Configuration Space Research Articles

Kirillov structures and reduction of Hamiltonian systems by scaling and standard symmetries

AbstractIn this paper, we discuss the reduction of symplectic Hamiltonian systems by scaling and standard symmetries which commute. We prove that such a reduction process produces a so‐called Kirillov Hamiltonian system. Moreover, we show that if we reduce first by the scaling symmetries and then by the standard ones or in the opposite order, we obtain equivalent Kirillov Hamiltonian systems. In the particular case when the configuration space of the symplectic Hamiltonian system is a Lie group , which coincides with the symmetry group, the reduced structure is an interesting Kirillov version of the Lie–Poisson structure on the dual space of the Lie algebra of . We also discuss a reconstruction process for symplectic Hamiltonian systems which admit a scaling symmetry. All the previous results are illustrated in detail with some interesting examples.

Is the spatial distribution of urban green space associated with crime in Chicago?

During past decades, much progress has been made to elucidate the relationship between the quantity of urban green space and crimes, but less is known about how their spatial distribution is associated with crimes. Therefore, this study aims to understand how the composition and configuration of urban green space are related to crimes in metropolitan cities in the United States. Our study performed landscape analysis using 756 census tracts for violent crimes and non-violent crimes in Chicago from 2017 to 2021 while controlling socioeconomic status. Spatial lag models showed that tree canopies were negatively associated with crime rates, while grass areas were positively associated with crime rates. In terms of the spatial distribution, there were more crime incidents in irregularly shaped green spaces compared to reguraraly shaped green spaces. On the contrary, disconnected tree canopies were more likely to have lower crime rates. Aggregated (i.e., a single large) also tended to have less crime rates. The results of our study provide some evidence of the role of the spatial distribution of urban green space on crimes and shed light on the ways to reduce crimes through effective urban green space planning

Confinement from distance in metric space and its relation to cosmological constant

We argue that, in a theory of quantum gravity, the gauge coupling and the confinement scale of a gauge theory are related to distance in the space of metric configurations, and in turn to the cosmological constant. To support the argument, we compute the gauge kinetic functions in variuos supersymmetric Heterotic and type II string compactifications and show that they depend on distance. According to the swampland program, the distance between two (anti) de Sitter vacua in the space of metric configurations is proportional to the logarithm of the ratio of cosmological constants and thus the confinement scale depends on the value of the cosmological constant. In this framework, for de Sitter space, we revisit the swampland Festina Lente bound and gauge theories in the dark dimension scenario. We show that if the Festina Lente bound is realized in a de Sitter vacuum and dependence on distance is strong enough, it will be realized in vacua with higher cosmological constants. In dark dimension scenario, as the value of cosmological constant is related to the decompactifying dimension, we find that the confinement scale is indeed related to radius of dark dimension. We show that in this scenario the Festina Lente bound holds for the standard model QCD, as well as all confining gauge groups with Nc ≲ 103.

Greenness and its composition and configuration in association with allergic rhinitis in preschool children

BackgroundFew studies focus on the associations of green space composition and configuration with children's allergic rhinitis (AR). MethodsA multi-center population-based cross-sectional study was performed in 7 cities in mainland of China between 2019 and 2020, recruiting 36,867 preschool children. Information on the current AR symptoms and demographics were collected by questionnaire. Exposure to residential greenness was estimated by Normalized Difference Vegetation Index (NDVI, 1000 m buffer) around the residences. Greenness composition was estimated in 3 main categories: forest, grassland, shrubland. Configuration of each category and total greenness (a spatial resolution of 10 m × 10 m) was estimated by 6 landscape pattern metrics to quantify their area, shape complexity, aggregation, connectivity, and patch density. Exposure to daily ambient particulate matter (PM1, PM2.5 and PM10, a spatial resolution of 1 km × 1 km) was estimated. Multilevel logistic regression models were applied to analyze the associations of greenness and its composition and configuration with AR, and mediation effects by PMs were examined by mediation analysis models. ResultsThe prevalence of self-reported current AR in preschool children was 33.1%. Two indicators of forest, Aggregation Index of forest patches (AIforest) (odds ratio (OR):0.92, 95% Confidential Interval (CI): 0.88–0.97), and Patch Cohesion of forest (COHESIONforest) (OR: 0.93, 95% CI:0.89–0.98) showed significantly negative associations with AR symptoms. Mediation analyses found the associations were partially mediated by PMs. Age, exclusive breastfeed duration and season were the potential effect modifiers. The associations varied across seven cities. ConclusionOur findings suggest the inverse associations of the aggregation and connectivity of forest patches surrounding residence addresses with AR symptoms. Since the cross-sectional study only provides associations rather than causation, further studies are needed to confirm our results as well as the underlying mechanisms.

