Related papers: Calculating Spectra by Sequential High-Pass Filter…
Understanding the evolution of the Milky Way calls for the precise abundance determination of many elements in many stars. A common perception is that deriving more than a few elemental abundances ([Fe/H], [$\alpha$/Fe], perhaps [C/H],…
Accurate and efficient calculations of absorption spectra of molecules and materials are essential for the understanding and rational design of broad classes of systems. Solving the Bethe-Salpeter equation (BSE) for electron-hole pairs…
Interpretation of time-resolved spectroscopies such as transient absorption (TA) or two-dimensional (2D) spectroscopy often relies on the perturbative description of light-matter interaction. In many cases the third order of nonlinear…
Retrieving the reflectance spectrum from objects is an essential task for many classification and detection problems, since many materials and processes have a unique spectral behaviour. In many cases, it is highly desirable to capture…
We show the effectiveness of automatic differentiation in efficiently and correctly computing and controlling the spectrum of implicitly linear operators, a rich family of layer types including all standard convolutional and dense layers.…
We propose a concept for production of high power coherent attosecond pulses in X-ray range. An approach is based on generation of 8th harmonic of radiation in a multistage HGHG FEL (high gain high harmonic free electron laser)…
It is shown that the copropagating three-wave-mixing parametric process, with appropriate type-II extended phase matching and pumped with a short second-harmonic pulse, can perform spectral phase conjugation and parametric amplification,…
Clustering short text embeddings is a foundational task in natural language processing, yet remains challenging due to the need to specify the number of clusters in advance. We introduce a scalable spectral method that estimates the number…
The resolution limits of classical spectroscopy can be surpassed by quantum-inspired methods leveraging the information contained in the phase of the complex electromagnetic field. Their counterpart in spatial imaging has been widely…
We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…
We place ourselves in the setting of high-dimensional statistical inference where the number of variables $p$ in a dataset of interest is of the same order of magnitude as the number of observations $n$. We consider the spectrum of certain…
Optical nonlinear Fourier transform-based communication systems require an accurate estimation of a signal's nonlinear spectrum, computed usually by piecewise approximation methods on the signal samples. We propose an algorithm, named…
Let $f(x)=x^{s(p^m-1)}$ be a power mapping over $\mathbb{F}_{p^n}$, where $n=2m$ and $\gcd(s,p^m+1)=t$. In \cite{kpm-1}, Hu et al. determined the differential spectrum and boomerang spectrum of the power function $f$, where $t=1$. So what…
When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…
A spatially varying blur kernel $h(\mathbf{x},\mathbf{u})$ is specified by an input coordinate $\mathbf{u} \in \mathbb{R}^2$ and an output coordinate $\mathbf{x} \in \mathbb{R}^2$. For computational efficiency, we sometimes write…
Complex field measurements are increasingly becoming the standard for state-of-the-art astronomical instrumentation. Complex field measurements have been used to characterize a suite of ground, airborne, and space-based heterodyne receiver…
This paper gives the pointwise H\"older (or multifractal) spectrum of continuous functions on the interval $[0,1]$ whose graph is the attractor of an iterated function system consisting of $r\geq 2$ affine maps on $\mathbb{R}^2$. These…
In conventional spectral/finite element methods, the triangulation/quadrilateralization of the domain produces many interior edges which require additional DOF. What if we could directly use the original hull without going to…
We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is…