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Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in…
Power spectral densities are a common, convenient, and powerful way to analyze signals. So much so that they are now broadly deployed across the sciences and engineering---from quantum physics to cosmology, and from crystallography to…
In this work, we consider the Fokker-Planck equation of the Nonlinear Noisy Leaky Integrate-and-Fire (NNLIF) model for neuron networks. Due to the firing events of neurons at the microscopic level, this Fokker-Planck equation contains…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
We propose a new model to account for the main structural characteristics of rock fracture networks (RFNs). The model is based on a generalization of the random neighborhood graphs to consider fractures embedded into rectangular spaces. We…
Understanding deep learning is increasingly emergent as it penetrates more and more into industry and science. In recent years, a research line from Fourier analysis sheds lights on this magical "black box" by showing a Frequency Principle…
We study the dynamics of dephasing in a quantum two-level system by modeling both 1/f and high-frequency noise by random telegraph processes. Our approach is based on a so-called spin-fluctuator model in which a noisy environment is modeled…
We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…
Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and…
A new method of accessing information on the symmetry free energy from yields of fragments produced in Fermi-energy heavy-ion collisions is proposed. Furthermore, by means of quantum fluctuation analysis techniques, correlations between…
The scanning electron microscope (SEM) recordings of dynamic nano-electromechanical systems (NEMS) are difficult to analyze due to the noise caused by low frame rate, insufficient resolution and blurriness induced by applied electric…
Mass spectrometry (MS) stands as a cornerstone analytical technique for molecular identification, yet de novo structure elucidation from spectra remains challenging due to the combinatorial complexity of chemical space and the inherent…
A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. Quantitative measurements of these rates are crucial for optimizing…
Anomaly detection is a key task across domains such as industry, healthcare, and cybersecurity. Many real-world anomaly detection problems involve analyzing multiple features over time, making time series analysis a natural approach for…
Electron energy loss spectroscopy is consolidating as a powerful tool to explore electronic (as well as vibrational) excitations of matter, including molecules. Performed in a scanning transmission electron microscope, this technique is…
Spin noise spectroscopy is an optical technique which can probe spin resonances non-perturbatively. First applied to atomic vapours, it revealed detailed information about nuclear magnetism and the hyperfine interaction. In solids, this…
Elastic light scattering has been extensively used to study samples showing a non uniform refraction index on lengthscales from a fraction of a micrometer to a fraction of a millimeter. Typically, a wide laser beam is sent through the…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
Fourier ptychographic microscopy (FPM) is a recently proposed computational imaging technique with both high resolution and wide field-of-view. In current FP experimental setup, the dark-field images with high-angle illuminations are easily…
Qubit noise spectroscopy (QNS) is a valuable tool for both the characterization of a qubit's environment and as a precursor to more effective qubit control to improve qubit fidelities. Existing approaches to QNS are what the classical…