Consideration oftransition-state (TS) conformer ensemblesis requiredto accurately model a reaction, and thus plays a key role in computationalcatalyst design. While CREST and GOAT are established methods forTS conformer ensemble generation, the associated computational costremains a major bottleneck in computational chemistry pipelines, includingfor the generation of large machine learning data sets for catalystdesign. To this end, we present racerTS (RApid Conformer Ensembles with RDKit for Transition States), a method forefficient TS conformer ensemble generation. In this work, we describethe algorithm behind racerTS, which is based on constraineddistance geometry. To benchmark the performance of racerTS against CREST and GOAT, we created conformer ensembles for transitionstates of 20 diverse reactions. To assess the utility of each conformergenerator in computational chemistry workflows, we optimize selectedlow-energy and diverse conformers at the DFT level. We use the generatedconformer ensembles and the results of this pipeline to assess conformergenerators according to the following metrics: computational cost,exhaustiveness, validity, and accuracy in low-energy regions. Consideringthe generated ensembles, we find that racerTS covers theconformer space similarly to CREST and slightly less comprehensivelythan GOAT, while the validity of the DFT-optimized TSs is better andthe accuracy in the low-energy region is sufficient for computationalchemistry applications (median error of 0.17 kcal/mol). Remarkably,racerTS achieves these results with a significant reductionin required wall-time. Our results demonstrate that racerTS is a highly efficient TS conformer ensemble generator, allowingfor rapid TS conformer sampling in computational chemistry pipelines.Additionally, racerTS paves the way to create meaningfulTS data sets to advance machine learning methods for the discoveryof novel and sustainable catalysts.

Protein loop modeling remains a fundamental challenge in computational biology due to the inherent flexibility of loops and their critical role in biological functions. In this work, we employ a discrete distance geometry formulation, efficiently solved using the Branch-and-Prune algorithm, with a key innovation being the incorporation of hydrogen atoms into the model. Hydrogen atoms bonded to N and C α in the protein backbone introduce additional geometric constraints, and their inclusion is particularly justified in the context of nuclear magnetic resonance (NMR) experiments, where short-range hydrogen-hydrogen distances can be detected and provide valuable structural information. By integrating these experimentally accessible constraints into the modeling process, we refine the representation of protein conformations. Computational experiments demonstrate that incorporating hydrogen atoms reduces the conformational space, leading to a more constrained and biologically realistic model. Comparisons with hydrogen-free formulations confirm that our approach improves agreement with known protein structures, further highlighting the relevance of distance geometry methods in structural refinement.

Hallux valgus (HV) is a prevalent three-dimensional foot deformity, yet it is primarily assessed in the anteroposterior plane radiographs. The role of the sagittal plane and specifically the plantar fat pad remains poorly understood. This study aimed to quantitatively explore the relationship between plantar fat-pad geometry and HV progression. In this retrospective study, we analysed 274 feet from 144 patients who underwent HV corrective surgery at Hasharon Hospital, Israel (2014-2024). Using custom Python-based software, we annotated 22 anatomical landmarks on preoperative, weight-bearing lateral radiographs (3 plantar fat pads and 19 plantar bony points). For each fat pad, 19 Distance features were generated (total 57), comprising 19 pairwise standardised distances. Associations between these distances and standard HV angles (HVA, IMA, DMAA, HIA) were assessed using Pearson and Spearman correlations, A subgroup analysis was carried out to compare patients aged below and above 40 years, as well as between male and female patients. In the full cohort, no distance feature correlated with standard HV angles at the prespecified threshold ([Formula: see text] or [Formula: see text], two-sided [Formula: see text]). Stratified analyses revealed subgroup-specific patterns: females showed three significant relationships (mainly involving the calcaneal fat pad), whereas males showed 29 predominantly negative forefoot-hindfoot correlations (e.g., base of 5th metatarsal fat pad [Formula: see text] calcaneal fat pad vs. HIA: [Formula: see text], [Formula: see text], both [Formula: see text]). The [Formula: see text] y group exhibited six significant features (including sesamoid-based positives), while the [Formula: see text] y group showed two first-ray-focused associations. Several effects were stronger on Spearman than Pearson, consistent with nonlinearity, and many between-group differences were significant by Fisher's [Formula: see text]-to-[Formula: see text] ([Formula: see text]). Progressive Distance Mapping (PDM) summarized these effects into composite, radiograph-overlaid maps. Progressive Distance Mapping (PDM) may suggest subgroup-dependent, progressive associations between plantar fat-pad-anchored distance geometry and hallux valgus (HV) severity. Despite no universal cohort-level correlations, PDM identifies four distinct morphologic subtypes within each subgroup (stratified by age and sex), this may suggest differing pathogenesis and patterns of plantar fat-pad involvement. These subtype-specific signatures are often nonlinear.

