Points In Space Research Articles

Spatial externalities, R&D spillovers, and endogenous technological change

Forward-looking economic agents operating in a finite continuous geographic area choose how much to innovate at each point in time and space. Based on this assumption, the present study incorporates spatial interactions in endogenous growth models, addressing the criticism that such models are inconsistent with empirical evidence. More specifically, we introduce spatial production spillovers, knowledge diffusion across space, and the capability for spatial heterogeneity into a standard expanding variety growth model based on R&D. We study the properties of equilibrium and optimal allocations and argue that the characteristics are different from those of the non-spatial model, which alter the appropriate policy measures. Finally, we provide numerical examples demonstrating the importance of spatial dependent policy measures in achieving a balanced regional development.

Physical-information model of the immune system as a development of P.K. Anokhin’s theory of functional systems

The article deals with the standard immunological model, which is based on the principles of random combination of molecules and cells and their random encounter with their complementary sites, which is accompanied by the formation of reversible complexes and/or a cascade of subsequent reactions. In its purity, such a model gives rise to various kinds of paradoxes that do not correspond to the reality of immune processes. As a rule, the development of immunology is expressed in the construction of more and more detailed links of immunologic events, but the addition of each new event to the chain of links should lead not to acceleration, but to slowing down of the final process within the combinatorial-complementary system. In this connection, the question of a new possible model of the immune system is raised, which is based on P.K. Anokhin’s theory of functional systems. As its further development the physical-information model (PhIM) of the immune system is proposed, which assumes two plans, informational and physical, of the immune system organization and their coordination on the basis of the ideas of organic potential and processes of conjugation. The information plan is represented as an abstract space of degrees of freedom of the system, analogous to phase space in physics. The current and final state of the system can be represented as points of the state space, the activity of the system with the transition from the current to the final state, as a trajectory in this space. The acceptor of the action result in the theory of functional systems of P.K. Anokhin is connected in this case with the image of the final state as the result of the system action. The construction of the trajectory of the system’s activity can be represented as the direction of reduction of the organic potential of the system, by analogy with that in the case of physical systems and their physical potentials. The organic potential reaches a minimum in the final state and expresses the need of the biosystem as a result of action.

Global Stochastic Comprehensive Sensitivity Analysis Based on Robustness Grouping and Improved Pelican Algorithm-Optimized Radial Basis Function Neural Network

Abstract Modeling analysis is one of the important means to analyze practical engineering, and as technology continues to evolve, various models are getting closer and closer to reality, while at the same time, there are more and more parameters in the models. It is important to analyse the impact of these parameters on the project to assist engineers in making plans or decisions. Sensitivity analysis (SA) can describe the effect of changes in these parameters on the model. However, complex models often have dozens or even hundreds of parameters, and most current SA methods struggle to deal reliably and effectively with these high-dimensional problems. In addition, it is difficult to obtain the sensitivity of continuous points in the parameter space with traditional SA methods. Therefore, this paper proposes a method that combines adaptive grouping and an Improved Pelican Optimization Algorithm for an optimal radial basis function (IPOA-RBF) agent model to solve these problems. Firstly, a clustering grouping method considering grouping robustness is established to obtain objective and stable parameter grouping results in high-dimensional sensitivity analysis. Secondly, a proxy model based on radial basis function neural network and an improved Pelican optimization algorithm are proposed to capture the logic of the proxy model to obtain the parameter sensitivity of continuous points in the parameter space. Finally, the superiority and applicability of this method is verified using an arch dam simulation model.

A study of the coupled dynamics of asymmetric absorbing clusters in a photophoretic trap

Abstract We report a study on the dynamics of absorbing asymmetric carbon clusters trapped by a loosely focused Gaussian beam using photophoretic force. At high laser powers, all the trapped clusters display rotation coupled with oscillation along the axial direction, with a majority spinning about a body fixed axis, while the rest display dual spin as well as orbital motion about a fixed point in space. The spinning and orbiting frequency is inversely proportional to the amplitude of the axial oscillation - with one growing at the expense of the other. Further, the frequencies of these rotations are not proportional to the laser power, but to the trap stiffnesses inferred from the corresponding natural frequencies. The clusters also stop rotating below a certain laser power, and execute random thermal fluctuations. Our work suggests that the dynamics of clusters trapped with photophoretic force are largely dependent on the cluster size and morphology, which could, in principle, be tuned to obtain various motional responses, and help in the design of rotating micromachines in air.

Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model

How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS2) field theory/ 3D Schwarzschild de Sitter (SdS3) space in [1–3], we study concrete complexity proposals in the microscopic models and their dual descriptions. First, we examine the spread complexity of the maximal entropy state of the doubled DSSYK model. We show that it counts the number of entangled chord states in its doubled Hilbert space. We interpret spread complexity in terms of a time difference between antipodal observers in SdS3 space, and a boundary time difference of the dual LdS2 CFTs. This provides a new connection between entanglement and geometry in dS space. Second, Krylov complexity, which describes operator growth, is computed for physical operators on all sides of the correspondence. Their late time evolution behaves as expected for chaotic systems. Later, we define the query complexity in the LdS2 model as the number of steps in an algorithm computing n-point correlation functions of boundary operators of the corresponding antipodal points in SdS3 space. We interpret query complexity as the number of matter operator chord insertions in a cylinder amplitude in the DSSYK, and the number of junctions of Wilson lines between antipodal static patch observers in SdS3 space. Finally, we evaluate a specific proposal of Nielsen complexity for the DSSYK model and comment on its possible dual manifestations.

Multi-spectral radiation thermometry of space point targets based on spectral image pixel binning

The temperature characteristics of space point targets are essential indicators of their operational status and performance. To address the issue of significant temperature measurement errors in space point targets caused by low temperatures and a low imaging signal-to-noise ratio (SNR), we propose a mathematical model for multi-spectral radiation thermometry, derived from the principles of dual-band radiation thermometry. Furthermore, a multi-spectral image pixel binning method is introduced to enhance the SNR and minimize measurement errors. The experimental results indicate that the proposed multi-spectral radiation thermometry outperforms dual-band radiation thermometry. After merging 2 to 20 pixels, multi-spectral radiation thermometry in the 3.75–4.1 and 4.3–4.62 µm bands demonstrates an enhanced SNR and reduced temperature measurement errors. For a 378.15 K blackbody, the relative errors decrease from 1.52% and 2.19% to 0.26% and 0.74%, respectively, after merging six and eight pixels in the two different bands, compared to unmerged images. This method provides a valuable reference for developing techniques to enhance the SNR and improve temperature measurement accuracy for space point targets.

A Theorem on k-Expansive Mapping and its Fixed Point in G𝐽 𝑆 – Metric Space

Objectives: To find a fixed point of k-expansive mapping on GJS-metric space by establishing a theorem on it and to prove the uniqueness of such a fixed point. Methods: A theorem for the k-expansive map on GJS-metric space is established by generalizing an existing contractive condition theorem. Generalization is done by replacing the contractive condition with an expansive type of condition. Findings: Certain conditions that have to be satisfied by a k-expansive mapping for the existence and uniqueness of fixed points in GJS-metric space were found in this article. An example is also given to illustrate the existence of a fixed point. Novelty: GJS-metric space is a new metric space that has been established recently. Furthermore, the fixed point theorem of k-expansive mapping on GJS - metric space has not yet been proved by anyone, and hence it is proved in this article. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: GJS-Metric space; Symmetric GJS-Metric space; GJS-Continuous function; GJS-Cauchy sequence; Expansive mapping; k-Expansive mapping

Experimental encircling of an exceptional point in a two degrees of freedom system: overview and application to noise control

When a resonator is added to an acoustic cavity or a vibrating structure, a new resonance frequency, or pole, is created in the system. When dissipation is present, this may breakdown when some parameters are finely tuned. This phenomenon, typical of non-Hermitian dynamics is called an exceptional point in the parametric space where two (or more) eigenvalues, as well as their associated eigenvectors, coalesce. In the recent years, EPs have gained interest in physics because of the counter-intuitive concepts associated with them. In the fields of acoustics and vibration, understanding EP may lead to a better comprehension of modal energy exchanges and decay. This work aims at exploring the key concepts related to EPs by revisiting the well-known coupled pendulums problem in the presence of damping. First, the free response of the experimental system is investigated after tuning it on an EP. Then an encircling is performed by varying the parameters through time. Our experimental results illustrate in a pedagogical manner nearly-optimal dissipation, energy exchange and chirality effects which have been recently evidenced in physics.