Matrix‐Product State Approach to the Generalized Nuclear Pairing Hamiltonian

AbstractIt is shown that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix‐product state) despite the presence of long‐range interactions. The ground state can be obtained using the density‐matrix renormalization group (DMRG) algorithm, which is accurate up to machine precision even for large nuclei, is numerically as cheap as the widely used Bardeen‐Cooper‐Schrieffer (BCS) approach, and does not suffer from any mean‐field artifacts. This framework is applied to compute the even‐odd mass differences of all known lead isotopes from to in a very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. Pairing with non‐zero angular momentum is also considered and the lowest excited states in the full configuration space of one major shell is determined, which is demonstrated for the , isotones. To demonstrate the capabilities of the method beyond low‐lying excitations, the first 100 excited states of with singlet pairing and the two‐neutron removal spectral function of are calculated, which relate to a two‐neutron pickup experiment.

Machine learning accelerated discovery of corrosion-resistant high-entropy alloys

Corrosion has a wide impact on society, causing catastrophic damage to structurally engineered components. An emerging class of corrosion-resistant materials are high-entropy alloys. However, high-entropy alloys live in high-dimensional composition and configuration space, making materials designs via experimental trial-and-error or brute-force ab initio calculations almost impossible. Here we develop a physics-informed machine-learning framework to identify corrosion-resistant high-entropy alloys. Three metrics are used to evaluate the corrosion resistance, including single-phase formability, surface energy and the compactness of oxide films formed on an alloy surface evaluated by Pilling–Bedworth ratios. We used random forest models to predict the single-phase formability, trained on an experimental dataset. Machine learning inter-atomic potentials were employed to calculate surface energies and Pilling–Bedworth ratios, which are trained on first-principles data fast sampled using embedded atom models. A combination of random forest models and high-fidelity machine learning potentials represents the first of its kind to relate chemical compositions to corrosion resistance of high-entropy alloys, paving the way for automatic design of materials with superior corrosion protection. This framework was demonstrated on AlCrFeCoNi high-entropy alloys and we identified composition regions with high corrosion resistance from a wide range of compositions. Machine learning predicted lattice constants and surface energies are consistent with values by first-principles calculations. The predicted single-phase formability and corrosion-resistant compositions of AlCrFeCoNi agree well with experiments. This framework provides a computationally efficient approach to navigate high-dimensional composition space of high-entropy alloys. It is general in its application and applicable to other complex materials, enabling high-throughput screening of material candidates and potentially accelerating the iteration of integrated computational materials engineering.

Topological Kolmogorov complexity and the Berezinskii-Kosterlitz-Thouless mechanism.

Topology plays a fundamental role in our understanding of many-body physics, from vortices and solitons in classical field theory to phases and excitations in quantum matter. Topological phenomena are intimately connected to the distribution of information content that, differently from ordinary matter, is now governed by nonlocal degrees of freedom. However, a precise characterization of how topological effects govern the complexity of a many-body state, i.e., its partition function, is presently unclear. In this paper, we show how topology and complexity are directly intertwined concepts in the context of classical statistical mechanics. We concretely present a theory that shows how the Kolmogorov complexity of a classical partition function sampling carries unique, distinctive features depending on the presence of topological excitations in the system. We confront two-dimensional Ising, Heisenberg, and XY models on several topologies and study the corresponding samplings as high-dimensional manifolds in configuration space, quantifying their complexity via the intrinsic dimension. While for the Ising and Heisenberg models the intrinsic dimension is independent of the real-space topology, for the XY model it depends crucially on temperature: across the Berezkinskii-Kosterlitz-Thouless (BKT) transition, complexity becomes topology dependent. In the BKT phase, it displays a characteristic dependence on the homology of the real-space manifold, and, for g-torii, it follows a scaling that is solely genus dependent. We argue that this behavior is intimately connected to the emergence of an order parameter in data space, the conditional connectivity, which displays scaling behavior. Our approach paves the way for an understanding of topological phenomena emergent from many-body interactions from the perspective of Kolmogorov complexity.

A slow feature analysis approach for the optimization of collective variables.

Molecular dynamics simulations have become increasingly important in understanding the microscopic mechanisms of various molecular systems. However, the high energy barriers in complicated molecules often make it difficult to observe events of interest within a reasonable timescale. To address this issue, researchers have developed a variety of enhanced sampling methods to explore configuration space by adding bias potentials along the slowly changing collective variables (CVs). In this study, we have developed a new tool that combines slow feature analysis and biasing-enhanced sampling methods to identify effective CVs and enhance the sampling efficiency of configuration space. We have demonstrated the effectiveness of this tool through three general examples.

Adaptive Bayesian contextual hyperband: A novel hyperparameter optimization approach

<p>Hyperparameter tuning plays a significant role when building a machine learning or a deep learning model. The tuning process aims to find the optimal hyperparameter setting for a model or algorithm from a pre-defined search space of the hyperparameters configurations. Several tuning algorithms have been proposed in recent years and there is scope for improvement in achieving a better exploration-exploitation tradeoff of the search space. In this paper, we present a novel hyperparameter tuning algorithm named adaptive Bayesian contextual hyperband (Adaptive BCHB) that incorporates a new sampling approach to identify best regions of the search space and exploit those configurations that produce minimum validation loss by dynamically updating the threshold in every iteration. The proposed algorithm is assessed using benchmark models and datasets on traditional machine learning tasks. The proposed Adaptive BCHB algorithm shows a significant improvement in terms of accuracy and computational time for different types of hyperparameters when compared with state-of-the-art tuning algorithms.</p>

Enhancing Development of Modular Application-Specific Configurable Space Robots

In many space activities, existing robotic systems are highly mission-specific and cannot be reused. On the other hand, there are several highly modular system designs, that lack the specialized hardware, yet. The MODKOM (Modular Components as Building Blocks for Application-specific Configurable Space Robots) project, aims to create a toolbox that allows to configure and recombine a robot for certain tasks, out of specialized and standardized building blocks; this also includes commercial off-the-shelf components. Therefore, MODKOM also focuses on providing a software framework to compose and configure such systems. Based on the proposed system modeling, all entities (hard- & software) can be represented, handled, and also be stored to reuse sub-systems. By providing adequate (graphical) user interfaces and thereby lowering the need for manually-typed files, this process is simplified benefiting accessibility to non-experts. First tests in parallel projects show already the reduced necessity for manual configuration work and thus, a decrease in mistakes in formerly error-prone tasks. MODKOM also provides a set of modular hardware building blocks, which will be used in the upcoming final demonstration scenario to evaluate the advances made.

Exploration-Exploitation Paradigm for Networked Biological Systems.

The stochastic exploration of the configuration space and the exploitation of functional states underlie many biological processes. The evolutionary dynamics stands out as a remarkable example. Here, we introduce a novel formalism that mimics evolution and encodes a general exploration-exploitation dynamics for biological networks. We apply it to the brain wiring problem, focusing on the maturation of that of the nematode Caenorhabditis elegans. We demonstrate that a parsimonious maxent description of the adult brain combined with our framework is able to track down the entire developmental trajectory.

Configuration, furniture layout, and earthquake hazards in campus buildings

Indonesia is the most disaster-prone country in the world because it is geographically located in the ring of fire and tectonic plate confluence. Campus buildings have large occupancy of up to 10,000 students at a time, increasing their vulnerability to disasters. The 2006 Yogyakarta earthquake affected several campuses, such as soft stories and short columns. It is clarified that the movement and shifting of furniture during the earthquake caused 90% of casualties and injuries. This study aims to identify the physical characteristics of the campus in general as well as the potential for earthquake hazards, specifically in the aspects of building configuration and furniture layout. This research was conducted using the campus-watching method that allows the students to identify the risks in the campus building. This research found that the campus buildings in Indonesia generally had an elongated space configuration with O, I, T, L, and U shapes with a ratio of more than 1:2, causing a higher risk of earthquake hazards. The risk of the soft story was identified in the lobby. The short columns in the campus building were formed due to a consecutive halved window-wall application in the classrooms and were observed to be prone to weakening. Using movable furniture, glass partitions, and racks raises the risk during the earthquake. Tables inside the room can be utilized as a temporary safe place during the earthquake. So, it is essential to use sturdy tables and ensure sufficient tables to be used as a temporary shelter during an earthquake.

