Geometric Framework Research Articles

Fitness of Nutrition Regulation in a Caterpillar Pest Mythimna separata (Walker): Insights from the Geometric Framework.

In nature, plants can contain variable nutrients depending upon the species, tissue, and developmental stage. Insect herbivores may regulate their nutrient intake behaviorally and physio- logically when encountering different foods. This study examined the nutritional regulation of the oriental armyworm, Mythimna separata, for the first time. In one experiment, we allowed the cater-pillars to choose between two nutritionally balanced but complementary diets. The caterpillars did not randomly consume the paired foods, but instead chose between the nutritionally balanced but complementary diets. This intake behavior was found to change with their developmental stages. Furthermore, the nutrient concentrations in food significantly impacted the insect's performance. In the other experiment, caterpillars were given one of eleven diets that reflected the different nutrient conditions in the field. The results showed that proteins were significantly associated with developmental time and fecundity. For example, by consuming protein-biased food, the caterpillars developed faster and produced more eggs. In contrast, carbohydrates were more strongly linked to lipid accumulation, and caterpillars accumulated more lipids when consuming the carbohydrate-biased food. Moreover, the caterpillars were also found to actively regulate their intake of proteins and carbohydrates based on food quality and to physiologically prepare for subsequent life stages. These findings enhance our understanding of how M. separata feeds and responds to different nutritional environments in the field, which could have implications for managing insect herbivores in agricultural settings.

Automated characterization and monitoring of material shape using Riemannian geometry

Shape affects both the physical and chemical properties of a material. Characterizing the roughness, convexity, and general geometry of a material can yield information on its catalytic efficiency, solubility, elasticity, porosity, and overall effectiveness in the application of interest. However, material shape can be defined in a multitude of conflicting ways where different aspects of a material’s geometry are emphasized over others, leading to bespoke measures of shape that are not easily generalizable. In this paper, we explore the use of Riemannian geometry in the analysis of shape, and show that a Riemannian geometric framework for shape analysis is generalizable, computationally scalable, and can be directly integrated into common data analysis methods. In this framework, material shapes are abstracted as points on a Riemannian manifold. This information can be used to construct statistical moments (e.g., means, variances) and perform tasks such as dimensionality reduction and statistical process control. We provide a practical introduction to the mathematics of shape analysis through Riemannian geometry and illustrate its application on a manufactured/mined granular material dataset provided by Covia Corp. We show that the Riemannian framework can be used to automatically extract and quantify the shape of granular materials in a statistically rigorous manner.

Fermion geometry and the renormalization of the Standard Model Effective Field Theory

The geometry of field space governs on-shell scattering amplitudes. We formulate a geometric description of effective field theories which extends previous results for scalars and gauge fields to fermions. The field-space geometry reorganizes and simplifies the computation of quantum loop corrections. Using this geometric framework, we calculate the fermion loop contributions to the renormalization group equations for bosonic operators in the Standard Model Effective Field Theory up to mass dimension eight.

Riemannian frameworks for the harmonization of resting-state functional MRI scans

Magnetic Resonance Imaging provides unprecedented images of the brain. Unfortunately, scanners and acquisition protocols can significantly impact MRI scans. The development of statistical methods able to reduce this variability without altering the relevant information in the scans, often coined harmonization methods, has been the topic of an increasing research effort supported by the recent growth of publicly available neuroimaging data sets and new possibilities for combining them to achieve greater statistical power. In this work, we focus on the challenges specifically raised by the harmonization of resting-state functional MRI scans. We propose to harmonize resting-state fMRI scans by reducing the impact of covariates such as scanner differences and scanning protocols on their associated functional connectomes and then propagating the changes back to the rs-fMRI time series. We use Riemannian geometric frameworks to preserve the mathematical properties of functional connectomes during their harmonization, and we demonstrate how state-of-the-art harmonization methods can be embedded within these frameworks to reduce covariates effects while preserving the relevant clinical information associated with aging or brain disorders. During our experiments, a large set of synthetic data was generated and processed to compare eighty variants of the proposed approach. The framework achieving the best harmonization was then applied to three low-dimensional data sets made of 712 sets of fMRI time series provided by the ABIDE consortium and two high-dimensional data sets obtained by processing 1527 rs-fMRI scans provided by the Human Connectome Project, the Framingham Heart Study and the Genetics of Brain Structure and Function study. These experiments established that our new framework could successfully harmonize low-dimensional connectomes and voxelwise functional time series and confirmed the need for preserving connectomes properties during their harmonization.