Anchor Space Optimal Transport as a Fast Solution to Multiple Optimal Transport Problems.

In machine learning, optimal transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel distributions. In practical scenarios, it is often necessary to solve multiple OT problems. Traditionally, these problems are treated independently, with each OT problem being solved sequentially. However, the computational complexity required to solve a single OT problem is already substantial, making the resolution of multiple OT problems even more challenging. Although many applications of fast solutions to OT are based on the premise of a single OT problem with arbitrary distributions, few efforts handle such multiple OT problems with multiple distributions. Therefore, we propose the anchor space OT (ASOT) problem: an approximate OT problem designed for multiple OT problems. This proposal stems from our finding that in many tasks the mass transport tends to be concentrated in a reduced space from the original feature space. By restricting the mass transport to a learned anchor point space, ASOT avoids pairwise instantiations of cost matrices for multiple OT problems and simplifies the problems by canceling insignificant transports. This simplification greatly reduces its computational costs. We then prove the upper bounds of its 1 -Wasserstein distance error between the proposed ASOT and the original OT problem under different conditions. Building upon this accomplishment, we propose three methods to learn anchor spaces for reducing the approximation error. Furthermore, our proposed methods present great advantages for handling distributions of different sizes with GPU parallelization.

Analytical and geometric interpretation of the flat arrangement of points by means of metric geometry in the study of metric spaces

Abstract When studying metric spaces, students of higher education often have difficulties with understanding the basic concepts and properties of these spaces. This, to a large extent, is a consequence of the significant level of formalization of such concepts on the one hand, and the preservation of the corresponding formulations and names familiar to students from a school mathematics course. To overcome these difficulties, it is advisable to use methods of geometric interpretation and visualization of these properties. At the same time, it is appropriate to use elements of metric geometry. Its methods make it possible to interpret the geometric features of the mutual placement of points of metric space in Cartesian (rectangular) coordinate systems, which are familiar to students of higher education. Moreover, it becomes possible to visualize these features with the help of graphic editors, since they, as a rule, use numerical values of the coordinates of points to visualize them. Based on the definition of an angle as an ordered trio of points of an arbitrary metric space, and the angular characteristic of this angle, the fact of the flat placement of four points of a non-Euclidean metric space is established, and examples of digital visualization of this arrangement using the dynamic geometric environment GeoGebra 3D are given.

Experimental and numerical study on focused wave generation using different energy modes

This paper reports an experimental and numerical study on the generation of freak waves related to the spatiotemporal focusing mechanism, where multiple water waves converge at a specific point in space and time to produce a large transient wave. A new energy distribution mode of constant-difference wave number (CDK) within the wave group is proposed and applied to both a physical and a numerical flume to generate focused waves, with primary attention given to the water surface elevation, underlying kinematics, and internal spectrum structure during the focused wave generation process. The classical experiment by Baldock et al. [“A laboratory study of nonlinear surface waves on water,” Philos. Trans. R. Soc., Ser. A 354, 649–676 (1996)], which used a constant-difference wave period within the wave group, is chosen for comparison. Spectral analysis shows that the CDK energy distribution mode can easily stimulate multiwave resonance in the focused wave group, where significant energy transfer from the main frequencies to higher harmonics is observed. Compared with the data from Baldock et al. [“A laboratory study of nonlinear surface waves on water,” Philos. Trans. R. Soc., Ser. A 354, 649–676 (1996)], the CDK wave group produces larger focused wave crests with higher propagation speeds and larger velocity gradients near the water surface due to strong multiwave resonance. The effects of the input spectrum, incident amplitude and initial water depth under different energy modes on focused-wave generation are analyzed. All the results indicate that the CDK energy distribution mode can produce larger focused waves compared to other energy distribution modes, which offers a novel approach for generating freak waves in the laboratory.