The photography distance and image network geometry are critical influencing factors on ground-based structure-from-motion photogrammetry (G-SfM) accuracy. However, their selection is often subjective, resulting in highly variable photogrammetric precision ranging from centimeters to sub-millimeters. Quantifying the influence of image network geometry and distance provides a scientific basis for designing G-SfM surveys across diverse applications, ensuring more reliable results. To address these uncertainties, this study systematically compares the commonly used Circumvent image network geometry (CING) with the Nadir (NING) and Nadir+Inclined (NIING) geometries—both widely adopted in drone-based SfM. Fifteen experiments were conducted under 3 geometries and 5 photography distances (0.6 m, 0.8 m, 1.0 m, 1.5 m, and 2.0 m). Results show that NIING achieved the highest accuracy, with an absolute bias of 0.04 mm at 0.6 m, representing a 55% improvement over CING and a 102% improvement over NING. Unlike CING and NING, whose accuracies remain insensitive to distance, NIING benefits from reduced photography distance, highlighting its potential for high-precision applications.

Context.Swift J1910.2–0546 (=MAXI J1910−057) is a Galactic X-ray transient discovered during a bright outburst in 2012. Its X-ray spectral and timing properties point to a black-hole accretor, yet the orbital period remains uncertain, and no reliable dynamical constraints on the binary parameters are available. The 2012 event, extensively monitored at X-ray and optical wavelengths, offers a rare opportunity to investigate the structure and dynamics of the system and to constrain its fundamental properties. Aims. We use time-series optical photometry and spectroscopy, obtained during outburst and quiescence, to estimate the orbital period, characterise the donor star, determine the interstellar extinction, distance, and system geometry, and constrain the component masses. Methods. Multi-site r -band and clear-filter light curves and WHT/ACAM spectra from the 2012 outburst were combined with time-series spectroscopy from GTC/OSIRIS and VLT/FORS2 in quiescence. Period searches were conducted using generalised Lomb–Scargle, phase-dispersion minimisation, and analysis-of-variance algorithms. We used diffuse interstellar bands to constrain E ( B − V ), while empirical correlations involving H α yielded estimates of K 2 , q , and i . Results. We detected a coherent, double-humped modulation with a period of 0.0941 ± 0.0007 d (2.26 ± 0.02 h) during the outburst. Its morphology is consistent with an early superhump, suggesting that the true orbital period may be slightly shorter than 4.52 h. The H α radial velocity curves do not yield a definitive orbital period. In quiescence, TiO bands indicate an M3−M3.5 donor contributing ≃70% of the red continuum. Diffuse interstellar bands give E ( B − V ) = 0.60 ± 0.05 and N H = (3.9 ± 1.3)×10 21 cm −2 , placing the system at a distance of 2.8−4.0 kpc. The H α line width in quiescence (FWHM 0 = 990 ± 45 km s −1 ), via a FWHM– K 2 calibration, provides an estimate of K 2 , while its double-peaked profile gives q and the orbital inclination. The latter appears much higher than estimates from X-ray studies. Adopting the resulting K 2 = 230 ± 17 km s −1 and q = 0.032 ± 0.010, along with two orbital period scenarios (2.25 and 4.50 h), Monte Carlo sampling returns a compact object mass of M 1 = 8 − 11 M ⊙ and an inclination of i = 13° −18° for plausible donor masses ( M 2 = 0.25 − 0.35 M ⊙ ). Overall, we favour an orbital period of 4.5 h. Conclusions.Swift J1910.2–0546 may be a short-period, low-inclination black hole X-ray transient, although the possibility of it being a neutron star accretor cannot be completely ruled out. Subsequent phase-resolved spectroscopy and photometry during quiescence are needed to better determine its fundamental parameters.

This study explores the use of carbon black nanofluids in solar thermal energy systems, specifically focusing on their application in direct absorption solar collectors, where the working fluid directly absorbs incoming radiation. This work presents a novel combination of long-term stability testing, geometrical effects, and multi-method analysis (experimental, theoretical, and numerical) to evaluate the thermal performance of nanofluids. Uniquely, carbon black nanofluids stored under ambient conditions for two years were tested and compared with freshly prepared samples, a comparison not previously reported in the research literature. The influence of nanoparticle concentration, irradiation distance, and system geometry was investigated using two simplistic container configurations: a test tube and a volumetric flask. Results demonstrated that the optimal concentration depended on geometry and irradiation conditions. Stability tests showed minimal performance degradation over time, confirming their viability for long-term operation. A theoretical model and CFD simulations further supported the findings, offering insight into heat transfer mechanisms and the sensitivity of system performance to physical parameters. The results highlight the practical potential of low-concentration carbon black nanofluids in scalable solar thermal systems and underscore the importance of system design in maximizing efficiency.

