Related papers: Interpolative fusions II: Preservation results
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
General results of interpolation (eg. Nevanlinna-Pick) by elements in the noncommutative analytic Toeplitz algebra $F^\infty$ (resp. noncommutative disc algebra $A_n$) with consequences to the interpolation by bounded operator-valued…
In this study, we have derived a thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects. This model accommodates variations in physical properties such as density, viscosity, heat capacity, and…
We develop a structure-preserving computational framework for optimal mixing control in incompressible flows. Our approach exactly conserves the continuous system's key invariants (mass and $L^2$-energy), while also maintaining discrete…
Noise has always been nonnegligible trouble in object detection by creating confusion in model reasoning, thereby reducing the informativeness of the data. It can lead to inaccurate recognition due to the shift in the observed pattern, that…
In this article, we consider the control of fusion in fusion systems, proving three previously known, non-trivial results in a new, largely elementary way. We then reprove a result of Aschbacher, that the product of two strongly closed…
The long-time relaxation of ideal two dimensional magnetohydrodynamic turbulence subject to the conservation of two infinite families of constants of motion---the magnetic and the "cross" topology invariants--is examined. The analysis of…
In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…
Infrared and visible images, as multi-modal image pairs, show significant differences in the expression of the same scene. The image fusion task is faced with two problems: one is to maintain the unique features between different…
Using molecular dynamics we study heat conduction and diffusion of hard disks in one dimensional narrow channels. When collisions preserve momentum the heat conduction $\kappa$ diverges with the number of disks $N$ as $\kappa\sim N^\alpha$…
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to the case of symmetric implication calculus $\mathsf{S^2IC}$,…
Model fusion seeks to combine independently trained neural networks into a single model without retraining, but is complicated by representational divergence arising from permutation invariance, random initialization, and heterogeneous…
The state of the art for mesh coupling at nonconforming interfaces is presented and reviewed. Mesh coupling is frequently applied to the modeling and simulation of motion in electromagnetic actuators and machines. The paper exploits Whitney…
In a complex disease such as tuberculosis, the evidence for the disease and its evolution may be present in multiple modalities such as clinical, genomic, or imaging data. Effective patient-tailored outcome prediction and therapeutic…
A thermodynamically consistent model of non-classical coupled non-linear thermoelasticity capable of accounting for thermal wave propagation is proposed. The heat flux is assumed to consist of both additive energetic and dissipative…
This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this third part,…
Cooperation information sharing is important to theories of human learning and has potential implications for machine learning. Prior work derived conditions for achieving optimal Cooperative Inference given strong, relatively restrictive…
We continue our study of open and closed languages. We investigate how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces;…
As a step towards establishing homotopy-theoretic foundations for topological data analysis (TDA), we introduce and study homotopy interleavings between filtered topological spaces. These are homotopy-invariant analogues of interleavings,…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…