Related papers: Interpolative fusions II: Preservation results
We develop a parabolic inf-sup theory for a modified TraceFEM semi-discretization in space of the heat equation posed on a stationary surface embedded in $\mathbb{R}^n$. We consider the normal derivative volume stabilization and add an…
The end-to-end image fusion framework has achieved promising performance, with dedicated convolutional networks aggregating the multi-modal local appearance. However, long-range dependencies are directly neglected in existing CNN fusion…
In this paper, we consider a nonlinear and nonlocal parabolic model for multi-species ionic fluids and introduce a semi-implicit finite volume scheme, which is second order accurate in space, first order in time and satisfies the following…
Deep learning based methods have penetrated many image processing problems and become dominant solutions to these problems. A natural question raised here is "Is there any space for conventional methods on these problems?" In this paper,…
Filtrations are certain transfinite sequences of topologies increasing in strength and interpolating between two given topologies $\sigma$ and $\tau$, with $\tau$ being stronger than $\sigma$. We prove general results on stabilization at…
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…
A number of key scientific computing applications that are based upon tensor-product grid constructions, such as numerical weather prediction (NWP) and combustion simulations, require property-preserving interpolation. Essentially…
Image fusion combines images from multiple domains into one image, containing complementary information from source domains. Existing methods take pixel intensity, texture and high-level vision task information as the standards to determine…
In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we reinterpret the work of Cendra et al. by substituting velocity…
Since no fusion theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects…
We refine a result of Matei and Meyer on stable sampling and stable interpolation for simple model sets. Our setting is model sets in locally compact abelian groups and Fourier analysis of unbounded complex Radon measures as developed by…
We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
In this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model…
The Cambrian explosion of easily accessible pre-trained diffusion models suggests a demand for methods that combine multiple different pre-trained diffusion models without incurring the significant computational burden of re-training a…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
Fusion is critical for a two-stream network. In this paper, we propose a novel temporal fusion (TF) module to fuse the two-stream joints' information to predict human motion, including a temporal concatenation and a reinforcement trajectory…