James Shipkowski · Zenodo (CERN European Organization for Nuclear Research) · 2026
Constraint–Density Scalar–Tensor Gravity presents a minimal scalar–tensor extension of General Relativity in which spacetime curvature is sourced not only by the matter stress–energy tensor, but also by a covariant scalar field χ interpreted as a constraint–density variable. The theory is formulated within standard covariant field theory using a Jordan-frame action in which the Ricci scalar is nonminimally coupled to a scalar-dependent function F(χ). The action includes a canonical kinetic term with positive-definite coefficient Z(χ) and a scalar potential V(χ). The nonminimal coupling allows spacetime curvature to respond to spatial and temporal variations in the constraint–density field, while the scalar potential enforces a finite viability window, χ_min ≤ χ ≤ χ_max. This ensures internal consistency and recoverability of General Relativity in appropriate limits. Field equations are derived from an action principle, and conditions for stability, ghost avoidance, and classical consistency are discussed. No teleological, observer-dependent, or metaphysical assumptions are introduced. The scalar field χ is treated strictly as a phenomenological covariant degree of freedom; no claim is made regarding its fundamental or ontological status. All equations and derivations are provided in the associated PDF.
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Bohua Sun · Results in Physics · 2018
This article attempts to clarify an issue regarding the proper definition of plastic dislocation density tensor. This study shows that the Ortiz’s and Berdichevsky’s plastic dislocation density tensors are equivalent with each other, but not with Kondo’s one. To fix the problem, we propose a modified version of Kondo’s plastic dislocation density tensor.
Cited by 1Open access
Yifan Peng, Siyao Yang, Yuehaw Khoo et al. · 2024
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Charles H. Conley, Christiane Martin · Journal of Algebra · 2006
Cited by 12
James P. Darby, Dávid Péter Kovács, Ilyes Batatia et al. · Physical Review Letters · 2023
Density-based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modeling, and the visualization and analysis of material datasets. The standard mechanism used to incorporate chemical element information is to create separate densities for each element and form tensor products between them. This leads to a steep scaling in the size of the representation as the number of elements increases. Graph neural networks, which do not explicitly use density representations, escape this scaling by mapping the chemical element information into a fixed dimensional space in a learnable way. By exploiting symmetry, we recast this approach as tensor factorization of the standard neighbour-density-based descriptors and, using a new notation, identify connections to existing compression algorithms. In doing so, we form compact tensor-reduced representation of the local atomic environment whose size does not depend on the number of chemical elements, is systematically convergable, and therefore remains applicable to a wide range of data analysis and regression tasks.
Cited by 38Open access
James Shipkowski · Zenodo (CERN European Organization for Nuclear Research) · 2026
Constraint–Density Scalar–Tensor Gravity presents a minimal scalar–tensor extension of General Relativity in which spacetime curvature is sourced not only by the matter stress–energy tensor, but also by a covariant scalar field χ interpreted as a constraint–density variable. The theory is formulated within standard covariant field theory using a Jordan-frame action in which the Ricci scalar is nonminimally coupled to a scalar-dependent function F(χ). The action includes a canonical kinetic term with positive-definite coefficient Z(χ) and a scalar potential V(χ). The nonminimal coupling allows spacetime curvature to respond to spatial and temporal variations in the constraint–density field, while the scalar potential enforces a finite viability window, χ_min ≤ χ ≤ χ_max. This ensures internal consistency and recoverability of General Relativity in appropriate limits. Field equations are derived from an action principle, and conditions for stability, ghost avoidance, and classical consistency are discussed. No teleological, observer-dependent, or metaphysical assumptions are introduced. The scalar field χ is treated strictly as a phenomenological covariant degree of freedom; no claim is made regarding its fundamental or ontological status. All equations and derivations are provided in the associated PDF.
Cited by 0Open access
Amrit Šorli · viXra · 2009
The study revealed a fluctuating growth trend in the number of publications and citations since 2007. As many as 147 institutions from 13 countries, with a total of 756 authors, have published 202 papers in 76 academic journals. Sichuan University in China and Tang Wenfu have been recognized as the most influential national institution and author. The most frequently published journal is "Pancreas", while the most cited is the "World Journal of Gastroenterology". Commonly used single herbs in this field include Baicalin, Emodin, Rhubarb, and Salvia miltiorrhizae. Frequently used herbal formulations include Da chengqi decoction, Chaiqin chengqi decoction, and Qing yi decoction. Current research hotspots primarily surround concepts like hmgb1, nf-kappab, nfr2, oxidative stress, exosomes, nlrp3, pyroptosis, etc. Potential future research themes could relate to pharmacology, reducing hmgb1, inflammatory response, cell activation, Qing Yi-decoction, etc. This review holds significant guiding importance for clinical and scientific research into TCM treatment for acute pancreatitis in the future.
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Balmer, Paul, Gallauer, Martin · ArXiv.org · 2025
The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology. We prove that patch-dense subsets detect tt-ideals and we prove that any infinite family of tt-functors that detects nilpotence provides such a patch-dense subset. We review several applications and examples in algebra, in topology and in the representation theory of profinite groups.
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Tao Xiang · Cambridge University Press eBooks · 2023
Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.
Cited by 33
Balmer, Paul, Gallauer, Martin · Warwick Research Archive Portal (University of Warwick) · 2025
The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology.We prove that patch-dense subsets detect tt-ideals and we prove that any infinite family of tt-functors that detects nilpotence provides such a patch-dense subset.We review several applications and examples in algebra, in topology and in the representation theory of profinite groups.