Microscale thermal variations in a walkable urban area during hot days: Analysis through mobile measurements and Day PET Signatures

This article analyzes the thermal variations of a small urban area recently transformed in the city center of Nantes, France, which has been designed to promote walkability and make it comfortable in summer. A measurement method based on mobile climate metrology, which offers high spatial resolution, was developed. Four measurements were conducted per day over five days between June and September 2023. The data was analyzed using the concept of the Day PET Signature (DPS), which reflects the dynamics of a point in space over the course of the day through variations in the Physiological Equivalent Temperature (PET) index. Four clusters of DPS were identified in the dataset, enabling the accurate assessment of the thermal diversity existing in the study area at different times of the day in summer. The results demonstrate that the observed differences between clusters are solely attributable to the radiative conditions at the distinct positions analyzed. The concept of a Radiative Portrait is introduced in order to characterize the thermal diversity of the study area. In contrast to the TMRT synthetic index, the Radiative Portrait provides a detailed breakdown of the fluxes, revealing the intensity of short- and long-wave radiation in top, bottom and lateral orientations. The combination of the Radiative Portrait and the PET class qualification provides a comprehensive understanding of the local climatescapes in summer.

Maxwell boundary condition for discrete velocity methods: macroscopic physical constraints and Lagrange multiplier-based implementation

In this paper, we propose an algorithm that imposes macroscopic physical constraints with Lagrange multiplier approach in implementing the Maxwell boundary condition within the framework of the discrete velocity method. For the simulation of rarefied gas flows in the presence of solid walls with complex geometry, the distribution function in the reflection region of the wall surface needs to be constructed in the discrete velocity space, to fulfill the specular reflection in the Maxwell boundary condition. The construction process should not consist of interpolation only, but include certain macroscopic physical constraints at the wall surface, so as to correctly account for gas-surface interaction on a macroscopic level. We demonstrate that for the specular reflection, keeping the symmetry of the first three moments of the distribution function between the incident and reflected region is sufficient for maintaining the conservation of mass, momentum, and energy at the wall surface. Furthermore, to strictly satisfy macroscopic physical constraints, a Lagrange multiplier method is introduced into the construction of the distribution function to correct the pure interpolation solution. In addition, the construction process requires the inversion of a large and sparse matrix (of dimension N × N, where N is the number of points in the velocity space). To improve the computational efficiency, the matrix inversion is converted into that of a much smaller matrix, i.e. (D+2) × (D+2) in the D-dimensional physical space. A series of numerical experiments are conducted to examine the performance of the proposed algorithm under different flow conditions. We demonstrate that the results obtained by the proposed algorithm are more accurate than the pure interpolation solution, comparing with the benchmark data. Moreover, after the validation of our results with previous studies, we find that the method significantly enhances the conservation of total mass and energy, especially for flows in an enclosed domain.

A Dynamic Path Planning Method for UAVs Based on Improved Informed-RRT* Fused Dynamic Windows

In recent years, navigating rotor drones in complex and dynamic environments has been a significant challenge. This paper proposes an improved path planning method by integrating the enhanced Informed-RRT* algorithm with the Dynamic Window Approach (DWA) algorithm. Firstly, the probability weight function for sampling direction is dynamically adjusted based on the Euclidean distance between the start and goal points to obtain higher-quality sampling points. Secondly, the Artificial Potential Field (APF) concept is introduced during the generation of new nodes, applying the improved APF method to the elliptical sampling area to guide the direction of new node generation. This significantly reduces the number of redundant nodes, enhances the convergence speed, and improves the obstacle avoidance efficiency. Then, a polynomial fitting method is employed to optimize the path, yielding a smoother trajectory. Finally, the improved DWA algorithm is integrated. Initially, the Informed-RRT* algorithm generates an optimal path from the starting point to the goal point in the global space, which is then provided as an initial reference path to the DWA algorithm. During actual operation, the DWA algorithm dynamically adjusts control inputs based on the current position, speed, and reference path of the drone, ensuring that the drone can avoid dynamic obstacles and unknown static obstacles in real time while staying as close to the reference path as possible.

