相关论文: Constructing Associative 3-folds by Evolution Equa…
A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based…
Methods that generate networks sharing a given degree distribution and global clustering can induce changes in structural properties other than that controlled for. Diversity in structural properties, in turn, can affect the outcomes of…
We construct a fully equivariant correspondence between Gromov-Witten and stable pairs descendent theories for toric 3-folds X. Our method uses geometric constraints on descendents, A_n surfaces, and the topological vertex. The rationality…
We study type III contractions of Calabi-Yau threefolds containing a ruled surface over a smooth curve. We discuss the conditions necessary for the image threefold to by smoothable. We describe the change in Hodge numbers caused by this…
Autoregressive models have achieved remarkable success across various domains, yet their performance in 3D shape generation lags significantly behind that of diffusion models. In this paper, we introduce OctGPT, a novel multiscale…
Aiming to generate easy-to-handle assembly sequences for robotic assembly, this study tackles assembly sequence generation by considering two tradeoff objectives: (1) insertion conditions and (2) degrees of constraints among assembled…
Given a closed real analytic Riemannian manifold, we construct and study a one parameter family of adapted complex structures on the manifold of its geodesics.
This work presents a unified framework for the unsupervised prediction of physically plausible interpolations between two 3D articulated shapes and the automatic estimation of dense correspondence between them. Interpolation is modelled as…
We construct a $14$-dimensional affine variety $\Sigma^{14}_{\mathbb{A}}$ with a $\rm{GL}_3$- and a $(\mathbb{C}^*)^6$-actions. We denote by $\Sigma^{13}_{\mathbb{A}}$ the affine variety obtained from $\Sigma^{14}_{\mathbb{A}}$ by setting…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
We prove an orbifold Riemann--Roch formula for a polarized 3--fold (X,D). As an application, we construct new families of projective Calabi--Yau threefolds.
Any smooth projective curve embeds into $\mathbb{P}^3$. More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a threefold $X$, then $X$ is…
Accurately drawing 3D objects is difficult for untrained individuals, as it requires an understanding of perspective and its effects on geometry and proportions. Step-by-step tutorials break the complex task of sketching an entire object…
We give some examples of Calabi-Yau 3-folds with $\rho=1$, defined over $\mathbb{Q}$ and constructed as 4-codimensional subvarieties of $\mathbb{P}^7$ via commutative algebra methods. We explain how to deduce their Hodge diamond and top…
The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed…
AlphaEvolve (Novikov et al., 2025) is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic…
Most decision tree induction algorithms are based on a greedy top-down recursive partitioning strategy for tree growth. In this paper, we propose several methods for induction of decision trees and their ensembles based on evolutionary…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…
This paper describes a way to subdivide a 3-manifold into angled blocks, namely polyhedral pieces that need not be simply connected. When the individual blocks carry dihedral angles that fit together in a consistent fashion, we prove that a…