Learning stochastic dynamics and predicting emergent behavior using transformers

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior under conditions not observed during training. We consider a lattice model of active matter undergoing continuous-time Monte Carlo dynamics, simulated at a density at which its steady state comprises small, dispersed clusters. We train a neural network called a transformer on a single trajectory of the model. The transformer, which we show has the capacity to represent dynamical rules that are numerous and nonlocal, learns that the dynamics of this model consists of a small number of processes. Forward-propagated trajectories of the trained transformer, at densities not encountered during training, exhibit motility-induced phase separation and so predict the existence of a nonequilibrium phase transition. Transformers have the flexibility to learn dynamical rules from observation without explicit enumeration of rates or coarse-graining of configuration space, and so the procedure used here can be applied to a wide range of physical systems, including those with large and complex dynamical generators.

Accelerating multi-tier storage cache simulations using knee detection

Storage cache hierarchies include diverse topologies, assorted parameters and policies, and devices with varied performance characteristics. Simulation enables efficient exploration of their configuration space while avoiding expensive physical experiments. Miss Ratio Curves (MRCs) efficiently characterize the performance of a cache over a range of cache sizes, revealing “key points” for cache simulation, such as knees in the curve that immediately follow sharp cliffs. Unfortunately, there are no automated techniques for efficiently finding key points in MRCs, and the cross-application of existing knee-detection algorithms yields inaccurate results.We present a multi-stage framework that identifies key points in any MRC, for both stack-based (e.g., LRU) and more sophisticated eviction algorithms (e.g., ARC). Our approach quickly locates candidates using efficient hash-based sampling, curve simplification, knee detection, and novel post-processing filters. We introduce Z-Method, a new multi-knee detection algorithm that employs statistical outlier detection to choose promising points robustly and efficiently.We evaluated our framework against seven other knee-detection algorithms, identifying key points in multi-tier MRCs with both ARC and LRU policies for 106 diverse real-world workloads. Compared to naïve approaches, our framework reduced the total number of points needed to accurately identify the best two-tier cache hierarchies by an average factor of approximately 5.5× for ARC and 7.7× for LRU.We also show how our framework can be used to seed the initial population for evolutionary algorithms. We ran 32,616 experiments requiring over three million cache simulations, on 151 samples, from three datasets, using a diverse set of population initialization techniques, evolutionary algorithms, knee-detection algorithms, cache replacement algorithms, and stopping criteria. Our results showed an overall acceleration rate of 34% across all configurations.

Robust training of machine learning interatomic potentials with dimensionality reduction and stratified sampling

Machine learning interatomic potentials (MLIPs) enable accurate simulations of materials at scales beyond that accessible by ab initio methods and play an increasingly important role in the study and design of materials. However, MLIPs are only as accurate and robust as the data on which they are trained. Here, we present DImensionality-Reduced Encoded Clusters with sTratified (DIRECT) sampling as an approach to select a robust training set of structures from a large and complex configuration space. By applying DIRECT sampling on the Materials Project relaxation trajectories dataset with over one million structures and 89 elements, we develop an improved materials 3-body graph network (M3GNet) universal potential that extrapolates more reliably to unseen structures. We further show that molecular dynamics (MD) simulations with the M3GNet universal potential can be used instead of expensive ab initio MD to rapidly create a large configuration space for target systems. We combined this scheme with DIRECT sampling to develop a reliable moment tensor potential for titanium hydrides without the need for iterative augmentation of training structures. This work paves the way for robust high-throughput development of MLIPs across any compositional complexity.

Accelerated Lignocellulosic Molecule Adsorption Structure Determination.

Here, we present a study combining Bayesian optimization structural inference with the machine learning interatomic potential Neural Equivariant Interatomic Potential (NequIP) to accelerate and enable the study of the adsorption of the conformationally flexible lignocellulosic molecules β-d-xylose and 1,4-β-d-xylotetraose on a copper surface. The number of structure evaluations needed to map out the relevant potential energy surfaces are reduced by Bayesian optimization, while NequIP minimizes the time spent on each evaluation, ultimately resulting in cost-efficient and reliable sampling of large systems and configurational spaces. Although the applicability of Bayesian optimization for the conformational analysis of the more flexible xylotetraose molecule is restricted by the sample complexity bottleneck, the latter can be effectively bypassed with external conformer search tools, such as the Conformer-Rotamer Ensemble Sampling Tool, facilitating the subsequent lower-dimensional global minimum adsorption structure determination. Finally, we demonstrate the applicability of the described approach to find adsorption structures practically equivalent to the density functional theory counterparts at a fraction of the computational cost.