Utilizing the geometric mechanics framework to predict attitude in a full ephemeris model of the Cislunar region

Predicting the attitude of spacecraft traveling within the Cislunar region is crucial to ensure the success of future missions planned within that realm of space. To consider the coupled nature of translational and rotational motion, the circular restricted full three-body problem (CRF3BP), previously proposed by the authors, is utilized to obtain an initial guess for the orbit and attitude motion of the spacecraft. Then, that initial guess is used to transition the trajectory into a full ephemeris model, which considers the additional perturbations due to the Sun’s gravitational effect and the eccentricity of the Moon’s orbit. Orbit/attitude coupling is studied for multiple orbits obtained within the CRF3BP considering spacecraft of different sizes. The trajectories selected for analysis are an L2 Lyapunov orbit, a distant retrograde orbit, a northern halo orbit, and a Lunar transfer from low-Earth orbit. The efficacy of the CRF3BP is demonstrated by studying how spacecraft motion, notably its attitude, is predicted in the full ephemeris model using this formalism.

Exploring accelerating hairy black holes in 2+1 dimensions: the asymptotically locally anti-de Sitter class and its holography

In the realm of lower-dimensional accelerating spacetimes, it is well-established that the presence of domain walls, which are co-dimension one topological defects, is a necessary condition for their construction. We expand upon the geometric framework employed in the generation of such spacetime solutions by incorporating a conformally coupled scalar field within the matter sector. This endeavor leads to the identification of several new families of three-dimensional accelerating spacetimes with asymptotically locally anti-de Sitter (AdS) behavior. Notably, one of these solutions showcases a hairy generalization of the accelerating BTZ black hole. This solution is constructed at both slow and rapid phases of acceleration, and its connection with established vacuum spacetime models is explicitly elucidated. The inclusion of the scalar field imparts a non-constant Ricci curvature to the domain wall, thereby rendering these configurations particularly suitable for the construction of two-dimensional quantum black holes. To establish a well-posed variational principle in the presence of the domain wall, two essential steps are undertaken. First, we extend the conventional renormalized AdS3 action to accommodate the presence of the scalar field. Second, we explicitly incorporate the Gibbons-Hawking-York term associated with the internal boundaries of our geometries and account for the tension of the domain wall in the action. This dual step process enables us to derive the domain wall field equations via the variational principle. Consequently, the action furnishes the appropriate quantum statistical relation. We engage in holographic computations, thereby determining the explicit form of the holographic stress tensor. In this context, the stress tensor can be expressed as that of a perfect fluid situated on a curved background. Additionally, it paves the road to ascertain the spacetime mass. Finally, we close by demonstrating the existence of three-dimensional accelerating spacetimes with asymptotically locally flat and asymptotically locally de Sitter geometries, particularly those embodying black holes.

Conformal gravitational theories in Barthel–Kropina-type Finslerian geometry, and their cosmological implications

We consider dark energy models obtained from the general conformal transformation of the Kropina metric, representing an (alpha , beta )-type Finslerian geometry, constructed as the ratio of the square of a Riemannian metric alpha and the one-form beta . Conformal symmetries appear in many fields of physics, and they may play a fundamental role in our understanding of the Universe. We investigate the possibility of obtaining conformal theories of gravity in the osculating Barthel–Kropina geometric framework, where gravitation is described by an extended Finslerian-type model, with the metric tensor depending on both the base space coordinates and a vector field. We show that it is possible to formulate a family of conformal Barthel–Kropina theories in an osculating geometry with second-order field equations, depending on the properties of the conformal factor, whose presence leads to the appearance of an effective scalar field of geometric origin in the gravitational field equations. The cosmological implications of the theory are investigated in detail by assuming a specific relation between the component of the one-form of the Kropina metric and the conformal factor. The cosmological evolution is thus determined by the initial conditions of the scalar field and a free parameter of the model. We analyze in detail three cosmological models corresponding to different values of the theory parameters. Our results show that the conformal Barthel–Kropina model can provide an acceptable description of the observational data, and may represent a theoretically attractive alternative to the standard Lambda CDM cosmology.

Automatic Detection of Tooth-Gingiva Trim Lines on Dental Surfaces.

Detecting the tooth-gingiva trim line from a dental surface plays a critical role in dental treatment planning and aligner 3D printing. Existing methods treat this task as a segmentation problem, which is resolved with geometric deep learning based mesh segmentation techniques. However, these methods can only provide indirect results (i.e., segmented teeth) and suffer from unsatisfactory accuracy due to the incapability of making full use of high-resolution dental surfaces. To this end, we propose a two-stage geometric deep learning framework for automatically detecting tooth-gingiva trim lines from dental surfaces. Our framework consists of a trim line proposal network (TLP-Net) for predicting an initial trim line from the low-resolution dental surface as well as a trim line refinement network (TLR-Net) for refining the initial trim line with the information from the high-resolution dental surface. Specifically, our TLP-Net predicts the initial trim line by fusing the multi-scale features from a U-Net with a proposed residual multi-scale attention fusion module. Moreover, we propose feature bridge modules and a trim line loss to further improve the accuracy. The resulting trim line is then fed to our TLR-Net, which is a deep-based LDDMM model with the high-resolution dental surface as input. In addition, dense connections are incorporated into TLR-Net for improved performance. Our framework provides an automatic solution to trim line detection by making full use of raw high-resolution dental surfaces. Extensive experiments on a clinical dental surface dataset demonstrate that our TLP-Net and TLR-Net are superior trim line detection methods and outperforms cutting-edge methods in both qualitative and quantitative evaluations.

A geometric framework for reaction enumeration in computational nucleic acid devices.

Cascades of DNA strand displacement reactions enable the design of potentially large circuits with complex behaviour. Computational modelling of such systems is desirable to enable rapid design and analysis. In previous work, the expressive power of graph theory was used to enumerate reactions implementing strand displacement across a wide range of complex structures. However, coping with the rich variety of possible graph-based structures required enumeration rules with complicated side-conditions. This paper presents an alternative approach to tackle the problem of enumerating reactions at domain level involving complex structures by integrating with a geometric constraint solving algorithm. The rule sets from previous work are simplified by replacing side-conditions with a general check on the geometric plausibility of structures generated by the enumeration algorithm. This produces a highly general geometric framework for reaction enumeration. Here, we instantiate this framework to solve geometric constraints by a structure sampling approach in which we randomly generate sets of coordinates and check whether they satisfy all the constraints. We demonstrate this system by applying it to examples from the literature where molecular geometry plays an important role, including DNA hairpin and remote toehold reactions. This work therefore enables integration of reaction enumeration and structural modelling.

A graph-based probabilistic geometric deep learning framework with online enforcement of physical constraints to predict the criticality of defects in porous materials

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as surrogates to approximate and extrapolate the solution of such multiscale simulations. These methodologies are usually limited to 2D problems due to the high computational cost of 3D voxel based CNNs. We propose a novel geometric learning approach based on a Graph Neural Network (GNN) that efficiently deals with three-dimensional problems by performing convolutions over 2D surfaces only. Following our previous developments using pixel-based CNN, we train the GNN to automatically add local fine-scale stress corrections to an inexpensively computed coarse stress prediction in the porous structure of interest. Our method is Bayesian and generates densities of stress fields, from which credible intervals may be extracted. As a second scientific contribution, we propose to improve the extrapolation ability of our network by deploying a strategy of online physics-based corrections. Specifically, we condition the posterior predictions of our probabilistic predictions to satisfy partial equilibrium at the microscale, at the inference stage. This is done using an Ensemble Kalman algorithm, to ensure tractability of the Bayesian conditioning operation. We show that this innovative methodology allows us to alleviate the effect of undesirable biases observed in the outputs of the uncorrected GNN, and improves the accuracy of the predictions in general.

Geometry of ecological coexistence and niche differentiation.

A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence. Historically, one important approach for addressing this question has been to analyze consumer resource models using geometric arguments. This has led to broadly applicable principles such as Tilman's R^{*} and species coexistence cones. Here, we extend these arguments by constructing a geometric framework for understanding species coexistence based on convex polytopes in the space of consumer preferences. We show how the geometry of consumer preferences can be used to predict species which may coexist and enumerate ecologically stable steady states and transitions between them. Collectively, these results provide a framework for understanding the role of species traits within niche theory.

Souriau’s general covariant formulation of Relativistic Hyperelasticity revisited

We present and modernize Souriau’s 1958 geometric framework for Relativistic continuous media, and enlighten the necessary and the ad hoc modeling choices made since. We focus as much as possible on the Continuum Mechanics point of view and describe the general covariant formulation of Hyperelasticity in (Variational) General Relativity. At this level of generality, different relativistic strain and stress tensors are formulated and discussed. Then, the choice of an observer, through the introduction of a spacetime structure allows us to make deeper insights into the foundations of Continuum Mechanics. We extend Souriau’s calculations, initially performed in the flat Minkowski spacetime, to the Schwarzschild spacetime accounting for gravitation. Finally, we recover the Classical Galilean Hyperelasticity with gravity, as the Newton–Cartan infinite light speed limit of this formulation.

GAGPT-2: A Geometric Attention-based GPT-2 Framework for Image Captioning in Hindi

Image captioning frameworks usually employ an encoder-decoder paradigm, with the encoder receiving abstract image feature vectors as input and the decoder for language modeling. Nowadays, most prominent architectures employ features from region proposals derived from object detection modules. In this work, we propose a novel architecture for image captioning. We employ the object detection module integrated with transformer architecture as an encoder and GPT-2 (Generative Pre-trained Transformer) as a decoder. The encoder utilizes the information of the spatial relationships among detected objects. We introduce a unique methodology for image caption generation in Hindi, which is widely spoken in South Asia and India and is the world’s third most spoken language as well as India’s official language. In terms of BLEU scores, the proposed approach’s performance is comparable to those of other baselines, and the results illustrate that the proposed approach outperforms the other baselines. The efficacy of the proposed approach in generating correct captions is further determined by human assessment in terms of adequacy and fluency.

Bianchi type cosmological models in f(T) tele-parallel gravity

Symmetry assumptions on the geometrical framework have provided successful mechanisms to develop physically meaningful solutions to many problems. In tele-parallel gravity, invariance of the frame and spin-connection under a group of motions defines an affine symmetry group. Here, we assume there exists a three-dimensional group of affine symmetries acting simply transitively on a spatial hypersurface and that this group of symmetry actions defines our affine frame symmetry group. We determine the general form of the co-frame and spin connection for each spatially homogeneous Bianchi type. We then construct the corresponding field equations for f(T) tele-parallel gravity. We show that if the symmetry group is of Bianchi type A (I, II, VI 0, VII 0, VIII or IX) then there exists a co-frame/spin connection pair that is consistent with the antisymmetric part of the field equations of f(T) tele-parallel gravity. For those geometries having a Bianchi type B symmetry group (IV, V, VIh , VIIh ), we find that in general these geometries are inconsistent with the antisymmetric part of the f(T) tele-parallel gravity field equations unless the theory reduces to an analog of General Relativity with a cosmological constant.

A geometric framework for multiclass ensemble classifiers

Ensemble classifiers have been investigated by many in the artificial intelligence and machine learning community. Majority voting and weighted majority voting are two commonly used combination schemes in ensemble learning. However, understanding of them is incomplete at best, with some properties even misunderstood. In this paper, we present a group of properties of these two schemes formally under a geometric framework. Two key factors, every component base classifier’s performance and dissimilarity between each pair of component classifiers are evaluated by the same metric—the Euclidean distance. Consequently, ensembling becomes a deterministic problem and the performance of an ensemble can be calculated directly by a formula. We prove several theorems of interest and explain their implications for ensembles. In particular, we compare and contrast the effect of the number of component classifiers on these two types of ensemble schemes. Some important properties of both combination schemes are discussed. And a method to calculate the optimal weights for the weighted majority voting is presented. Empirical investigation is conducted to verify the theoretical results. We believe that the results from this paper are very useful for us to understand the fundamental properties of these two combination schemes and the principles of ensemble classifiers in general. The results are also helpful for us to investigate some issues in ensemble classifiers, such as ensemble performance prediction, diversity, ensemble pruning, and others.

Training and Guidance in Use Software Wingeom 2D and 3D in Learning Geometry to Improve the Professionalism of Junior High School Teachers In Tanggetada District, Kolaka District, Southeast Sulawesi Province

This service aims to increase the professionalism of junior high school teachers in learning geometry by using Mathematics Learning Media, namely the use Sofware Wingeom 2D and 3D. This was done because looking at the problems that are generally faced by teachers in research, namely the lack of utilization and knowledge of teachers in the use of Wingeom-Based Mathematics Learning Media, in schools teachers are known that one of their weaknesses is the lack of work in the field of scientific work and research caused by erroneous one of them is the inadequacy of teachers in using mathematics learning media which can make it easier for them to be able to work. Program Wingeom 2D and 3D is a computer application program designed to support geometry learning, both two-dimensional and three-dimensional. This program can be used asmind tools in learning geometry, where teachers can use it to develop a dimensional geometric framework. With programs Wingeom It is hoped that later the teacher will be able to explore, observe, do shape animation and display dimensional geometry material, in addition to the program Wingeom 2D and 3D are expected to help visualize a geometric concept clearly so that teachers will more easily understand geometric concepts so that it will have an impact on improving the quality of teachers in the learning process, especially learning geometry. The mandatory outputs to be achieved are (1). One scientific article published in a journal with ISSN or proceedings from a national seminar. (2) Publication in print/online/repocitory mass media PT. (3). Increased competitiveness (increase quality, quantity, and added value of goods, services, product diversification, or other resources depending on the type of activity proposed. (4). Increasing the application of science and technology in society (mechanization, IT, and management). (5) Improvement of community values (art, culture, social, politics, security, peace, education, and health. Meanwhile, Additional Outcomes are in the form of (1). method or system; product (goods or services). (2). HKI, (3). Books with ISSN, (4). TTG Innovation, and, (5). International Publications. Method used in this training and mentoring include: (1) talk and question and answer about steps usage stepssoftware Wingeom 2D and 3D in learning geometry, (2) discussion groups directed on the steps of use software Wingeom 2D and 3D in learning geometry, (3) guidance and each simulation usage stepssoftware Wingeom 2d and 3D in learning geometry, (4) practice direct use of each step usage software Wingeom 2D and 3D dalam learning geometry, (5) giving related assignments usage software Wingeom 2D and 3D dalam geometry learning.

