Geometric Framework Research Articles

The Geometric Framework for Nutrition and Its Application to Rodent Models.

Rodents have been the primary model for mammalian nutritional physiology for decades. Despite an extensive body of literature, controversies remain around the effects of specific nutrients and total energy intake on several aspects of nutritional biology, even in this well-studied model. One approach that is helping to bring clarity to the field is the geometric framework for nutrition (GFN). The GFN is a multidimensional paradigm that can be used to conceptualize nutrition and nutritional effects, design experiments, and interpret results. To date, more than 30 publications have applied the GFN to data from rodent models of nutrition. Here we review the major conclusions from these studies. We pay particular attention to the effects of macronutrients on satiety, glucose metabolism, lifespan and the biology of aging, reproductive function, immune function, and the microbiome. We finish by highlighting several knowledge gaps that became evident upon reviewing this literature.

Geometric Relational Framework for General‐Relativistic Gauge Field Theories

AbstractIt is recalled how relationality arises as the core insight of general‐relativistic gauge field theories from the articulation of the generalized hole and point‐coincidence arguments. Hence, a compelling case for a manifestly relational framework ensues naturally. A formulation for such a framework is proposed, based on a significant development of the dressing field method of symmetry reduction. A version for the group of automorphisms of a principal bundle over a manifold is first developed, as it is the most natural and elegant, and as hosts all the mathematical structures relevant to general‐relativistic gauge field theory. However, as the standard formulation is local, on , the relational framework for local field theory is then developed. The generalized point‐coincidence argument is manifestly implemented, whereby the physical field‐theoretical degrees of freedoms co‐define each other and define, coordinatize, the physical spacetime itself. Applying the framework to General Relativity, relational Einstein equations are obtained, encompassing various notions of “scalar coordinatization” à la Kretschmann–Komar and Brown–Kuchař.

Integration of molecular coarse-grained model into geometric representation learning framework for protein-protein complex property prediction

Structure-based machine learning algorithms have been utilized to predict the properties of protein-protein interaction (PPI) complexes, such as binding affinity, which is critical for understanding biological mechanisms and disease treatments. While most existing algorithms represent PPI complex graph structures at the atom-scale or residue-scale, these representations can be computationally expensive or may not sufficiently integrate finer chemical-plausible interaction details for improving predictions. Here, we introduce MCGLPPI, a geometric representation learning framework that combines graph neural networks (GNNs) with MARTINI molecular coarse-grained (CG) models to predict PPI overall properties accurately and efficiently. Extensive experiments on three types of downstream PPI property prediction tasks demonstrate that at the CG-scale, MCGLPPI achieves competitive performance compared with the counterparts at the atom- and residue-scale, but with only a third of computational resource consumption. Furthermore, CG-scale pre-training on protein domain-domain interaction structures enhances its predictive capabilities for PPI tasks. MCGLPPI offers an effective and efficient solution for PPI overall property predictions, serving as a promising tool for the large-scale analysis of biomolecular interactions.

Geometric deep learning framework for de novo genome assembly.

The critical stage of every de novo genome assembler is identifying paths in assembly graphs that correspond to the reconstructed genomic sequences. The existing algorithmic methods struggle with this, primarily due to repetitive regions causing complex graph tangles, leading to fragmented assemblies. Here, we introduce GNNome, a framework for path identification based on geometric deep learning that enables training models on assembly graphs without relying on existing assembly strategies. By leveraging only the symmetries inherent to the problem, GNNome reconstructs assemblies from PacBio HiFi reads with contiguity and quality comparable to those of the state-of-the-art tools across several species. With every new genome assembled telomere-to-telomere, the amount of reliable training data at our disposal increases. Combining the straightforward generation of abundant simulated data for diverse genomic structures with the AI approach makes the proposed framework a plausible cornerstone for future work on reconstructing complex genomes with different ploidy and aneuploidy degrees. To facilitate such developments, we make the framework and the best-performing model publicly available, provided as a tool that can directly be used to assemble new haploid genomes.