GABoost: Graph Alignment Boosting via Local Optimum Escape

Heterogeneous graphs provide a universal data structure for representing various kinds of structured data in numerous domains. The graph alignment problem aims to find the correspondences of vertices in different graphs, playing a fundamental role in many downstream tasks of heterogeneous graph mining. In recent years, many graph alignment methods have been proposed, ranging from classical optimization methods , spectral methods , to embedding learning based-methods . Due to the problem's complexity, the result found by most existing methods is either a heuristic solution or a critical point in the solution space. In this paper, we propose GABoost, a graph alignment boosting algorithm that takes as input an initial alignment between two heterogeneous graphs and outputs a boosted alignment via an iterative local-optimum-escape process. One of the distinctive features of GABoost is that it can be sequentially composed with any graph alignment methods to improve the output of upstream methods. To examine the effectiveness of GABoost, we select 7 upstream methods of graph alignment as well as 6 real-world datasets, and quantitatively investigate the degree to which GABoost boosts these methods. The results show that GABoost improves the alignment accuracy of the 7 upstream methods by 25.25% on average with acceptable time overhead.

Understanding the Effects of Spacecraft Trajectories through Solar Coronal Mass Ejection Flux Ropes Using 3DCOREweb

This study investigates the impact of spacecraft positioning and trajectory on in situ signatures of coronal mass ejections (CMEs). Employing the 3DCORE model, a 3D flux rope model that can generate in situ profiles for any given point in space and time, we conduct forward modeling to analyze such signatures for various latitudinal and longitudinal positions, with respect to the flux rope apex, at 0.8 au. Using this approach, we explore the appearance of the resulting in situ profiles for different flux rope types, with different handedness and inclination angles, for both high- and low-twist CMEs. Our findings reveal that CMEs exhibit distinct differences in signatures between apex hits and flank encounters, with the latter displaying elongated profiles with reduced rotation. Notably, constant, nonrotating in situ signatures are only observed for flank encounters of low-twist CMEs, suggesting the existence of untwisted magnetic field lines within CME legs. Additionally, our study confirms the unambiguous appearance of different flux rope types in in situ signatures in all of the cases, barring some indistinguishable cases, contributing to the broader understanding and interpretation of observational data. Given the model assumptions, this may refute trajectory effects as the cause for mismatching flux rope types as identified in solar signatures. While acknowledging limitations inherent in our model, such as the assumption of constant twist and a nondeformable torus-like shape, we still draw relevant conclusions within the context of the global magnetic field structures of CMEs and the potential for distinguishing flux rope types based on in situ observations.

Favorable phase transitions induced by spinful electron–electron interactions in two-dimensional semimetal with a quadratic band crossing point

We study the effects of marginally spinful electron–electron interactions on the low-energy instabilities and favorable phase transitions in a two-dimensional (2D) spin-1/2 semimetal that owns a quadratic band crossing point (QBCP) parabolically touched by the upper and lower bands. In the framework of a renormalization group procedure, all sorts of interactions are treated on the equal footing to derive the coupled energy-dependent evolutions of all interaction couplings that govern the low-energy properties. Deciphering the essential physical information of such flows, we at first find that the tendencies of interaction parameters fall into three categories including Limit case, Special case, and General case based on the initial conditions. In addition, the 2D QBCP system is attracted to several distinct kinds of fixed points (FPs) in the interaction-parameter space, namely FP1+/FP2−, FP1±/ FP2±/FP3±, and FP1±/FP3±/FP41,42,43± with the subscripts characterizing the features of FPs for the Limit, Special, and General cases, respectively. Furthermore, as approaching these FPs, we demonstrate that the spinful fermion–fermion interactions can induce a number of favorable instabilities accompanied by certain phase transitions. Specifically, the quantum anomalous Hall (QAH), quantum spin Hall (QSH), and nematic (Nem.) site(bond) states are dominant for FP1±, FP2±, and FP3±, respectively. Rather, QSH becomes anisotropic nearby FP41,42,43± with one component leading and the others subleading. Besides, Nem.site(bond), chiral superconductivity, and nematic-spin-nematic (NSN.) site(bond) are subleading candidates around these FPs. Our findings provide valuable insights for further research into the 2D QBCP and similar systems.