The Upper Cretaceous petroleum system of the East Beni Suef Basin, Egypt: an integrated geological and 2D basin modelling approach

We integrated geological and 2D basin modelling to investigate the tectonostratigraphic evolution of the East Beni Suef Basin (EBSB) of north central Egypt and its implications for the Upper Cretaceous petroleum system. Two intersecting seismic sections and three exploration wells were used for this study. The geological model defines the structural and geometrical framework of the basin, which formed the basis for subsequent 2D basin modelling. The developed basin models were calibrated and fine-tuned using vitrinite reflectance and corrected temperature data. Modelling results indicate that the Abu Roash ‘F’ source-rock maturity ranges from the early oil window at the basin margins to the main oil window in the centre. The main phase of hydrocarbon generation occurred during the Eocene after trap formation in the Late Cretaceous. Generated hydrocarbons have migrated both laterally and vertically, most likely from the central part of the basin towards the basin margins, particularly eastwards to the structural traps. The model predicts low accumulation rates for the EBSB, which are caused by the ineffective sealing capacity of the overburden rocks and normal faults. In addition to the proven kitchen for the charging of the Abu Roash ‘E’ reservoirs, an additional kitchen area to the NW of the basin is suggested for the Abu Roash ‘G’ reservoirs.

Invited Session III: Neural network models of the visual system: Neural population geometry: An approach for understanding biological and artificial neural networks.

A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the 'black box' of representations in neural circuits. In this talk, we will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from the structure in neural populations and from biologically plausible neural networks. First, we will introduce an analytic theory that connects geometric structures that arise from neural responses (i.e., neural manifolds) to the neural population's efficiency in implementing a task. In particular, this theory describes a perceptron's capacity for linearly classifying object categories based on the underlying neural manifolds' structural properties. Next, we will describe how such methods can, in fact, open the 'black box' of distributed neuronal circuits in a range of experimental neural datasets. In particular, our method overcomes the limitations of traditional dimensionality reduction techniques, as it operates directly on the high-dimensional representations, rather than relying on low-dimensionality assumptions for visualization. Furthermore, this method allows for simultaneous multi-level analysis, by measuring geometric properties in neural population data, and estimating the amount of task information embedded in the same population. These geometric frameworks are general and can be used across different brain areas and task modalities, as demonstrated in the work of ours and others, ranging from the visual cortex to parietal cortex to hippocampus, and from calcium imaging to electrophysiology to fMRI datasets. Finally, we will discuss our recent efforts to fully extend this multi-level description of neural populations, by (1) investigating how single neuron properties shape the representation geometry in early sensory areas, and by (2) understanding how task-efficient neural manifolds emerge in biologically-constrained neural networks. By extending our mathematical toolkit for analyzing representations underlying complex neuronal networks, we hope to contribute to the long-term challenge of understanding the neuronal basis of tasks and behaviors.

A geometric framework for discrete time port‐Hamiltonian systems

AbstractPort‐Hamiltonian systems provide an energy‐based formulation with a model class that is closed under structure preserving interconnection. For continuous‐time systems, these interconnections are constructed by geometric objects called Dirac structures. In this paper, we derive this geometric formulation and the interconnection properties for scattering passive discrete‐time port‐Hamiltonian systems.

MpbPPI: a multi-task pre-training-based equivariant approach for the prediction of the effect of amino acid mutations on protein-protein interactions.

The accurate prediction of the effect of amino acid mutations for protein-protein interactions (PPI $\Delta \Delta G$) is a crucial task in protein engineering, as it provides insight into the relevant biological processes underpinning protein binding and provides a basis for further drug discovery. In this study, we propose MpbPPI, a novel multi-task pre-training-based geometric equivariance-preserving framework to predict PPI $\Delta \Delta G$. Pre-training on a strictly screened pre-training dataset is employed to address the scarcity of protein-protein complex structures annotated with PPI $\Delta \Delta G$ values. MpbPPI employs a multi-task pre-training technique, forcing the framework to learn comprehensive backbone and side chain geometric regulations of protein-protein complexes at different scales. After pre-training, MpbPPI can generate high-quality representations capturing the effective geometric characteristics of labeled protein-protein complexes for downstream $\Delta \Delta G$ predictions. MpbPPI serves as a scalable framework supporting different sources of mutant-type (MT) protein-protein complexes for flexible application. Experimental results on four benchmark datasets demonstrate that MpbPPI is a state-of-the-art framework for PPI $\Delta \Delta G$ predictions. The data and source code are available at https://github.com/arantir123/MpbPPI.