Lensing Point-spread Function of Coherent Astrophysical Sources and Nontrivial Wave Effects

Most research on astrophysical lensing has been conducted using the geometric optics framework, where there exists a clear concept of lensing images. However, wave optics effects can be important for coherent sources, e.g., pulsars, fast radio bursts, and gravitational waves observed at long wavelengths. There, the concept of lensing images needs an extension. We introduce the concept of the “lensing point-spread function” (LPSF), the smoothed flux density distribution of a coherent point source after being lensed, as a generalization of the lensing image concept at finite frequencies. The frequency-dependent LPSF captures the gradual change of the flux density distribution of the source from discrete geometric images at high frequencies to a smooth distribution at low frequencies. It complements other generalizations of lensing images, notably the imaginary images and the Lefschetz thimbles. Being a footprint of a lensing system, the LPSF is useful for theoretical studies of lensing. Using the LPSF, we identify a frequency range with nontrivial wave effects, where both geometric optics and perturbative wave optics fail, and determine this range to be ∣κ∣−1 ≲ ν ≲ 10, with κ and ν being the dimensionless lens amplitude and the reduced observing frequency, respectively. Observation of LPSFs with nontrivial wave effects requires either very close-by lenses or very large observing wavelengths. The potential possibilities are the lensing of gravitational waves, the plasma lensing of Milky Way pulsars, and lensing by the solar gravitational lens.

Symmetry Preservation in Hamiltonian Systems: Simulation and Learning

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system respecting its dynamics and, as a consequence, Noether’s theorem, conserved quantities are observed. We propose to simulate and learn the mappings of interest through the construction of G-invariant Lagrangian submanifolds, which are pivotal objects in symplectic geometry. A notable property of our constructions is that the simulated/learned dynamics also preserves the same conserved quantities as the original system, resulting in a more faithful surrogate of the original dynamics than non-symmetry aware methods, and in a more accurate predictor of non-observed trajectories. Furthermore, our setting is able to simulate/learn not only Hamiltonian flows, but any Lie group-equivariant symplectic transformation. Our designs leverage pivotal techniques and concepts in symplectic geometry and geometric mechanics: reduction theory, Noether’s theorem, Lagrangian submanifolds, momentum mappings, and coisotropic reduction among others. We also present methods to learn Poisson transformations while preserving the underlying geometry and how to endow non-geometric integrators with geometric properties. Thus, this work presents a novel attempt to harness the power of symplectic and Poisson geometry toward simulating and learning problems.

Transverse energy absorption performance of sandwich tubes with various origami foldcores

Nowadays, composite sandwich tubes are extensively utilized in the civil and aerospace industries due to their superior strength-to-weight mechanical properties. Origami-based core offers a large enhancement of the mechanical properties, yet little study research focuses on the effect of various foldcore configurations on the transverse mechanical properties of sandwich tubes, necessitating the design method for applications. This study introduces an innovative approach by incorporating origami into the composite sandwich core to enhance the transverse energy absorption capacity. The quasi-static transverse mechanical properties of carbon fibre-reinforced polymer (CFRP) sandwich tubes with foldcores are studied under three-point bending-like local compression and transverse structural compression. A systematic geometric design framework and numerical modelling technique are provided. By integrating finite element analysis and experiments, the research investigates the effects of various origami foldcore configurations and geometric parameters on transverse energy absorption capacity. The experiment setup is provided by sandwich tubular specimens with a full-diamond configuration as the foldcore. The cylindrical tubes (foldcore) of the sandwich structures were manufactured using four plies [0°]4 of T700 (T300) woven CFRP with the hot press moulding (vacuum bag using female and male moulds) technique respectively. Then, the parametric study and damage mode analysis of eight different foldcore patterns (axial Miura, circumferential Miura, diamond, Kresling, and their curved-creased counterparts) were studied. The results showed the superior energy absorption performance of the sandwich tube with Miura-pattern foldcore over the origami-pattern counterparts, nested tube, and traditional honeycomb sandwich tube with CFRP or aluminium-made cores. Therefore, the structural parameters optimisation of the Miura pattern tube was carried out by the Response Surface method (RSM) and a design strategy for increasing the energy absorption capacity was found. The findings offer guidance for designing high-specific energy absorption tubular structures for future advanced engineering applications.

