Related papers: Adjoint characteristic decomposition of one-dimens…
A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple,…
The effect of a standing acoustic wave on the diffusion of an ad-atom on a crystalline surface is theoretically studied. We used an unidimensional space model to study the ad-atom+substrate system. The dynamic equation of the ad-atom, a…
This article presents a unified theory for analysis of components in discrete data, and compares the methods with techniques such as independent component analysis, non-negative matrix factorisation and latent Dirichlet allocation. The main…
We present an adjoint sensitivity method for hybrid discrete -- continuous systems, extending previously published forward sensitivity methods. We treat ordinary differential equations and differential-algebraic equations of index up to two…
We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in $R^n$, n = 1, 2, 3. We characterize their self-adjoint extensions and, in the unidimensional case, present a discussion of controversies in…
Collective diffusion coefficient in a one dimensional lattice gas adsorbate is calculated using variational approach. Particles interact via either a long-range, or a long range electron-gas-mediated (for a metallic substrate), or a…
In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge,…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
In recent years, it has been convincingly shown that weather forecasting models can be run in single-precision arithmetic. Several models or components thereof have been tested with even lower precision than this. This previous work has…
Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…
With the benefit of deep learning techniques, recent researches have made significant progress in image compression artifacts reduction. Despite their improved performances, prevailing methods only focus on learning a mapping from the…
In this paper we prove an optimal $L^2-L^{2d}$ decay estimate of the adjoint Radon transform of compactly supported data in $d$-dimensional space via a geometric method. A similar problem in dimension $3$ has be considered in the author's…
The sharp increasing in fabrication capabilities of nanomaterials, and complex structures such as meta-surfaces and metalens, has opened to the possibility of employing them for accurately control the electromagnetic field, beyond the…
The emergence of "acoustic diode" (AD) capable of rectifying acoustic wave like electrical diodes do to electricity has been believed to be able to offer unconventional manipulation on sound, e.g., to isolate the wrong-way reflection, and…
Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulations for design. However, the conventional adjoint method breaks down for scale-resolving simulations like large-eddy simulation (LES) or direct…
Emotion and expressivity in music have been topics of considerable interest in the field of music information retrieval. In recent years, mid-level perceptual features have been suggested as means to explain computational predictions of…
A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and…
The low-frequency acoustic-like modes in a pair plasma (electron-positron or pair-ion) is studied by employing a kinetic theory model based on the Vlasov and Poisson's equation with emphasizing the Tsallis's nonextensive statistics. The…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality…