Configuration Space Research Articles

Multisimplicial chains and configuration spaces

We define an E∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_\\infty $$\\end{document}-coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of E∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_\\infty $$\\end{document}-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.

Deep Learning-Enhanced Sampling-Based Path Planning for LTL Mission Specifications.

The presented paper introduces a novel path planning algorithm designed for generating low-cost trajectories that fulfill mission requirements expressed in Linear Temporal Logic (LTL). The proposed algorithm is particularly effective in environments where cost functions encompass the entire configuration space. A core contribution of this paper is the presentation of a refined approach to sampling-based path planning algorithms that aligns with the specified mission objectives. This enhancement is achieved through a multi-layered framework approach, enabling a simplified discrete abstraction without relying on mesh decomposition. This abstraction is especially beneficial in complex or high-dimensional environments where mesh decomposition is challenging. The discrete abstraction effectively guides the sampling process, influencing the selection of vertices for extension and target points for steering in each iteration. To further improve efficiency, the algorithm incorporates a deep learning-based extension, utilizing training data to accurately model the optimal trajectory distribution between two points. The effectiveness of the proposed method is demonstrated through simulated tests, which highlight its ability to identify low-cost trajectories that meet specific mission criteria. Comparative analyses also confirm the superiority of the proposed method compared to existing methods.

Machine learning-enabled chemical space exploration of all-inorganic perovskites for photovoltaics

The vast compositional and configurational spaces of multi-element metal halide perovskites (MHPs) result in significant challenges when designing MHPs with promising stability and optoelectronic properties. In this paper, we propose a framework for the design of B-site-alloyed ABX3 MHPs by combining density functional theory (DFT) and machine learning (ML). We performed generalized gradient approximation with Perdew–Burke–Ernzerhof functional for solids (PBEsol) on 3,159 B-site-alloyed perovskite structures using a compositional step of 1/4. Crystal graph convolution neural networks (CGCNNs) were trained on the 3159 DFT datasets to predict the decomposition energy, bandgap, and types of bandgaps. The trained CGCNN models were used to explore the compositional and configurational spaces of 41,400 B-site-alloyed ABX3 MHPs with a compositional step of 1/16, by accessing all possible configurations for each composition. The electronic band structures of the selected compounds were calculated using the hybrid functional (PBE0). Then, we calculated the optical absorption spectra and spectroscopic limited maximum efficiency of the selected compounds. Based on the DFT/ML-combined screening, 10 promising compounds with optimal bandgaps were selected, and from among these 10 compounds, CsGe0.3125Sn0.6875I3 and CsGe0.0625Pb0.3125Sn0.625Br3 were suggested as photon absorbers for single-junction and tandem solar cells, respectively. The design framework presented herein is a good starting point for the design of mixed MHPs for optoelectronic applications.

Comparative Life-Cycle Assessment of Steel and GFRP Rebars for Procurement Sustainability in the Construction Industry

This research examines the potential impact on the procurement sustainability of replacing steel rebars with Glass Fiber-Reinforced Polymer (GFRP) rebars in the construction industry, focusing on screed pre-cast hollow core topping in a project in the Kingdom of Saudi Arabia. A comparative life cycle assessment (LCA) is conducted using One Click LCA (Version 0.26.0) software for cradle-to-grave analysis. The assessment covers various stages, including raw material extraction, manufacturing, transportation, usage, and recycling. The comprehensive LCA highlights GFRP rebars as a more sustainable alternative to steel, emitting 17% less CO2 equivalent (2e) per kilogram throughout its life cycle. Additionally, GFRP requires substantially less mass compared to steel, resulting in a dramatic reduction in CO2e emissions ranging from 77.89% to 85.26% across different spacing configurations in real-world construction scenarios, as presented in this research case study. These findings suggest that GFRP rebars offer a promising solution for reducing the environmental impact of construction activities while potentially yielding significant cost savings over the project’s life cycle. Integrating environmental considerations into material selection processes can prioritize sustainability without compromising performance or safety, contributing to a more sustainable future for the construction industry globally.

In-silico Studies, Design, and Synthesis of Pyrimidine-linked Benzothiazoles for its Anticonvulsant Potential.

The objective of the study was to design and synthesize a series of N-(6-substituted-1,3-benzothiazole- 2-yl)-2-{[6-(3-substitutedphenyl)-5-cyano-2-sulfanylpyrimidine-4-yl)]amino}acetamide derivatives BPD (1-15) that contains key pharmacophores required for anticonvulsant action. The titled compounds (BPD 1-15) were synthesized by reacting 2-substituted-N-(6-chlorobenzo[d]thiazol2-yl)acetamide with 4-amino-6-(4-substituted phenyl)-2-mercapto pyrimidine 5-carbonitrile in the presence of potassium carbonate and dry acetone. The synthesized compounds BPD (1-15) were assessed in vivo by the maximum electric shock (MES) test and the subcutaneous pentylenetetrazol (scPTZ) test in mice. The neurotoxicity test was performed by the rotarod test. A molecular docking study of title compounds with a sodium channel receptor (PDB ID: 1BYY) was carried out using the SP Docking protocol of the Glide module of the Maestro. Pharmacophore modeling was used to qualitatively identify the chemical characteristics for ligand binding and their spatial configurations in the 3D space of the active site. Among the studied compounds, BPD-15 and BPD-5 compounds showed significant action in both the MES and scPTZ models, with no neurotoxicity. BPD-15 & BPD-5 were relatively safe in acute toxicity testing. Compounds BPD-15 and BPD-5 showed good dock scores of -6.434 and -6.191, respectively. Thus, the compounds BPD-15 and BPD-5 have shown a considerable affinity towards the sodium channel as compared to the standard drug Riluzole. Compound BPD-14 showed good drug compatibility, and compounds BPD-1, BPD-2, BPD-11, BPD-12, BPD-13, BPD-14, BPD-15 showed good ADME values.

The anti-dogbone: Evaluating and designing optimal tensile specimens for deep learning of constitutive relations

Traditional tensile testing with “dogbone”-shaped specimen (ASTM E8, first standardized in 1924) strives for strain uniformity. Multiple tests with such samples help fit simple constitutive relation parameters on real materials. With the development of deep learning, the concept of employing entirely data-driven constitutive relations to capture more intricate material behavior has arisen. Nevertheless, these methods demand experimental data that are distributed throughout the complete stress–strain configuration space to effectively train the machine learning models. This is particularly crucial for mechanisms like hardening, which are time-dependent and sensitive to loading history. In this work, we investigate the potential to efficiently gather a wider range of experimental data points in the stress–strain configuration space using non-uniform samples and displacement-field mapping, leveraging advancements in computer vision techniques. We developed a metric to quantify stress state diversity in 2D tensile experiments and used it to optimize the shape of the sheet sample. The goal was to increase stress–strain diversity obtained within a single test, particularly in the linear elastic regime. Additional geometric constraints can be introduced on the design features, considering factors such as size and curvature to adapt to the microstructural characteristics of the sample material.

Network science: Ising states of matter.

Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction power of network science has not yet been systematically explored in this context. Here we fill this gap by providing an in-depth statistical, combinatorial, geometrical, and topological characterization of 2D Ising snapshot networks (IsingNets) extracted from Monte Carlo simulations of the 2D Ising model at different temperatures, going across the phase transition. Our analysis reveals the complex organization properties of IsingNets in both the ferromagnetic and paramagnetic phases and demonstrates the significant deviations of the IsingNets with respect to randomized null models. In particular percolation properties of the IsingNets reflect the existence of the symmetry between configurations with opposite magnetization below the critical temperature and the very compact nature of the two emerging giant clusters revealed by our persistent homology analysis of the IsingNets. Moreover, the IsingNets display a very broad degree distribution and significant degree-degree correlations and weight-degree correlations demonstrating that they encode relevant information present in the configuration space of the 2D Ising model. The geometrical organization of the critical IsingNets is reflected in their spectral properties deviating from the one of the null model. This work reveals the important insights that network science can bring to the characterization of phases of matter. The set of tools described hereby can be applied as well to numerical and experimental data.

Homology and Euler characteristic of generalized anchored configuration spaces of graphs

AbstractIn this paper we consider the generalized anchored configuration spaces on n labeled points on a graph. These are the spaces of all configurations of n points on a fixed graph G, subject to the condition that at least q vertices in some pre-determined set K of vertices of G are included in each configuration. We give a non-alternating formula for the Euler characteristic of such spaces for arbitrary connected graphs, which are not trees. Furthermore, we completely determine the homology groups of the generalized anchored configuration spaces of n points on a circle graph.

