Related papers: Integrable cross-field generation based on imposed…
The characterization of a six- (or seven)-dimensional internal manifold with metric as having positive, zero or negative curvature is expected to be an important aspect of warped compactifications in supergravity. In this context, Douglas…
We propose a method for computing integrable orthogonal frame fields on planar surfaces. Frames and their symmetries are implicitly represented using orthogonally decomposable (odeco) tensors. To formulate an integrability criterion, we…
We present Twisted Edges, a unified framework for designing Linked Knot (LK) structures using labeled non-manifold surface meshes. While the concept of edge twists, originating in topological graph theory, is foundational to these designs,…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
We review some properties of N=8 gauged supergravity in four dimensions with modified, but AdS invariant boundary conditions on the m^2=-2 scalars. There is a one-parameter class of asymptotic conditions on these fields and the metric…
We propose the notion of integrable boundary in the context of discrete integrable systems on quad-graphs. The equation characterizing the boundary must satisfy a compatibility equation with the one characterizing the bulk that we called…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and…
We present a framework for constructing examples of smooth projective curves over number fields with explicitly given elements in their second K-group using elementary algebraic geometry. This leads to new examples for hyperelliptic curves…
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…
Artificial intelligence (AI) and machine learning (ML) models in materials science are predominantly trained on ideal bulk crystals, limiting their transferability to real-world applications where surfaces, interfaces, and defects dominate.…
Let $(M,\Omega)$ be a connected symplectic 4-manifold and let $F=(J,H) : M \to \mathbb{R}^2$ be a completely integrable system on $M$ with only non-degenerate singularities and for which $J : M \to \mathbb{R}$ is a proper map. Assume that…
We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $ n$-particle contributions $\chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear…
Explainability in AI is crucial for model development, compliance with regulation, and providing operational nuance to predictions. The Shapley framework for explainability attributes a model's predictions to its input features in a…
Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has…
The overall behavior of a 2D lattice of voids embedded in an anisotropic matrix is investigated in the limit of vanishing porosity f. An effective-medium model (of the Hashin-Shtrikman type) which accounts for elastic interactions between…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
Generative modelling for shapes is a prerequisite for In-Silico Clinical Trials (ISCTs), which aim to cost-effectively validate medical device interventions using synthetic anatomical shapes, often represented as 3D surface meshes. However,…
The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…