Cited by 0Open access
Yifan Peng, Siyao Yang, Yuehaw Khoo et al. · SSRN Electronic Journal · 2025
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Boxiang Wang, Le Zhou, Jian Yang et al. · Statistics and Its Interface · 2024
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Marco Reisert, Henrik Skibbe, Valerij G. Kiselev · Lecture notes in computer science · 2012
Cited by 7
Michael Lubasch, Johanna I. Fuks, Heiko Appel et al. · DIGITAL.CSIC (Spanish National Research Council (CSIC)) · 2013
Trabajo presentado al CECAM Workshop on "Density Functional Theory: learning from the past, looking to the future" celebrado en Berlín (Alemania) del 2 al 5 de Julio de 2013.
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Jiří Ajgl, Ondřej Straka · 2025
Point-mass filters solve Bayesian recursive relations by approximating probability density functions of a system state over grids of discrete points. The approach suffers from the curse of dimensionality. The exponential increase of the number of the grid points can be mitigated by application of low-rank approximations of multidimensional arrays. Tensor train decompositions represent individual values by the product of matrices. This paper focuses on selected issues that are substantial in state estimation. Namely, the contamination of the density approximations by negative values is discussed first. Functional decompositions of quadratic functions are compared with decompositions of discretised Gaussian densities next. In particular, the connection of correlation with tensor train ranks is explored. Last, the consequences of interpolating the density values from one grid to a new grid are analysed.
Cited by 0
The Conference on Uncertainty in Artificial Intelligence (UAI) 2021 2021, Novikov, Georgii, Oseledets, Ivan et al. · Underline Science Inc. · 2021
Full paper: https://www.auai.org/uai2021/pdf/uai2021.512.pdf Abstract: Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter selection and are often prone to instabilities during training and inference. We propose a new efficient tensor train-based model for density estimation (TTDE). Such density parametrization allows exact sampling, calculation of cumulative and marginal density functions, and partition function. It also has very intuitive hyperparameters. We develop an efficient non-adversarial training procedure for TTDE based on the Riemannian optimization. Experimental results demonstrate the competitive performance of the proposed method in density estimation and sampling tasks, while TTDE significantly outperforms competitors in training speed. Authors: Georgii Novikov (Skolkovo Institute of Science and Technology); Maxim Panov (Skolkovo Institute of Science and Technology); Ivan Oseledets (Skolkovo Institute of Science and Technology)
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Julia Hörrmann, Daniel Hug, Michael A. Klatt et al. · arXiv (Cornell University) · 2013
A stationary Boolean model is the union set of random compact particles which are attached to the points of a stationary Poisson point process. For a stationary Boolean model with convex grains we consider a recently developed collection of shape descriptors, the so called Minkowski tensors. By combining spatial and probabilistic averaging we define Minkowski tensor densities of a Boolean model. These densities are global characteristics of the union set which can be estimated from observations. In contrast local characteristics like the mean Minkowski tensor of a single random particle cannot be observed directly, since the particles overlap. We relate the global to the local properties by density formulas for the Minkowski tensors. These density formulas generalize the well known formulas for intrinsic volume densities and are obtained by applying results from translative integral geometry. For an isotropic Boolean model we observe that the Minkowski tensor densities are proportional to the intrinsic volume densities, whereas for a non-isotropic Boolean model this is usually not the case. Our results support the idea that the degree of anisotropy of a Boolean model may be expressed in terms of the Minkowski tensor densities. Furthermore we observe that for smooth grains the mean curvature radius function of a particle can be reconstructed from the Minkowski tensor densities. In a simulation study we determine numerically Minkowski tensor densities for non-isotropic Boolean models based on ellipses and on rectangles in two dimensions and find excellent agreement with the derived analytic density formulas. The tensor densities can be used to characterize the orientational distribution of the grains and to estimate model parameters for non-isotropic distributions.
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Fatin El Ajjouri · Zenodo (CERN European Organization for Nuclear Research) · 2025
Dislocations create elastic fields, detectable by surface-sensitive techniques like EBSD and ECCI. In this report, a field dislocation mechanics (FDM) model to compare surface and bulk dislocation signatures in GaN layers on Si substrates is used. Significant differences between surface and bulk fields highlight potential misinterpretations in surface-based dislocation characterization. Metrics for accurate dislocation characterization and perform virtual ECCI are established.
Cited by 0Open access
Jiří Ajgl, Ondřej Straka · ArXiv.org · 2025
Point-mass filters solve Bayesian recursive relations by approximating probability density functions of a system state over grids of discrete points. The approach suffers from the curse of dimensionality. The exponential increase of the number of the grid points can be mitigated by application of low-rank approximations of multidimensional arrays. Tensor train decompositions represent individual values by the product of matrices. This paper focuses on selected issues that are substantial in state estimation. Namely, the contamination of the density approximations by negative values is discussed first. Functional decompositions of quadratic functions are compared with decompositions of discretised Gaussian densities next. In particular, the connection of correlation with tensor train ranks is explored. Last, the consequences of interpolating the density values from one grid to a new grid are analysed.
Cited by 0Open access
Fatin El Ajjouri · Zenodo (CERN European Organization for Nuclear Research) · 2025
Dislocations create elastic fields, detectable by surface-sensitive techniques like EBSD and ECCI. In this report, a field dislocation mechanics (FDM) model to compare surface and bulk dislocation signatures in GaN layers on Si substrates is used. Significant differences between surface and bulk fields highlight potential misinterpretations in surface-based dislocation characterization. Metrics for accurate dislocation characterization and perform virtual ECCI are established.
Cited by 0Open access