Configuration Space Research Articles

A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking

We construct the hyper-Kähler moduli space of framed monopoles over R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^3$$\\end{document} for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence arbitrary symmetry breaking. In order to do so, we define a configuration space of pairs with appropriate asymptotic conditions and perform an infinite-dimensional quotient construction. We make use of the b and scattering calculuses to study the relevant differential operators.

Correlating Nitrate Adsorption with the Local Environments of FeCoNiCuZn High-Entropy Alloy Catalysts Using Machine Learning.

The electrocatalytic nitrate reduction to ammonia holds significant values for water remediations and energy applications, which quests for the development of highly effective catalysts with considerable stability and selectivity. Recently, high-entropy alloys (HEAs) are attracting growing attention for electrocatalytic processes. Nonetheless, studies of HEA-based nitrate reduction to ammonia are still at the early stage, and it remains unclear how the HEA compositions affect the adsorption and activation of the reaction intermediates. Herein, high-throughput density functional theory (DFT) calculations were integrated with machine learning to investigate the dependence of nitrate adsorption on the FeCoNiCuZn HEA structures. In particular, a total of 1268 different structures were sampled and constructed from the multidimensional configuration space, followed by the DFT calculations to investigate the Gibbs free energy of nitrate adsorption (i.e., ΔGNO3) on different surface microstructures. Four regression models were successfully developed, which can accurately predict ΔGNO3 using the HEA structures as the input features. Through the analysis of the feature importance, it was found that the active sites are crucial for nitrate adsorption; meanwhile, the local environments also play a considerable role. The dependence of the ΔGNO3 and adsorption geometries on the HEA compositions demonstrates that the compositional modulation of the HEA catalysts could be a promising avenue for facile adsorption and activation of reaction intermediates. Overall, this work will contribute to the probabilistic optimization of the HEA microstructures for enhanced electrochemical nitrate reduction.

A non-Archimedean approach to K-stability, I: Metric geometry of spaces of test configurations and valuations

A non-Archimedean approach to K-stability, I: Metric geometry of spaces of test configurations and valuations

Turbulence scaling from deep learning diffusion generative models

Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehension necessitates an understanding of the space of turbulent fluid flow configurations. We employ a diffusion-based generative model to learn the distribution of turbulent vorticity profiles and generate snapshots of turbulent solutions to the incompressible Navier-Stokes equations. We consider the inverse cascade in two spatial dimensions and generate diverse turbulent solutions that differ from those in the training dataset. We analyze the statistical scaling properties of the new turbulent profiles, calculate their structure functions, energy power spectrum, velocity probability distribution function and moments of local energy dissipation. All the learnt scaling exponents are consistent with the expected Kolmogorov scaling This agreement with established turbulence characteristics provides strong evidence of the model's capability to capture essential features of real-world turbulence.

Hidden Semi-Markov models for semantic-graph language modeling

Semantic communication is expected to play a critical role in reducing traffic load in future intelligent large-scale sensor networks. With advances in Machine Learning (ML) and Deep Learning (DL) techniques, design of semantically-aware systems has become feasible in recent years. This work focuses on improving the reliability of the semantic information represented in a graph-based language that has been recently proposed. Inaccuracies in the representation of the semantic information can arise due to multiple factors, such as algorithmic shortcomings or sensory errors, decreasing the performance of the semantic extractor. This study aims to model the temporal evolution of semantic information, represented using the graph language, to enhance its reliability. Each unique graph configuration is treated as a distinct state, leading to a Hidden Semi-Markov Model (HSMM) defined over the state space of the graph configurations. The HSMM formulation enables the integration of prior knowledge on the semantic signal into the graph sequences, enhancing the accuracy in identifying semantic innovations. Within the HSMM framework, algorithms designed for graph smoothing, semantic information fusion, and model learning are introduced. The efficacy of these algorithms in improving the reliability of the extracted semantic-graphs is demonstrated through simulations and video streams generated in the CARLA simulation environment.

