Related papers: From PDEs to Pfaffian fibrations
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms…
Jets are extended multipartonic systems and serve as a powerful tool for investigating the dynamics of emergent phenomena driven by many body QCD interactions. In heavy ion collisions, starting from their production during the perturbative…
In an aerial hybrid massive multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) system, how to design a spectral-efficient broadband multi-user hybrid beamforming with a limited pilot and feedback…
We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the…
Finding the general solution of partial differential equations (PDEs) is essential for controller design in newly developed methods. Interconnection and damping assignment passivity based control (IDA-PBC) is one of such methods in which…
Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent,…
Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to…
The increasing concerns about data privacy and security drive an emerging field of studying privacy-preserving machine learning from isolated data sources, i.e., federated learning. A class of federated learning, vertical federated…
This paper presents a novel method for synthesizing new physical layer modulation and coding schemes for communications systems using a learning-based approach which does not require an analytic model of the impairments in the channel. It…
The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot…
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…
In this paper we review the hole argument for the space-time points and elementary particles and generalize the hole argument to include all geometric object fields and diffeomorphisms; and, by application of forgetful functors to abstract…
In this paper we shall prove that the plane of financial events, introduced and applied to financial problems by the author himself (see [2], [3] and [4]) can be considered as a fibration in two different ways. The first one, the natural…
We give a new construction of the holonomy groupoid of a regular foliation in terms of a partial connection on a diffeological principal bundle of germs of transverse parametrisations. We extend these ideas to construct a novel holonomy…
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
The polarizable embedding (PE) model is a fragment-based quantum-classical approach aimed at accurate inclusion of environment effects in quantum-mechanical response property calculations. The aim of this tutorial is to give insight into…
Permanent Data Encoding (PDE) is a visual language framework designed for long-term, human-readable, and electrically independent knowledge preservation. By encoding semantic content into compact 2-3 character alphanumeric codes, paired…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
Medical ultrasound provides images which are the spatial map of the tissue echogenicity. Unfortunately, an ultrasound image is a low-quality version of the expected Tissue Reflectivity Function (TRF) mainly due to the non-ideal Point Spread…