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In critical lattice models, distance ($r$) dependent correlation functions contain power laws $r^{-2\Delta}$ governed by scaling dimensions $\Delta$ of an underlying continuum field theory. In Monte Carlo simulations, the leading dimensions…
We present a detailed study of the applications of two stochastic approaches, stochastic optimization method (SOM) and stochastic analytical inference (SAI), to extract spectral functions from Euclidean correlation functions. SOM has the…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking…
Extracting pulsive temporal patterns from a small dataset without their repetition or singularity shows significant importance in manufacturing applications but does not sufficiently attract scientific attention. We propose to quantify how…
We illustrate a technique for fitting lattice QCD correlators to sums of exponentials that is significantly faster than traditional fitting methods --- 10--40 times faster for the realistic examples we present. Our examples are drawn from a…
We present results for lattice QCD in the limit of infinite gauge coupling on a discrete spatial but continuous Euclidean time lattice. A worm type Monte Carlo algorithm is applied in order to sample two-point functions which gives access…
Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
We present a new supervised deep-learning approach to the problem of the extraction of smeared spectral densities from Euclidean lattice correlators. A distinctive feature of our method is a model-independent training strategy that we…
The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the Wilson loop. General arguments tell us that the lowest lying spectral peak encodes, through its position and shape, the…
As semiconductor devices continue to scale down, process vari- ations become more relevant for circuit design. Facing such variations, statistical static timing analysis is introduced to model variations more accurately so that the…
We present a new method to calculate moments of parton distribution functions of any order with lattice QCD computations. This method leverages the gradient flow for fermion and gauge fields. The flowed matrix elements of twist-2 operators…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…
The analysis of lattice simulation correlation function data is notoriously hindered by the ill-conditioning of the Euclidean time covariance matrix. Additionally, the isolation of a single physical state in such functions is generally…
In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of…
One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically…
Lattice Field theory allows to extract properties of particles in strongly coupled quantum field theories by studying Euclidean vacuum expectation values. When estimated from numerical Monte Carlo simulations these are typically affected by…