A constraint programming framework for preliminary mission analysis: Applications for constellation-servicing active debris removal

Constraint Programming is a classical artificial intelligence paradigm characterised by its flexibility for the modelling of complex problems. In the field of space operations, this approach has been successfully used for mission planning and scheduling. This manuscript proposes a framework that leverages the strengths of Constraint Programming for the preliminary analysis of space missions, introducing some modifications to tailor it to the application at hand. Specifically, it uses constraint propagation and search techniques to thoroughly explore the configuration space of a mission in an efficient manner. Consequently, it is able to quantify the performance of precomputed mission choices with respect to the mission requirements, as well as generate new ones that optimise such performance. The proposed methodology has been particularised for two application cases involving active debris removal missions for large constellations in low Earth orbit, namely, a chaser case and a mothership case. The chaser case considers a servicing satellite that rendezvouses with the failed satellites of the constellation and directly transports them to a disposal orbit. The mothership case comprises a servicing satellite that installs deorbiting kits in each of the failed satellites, except for the one removed in the last place. This way, the servicing satellite will only transport this object, while the deorbiting kits will carry out the disposal of the rest of them. This methodology has been successfully used to evaluate a preliminary mission analysis of both application cases developed under ESA’s Sunrise project.

Behavior of Correlation Functions in the Dynamics of the Multiparticle Quantum Arnol’d Cat

The multi-particle Arnol’d cat is a generalization of the Hamiltonian system, both classical and quantum, whose period evolution operator is the renowned map that bears its name. It is obtained following the Joos–Zeh prescription for decoherence by adding a number of scattering particles in the configuration space of the cat. Quantization follows swiftly if the Hamiltonian approach, rather than the semiclassical approach, is adopted. The author has studied this system in a series of previous works, focusing on the problem of quantum–classical correspondence. In this paper, the dynamics of this system are tested by two related yet different indicators: the time autocorrelation function of the canonical position and the out-of-time correlator of position and momentum.

Renormalization group flows from the Hessian geometry of quantum effective actions

We explore a geometric perspective on quantum field theory by considering the configuration space spanned by the correlation functions. Employing n-particle irreducible effective actions constructed via Legendre transforms of the Schwinger functional, this configuration space can be associated with a Hessian manifold. This allows for various properties and uses of the n-particle irreducible effective actions to be re-cast in geometrical terms. In the 2PI case, interpreting the two-point source as a regulator, this approach can be readily connected to the functional renormalization group. Renormalization group flows are then understood in terms of geodesics on this Hessian manifold.

The Uchuu-glam BOSS and eBOSS LRG lightcones: exploring clustering and covariance errors

ABSTRACT This study investigates the clustering and bias of Luminous Red Galaxies (LRG) in the BOSS-LOWZ, -CMASS, -COMB, and eBOSS samples, using two types of simulated lightcones: (i) high-fidelity lightcones from UchuuN-body simulation, employing SHAM technique to assign LRG to (sub)haloes, and (ii) 16 000 covariance lightcones from GLAM-UchuuN-body simulations, including LRG using HOD data from Uchuu. Our results indicate that Uchuu and glam lightcones closely replicate BOSS/eBOSS data, reproducing correlation function and power spectrum across scales from redshifts 0.2 to 1.0, from 2 to $150 \,h^{-1}\,\mathrm{Mpc}$ in configuration space, from 0.005 to $0.7\, h\,\mathrm{Mpc}^{-1}$ in Fourier space, and across different LRG stellar masses. Furthermore, comparing with existing MD-Patchy and EZmock BOSS/eBOSS lightcones based on approximate methods, our GLAM-Uchuu lightcones provide more precise clustering estimates. We identify significant deviations from observations within $20 \,h^{-1}\,\mathrm{Mpc}$ scales in MD-Patchy and EZmock, with our covariance matrices indicating that these methods underestimate errors by between 10 per cent and 60 per cent. Lastly, we explore the impact of cosmology on galaxy clustering. Our findings suggest that, given the current level of uncertainties in BOSS/eBOSS data, distinguishing models with and without massive neutrino effects on large-scale structure (LSS) is challenging. This paper highlights the Uchuu and GLAM-Uchuu simulations’ robustness in verifying the accuracy of Planck cosmological parameters, providing a strong foundation for enhancing lightcone construction in future LSS surveys. We also demonstrate that generating thousands of galaxy lightcones is feasible using N-body simulations with adequate mass and force resolution.

