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A space-filling curve (SFC) maps points in a multi-dimensional space to one-dimensional points by discretizing the multi-dimensional space into cells and imposing a linear order on the cells. This way, an SFC enables the indexing of…
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commutation relations between double-row operators, we prove a skew…
In this study, we investigate the potential of mark-weighted angular correlation functions (MACFs), which integrate $\beta$-cosmic-web classification with angular correlation function analysis to improve cosmological constraints. Using SDSS…
We calculate four-point correlation functions of two weight-2 and two weight-3 1/2-BPS operators in \mathcal{N}=4 SYM in the large N limit in supergravity approximation. By the AdS/CFT conjecture, these operators are dual to AdS…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…
The self-attention mechanism, now central to deep learning architectures such as Transformers, is a modern instance of a more general computational principle: learning and using pairwise affinity matrices to control how information flows…
Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many of the statistical methods used to account for autocorrelation can be viewed as regression models that include basis…
A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising…
N-Point Correlation Functions, usually with N = 2, 3, and their Fourier-space analogs power spectrum and bispectrum, are major tools used in cosmology to capture the clustering of large-scale structure. We outline how the clustering these…
We use the correspondence between scalar field theory on AdS and induced conformal field theory on its boundary to calculate correlation functions of logarithmic conformal field theory in arbitrary dimensions.Our calculations utilize the…
For stationary time series, it is common to use the plots of partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of such processes. To our best knowledge, such analogs for non-stationary…
After a brief outline of general aspects of conformal field theories in coordinate space, in a first part we review the solution of the conformal constraints of three- and four-point functions in momentum space in dimensions $d\geq 2$, in…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
The affinity dimension is a number associated to an iterated function system of affine maps, which is fundamental in the study of the fractal dimensions of self-affine sets. De-Jun Feng and the author recently solved a folklore open…
Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in…
We propose a new autocorrelation measure for functional time series that we term spherical autocorrelation. It is based on measuring the average angle between lagged pairs of series after having been projected onto the unit sphere. This new…
The design of training objective is central to training time-series forecasting models. Existing training objectives such as mean squared error mostly treat each future step as an independent, equally weighted task, which we found leading…
We apply the numerical bootstrap program to chiral operators in four-dimensional ${\mathcal N}=2$ SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special…
A new method for local and global explanation of the machine learning black-box model predictions by tabular data is proposed. It is implemented as a system called AFEX (Attention-like Feature EXplanation) and consisting of two main parts.…
We developed two new alternatives to signature-based, spatial autoregressive models. In a simulation study, we found that the new models performed at least as well as existing approaches but presented shorter computation times. We then used…