NLOphoric unsymmetrically substituted D-π-A benzodifuranone dyes: Density functional theory, time dependent-density functional theory, and non-linear optical studies

The linear and non-linear optical properties of thirty-five unsymmetrically substituted compounds are studied using density functional theory and time-dependent density functional theory methods (B3LYP/6311++G(d,p), CAM-B3LYP/6311++G(d,p) and M06-2X/6311++G(d,p)). A comparable set of functionals is also used to investigate vertical excitation. It is observed that the inclusion of the nitrogen-substituted electron-donating group along with the electron-withdrawing group led to more red-shifted absorption maxima and exhibited an excellent (non-linear optical) NLO response. The geometrical framework, dipole moment, and other descriptors, HOMO-LUMO energy gaps, linear polarizability, first-order and second-order hyperpolarizability are calculated to investigate the effect of different electron donating and accepting substituents on the NLO properties of benzodifuranone chromophores. In cases where nitrogen substituents are added, the electron density is more widely spread throughout the donor in HOMO and more displaced to the acceptor in LUMO. The computed first-order and second-order hyperpolarizability values and decreasing HOMO-LUMO energy gaps in disubstituted nitrogen-containing compounds show that 1a-1e, 4a-4e, 5a-5e are promising candidates in all functionals for better NLO properties.

Predictive Framework for Flow Reversals and Excursions in Turbulence.

We present a dynamical framework for intermittent reversals and excursions (R&Es) of large-scale circulations in turbulence. We show that R&Es can occur when turbulent trajectories in phase space shadow invariant manifolds of certain unstable periodic orbits (UPOs). Consequently, substantial flow reorganization and extreme fluctuations in flow metrics observed during R&Es can be reconstructed by splicing the unstable manifolds of such dynamically relevant UPOs. Using this geometrical framework, we predict imminent R&Es and preemptively avert these extreme events using closed-loop control.

Device response principles and the impact on energy resolution of epitaxial quantum dot scintillators with monolithic photodetector integration

Epitaxial quantum dot (QD) scintillator crystals with picosecond-scale timing and high light yield have been created for medical imaging, high energy physics and national security applications. Monolithic photodetector (PD) integration enables the sensing of photons generated within the waveguiding crystal and allows a wide range of scintillator-photodetector coupling geometries. Until recently, these doubly novel devices have suffered from complex, high variance responses to monoenergetic sources which significantly reduces their precision and accuracy. The principles governing the overall device response have now been discerned and embodied by an expression derived within a geometrical optics framework which considers optical properties, surface roughness and photodetector coupling geometry. Response variation due to these factors was sufficiently reduced to obtain material-related energy resolution values of 2.4% with alpha particles. These findings place energy resolution alongside luminescence timescale, photon yield, and radiation hardness as outstanding properties of these engineered materials.

Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation

We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such a term is that the Legendre transformation is an affine, instead of linear, bundle isomorphism between the tangent and cotangent bundles of the configuration space and some care is needed in the development of the geometric formalism. At the end of the day, the affine nature of the Legendre transform is reflected in the affine dependence of the brackets that we construct on the momentum variables. Our study is motivated by a wide class of nonholonomic systems involving rigid bodies with internal rotors which are of interest in control. Our construction provides a natural geometric framework for the (known) Hamiltonisations of the gyrostatic generalisations of the Suslov and Chaplygin sphere problems.

A geometric framework for asymptoticity and expansivity in topological dynamics

In this paper we develop a geometric framework to address asymptoticity and nonexpansivity in topological dynamics when the acting group is second countable and locally compact. As an application, we show extensions of Schwartzman’s theorem in this context. Also, we get new results when the acting group is Z d {\mathbb Z}^d : any half-space of R d \mathbb {R}^d contains a vector defining a (oriented) nonexpansive direction in the sense of Boyle and Lind. Finally, we deduce rigidity properties of distal Cantor systems.

