are represented as attracting valleys resulting from a complex regulatory network. Here, we introduce a framework for explicitly constructing…
We consider the problem of enumerating d-irreducible maps, i.e. planar maps whose all cycles have length at least d, and such that any cycle of length d is the boundary of a face of degree d. We develop two approaches in parallel: the…
Reconstructing accurate 3D models of large-scale real-world scenes from unstructured, in-the-wild imagery remains a core challenge in computer vision, especially when the input views have little or no overlap. In such cases, existing…
Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning…
Meromorphic connections on Riemann surfaces originate and are closely related to the classical theory of linear ordinary differential equations with meromorphic coefficients. Limiting behaviour of geodesics of such connections has been…
In traditional recognition tasks of neural networks, a potential landscape or cost function guides the system toward patterns using gradient dynamics. That is not how the brain works as its dynamics is far from equilibrium. We present an…
We study end-to-end learning strategies for 3D shape inference from images, in particular from a single image. Several approaches in this direction have been investigated that explore different shape representations and suitable learning…
We consider problems in which a simple path of fixed length, in an undirected graph, is to be shifted from a start position to a goal position by moves that add an edge to either end of the path and remove an edge from the other end. We…
In this paper we show that following Nachman's method we can still reconstruct complex conductivities in $C^{1,1}$ from its Dirichlet-to-Neumann map in three and higher dimensions. For such, we analyze all of the results in Nachman and…
Directed networks are essential for representing complex systems, capturing the asymmetry of interactions in fields such as neuroscience, transportation, and social networks. Directionality reveals how influence, information, or resources…
Landscapes are meaningful ecological units that strongly depend on the environmental conditions. Such dependencies between landscapes and the environment have been noted since the beginning of Earth sciences and cast into conceptual models…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
Semi-structured regression models enable the joint modeling of interpretable structured and complex unstructured feature effects. The structured model part is inspired by statistical models and can be used to infer the input-output…
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…