Related papers: Benford Analysis: A useful paradigm for spectrosco…
In this paper, we propose a Bayesian spectral deconvolution method for absorption spectra. In conventional analysis, the noise mechanism of absorption spectral data is never considered appropriately. In that analysis, the least-squares…
A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…
Deep graph models (e.g., graph neural networks and graph transformers) have become important techniques for leveraging knowledge across various types of graphs. Yet, the neural scaling laws on graphs, i.e., how the performance of deep graph…
The detection reliability of weak signals is a critical issue in many astronomical contexts and may have severe consequences for determining number counts and luminosity functions, but also for optimising the use of telescope time in…
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…
In this paper, we establish a new law of large numbers with the rate of convergence for special partial sums in a probability space. The proof relies on nonlinear expectation theory, as the uncertainty of random variables in the special…
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…
This article presents a modern deterministic framework for the study of leading significant digit distributions in numerical data. Rather than relying on traditional probabilistic or mixture-based explanations, we demonstrate that the…
We study multi-digit correlations in Benford sequences b^n for integer bases 2 <= b <= 1000, measuring dependence via conditional mutual information (CMI). A resonance ratio derived from the continued fraction expansion of log_10(b)…
This paper explores a real-world fundamental theme under a data science perspective. It specifically discusses whether fraud or manipulation can be observed in and from municipality income tax size distributions, through their aggregation…
We examine the relationship between two different types of ranked data, frequencies and magnitudes. We consider data that can be sorted out either way, through numbers of occurrences or size of the measures, as it is the case, say, of moon…
Nuclear magnetic resonance (NMR) is a powerful spectroscopic technique that is sensitive to the local atomic structure of matter. Computational predictions of NMR parameters can help to interpret experimental data and validate structural…
This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameter-dependent normalising constant of the Bingham distribution,…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
In pattern recognition, digit recognition has always been a very challenging task. This paper aims to extracting a correct feature so that it can achieve better accuracy for recognition of digits. The applications of digit recognition such…
The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also…