Application of geometric deep learning in disease-gene relationship prediction

The correlation between diseases and genetic factors represents a pivotal challenge in the biomedical field, often conceptualized as a task of link prediction. Conventional methods employed for prediction, such as statistical models and various machine learning algorithms, frequently fall short in terms of accuracy when confronted with the intricacies of biological network data. These methods also tend to inadequately represent the complex relationships inherent in such data. In contrast, recent advances in geometric deep learning have introduced a powerful tool within artificial intelligence, particularly adept at processing non-Euclidean data structures. This study delves into the potential of leveraging geometric deep learning techniques to enhance the prediction of disease-gene associations. Initially, we conduct a thorough review of existing research related to link prediction, encompassing both traditional approaches and contemporary methods grounded in deep learning. Subsequently, we propose a geometric deep learning framework, incorporating Graph Convolutional Networks (GCN) and Graph Auto-Encoder (GAE), to develop and assess our predictive model. The results of our experiments demonstrate that the proposed geometric deep learning model surpasses conventional techniques in accurately predicting disease-gene associations. In conclusion, we evaluate the implications of our findings, discuss their practical applications in the biomedical domain, and suggest possible avenues for future research.

Cosmological tests of the dark energy models in Finsler-Randers space-time

The Finsler-Randers space-time offers a novel perspective on cosmic dynamics, departing from the constraints of General Relativity. This paper thoroughly investigates two dark energy models resulting from the parametrization of H within this geometric framework. We have conducted some geometrical and physical analysis of the dark energy models in Finslerian geometry. First, we have derived the field equations governing the universe's evolution within the Finsler-Randers formalism, incorporating the presence of dark energy. Through this, we explore its implications on cosmological phenomena, including cosmic expansion, late-time behavior of the universe, cosmological phase transition, and a few more. Also, we employ observational data such as Cosmic Chronometer, Supernovae, Gamma-Ray Bursts, Quasar, and baryon acoustic oscillations to constrain the parameters associated with dark energy in the Finsler-Randers universe. Comparing theoretical predictions with empirical observations, we assess the model viability and discern any deviations from the standard ΛCDM cosmology. Our findings offer intriguing insights into the nature of dark energy within this alternative gravitational framework, providing a deeper understanding of its role in shaping cosmic evolution. The implications of our results extend to fundamental cosmology, hinting at new avenues for research to unravel the mysteries surrounding dark energy and the geometric structure of the universe within non-standard gravitational theories.

MuToN Quantifies Binding Affinity Changes upon Protein Mutations by Geometric Deep Learning.

Assessing changes in protein-protein binding affinity due to mutations helps understanding a wide range of crucial biological processes within cells. Despite significant efforts to create accurate computational models, predicting how mutations affect affinity remains challenging due to the complexity of the biological mechanisms involved. In the present work, a geometric deep learning framework called MuToN is introduced for quantifying protein binding affinity change upon residue mutations. The method, designed with geometric attention networks, is mechanism-aware. It captures changes in the protein binding interfaces of mutated complexes and assesses the allosteric effects of amino acids. Experimental results highlight MuToN's superiority compared to existing methods. Additionally, MuToN's flexibility and effectiveness are illustrated by its precise predictions of binding affinity changes between SARS-CoV-2 variants and the ACE2 complex.

A-priori framework of viscosity and ionic conductivity estimation of ionogel

A-priori framework has been developed to estimate the viscosity and ionic conductivity of ionogel. Six imidazolium-class of ionic liquids (ILs) form ionogels with tetraethyl orthosilicate (TEOS) matrix. Group contribution parameters of TEOS are estimated with the fitting of the density dataset in the predictive Soave−Redlich−Kwong equation of state with the NSM1 alpha function model. Later the parameters are used to estimate the critical property of ILs and TEOS. These facilitate the formulation of the predictive framework of viscosity estimation through the geometric similitude concept with the Valderrama-Patel-Teja cubic equation of state. Later the viscosity of ionogels is estimated through a mixture form of geometric similitude framework as well as the Arrhenius model. Additionally, the estimated viscosities from both frameworks are used to estimate the ionic conductivities of ionogels. The compositional and temperature variance of ionic conductivity reveals the superior ionic conductivity of tetrafluoroborate-based ionogels than the bis(trifluoromethanesulfonyl) imide-based counterparts. Both models estimate the decrease in viscosity as well as incremental trends in ionic conductivity with temperature. However, the concentration of IL rather plays a different trend in the estimation model as well as the class of IL. Such a priori framework shall lead to the design of the ionogels focusing on the physicochemical properties.