Two fast finite difference methods for a class of variable-coefficient fractional diffusion equations with time delay

This paper introduces the fast Crank–Nicolson (CN) and compact difference schemes for solving the one- and two-dimensional fractional diffusion equations with time delay. The CN method is employed for temporal discretization, while the fractional centered difference (FCD) formula discretizes the Riesz space derivative. Additionally, a novel fourth-order scheme is developed using compact difference operators to improve accuracy. The convergence and stability of these schemes are rigorously proven. The discretized systems combining Toeplitz-like structures can be effectively solved by Krylov subspace solvers with suitable preconditioners. Each time level of these methods requires a computational complexity of O(plogp) per iteration and a memory of O(p), where p represents the total number of grid points in space. Numerical examples are given to illustrate both the theoretical results and the computational efficiency of the fast algorithm.

Prediction of directional solidification in freeze casting of biomaterial scaffolds using physics-informed neural networks

Freeze casting, a manufacturing technique widely applied in biomedical fields for fabricating biomaterial scaffolds, poses challenges for predicting directional solidification due to its highly nonlinear behavior and complex interplay of process parameters. Conventional numerical methods, such as computational fluid dynamics (CFD), require adequate and accurate boundary condition knowledge, limiting their utility in real-world transient solidification applications due to technical limitations. In this study, we address this challenge by developing a physics-informed neural networks (PINNs) model to predict directional solidification in freeze-casting processes. The PINNs model integrates physical constraints with neural network predictions, requiring significantly fewer predetermined boundary conditions compared to CFD. Through a comparison with CFD simulations, the PINNs model demonstrates comparable accuracy in predicting temperature distribution and solidification patterns. This promising model achieves such a performance with only 5000 data points in space and time, equivalent to 250,000 timesteps, showcasing its ability to predict solidification dynamics with high accuracy. The study’s major contributions lie in providing insights into solidification patterns during freeze-casting scaffold fabrication, facilitating the design of biomaterial scaffolds with finely tuned microstructures essential for various tissue engineering applications. Furthermore, the reduced computational demands of the PINNs model offer potential cost and time savings in scaffold fabrication, promising advancements in biomedical engineering research and development.

Quality control of elbow joint radiography using a YOLOv8-based artificial intelligence technology

BackgroundTo explore an artificial intelligence (AI) technology employing YOLOv8 for quality control (QC) on elbow joint radiographs.MethodsFrom January 2022 to August 2023, 2643 consecutive elbow radiographs were collected and randomly assigned to the training, validation, and test sets in a 6:2:2 ratio. We proposed the anteroposterior (AP) and lateral (LAT) models to identify target detection boxes and key points on elbow radiographs using YOLOv8. These identifications were transformed into five quality standards: (1) AP elbow positioning coordinates (XA and YA); (2) olecranon fossa positioning distance parameters (S17 and S27); (3) key points of joint space (Y3, Y4, Y5 and Y6); (4) LAT elbow positioning coordinates (X2 and Y2); and (5) flexion angle. Models were trained and validated using 2,120 radiographs. A test set of 523 radiographs was used for assessing the agreement between AI and physician and to evaluate clinical efficiency of models.ResultsThe AP and LAT models demonstrated high precision, recall, and mean average precision for identifying boxes and points. AI and physicians showed high intraclass correlation coefficient (ICC) in evaluating: AP coordinates XA (0.987) and YA (0.991); olecranon fossa parameters S17 (0.964) and S27 (0.951); key points Y3 (0.998), Y4 (0.997), Y5 (0.998) and Y6 (0.959); LAT coordinates X2 (0.994) and Y2 (0.986); and flexion angle (0.865). Compared to manual methods, using AI, QC time was reduced by 43% for AP images and 45% for LAT images (p < 0.001).ConclusionYOLOv8-based AI technology is feasible for QC of elbow radiography with high performance.Relevance statementThis study proposed and validated a YOLOv8-based AI model for automated quality control in elbow radiography, obtaining high efficiency in clinical settings.Key PointsQC of elbow joint radiography is important for detecting diseases.Models based on YOLOv8 are proposed and perform well in image QC.Models offer objective and efficient solutions for QC in elbow joint radiographs.Graphical