Configuration space partitioning in tilings of a bounded region of the plane

Configuration space partitioning in tilings of a bounded region of the plane

Homology of configuration spaces of surfaces modulo an odd prime

Abstract For a compact orientable surface Σ g , 1 \Sigma_{g,1} of genus 𝑔 with one boundary component and for an odd prime number 𝑝, we study the homology of the unordered configuration spaces C ∙ ( Σ g , 1 ) : = ∐ n ≥ 0 C n ( Σ g , 1 ) C_{\bullet}(\Sigma_{g,1}):=\coprod_{n\geq 0}C_{n}(\Sigma_{g,1}) with coefficients in F p \mathbb{F}_{p} . We describe H ∗ ⁢ ( C ∙ ⁢ ( Σ g , 1 ) ; F p ) H_{*}(C_{\bullet}(\Sigma_{g,1});\mathbb{F}_{p}) as a bigraded module over the Pontryagin ring H ∗ ⁢ ( C ∙ ⁢ ( D ) ; F p ) H_{*}(C_{\bullet}(D);\mathbb{F}_{p}) , where 𝐷 is a disc, and compute in particular the bigraded dimension over F p \mathbb{F}_{p} . We also consider the action of the mapping class group Γ g , 1 \Gamma_{g,1} and prove that the mod-𝑝 Johnson kernel K g , 1 ⁢ ( p ) ⊆ Γ g , 1 \mathcal{K}_{g,1}(p)\subseteq\Gamma_{g,1} is the kernel of the action on H ∗ ⁢ ( C ∙ ⁢ ( Σ g , 1 ; F p ) ) H_{*}(C_{\bullet}(\Sigma_{g,1};\mathbb{F}_{p})) .

Generalized permutohedra in the kinematic space

In this note, we study the permutohedral geometry of the singularities of a certain differential form introduced in recent work of Arkani-Hamed, Bai, He and Yan. There it was observed that the poles of the form determine a family of polyhedra which have the same face lattice as that of the permutohedron. We realize that family explicitly, proving that it in fact fills out the configuration space of a particularly well-behaved family of generalized permutohedra, the zonotopal generalized permutohedra, that are obtained as the Minkowski sums of line segments parallel to the root directions ei − ej.Finally we interpret Mizera’s formula for the biadjoint scalar amplitude m(\U0001d540n, \U0001d540n), restricted to a certain dimension n − 2 subspace of the kinematic space, as a sum over the boundary components of the standard root cone, which is the conical hull of the roots e1 − e2, … , en−2 − en−1.

Comparing receptor binding properties of SARS-CoV-2 and of SARS-CoV virus by using unsupervised machine learning models

This work continues our recent molecular dynamics investigation of the three systems of the human ACE2 receptor interacting with the viral RBDs of SARS-CoV virus and two variants of SARS-CoV-2 viruses. The simulations are extended and analyzed using unsupervised machine learning models to give complementary descriptions of hidden features of the viral binding mechanism. Specifically, the principal component analysis (PCA) and the variational autoencoder (VAE) models are employed, both are classified as dimensionality reduction approaches with different focuses. The results support the molecular dynamics results that the two variants of SARS-CoV-2 bind stronger and more stable to the human ACE2 receptor than SARS-CoV virus does. Moreover, stronger bindings also affect the structure of the human receptor, making it fluctuate more, a sensitive feature which is hard to detect using standard analyses. Unexpectedly, it is found that the VAE model can learn and arrange randomly shuffled protein structures obtained from molecular dynamics in time order in the latent space representation. This result potentially has promising application in computational biomolecules. One could use this VAE model to jump forward in time during a molecular dynamics simulation, and to enhance the sampling of protein configuration space.

