A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New scheme optimizes BMI through probabilistic and geometric shaping.
In this paper, an unsupervised machine learning method for geometric constellation shaping is investigated. By embedding a differentiable fiber channel model within two neural networks, the learning algorithm is optimizing for a geometric constellation shape. The learned constellations yield improved performance to sta…
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a da…
Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.
Minimal surfaces help compare geometric shapes.
Python tools for 3D shape analysis on Kendall's space.
Study fourth-order geometric flow of shape operator for co-dimension one immersions.
SVarM uses varifold representations for shape classification and regression.
The choice of constellations largely affects the performance of communication systems. When designing constellations, both the locations and probability of occurrence of the points can be optimized. These approaches are referred to as geometric and probabilistic shaping, respectively. Usually, the geometry of the const…
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by Morse Theory, we algorithmically produce a PL approximation of the original shape …
The paper presents a method for analyzing shape graphs using specific features.
Study examines heart and football-shaped metrics, verifying geometric structure.
A framework for generating 3D shapes by sequentially assembling primitives.
A new geometric shaping method is proposed, leveraging unsupervised machine learning to optimize the constellation design. The learned constellation mitigates nonlinear effects with gains up to 0.13 bit/4D when trained with a simplified fiber channel model.
These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an inter-disciplinary area of research with theoretical foundations in infinite-dimensional Riemannian geometry, geometric statistics, and geo…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed…
In this paper, we are concerned with the 2D and 3D geometric shape generation by prescribing a set of characteristic values of a specific geometric body. One of the major motivations of our study is the 3D human body generation in various applications. We develop a novel method that can generate the desired body with c…
Autoencoder-based geometric shaping is proposed that includes optimizing bit mappings. Up to 0.2 bits/QAM symbol gain in GMI is achieved for a variety of data rates and in the presence of transceiver impairments. The gains can be harvested with standard binary FEC at no cost w.r.t. conventional BICM.
Geometric reduction of the Newtonian planar three-body problem is investigated in the framework of equivariant Riemannian geometry, which reduces the study of trajectories of three-body motions to the study of their moduli curves, that is, curves which record the change of size and shape, in the moduli space of oriente…
Optimizes shapes in uncertain Navier-Stokes flow problems.
LIMP learns latent shapes with metric preservation, improving generative models.
The paper introduces a new method to measure the shape relations between biological objects using r-parallel sets.
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time sy…
Deep learning models complex multivariate extremes using geometric shapes.
We address the geometric Cauchy problem for surfaces associated to the membrane shape equation describing equilibrium configurations of vesicles formed by lipid bilayers. This is the Euler-Lagrange equation of the Canham-Helfrich-Evans elastic curvature energy subject to constraints on the enclosed volume and the surfa…
The paper uses 3D shapes to reveal sundial design adjustments based on latitude.
We consider the problem of modelling noisy but highly symmetric shapes that can be viewed as hierarchies of whole-part relationships in which higher level objects are composed of transformed collections of lower level objects. To this end, we propose the stochastic wreath process, a fully generative probabilistic model…
Transforms curves and surfaces for efficient geometric analysis.
Enhanced 3D shape analysis using information geometry.
In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.
We consider a shape optimization problem for the first mixed Steklov-Dirichlet eigenvalues of domains bounded by two balls in two-point homogeneous space. We give a geometric proof which is motivated by Newton's shell theorem
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of t…
New approach reduces shape optimization anomalies and improves design quality.
A new geometric perceptron model improves 3D shape classification.
The paper proves inequalities for star-shaped and -mean convex hypersurfaces in .
GNPs learn operators on non-Euclidean geometries using neural networks.
New method learns shape correspondences robustly from raw geometry.
This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on varying geometrical supports. Analysing variability of fshapes' ensembles requir…
Simplifies Wulff theorem for crystalline shapes using Minkowski Theory.
Topology-enhanced loss improves 3D object reconstruction from 2D images.
Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations; or (ii) loss functions explicitly defined over the neural level sets…
We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary g…
A new method monitors unstructured 3D shapes without registration.
CupNet prunes neural nets for cup-shaped data.
New friction model for geometric locomotion systems.
Paper analyzes shapes of brain arterial networks using statistical methods.
Paper finds new 3D shapes that can be inside a 4D space.
Study compares geometric approaches for shape and deformation statistics.