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In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown…
Throughput optimization of optical communication systems is a key challenge for current optical networks. The use of gain-flattening filters (GFFs) simplifies the problem at the cost of insertion loss, higher power consumption and…
In this paper we analyze a simple spectral method (EIG1) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given two matrices $A$ and $B$, we compute $v_1$ and $v'_1$ two corresponding leading…
We propose and explore the potential of a method to extract high signal-to-noise (S/N) integrated spectra related to physical and/or morphological regions on a 2-dimensional field using Integral Field Spectroscopy (IFS) observations by…
Fabry-P\'erot interferometers (FPIs) have become very popular in solar observations because they offer a balance between cadence, spatial resolution, and spectral resolution through a careful design of the spectral sampling scheme according…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
Photon counting lidar has become an invaluable tool for 3D depth imaging due to the fine-precision it can achieve over long ranges. However, high frame rate, high resolution lidar devices produce an enormous amount of time-of-flight (ToF)…
We have developed observation control software for the Immersion GRating INfrared Spectrometer (IGRINS) slit-viewing camera module, which maintains the position of an astronomical target on the spectroscopic slit. It is composed of several…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
The Bayesian gravitational shear estimation algorithm developed by Bernstein and Armstrong (2014) can potentially be used to overcome multiplicative noise bias and recover shear using very low signal-to-noise ratio (S/N) galaxy images. In…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…
With the large amounts of spectroscopic data available today and the very large surveys to come (e.g. Gaia), the need for automatic data analysis software is unquestionable. We thus developed an automatic spectra analysis program for the…
Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad…
Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…
Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data…
The SIRTF InfraRed Spectrograph (IRS) is faced with many of the same calibration challenges that were experienced in the ISO SWS calibration program, owing to similar wavelength coverage and overlapping spectral resolutions of the two…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
Graph Spectral Sparsification (GSS) identifies an ultra-sparse subgraph, or sparsifier, whose Laplacian matrix closely approximates the spectral properties of the original graph, enabling substantial reductions in computational complexity…
Graph neural networks (GNNs) are commonly used in semi-supervised settings. Previous research has primarily focused on finding appropriate graph filters (e.g. aggregation methods) to perform well on both homophilic and heterophilic graphs.…