Unveiling the geometrical and mechanical properties of Σ3 (111) grain boundaries in Ni-based alloys: From interfacial insights

Understanding the properties of interfaces and grain boundaries is pivotal for advancing the design and performance of modern materials and devices. The mechanical strength and durability of materials are significantly influenced by the integrity of these interfaces and grain boundaries. In this study, we employ density functional theory calculations to investigate the geometries, electronic properties, and mechanical behaviors of Σ3 (111) grain boundaries in Ni, AlNi3, and FeNi3 systems. Result reveals that these grain boundaries exhibit trigonal, hexagonal, and hexagonal close-packed structures with minimal bond length distortions, attributed to specific misorientation angles of 60°. They also demonstrate bonding characteristics akin to their corresponding polycrystalline bulk materials, indicating stability and twist character with anti-phase boundaries. Evaluation of grain boundary energetics indicates low energy values and stability across the studied systems. Furthermore, we conduct a detailed examination of the interfacial grain boundary structures of Σ3 (111) Ni/AlNi3 and Σ3 (111) Ni/FeNi3, revealing trigonal closed space configurations with twist character and anti-phase boundaries. Electron localization in interfacial regions suggests a metallic nature of interfacial bonds, supported by density of state calculations and positive Cauchy pressure. Assessment of mechanical properties indicate ductile behavior due to structural heterogeneity, moderate anisotropy. Overall, present study underscores the enhanced mechanical properties resulting from heterogeneity, offering promise for future applications in advanced materials and devices. Additionally, a comparative analysis with highlights the advancements and contributions of this study to the existing body of knowledge.

Optimizing canopy spacing configuration enhances foxtail millet grain yield and water productivity by improving stalk lodging resistance in the North China Plain

Optimizing canopy spacing configuration can enhance resources utilization, supporting robust growth and dry matter production, while mitigating the risk of lodging and improving crop yield and quality. However, research specifically addressing optimal canopy spacing configurations for foxtail millet remains limited. Over a two-year period, a field experiment in the North China Plain assessed the impacts of four-row spacing configurations (T0: 40 + 40 cm; T1: 30 + 50 cm; T2: 20 + 60 cm; T3: 10 + 70 cm), to investigate the effects of row spacing configuration on lodging resistance, canopy spatial configuration, stem characteristics, yield, and water productivity (WP) of foxtail millet, aiming to elucidate the underlying regulatory mechanisms. Row spacing configurations significantly influenced lodging resistance, yield, and WP. Under T1, improvements were observed in stem morphology and mechanical properties, particularly in the 2nd-6th basal internodes (I2-I6). The light interception rate in T1 at wide rows in the middle canopy (30–90 cm aboveground) increased by 97.89 %, compared to T0. Partial least squares-structural equation modeling revealed that improved light interception in wide rows in the middle canopy contributed to a rise in diameter and dry plumpness of I2. This, in turn, promoted greater breaking resistance of I2 and tensile resistance, ultimately reducing the lodging likelihood. Simultaneously, the decrease in lodging resulted in higher yield and WP at yield level of foxtail millet. Therefore, T1 demonstrated the lowest lodging rate (67.34 %–91.92 % lower than T0), and the highest yield and WP at yield level (4.10 %–8.03 % and 20.79 %–22.46 % higher than T0). Optimizing canopy spacing configuration is essential for cultivating high-yielding and water-efficient foxtail millet populations. The results indicated that the 30 + 50 cm row spacing configuration improves light distribution in the middle canopy, enhancing lodging resistance and consequently increasing both yield and WP. This research offers a theoretical foundation for foxtail millet breeding and agronomic practices to achieve lower lodging rate, higher yields, and enhanced WP in the North China Plain.

