Related papers: Learning Lineage-guided Geodesics with Finsler Geo…

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…

A core challenge for modern biology is how to infer the trajectories of individual cells from population-level time courses of high-dimensional gene expression data. Birth and death of cells present a particular difficulty: existing…

Self-driving vehicles rely on sensory input to monitor their surroundings and continuously adapt to the most likely future road course. Predictive trajectory planning is based on snapshots of the (uncertain) road course as a key input.…

Predicting the future trajectories of the traffic agents is a gordian technique in autonomous driving. However, trajectory prediction suffers from data imbalance in the prevalent datasets, and the tailed data is often more complicated and…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…

Phylogenetic tree reconstruction is traditionally based on multiple sequence alignments (MSAs) and heavily depends on the validity of this information bottleneck. With increasing sequence divergence, the quality of MSAs decays quickly.…

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions…

A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this…

Existing subset selection methods for efficient learning predominantly employ discrete combinatorial and model-specific approaches which lack generalizability. For an unseen architecture, one cannot use the subset chosen for a different…

Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…

This paper explores the generalized projective Riemann curvature in Finsler geometry, focusing on the properties of projectively equivalent Finsler metrics and the invariance of their curvature structures under projective transformations.…

Modern formulation of Finsler geometry of a manifold M utilizes the equivalence between this geometry and the Riemannian geometry of VTM, the vertical bundle over the tangent bundle of M, treating TM as the base space. We argue that this…

We show that a small perturbation of the boundary distance function of a simple Finsler metric on the $n$-disc is also the boundary distance function of some Finsler metric. (Simple metric form an open class containing all flat metrics.)…

Using movement primitive libraries is an effective means to enable robots to solve more complex tasks. In order to build these movement libraries, current algorithms require a prior segmentation of the demonstration trajectories. A…

We demonstrate the use of computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicast-based delay inference, i.e. the problem of…

This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly…

Due to the advent of new mobile devices and tracking sensors in recent years, huge amounts of data are being produced every day. Therefore, novel methodologies need to emerge that dive through this vast sea of information and generate…

Predicting the evolution of spatiotemporal physical systems from sparse and scattered observational data poses a significant challenge in various scientific domains. Traditional methods rely on dense grid-structured data, limiting their…

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…