Configuration Space Research Articles

Structural Designs Meet Optimality: Exploring Optimized LSM-tree Structures in a Colossal Configuration Space

Mainstream LSM-tree-based key-value stores face challenges in optimizing performance for point lookup, range lookup, and update operations concurrently due to their constrained configurations. They typically follow fixed patterns to specify the level capacity and the number of sorted runs per-level. This confines their designs to a restricted space, limiting opportunities for broader optimizations. To address this challenge, we consider a more flexible configuration that enables independent adjustments of the number of runs per-level, size ratio, and Bloom filter settings at each LSM-tree level. By carefully analyzing the cost of each operation based on the new design space, we unveil two critical insights for optimizing the tradeoff among the three operations. Firstly, achieving efficient point lookup requires a large last level. Secondly, there is a specific correlation between the number of runs per level and size ratio that is advantageous for overall update and range lookup performance. Based on these insights, we introduce Moose, a structure delivering an impressive overall performance for point lookup, range lookup, and update concurrently. Furthermore, we also introduce a new framework, Smoose, to navigate the design space for adapting specific workloads. We implemented Moose and Smoose on top of RocksDB and experimental results demonstrate that our proposed approach outperforms state-of-the-art LSM-tree structures across diverse workloads.

Glassy Word Problems: Ultraslow Relaxation, Hilbert Space Jamming, and Computational Complexity

We introduce a family of local models of dynamics based on “word problems” from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random circuit or local Hamiltonian dynamics and include many familiar examples of constrained dynamics as special cases. The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must “work out” the other states in the sector to which they belong. When this problem has a high time complexity, relaxation is slow. In some of the cases we study, this problem also has high space complexity. When the space complexity is larger than the system size, an unconventional type of jamming transition can occur, whereby a system of a fixed size is not ergodic but can be made ergodic by appending a large reservoir of sites in a trivial product state. This finding manifests itself in a new type of Hilbert space fragmentation that we call fragile fragmentation. We present explicit examples where slow relaxation and jamming strongly modify the hydrodynamics of conserved densities. In one example, density modulations of wave vector q exhibit almost no relaxation until times O(exp(1/q)), at which point they abruptly collapse. We also comment on extensions of our results to higher dimensions. Published by the American Physical Society 2024

Unveiling the Structure of Oxygen Vacancies in Bulk Ceria and the Physical Mechanisms behind Their Formation.

Understanding the structures of oxygen vacancies in bulk ceria is crucial as they significantly impact the material's catalytic and electronic properties. The complex interaction between oxygen vacancies and Ce3+ ions presents challenges in characterizing ceria's defect chemistry. We introduced a machine learning-assisted cluster-expansion model to predict the energetics of defective configurations accurately within bulk ceria. This model effectively samples configurational spaces, detailing oxygen vacancy structures across different temperatures and concentrations. At lower temperatures, vacancies tend to cluster, mediated by Ce3+ ions and electrostatic repulsion, while at higher temperatures, they distribute uniformly due to configurational entropy. Our analysis also reveals a correlation between thermodynamic stability and the band gap between occupied O 2p and unoccupied Ce 4f orbitals, with wider band gaps indicating higher stability. This work enhances our understanding of defect chemistry in oxide materials and lays the groundwork for further research into how these structural properties affect ceria's performance.

Prediction of two-dimensional carbon nitride materials with semimetal states and flat bands

The search for new two-dimensional (2D) carbon nitride (CN) materials with desirable properties is an important and critical area of research. This study presents a series of 2D CN materials with appealing features such as semimetal or flat bands. By utilizing group theory and graph theory, we perform a random search of the configurational space of 2D CN monolayers, leading to the identification of 721 new CN materials. Extensive density functional theory calculations were then conducted to evaluate their properties. We found that 57 materials exhibit semimetal behavior, while 664 display characteristics of semiconductors and normal metals. Notably, materials such as 51-5-16-C3N-r568 and 55-5-20-C4N-r568 feature topological Dirac semimetals with protected 1D topological boundary states. Moreover, 31 materials possess flat bands near their Fermi level, including two with kagome-like flat bands that induce intrinsic spontaneous magnetization due to partially-occupied flat bands. Our results offer several promising candidates for exploring physical phenomena related to semimetals or flat bands in 2D CN materials.

Effect of Different Spacing Levels on Yield and Yield Contributing Characters in Cocoa (Theobroma cacao L.)