Effect of Different Planting Density in Cocoa (Theobroma cacao l.) on Leaf Macro and Micronutrient Levels Grown under Coconut Ecosystem

An experiment investigating the impact of different cocoa densities on leaf macro and micronutrient levels within a coconut ecosystem was conducted at the Coconut Farm of the Horticultural College and Research Institute, Tamil Nadu Agricultural University, Coimbatore. The study employed a Randomized Block Design (RBD) comprising eight treatments, each replicated three times. Notably, among the various spacing configurations, T1 (3m x 1.2m) exhibited the highest levels of leaf nitrogen (1.86%), phosphorus (0.084%), potassium (1.39%), and boron (91.33 ppm) content. This suggests that under Tamil Nadu conditions, high-density planting in the T1 treatment not only resulted in elevated nutrient levels but also correlated with a notable increase in revenue. These findings underscore the potential benefits of adopting high-density planting practices in cocoa cultivation within coconut ecosystems. Further research is warranted to explore the long-term implications of spacing configurations and nutrient interactions on crop productivity and profitability.

A fast and smooth one-electron approach for investigating charge transfer states and D1-D0 crossings for systems with odd numbers of electrons.

We propose an efficient version of ensemble Hartree-Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions-even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for abinitio non-adiabatic dynamics in the near future.

WFOT: A Wave Function Overlap Tool between Single- and Multi-Reference Electronic Structure Methods for Spectroscopy Simulation.

We report the development of a novel diagnostic tool, named wave function overlap tool (WFOT), designed to evaluate the overlap between wave functions computed at single-reference [i.e., time-dependent density functional theory or configuration interaction singles (CIS)] and multireference (i.e., CASSCF/CASPT2) electronic structure levels of theory. It relies on truncating the single- and multireference WFs to CIS-like expansions spanning the same configurational space and maximizing the molecular orbital overlap by means of a unitary transformation. To demonstrate the functionality of the tool, we calculate the transient spectrum of acetylacetone by evaluating excited state absorption signals with multireference quality on top of single-reference on-the-fly dynamics simulations. Semiautomatic spectra generation is facilitated by interfacing the tool with the COBRAMM package, which also allows one to use WFOT with several quantum chemistry codes such as Gaussian, NWChem, and OpenMolcas. Other exciting possibilities for the utilization of the code beyond the simulation of transient absorption spectroscopy are eventually discussed.

Input‐output linearization and decoupling of mechanical control systems

AbstractIn this article, we present the problem of simultaneous input‐output feedback linearization and decoupling (noninteracting) for mechanical control systems with outputs. We show that the natural requirement of preserving mechanical structure of the system and of transformations imposes supplementary conditions when compared to the classical solution of the same problem for general control systems. These conditions can be expressed using objects on the configuration space only. We illustrate our results with several examples of mechanical control systems.

Multistable compliant linkages with multiple kinematic paths separated by energy barriers

Multistable morphing structures can reconfigure between different stable states that are separated by energy barriers, and one-degree-of-freedom (1-DOF) mechanisms have many merits, like simple actuation. This paper combines the two and proposes a new family of reconfigurable compliant linkages with many (2−6) 1-DOF kinematic paths that are separated by energy barriers. This new type of design is an extension of multistable structures, where each stable state corresponds to not just one configuration but a 1-DOF configuration space, i.e., a kinematic path. Components of the linkages are made elastically compliant, therefore enabling the switch between two isolated compatible paths with multi-stability. A generation-selection hybrid design algorithm to follow prescribed reconfigurable paths is proposed, and a minimum energy path (MEP) finding method to guide actuation to switch between different kinematic paths is developed. Four design examples with 2–3 reconfigurable paths and their experiments are presented, and the effectiveness of this method is verified. This work provides a fresh perspective to design the single-DOF reconfigurable mechanisms with larger design space, more reconfigurable kinematic paths, and easier reconfiguration actuation.