Related papers: Benford Analysis: A useful paradigm for spectrosco…
We study the individual digits for the absolute value of the characteristic polynomial for the Circular $\beta$-Ensemble. We show that, in the large $N$ limit, the first digits obey Benford's Law and the further digits become uniformly…
Model-independent searches in particle physics aim at completing our knowledge of the universe by looking for new possible particles not predicted by the current theories. Such particles, referred to as signal, are expected to behave as a…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
Nuclear Magnetic Resonance (NMR) spectra are widely used in metabolomics to obtain profiles of metabolites dissolved in biofluids such as cell supernatants. Methods for estimating metabolite concentrations from these spectra are presently…
Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can…
Both sampling a time-varying signal, and its spectral analysis are activities subjected to theoretically compelling, such as Shannon's theorem and the objectively limiting of the frequency's resolution. Usually, the signals' spectra are…
Data mining is wide spreading its applications in several areas. There are different tasks in mining which provides solutions for wide variety of problems in order to discover knowledge. Among those tasks association mining plays a pivotal…
Just as semantic hashing can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for…
The inverse eigenvalue problem of a graph studies the real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of the graph. The strong spectral property (SSP) is an important tool for this problem. This note…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
The high performance of denoising diffusion models for image generation has paved the way for their application in unsupervised medical anomaly detection. As diffusion-based methods require a lot of GPU memory and have long sampling times,…
A universal First-Letter Law (FLL) is derived and described. It predicts the percentages of first letters for words in novels. The FLL is akin to Benford's law (BL) of first digits, which predicts the percentages of first digits in a data…
We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the…
Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in…
For arbitrary Borel probability measures with compact support on the real line, characterizations are established of the best finitely supported approximations, relative to three familiar probability metrics (Levy, Kantorovich, and…
In relation to recent experimental data [1], we develop a theory framework for demonstrating the feasibility of detecting sharp Nuclear Magnetic Resonance (NMR) oscillations in a real time ESR data. The procedure is to follow real time…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely…
The spectrogram is a classical DSP tool used to view signals in both time and frequency. Unfortunately, the Heisenberg Uncertainty Principal limits our ability to use them for detecting and measuring narrowband signal modulation in wideband…