Variability modeling of products, processes, and resources in cyber–physical production systems engineering

Cyber-Physical Production Systems (CPPSs), such as automated car manufacturing plants, execute a configurable sequence of production steps to manufacture products from a product portfolio. In CPPS engineering, domain experts start with manually determining feasible production step sequences and resources based on implicit knowledge. This process is hard to reproduce and highly inefficient. In this paper, we present the Extended Iterative Process Sequence Exploration (eIPSE) approach to derive variability models for products, processes, and resources from a domain-specific description. To automate the integrated exploration and configuration process for a CPPS, we provide a toolchain which automatically reduces the configuration space and allows to generate CPPS artifacts, such as control code for resources. We evaluate the approach with four real-world use cases, including the generation of control code artifacts, and an observational user study to collect feedback from engineers with different backgrounds. The results confirm the usefulness of the eIPSE approach and accompanying prototype to straightforwardly configure a desired CPPS.

Space Layout Simulation of Assembled Nanoarchitecture Based on Improved Particle Swarm Optimization

In order to solve the problem that the traditional building space configuration model cannot meet the optimization of building space characteristics, the author proposes the optimization of building space utilization based on spatialized particle swarm optimization. First, to solve the problem of optimal allocation of space units, the PSO algorithm is modified to encode the space units by means of character coding.Secondly, the maximum standardization method is used for data processing, and the factors affecting space utilization are summarized, the objective function of optimal allocation of architectural space is given from three aspects: economic benefits, social benefits and ecological benefits; Finally, by analyzing the advantages and disadvantages of master-slave parallel model and point-to-point parallel model, a chained parallel structure is proposed. The experimental results show that: The experimental data is based on the utilization of building space in these three regions in 2015, and the vector map is divided into 30 m × A grid of 30 m in size, and all statistical data and spatial data are projected on each grid cell. The difference between the fitness values of the final convergence of the three parallel models is small, and the main difference is the convergence speed. During the run time test, set the three parallel models to run under the conditions of 8, 16, 32 and 64 nodes respectively. Because of the combination of the advantages of master-slave model and point-to-point model, the running time of chained parallel model is significantly lower than that of the other two parallel models. Conclusion: Through data simulation test, it is verified that the chained parallel model has higher fitness, convergence speed and shorter running time, and its performance is better than the other two, indicating that the optimization algorithm proposed by the author has good performance.

Micrometer-size spatial superpositions for the QGEM protocol via screening and trapping

The quantum gravity-induced entanglement of masses (QGEM) protocol for testing quantum gravity using entanglement witnessing utilizes the creation of spatial quantum superpositions of two neutral, massive matter-wave interferometers kept adjacent to each other, separated by a distance d. The mass and the spatial superposition should be such that the two quantum systems can entangle solely via the quantum nature of gravity. Despite being charge-neutral, many electromagnetic backgrounds can also entangle the systems such as the dipole-dipole and Casimir-Polder interactions. To minimize electromagnetic-induced interactions between the masses, it is pertinent to isolate the two superpositions by a conducting plate. However, the conducting plate will also exert forces on the masses and hence the trajectories of the two superpositions would be affected. To minimize this effect, we propose to trap the two interferometers such that the trapping potential dominates over the attraction between the conducting plate and the matter-wave interferometers. The superpositions can still be created via the Stern-Gerlach effect in the direction parallel to the plate, where the trapping potential is negligible. The combination of trapping and shielding provides a better parameter space for the parallel configuration of the experiment, where the requirement on the size of the spatial superposition, to witness the entanglement between the two masses purely due to their quantum nature of gravity, decreases by at least two orders of magnitude as compared to the original protocol paper. Published by the American Physical Society 2024

On the dynamics of spring-pendulum system: an overview of configuration space and phase space

The dynamics of the spring-pendulum system with two degrees of freedom were studied. The motion of this system is restricted to be in a vertical plane so that the chosen generalized coordinates are the increased length of the spring and the swing angle of pendulum . Hamiltonian of the system is obtained from the Legendre transformation of Lagrangian. Hamilton’s equation yields four differential equations that represent the dynamic of the system. The obtained results were visualized in configuration space and phase space trajectories. It is shown that generally the greater the initial swing angle, the more complex pattern will occur followed by the appearance of chaotic phenomena.