The experiment titled "Effect of different spacing levels on yield and yield contributing characters in cocoa" was conducted at the Coconut Farm of the Horticultural College and Research Institute, Tamil Nadu Agricultural University, Coimbatore. Utilizing a Randomized Block Design (RBD) with eight treatments replicated three times, the study aimed to investigate the impact of spacing levels on cocoa yield traits. The treatments involved in the experiment included a double row of cocoa planted between two rows of coconut trees, with spacing configurations as follows: T1 (3m x 1.2m), T2 (3m x 2m), T3 (3m x 2.5m), and T4 (3m x 3m). Additionally, a single row of cocoa between two coconut rows was examined, with spacings represented by T5 (1.5m), T6 (2m), T7 (2.5m), and T8 (3m). Results revealed significant variations among spacing treatments, with cocoa at 3m spacing demonstrating the highest productivity, yielding 43.47 pods per tree and 1021.48 g of dry beans per tree. Noteworthy findings included T1 (3m x 1.2m) exhibiting the longest pods (16.64 cm), T6 (2m) the widest pod girth (21.67 cm), and T8 (3m) producing the heaviest pods (204.50 g). Additionally, T6 yielded the highest total beans per pod (37.34) and dry bean weight (25.44 g), T4 had the heaviest single fresh bean (1.63 g), and T2 demonstrated the highest single dry bean weight (0.70 g). These findings offer valuable insights for optimizing cocoa cultivation practices, emphasizing the importance of spacing configurations in maximizing yield and bean characteristics.

Photocatalytic degradation of metformin on a rectangular baffled reactor: CFD modeling and validation investigation

Solar-irradiated photocatalysis is an advanced oxidation process (AOP) commonly used for water purification due to its excellent potential to break down a diverse range of persistent organic compounds into non-toxic byproducts. Reactor design is crucial in the photocatalysis process's efficiency, effectiveness, and scalability. Computational fluid dynamics (CFD) is an effective tool to study and comprehend reactor designs, reduce system cost, design time, and optimise reactor performance. This investigation focuses on designing and developing a rectangular baffled photocatalytic reactor that can effectively degrade metformin (MTF). The experimental study optimized the value of pH and catalyst dosage for efficient removal. The photoreactor demonstrated an efficiency of 58.14 % and was validated. The CFD results, including velocity profile and mass fraction of metformin, strongly agreed with the experimental results with an R2 value of 0.9826. The combination of various baffle sizes and spacing configurations was modeled and analyzed to develop a rectangular baffled photocatalytic reactor with maximum removal efficiency. The inclusion of baffles increased the flow path, improved mixing and enhanced the degrading efficiency. The investigation findings indicated the highest degradation efficiency of 78.03 % with the seven number of baffles.

Constructing and Evaluating Machine-Learned Interatomic Potentials for Li-Based Disordered Rocksalts.

Lithium-based disordered rocksalts (LDRs), which are an important class of positive electrode materials that can increase the energy density of current Li-ion batteries, represent a significantly complex chemical and configurational space for conventional density functional theory (DFT)-based high-throughput screening approaches. Notably, atom-centered machine-learned interatomic potentials (MLIPs) are a promising pathway to accurately model the potential energy surface of highly disordered chemical spaces, such as LDRs, where the performance of such MLIPs has not been rigorously explored yet. Here, we represent a comprehensive evaluation of the accuracy, transferability, and ease of training of five atom-centered MLIPs, including the artificial neural network potentials developed by the atomic energy network (AENET), the Gaussian approximation potential (GAP), the spectral neighbor analysis potential (SNAP) and its quadratic extension (qSNAP), and the moment tensor potential (MTP), in modeling a 11-component LDR chemical space. Specifically, we generate a DFT-calculated data set of 10,842 configurations of disordered LiTMO2 and TMO2 compositions, where TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and/or Cu. To provide a point-of-comparison on the performance of atom-centered MLIPs, we also trained the neural equivariant interatomic potential (NequIP) on a subset of our data. Importantly, we find AENET to be the best potential in terms of accuracy and transferability for energy predictions, while MTP is the best for atomic forces. While AENET is the fastest to train among the MLIPs considered at low number of epochs (300), the training time increases significantly as epochs increase (3300), with a corresponding reduction in training errors (∼60%). Note that AENET and GAP tend to overfit in small data sets, with the extent of overfitting reducing with larger data sets. Finally, we observe AENET to provide reasonable predictions of average Li-intercalation voltages in layered, single-TM LiTMO2 frameworks, compared to DFT (∼10% error on average). Our study should pave the way both for discovering novel disordered rocksalt electrodes and for modeling other configurationally complex systems, such as high-entropy ceramics and alloys.

Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking.

Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) has been proposed as a reformulation of the second-order ADC scheme for the polarization propagator within the projection quantum Monte Carlo formalism. Dense-sparse partitioning and importance ranking filtering strategies are now exploited to accelerate its convergence and to alleviate the signproblem inherent in such calculations. By splitting the configuration space into dense and sparse subsets, the corresponding projection operator is decomposed into four distinct blocks. Deterministic calculations handle the dense-to-dense and sparse-to-dense blocks, while the remaining blocks, dense-to-sparse and sparse-to-sparse, are stochastically evaluated. The dense set is efficiently stored in a fixed-size array, and the sparse set is represented through conventional floating random Monte Carlo walks. The stochastic projection is further refined through importance ranking criteria, enabling a reduction in the required number of walkers with a controllable bias. Our results demonstrate the integration of dense-sparse partitioning with importance ranking filtering to significantly enhance the efficiency of QMCADC, enabling large-scale molecular excited-state calculations. Furthermore, this novel approach maximizes the utilization of the sparsity of ADC(2), transforming QMCADC into a tailored framework for ADC calculations.

Wave Function and Information

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e., its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called “quantum potential” in this context is briefly discussed.

Development of Parallel On-the-Fly Crystal Algorithm for Global Exploration of Conical Intersection Seam Space.

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

On the canonicity of the singularities of quotients of the Fulton-MacPherson compactification

We prove that quotients of the Fulton-MacPherson compactification of configuration spaces of smooth projective varieties of dimension > 1 >1 by permutation groups have canonical singularities.

Variational Integrators on Manifolds for Constrained Mechanical Systems

Abstract Variational integrators play a pivotal role in the simulation and control of constrained mechanical systems. Current Lagrange multiplier-free variational integrators for such systems are concise but inevitably face issues with parameterization singularities, hindering global integration. To tackle this problem, this paper proposes a novel method for constructing variational integrators on manifolds without introducing Lagrange multipliers, offering the benefit of avoiding singularities. Our approach unfolds in three key steps: (1) the local parameterization of configuration space; (2) the formulation of forced discrete Euler–Lagrange equations on manifolds; and (3) the construction and implementation of high-order variational integrators. Numerical tests are conducted for both conservative and forced mechanical systems, demonstrating the excellent global energy behavior of the proposed variational integrators.

Quotient singularities in the Grothendieck ring of varieties

Let G G be a finite group, X X be a smooth complex projective variety with a faithful G G -action, and Y Y be a resolution of singularities of X / G X/G . Larsen and Lunts asked whether [ X / G ] − [ Y ] [X/G]-[Y] is divisible by [ A 1 ] [\mathbb {A}^1] in the Grothendieck ring of varieties. We show that the answer is negative if B G BG is not stably rational and affirmative if G G is abelian. The case when X = Z n X=Z^n for some smooth projective variety Z Z and G = S n G=S_n acts by permutation of the factors is of particular interest. We make progress on it by showing that [ Z n / S n ] − [ Z ⟨ n ⟩ / S n ] [Z^n/S_n]-[Z\langle n\rangle / S_n] is divisible by [ A 1 ] [\mathbb {A}^1] , where Z ⟨ n ⟩ Z\langle n\rangle is Ulyanov’s polydiagonal compactification of the n n th configuration space of Z Z .

Assessment of Anharmonicities in Clusters: Developing and Validating a Minimum-Information Partition Function.

Precise thermodynamic calculations are essential for understanding the dynamics of cluster systems and new particle formation. However, the widely employed harmonic statistical mechanical approach often falls short in terms of accuracy. In this study, we present an improved statistical model that incorporates vibrational anharmonicity via a novel partition function that requires only one additional system-specific input parameter. In addition to considering vibrational aspects, we also account for anharmonicity related to the configurational space. The role of anharmonicities is thoroughly examined in the case of general clusters, where the complete sets of conformers, mechanically stable spatial arrangements, are known up to clusters composed of 14 monomers. By performing consistent Monte Carlo simulations on these systems, we benchmark the statistical model's efficacy in reproducing key thermodynamic properties (formation free energy and potential energy) in the classical limit. The model exhibits exceptional alignment with simulations, accurately reproducing free energies within a precision of 2kBT and reliably capturing cluster melting temperatures. Furthermore, we demonstrate the significance and applicability of the model by reproducing thermodynamic barriers in homogeneous gas-phase nucleation of larger clusters. The transferability of our developed approach extends to more complex molecular systems and bears relevance for atmospheric multicomponent clusters, in particular.