A realist interpretation of unitarity in quantum gravity

Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalisability and the problem of time. We take a realist approach based on pilot-wave theory to address this issue in the Ashtekar formulation of the Wheeler–DeWitt equation. We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system recently discussed in Alexander et al (2022 Phys. Rev. D 106 106012), by parameterising a variation of a Weyl-spinor that depends on the Kodama state. The total Hamiltonian constraint yields a time-dependent Schrodinger equation, without semi-classical approximations, which we use to derive a local continuity equation over the configuration space. We implement the reality conditions at the level of the guidance equation, and obtain a real spin-connection, extrinsic curvature and triad along the system trajectory. We obtain quantum corrections to deSitter spacetime from the guidance equation. The non-normalisable Kodama state is naturally factored out of the full quantum state in the conserved current density, opening the possibility for quantum-mechanical unitarity. We also give a pilot-wave generalisation of the notion of unitarity applicable to non-normalisable states, and show the existence of equilibrium density for our system. Lastly, we find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.

Effects of general relativistic post-Newtonian approximations on the configuration space properties of elliptical orbital trajectories

Post-Newtonian approximations have been successful in describing various astronomical phenomena that classical Newtonian gravity could not. One such phenomenon is the precession of the periapsis of elliptical orbits. Einstein originally solved the problem in 1916 and since then others have been applying the technique to numerous complex systems. However, not much attention has been given to studying the changes in the configuration space when switching from Newtonian to post-Newtonian mechanics. Here, we compare the sizes and topologies of the configuration spaces of both these approaches and further explore the likelihood of planetary collisions in other star systems when configuration space expansion due to general relativity is taken into account.

Optimization for bilevel spatial configuration of underground space surrounding high-speed railway station in China from the perspective of urban morphology

The rapid growth of high-speed railways has led to the development of underground spaces surrounding high-speed railway stations (USSHRSs). The evolution of USSHRS has enhanced the space utilization efficiency. As USSHRSs expand, the layout of the underground connectivity network becomes increasingly intricate. Additionally, pedestrian behavior in USSHRSs transitions from mere passing to longer stays, and its spatial configuration becomes more difficult to evaluate. To date, studies have mostly focused on the structural analysis or inner underground space relationship of USSHRSs. A research gap exists in the field of USSHRS spatial configuration from the perspective of urban development. To fill this research gap, this study focused on the spatial configuration of the USSHRS from the perspective of urban morphology and established a quantitative analysis method for USSHRSs at both global and local levels. At the global level, we devised a method for measuring the USSHRS spatial configuration using pedestrian composite accessibility based on a complex network. At the local level, we used space syntax to study the inner spatial configuration problems of USSHRSs. Finally, we used the Shanghai Hongqiao Station (Shanghai, China) as a case study. The results revealed that the spatial configuration optimization of the USSHRS must improve the connectivity efficiency of the USSHRS, and the corresponding functional layout should also be optimized towards a centralized layout. This study aims to provide decision-making support for the planning and layout of complicated USSHRS and to highlight the role of USSHRS in urban sustainable development.

Model predictive manipulation of compliant objects with multi-objective optimizer and adversarial network for occlusion compensation

Background:The manipulation of compliant objects by robotic systems remains a challenging task, largely due to their variable shapes and the complex, high-dimensional nature of their interaction dynamics. Traditional robotic manipulation strategies struggle with the accurate modeling and control necessary to handle such materials, especially in the presence of visual occlusions that frequently occur in dynamic environments. Meanwhile, for most unstructured environments, robots are required to have autonomous interactions with their surroundings. Methods:To solve the shape manipulation of compliant objects in an unstructured environment, we begin by exploring the regression-based algorithm of representing the high-dimensional configuration space of deformable objects in a compressed form that enables efficient and effective manipulation. Simultaneously, we address the issue of visual occlusions by proposing the integration of an adversarial network, enabling guiding the shaping task even with partial observations of the object. Afterwards, we propose a receding-time estimator to coordinate the robot action with the computed shape features while satisfying various performance criteria. Finally, model predictive controller is utilized to compute the robot’s shaping motions subject to safety constraints. Detailed experiments are presented to evaluate the proposed manipulation framework. Significant findings:Our MPC framework utilizes the compressed representation and occlusion-compensated information to predict the object’s behavior, while the multi-objective optimizer ensures that the resulting control actions meet multiple performance criteria. Through rigorous experimental validation, our approach demonstrates superior manipulation capabilities in scenarios with visual obstructions, outperforming existing methods in terms of precision and operational reliability. The findings highlight the potential of our integrated approach to significantly enhance the manipulation of compliant objects in real-world robotic applications.

