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Deformable image registration is a fundamental task in medical image processing. Traditional optimization-based methods often struggle with accuracy in dealing with complex deformation. Recently, learning-based methods have achieved good…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
In this paper we present a novel approach to interpretable AI inspired by Quantum Field Theory (QFT) which we call the NCoder. The NCoder is a modified autoencoder neural network whose latent layer is prescribed to be a subset of $n$-point…
Effective and accurate characterization and quantification of complex microstructure of a heterogeneous material and its evolution under external stimuli are very challenging, yet crucial to achieving reliable material performance…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…
We compute exact three and four point functions in the W_N minimal models that were recently conjectured to be dual to a higher spin theory in AdS_3. The boundary theory has a large number of light operators that are not only invisible in…
By use of conformal field theory, we discover several exact factorizations of higher-order density correlation functions in critical two-dimensional percolation. Our formulas are valid in the upper half-plane, or any conformally equivalent…
Theory of non-equilibrium Green's function (NGF) provides a practical framework for studying quantum many-body systems out of equilibrium. Extending the previous mean field approach developed for nuclear systems in one dimension with NGF,…
In this short note we publish the analytic quantile function for the Navarro, Frenk & White (NFW) profile. All known published and coded methods for sampling from the 3D NFW PDF use either accept-reject, or numeric interpolation (sometimes…
Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…
We introduce new algorithms for computing non-termination sensitive control dependence (NTSCD) and decisive order dependence (DOD). These relations on control flow graph vertices have many applications including program slicing and compiler…
We propose a simple iterative algorithm to construct the optimal multi-configuration approximation of an $N$-fermion wave function. That is, $M\geq N $ single-particle orbitals are sought iteratively so that the projection of the given wave…
The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…
We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the algorithms are derived, simulation results and error analysis…
Discrete Hahn polynomials (DHPs) and their moments are considered to be one of the efficient orthogonal moments and they are applied in various scientific areas such as image processing and feature extraction. Commonly, DHPs are used as…
This chapter provides a comprehensive review of fundamental concepts related to approximate natural orbital functionals (NOFs), emphasizing their significance in quantum chemistry and physics. Focusing on fermions, the discussion excludes…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
Correlation functions, such as static and dynamic structure factors, offer a versatile approach to analyzing atomic-scale structure and dynamics. By having access to the full dynamics from atomistic simulations, they serve as valuable tools…