Enhancing thermal stability of optimal magnetization reversal in nanoparticles

Energy-efficient switching of nanoscale magnets requires application of a time-varying magnetic field characterized by microwave frequency. At finite temperatures, even weak thermal fluctuations induce perturbations in the magnetization that can accumulate in time, disrupt the phase locking between the magnetization and the applied field, and eventually compromise magnetization switching. It is demonstrated here that the magnetization reversal is mostly disturbed by unstable perturbations arising in a certain domain of the configuration space of a nanomagnet. The instabilities can be suppressed and the probability of magnetization switching enhanced by applying an additional stimulus such as a weak longitudinal magnetic field that ensures bounded dynamics of the perturbations. Application of the stabilizing longitudinal field to a uniaxial nanomagnet makes it possible to reach a desired probability of magnetization switching even at elevated temperatures. The principle of suppressing instabilities provides a general approach to enhancing thermal stability of magnetization dynamics. Published by the American Physical Society 2024

Effect of Dynamic and Preferential Decoration of Pt Catalyst Surfaces by WOx on Hydrodeoxygenation Reactions.

Catalysts containing Pt nanoparticles and reducible transition-metal oxides (WOx, NbOx, TiOx) exhibit remarkable selectivity to aromatic products in hydrodeoxygenation (HDO) reactions for biomass valorization, contrasting the undesired aromatic hydrogenation typically observed for metal catalysts. However, the active site(s) responsible for the high selectivity remains elusive. Here, theoretical and experimental analyses are combined to explain the observed HDO reactivity by interrogating the organization of reduced WOx domains on Pt surfaces at sub-monolayer coverage. The SurfGraph algorithm is used to develop model structures that capture the configurational space (∼1000 configurations) for density functional theory (DFT) calculations of a W3O7 trimer on stepped Pt surfaces. Machine-learning models trained on the DFT calculations identify the preferential occupation of well-coordinated Pt sites (≥8 Pt coordination number) by WOx and structural features governing WOx-Pt stability. WOx/Pt/SiO2 catalysts are synthesized with varying W loadings to test the theoretical predictions and relate them to HDO reactivity. Spectroscopy- and microscopy-based catalyst characterizations identify the dynamic and preferential decoration of well-coordinated sites on Pt nanoparticles by reduced WOx species, consistent with theoretical predictions. The catalytic consequences of this preferential decoration on the HDO of a lignin model compound, dihydroeugenol, are clarified. The effect of WOx decoration on Pt nanoparticles for HDO involves WOx inhibition of aromatic ring hydrogenation by preferentially blocking well-coordinated Pt sites. The identification of preferential decoration on specific sites of late-transition-metal surfaces by reducible metal oxides provides a new perspective for understanding and controlling metal-support interactions in heterogeneous catalysis.

Collision-free Tool Motion Planning for 5-Axis CNC Machining with Toroidal Cutters

Collision detection is a crucial part of CNC machining, however, many state-of-the-art algorithms test collisions as a post-process, after the path-planning stage, or use conservative approaches that result in low machining accuracy in the neighborhood of the cutter’s contact paths. We propose a fast collision detection test that does not require a costly construction of the configuration space nor high-resolution sampling of the cutter’s axis and uses the information of the neighboring points to efficiently prune away points of the axis that cannot cause collisions. The proposed collision detection test is incorporated directly as a part of the tool motion-planning stage, enabling design of highly-accurate motions of a toroidal cutting tool along free-form geometries. We validate our algorithm on a variety of benchmark surfaces, showing that our results provide high-quality approximations with provably non-colliding motions.

Tuning structural and electronic properties of metal-organic framework 5 by metal substitution and linker functionalization.

The chemical flexibility of metal-organic frameworks (MOFs) offers an ideal platform to tune structure and composition for specific applications, from gas sensing to catalysis and from photoelectric conversion to energy storage. This variability gives rise to a large configurational space that can be efficiently explored using high-throughput computational methods. In this work, we investigate from first principles the structural and electronic properties of MOF-5 variants obtained by replacing Zn with Be, Mg, Cd, Ca, Sr, and Ba and by functionalizing the originally H-passivated linkers with CH3, NO2, Cl, Br, NH2, OH, and COOH groups. To build and analyze the resulting 56 structures, we employ density-functional theory calculations embedded in an in-house developed library for automatized calculations. Our findings reveal that structural properties are mainly defined by metal atoms and large functional groups, which distort the lattice and modify coordination. The formation energy is largely influenced by functionalization and enhanced by COOH and OH groups, which promote the formation of hydrogen bonds. The charge distribution within the linker is especially influenced by functional groups with electron-withdrawing properties, while the metal nodes play a minor role. Likewise, the bandgap size is crucially determined by ligand functionalization. The smallest gaps are found with NH2 and OH groups, which introduce localized orbitals at the top of the valence band. This characteristic makes these functionalizations particularly promising for the design of MOF-5 variants with enhanced gas uptake and sensing properties.

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.