Unified invariant of knots from homological braid action on Verma modules

AbstractWe re‐build the quantum unified invariant of knots from braid groups' action on tensors of Verma modules. It is a two variables series having the particularity of interpolating both families of colored Jones polynomials and ADO polynomials, that is, semisimple and non‐semisimple invariants of knots constructed from quantum . We prove this last fact in our context that re‐proves (a generalization of) the famous Melvin–Morton–Rozansky conjecture first proved by Bar‐Natan and Garoufalidis. We find a symmetry of nicely generalizing the well‐known one of the Alexander polynomial, ADO polynomials also inherit this symmetry. It implies that quantum non‐semisimple invariants are not detecting knots' orientation. Using the homological definition of Verma modules we express as a generating sum of intersection pairing between fixed Lagrangians of configuration spaces of disks. Finally, we give a formula for using a generalized notion of determinant, that provides one for the ADO family. It generalizes that for the Alexander invariant.

Configuration space of helical chiral self-assembly of micro/nano-fibers

As undertaking various key functions, helical chiral structures are widely presented in nature. Herein, we develop a general theoretical framework to guide the formation of helical chiral structures through self-assembly of micro/nano-fibers driven by adhesion. By analyzing the spiral contact geometric characteristics of multiple fibers and extending the JKR theory, an analytical model for adhesive contact between helical interfaces is proposed. Further, the complete configuration space of self-assembled fibers depending on the adhesion work, elastic modulus, aspect ratio, and initial helix angle is theoretically obtained. A diversity of helical configurations that far beyond existing experimental findings are predicted, which stems from the existence of multiple energy minimum points on the configuration-energy map. This work reveals the mechanism of adhesion-driven helical chiral structures, and provides theoretical foundation for guiding high-efficient fabrication of helical chiral structures through self-assembly method, which could promote the wide application of chiral structures in fields such as optics, catalysis and drug screening.

Electric field and higher harmonics of RF plasma slit jet measured by antennas and VI probes

The cold atmospheric plasma jets change their character when interacting with the different surfaces. Since such interaction is the primary area of plasma jet applications, it is essential to monitor the process. The non-linearity of the RF plasma slit jet (PSJ) was analyzed using the VI probes and a novel method, the non-intrusive antenna measurements. Regardless of the experimental setup and gas mixture (Ar, Ar/O2, Ar/N2), the PSJ frequency spectrum consisted of the following main features: dominant fundamental frequency peak, relatively strong odd harmonics, and significantly weaker even harmonics. The lowest degree of non-linearity was recorded for the Ar PSJ ignited against a grounded target. Admixing a molecular gas increased the discharge non-linearity. It was attributed to the enhancement of secondary electron emission from the dielectric surfaces. In addition to the non-linearity analysis, the antenna spectra were for the first time used to determine the semi-quantitative values of the PSJ-radiated electric field. The electric fields decreased by a factor of 2 after the admixing of nitrogen and oxygen molecular gases. Out of the studied targets, the highest electric fields were observed when plasma impinged on the grounded targets, followed by the floating target (2× lower) and the PSJ ignited in the open space configuration (4× lower than in the grounded target configuration).

Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials

Efficiently creating a concise but comprehensive data set for training machine-learned interatomic potentials (MLIPs) is an under-explored problem. Active learning, which uses biased or unbiased molecular dynamics (MD) to generate candidate pools, aims to address this objective. Existing biased and unbiased MD-simulation methods, however, are prone to miss either rare events or extrapolative regions—areas of the configurational space where unreliable predictions are made. This work demonstrates that MD, when biased by the MLIP’s energy uncertainty, simultaneously captures extrapolative regions and rare events, which is crucial for developing uniformly accurate MLIPs. Furthermore, exploiting automatic differentiation, we enhance bias-forces-driven MD with the concept of bias stress. We employ calibrated gradient-based uncertainties to yield MLIPs with similar or, sometimes, better accuracy than ensemble-based methods at a lower computational cost. Finally, we apply uncertainty-biased MD to alanine dipeptide and MIL-53(Al), generating MLIPs that represent both configurational spaces more accurately than models trained with conventional MD.

