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This study introduces a novel hierarchical divisive clustering approach with stochastic splitting functions (SSFs) to enhance classification performance in multi-class datasets through hierarchical classification (HC). The method has the…
We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with…
A new method ( PI-DFT ) which combines path integrals and density functional theory is proposed as a pathway to many fields of physics. Within path integral theory it is possible to construct particle densities without explicitly…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
Studying $e^-e^+\to W^- W^+$ at the 1loop electroweak (EW) order, we derive very accurate and simple expressions for the four Helicity Conserving (HC) amplitudes, which dominate this process at high energies. The calculations are done in…
Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi's results on $H^{\8}$…
The $H^\infty$-functional calculus is a two-step procedure, introduced by A. McIntosh, that allows the definition of functions of sectorial operators in Banach spaces. It plays a crucial role in the spectral theory of differential…
Ranking groups of researchers is important in several contexts and can serve many purposes such as the fair distribution of grants based on the scientist's publication output, concession of research projects, classification of journal…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…
In HCI, frameworks function as a type of theoretical contribution, often supporting ideation, design, and evaluation. Yet, little is known about how they are actually used, what functions they serve, and which scholarly practices that shape…
We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
The Hilbert-Einstein equations are derived in the formalism employing the imbedding of the space-time into linear 10-dimensional space. An extra antisymmetric tensor field is needed for this task.
We probe the cosmic expansion scenario within the framework of $f(R, L_{m})$ gravity by employing a well-motivated functional form of $f(R, L_{m}) = \frac{R}{2} + L_{m}^{\lambda}$. Specifically, we introduce three novel cosmological models…
The symmetry-adapted-cluster configuration interaction (SAC-CI) method is used for ab initio calculation of electronic structure of HCl+ and HBr+ molecular ions. Potential energy curves (PEC) are obtained for a series of low-lying…
The Equivalence Theorem is commonly used to calculate perturbatively amplitudes involving gauge bosons at energy scales higher than gauge boson masses. However, when the scalar sector is strongly interacting the theory is non-perturbative.…
The PAH family of organic compounds (polycyclic aromatic hydrocarbons), involved in several fields of chemistry, has received particular attention in astrochemistry, where their vibrational spectroscopy, thermodynamic, dynamic, and…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we…