The association between dietary patterns before pregnancy and gestational diabetes mellitus: a matched case-control study in China.

We aimed to explore the relationship between dietary patterns and gestational diabetes mellitus (GDM) during pre-pregnancy six months using principal component analysis (PCA) and the geometric framework for nutrition (GFN). We conducted a case-control study that included 210 GDM pregnant women and 210 controls. The dietary intake of all participants was assessed by a validated semi-quantitative food frequency questionnaire (FFQ). Major dietary patterns were extracted by PCA. A conditional logistic regression model was used to determine whether specific dietary patterns are associated with the risk of GDM. Meanwhile, the relationship between dietary patterns and GDM was visualized using GFN. Four major dietary patterns were identified: "protein-rich pattern," "plant-based pattern," "oil-pickles-desserts pattern," and "cereals-nuts pattern." After adjustment for confounders, the "plant-based pattern" was associated with decreased risk of GDM (Q4 vs. Q1: OR = 0.01, 95% CI: 0.00-0.08), whereas no significant association was found in other dietary patterns. Moreover, there was no dietary intake of ice cream cones and deep-fried dough sticks for the population, which would produce fewer patients with GDM. Deep-fried dough sticks had statistically significant differences in the case and control groups (p < 0.001), while ice cream cones had the opposite result. The "plant-based pattern" may reduce the risk of GDM. Besides, although the "cereals-nuts pattern" had no association with GDM risk, avoiding the intake of deep-fried dough sticks could decrease GDM risk.

Symmetries in Riemann-Cartan Geometries

Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics including quantum gravity theories and have many important differences when compared to Riemannian geometries. One notable difference, is the number of symmetries for a Riemann-Cartan geometry is potentially smaller than the number of Killing vector fields for the metric. In this paper, we will review the investigation of symmetries in Riemann-Cartan geometries and the mathematical tools used to determine geometries that admit a given group of symmetries. As an illustration, we present new results by determining all static spherically symmetric and all stationary spherically symmetric Riemann-Cartan geometries. Furthermore, we have determined the subclasses of spherically symmetric Riemann-Cartan geometries that admit a seven-dimensional group of symmetries.

Energy Localization and Topological Defect in Spherical Non‐Hermitian Topolectrical Circuits

AbstractThis work examines the energy localization in non‐Hermitian systems, with a particular focus on the influence of topological defects in spherical models. Alterations in the mode distribution are explored within non‐Hermitian Su‐Schrieffer‐Heeger (SSH) chains affected by these defects, utilizing the Maximum Skin Corner Weight (MaxWSC) metric. An innovative spherical model is introduced, created by segmenting spheres into 1D chain structures, to study the non‐Hermitian skin effect (NHSE) within a spherical geometric framework. Experimental validations conducted on Printed Circuit Boards (PCBs) corroborate the theoretical insights. These findings not only substantiate the theoretical approach but also illustrate the capability of engineered circuit systems to mimic complex non‐Hermitian phenomena, highlighting the utility of spherical geometries in exploring NHSE and topological phenomena in non‐Hermitian systems.

A Point Cloud Graph Neural Network for Protein-Ligand Binding Site Prediction.

Predicting protein-ligand binding sites is an integral part of structural biology and drug design. A comprehensive understanding of these binding sites is essential for advancing drug innovation, elucidating mechanisms of biological function, and exploring the nature of disease. However, accurately identifying protein-ligand binding sites remains a challenging task. To address this, we propose PGpocket, a geometric deep learning-based framework to improve protein-ligand binding site prediction. Initially, the protein surface is converted into a point cloud, and then the geometric and chemical properties of each point are calculated. Subsequently, the point cloud graph is constructed based on the inter-point distances, and the point cloud graph neural network (GNN) is applied to extract and analyze the protein surface information to predict potential binding sites. PGpocket is trained on the scPDB dataset, and its performance is verified on two independent test sets, Coach420 and HOLO4K. The results show that PGpocket achieves a 58% success rate on the Coach420 dataset and a 56% success rate on the HOLO4K dataset. These results surpass competing algorithms, demonstrating PGpocket's advancement and practicality for protein-ligand binding site prediction.