Related papers: From PDEs to Pfaffian fibrations
Phage display is a powerful laboratory technique used to study the interactions between proteins and other molecules, whether other proteins, peptides, DNA or RNA. The under-utilisation of this data in conjunction with deep learning models…
We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…
As the loop space of a Riemannian manifold is infinite-dimensional, it is a non-trivial problem to make sense of the "top degree component" of a differential form on it. In this paper, we show that a formula from finite dimensions…
Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…
Let \pi : V \rightarrow M be a (real or holomorphic) vector bundle whose base has an almost Frobenius structure (\circ_{M},e_{M}, g_{M}) and typical fiber has the structure of a Frobenius algebra (\circ_{V},e_{V},g_{V}). Using a connection…
Jet substructure provides one of the most exciting new approaches for searching for physics in and beyond the Standard Model at the Large Hadron Collider. Modern jet substructure searches are often performed with Neural Network (NN) taggers…
In this report, we present and compare the results of an improved fractional and integer order partial differential equation (PDE)-based binarization scheme. The improved model incorporates a diffusion term in addition to the edge and…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…
Boosted resonances is a highly probable and enthusiastic scenario in any process probing the electroweak scale. Such objects when decaying into jets can easily blend with the cornucopia of jets from hard relative light QCD states. We review…
We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…
The high-dimensional nature of the 4-D light field (LF) poses great challenges in achieving efficient and effective feature embedding, that severely impacts the performance of downstream tasks. To tackle this crucial issue, in contrast to…
In this paper, the Painlev\'e property to fractional differential equations (FDEs) are extended and the existence and uniqueness theorems for both linear and nonlinear FDEs are established. The results contribute to the research of…
This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order…
Inpainting-based image compression is emerging as a promising competitor to transform-based compression techniques. Its key idea is to reconstruct image information from only few known regions through inpainting. Specific partial…
We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of…
As edge devices become increasingly powerful, data analytics are gradually moving from a centralized to a decentralized regime where edge compute resources are exploited to process more of the data locally. This regime of analytics is…
Although organizations are continuously making concerted efforts to harden their systems against network attacks by air-gapping critical systems, attackers continuously adapt and uncover covert channels to exfiltrate data from air-gapped…
We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate…
Feature engineering is the process of using domain knowledge to extract features from raw data via data mining techniques and is a key step to improve the performance of machine learning algorithms. In the multi-party feature engineering…
Developing effective representations of protein structures is essential for advancing protein science, particularly for protein generative modeling. Current approaches often grapple with the complexities of the SE(3) manifold, rely on…