Low fidelity data driven machine learning based optimisation method for box-wing configuration

Wing design optimization traditionally involves computationally expensive high-fidelity simulations, limiting the exploration of design spaces. In this study, we propose a methodology that combines low-fidelity numerical models with machine learning algorithms to efficiently navigate the complex parameter space of box-wing configurations. Through the utilisation of a surrogate model trained on a limited dataset derived from low-fidelity simulations, our method strives to predict results within an acceptable range, significantly curtailing computational costs and time. The effectiveness of this methodology is demonstrated through a series of case studies, involving the Onera M6 and NASA CRM wing as test cases and Bionica box-wing optimization as an application case. The initial application of the proposed methodology to the box-wing case successfully achieved an almost 9.82 % increase in overall aerodynamic efficiency. Its competitive performance compared to conventional optimization methods, along with its substantial reduction in computational time and resource requirements, is evident. This efficient methodology holds promise for enhancing the design optimization process for aviation start-ups by efficiently exploring complex design spaces with reduced computational burden.

Topological actions of Temperley–Lieb monoids and representation stability

In this paper, we consider the Temperley–Lieb algebras [Formula: see text] at [Formula: see text]. Since [Formula: see text], we can consider the multiplicative monoid structure and ask how this monoid acts on topological spaces. Given a monoid action on a topological space, we get an algebra action on each homology group. The main theorem of this paper explicitly deduces the representation structure of the homology groups in terms of a natural filtration associated with our [Formula: see text]-space. As a corollary of this result, we are able to study stability phenomena. There is a natural way to define representation stability in the context of [Formula: see text], and the presence of filtrations enables us to define a notion of topological stability. We are able to deduce that a filtration-stable sequence of [Formula: see text]-spaces results in representation-stable sequence of homology groups. This can be thought of as the analogue of the statement that the homology of configuration spaces forms a finitely generated FI-module.

Generalized color orderings: CEGM integrands and decoupling identities

In a recent paper, we defined generalized color orderings (GCO) and Feynman diagrams (GFD) to compute color-dressed generalized biadjoint amplitudes. In this work, we study the Cachazo-Early-Guevara-Mizera (CEGM) representation of generalized partial amplitudes and “decoupling” identities. This representation is a generalization of the Cachazo-He-Yuan (CHY) formulation as an integral over the configuration space X(k,n) of n points on CPk−1 in generic position.Unlike the k=2 case, Parke-Taylor-like integrands are not enough to compute all partial amplitudes for k>2. Here we give a set of constraints that integrands associated with GCOs must satisfy and use them to construct all (3,n<9) integrands, all (3,9) integrands up to four undetermined constants, and 95% of (4,8) integrands up to 24 undetermined constants.k=2 partial amplitudes are known to satisfy identities. Among them, the so-called U(1) decoupling identities are the simplest ones. These are characterized by a label i and a color ordering in X(2,|[n]∖{i}|). Here we introduce decoupling identities for k>2 determined combinatorially using GCOs. Moreover, we identify the natural analog of U(1) identities as those characterized by a pair of labels i≠j, and a pair of GCOs, one in X(k,|[n]∖{i}|) and the other in X(k−1,|[n]∖{j}|). We call them double extension identities.We also provide explicit connections among different ways of representing GCOs, such as configurations of lines, configurations of points, and reorientation classes of uniform oriented matroids (chirotopes).

Automatic Determination of the Non-Covalent Stable Conformations of the NO2-Pyrene Cluster in Full Dimensionality (81D) Using the vdW-TSSCDS Approach.

We present the detailed topographical characterisation (stationary points and minimum energy paths connecting them) of the full dimensional (81D) intermolecular potential energy surface associated with the non-covalent interactions between the NO2 radical and the pyrene (C16H10) molecule. The whole procedure is (quasi) fully automated. We have used our recent algorithm vdW-TSSCDS as implemented on the freely-available AutoMekin software package. To this end, a series of inexpensive classical trajectories using forces from a low-level (semi-empirical) theory are used to sample the configuration space of the system in the search for candidates to first order saddle points. These guess structures are determined by means of a graph-theory based algorithm using the concept of adjacency matrix. Low-level optimizations are followed by re-optimizations at a final high-level of theory (DFT and CCSD(T)-F12 in our case.). The resulting set of stationary points and paths connecting them constitutes the so-called reaction network. In the case of NO2-pyrene, this network exhibits four major basins which can be characterized by their point-group symmetry. A central one, of global C2 symmetry, comprises the global minimum (as well as all other permutationally related conformers) together with the corresponding C2v saddle points connecting them. This central basin is connected to three others of lower C1 symmetry. The latter can be distinguished by the projection of the position of the NO2 nitrogen atom on the pyrene plane in combination with the relative orientation of the oxygen pair pointing either inwards, outwards, upwards or downwards.