ABSTRACT In interdisciplinary built environment projects, cognitive distances between team members can hinder effective collaboration and project success. This study proposes a method for mapping and measuring these cognitive distances using natural language processing techniques. The study used a case study to develop the measurement metrics and four interdisciplinary design teams consisting of 28 master's students from the disciplines of architecture, civil engineering, environmental design, and historic preservation. The findings highlight that cognitive distance is a multi-dimensional indicator, emphasizing conceptual diversity in breadth and complexity of thinking in length. At the same time, the study concludes that visualizing cognitive distance is important for facilitating innovative interdisciplinary collaboration, and that future research could build on this methodology to conduct empirical studies to systematically assess teams’ multidimensional cognitive distance in order to facilitate collaboration and improve overall project performance.

A hybrid wave energy conversion (WEC) system, integrating a backward bent duct buoy (BBDB) with an oscillating buoy (OB) via a flexible mooring chain, is introduced in this study. Unlike existing hybrid WECs, the proposed system dispenses with rigid mechanical linkages and enables flexible offshore deployment. Flared BBDB and buoy models with spherical, cylindrical, and semi-capsule shapes are designed and tested experimentally in a wave flume using both regular and irregular wave conditions. The effects of nozzle ratio (NR), coupling distance, buoy draft, and buoy geometry are systematically examined to investigate the hydrodynamic performance and energy conversion characteristics. It is found that NR at 110 under unidirectional airflow produces an optimal balance between pressure response, free surface displacement, and energy conversion efficiency. Energy extraction is significantly influenced by the coupling distance, with the hybrid system achieving maximum performance at a specific normalized spacing. The semi-capsule buoy improves power extraction ability and expands effective bandwidth due to asymmetric shape and coupled motion. These findings provide valuable insights into the coupling mechanism and geometric optimization for hybrid WECs.

Abrasive Waterjet (AWJ) machining is a highly versatile non-conventional manufacturing technology, increasingly adopted across diverse industries due to its capability of processing a wide spectrum of materials, including metals, alloys, ceramics, composites, and polymers. Unlike conventional methods, AWJ utilizes high-pressure water mixed with abrasive particles to remove material by erosion, significantly reducing thermal effects, mechanical distortion, and material degradation. The performance and efficiency of AWJ machining are directly influenced by critical process parameters such as waterjet pressure, traverse speed, abrasive mass flow rate, stand-off distance, and nozzle geometry. Recent studies have shown that optimizing these parameters is essential to enhance surface finish, improve material removal rates, and reduce kerf defects such as taper angles and burr formation. This comprehensive review systematically synthesizes recent advancements and essential findings from the existing literature on AWJ machining. It emphasizes material-specific optimization strategies, explores critical interactions between machining parameters, and summarizes methodologies such as experimental designs, numerical modeling, response surface methodology, and artificial neural networks frequently used to optimize the AWJ process. Particular attention is given to identifying the underlying mechanisms influencing outcomes, such as material erosion phenomena, abrasive particle interactions with the material surface, crack initiation and propagation, as well as abrasive embedment. Furthermore, the review addresses current challenges, including achieving precision machining for hard-to-cut materials like superalloys (e.g., Inconel 718, Ti-6Al-4V) and fiber-reinforced polymer composites, highlighting recent solutions and future research directions. This extended synthesis provides valuable insights and standardized guidelines for industrial practitioners and researchers, facilitating broader adoption and continuous innovation within AWJ machining technology.

Diffusion-based generative models have recently excelled in generating molecular conformations but struggled with the generalization issue -- models trained on one dataset may produce meaningless conformations on out-of-distribution molecules. On the other hand, distance geometry serves as a generalizable tool for the traditional computational chemistry methods of molecular conformation, which is predicated on the assumption that it is possible to adequately define the set of all potential conformations of any non-rigid molecular system using purely geometric constraints. In this work, we for the first time explicitly incorporate distance geometry constraints into pretraining phase of diffusion-based molecular generation models to improve the generalizability. Inspired by the classical distance geometry solution designed for solving the molecular distance geometry problem, we propose MiGDiff, a Metrization-Informed Geometric Diffusion framework. MiGDiff injects distance geometry constraints by pretraining the deep geometric diffusion backbone within the Metrization sampling approach, yielding a "Metrization-driven pretraining + Data-driven finetuning" paradigm. Experimental results demonstrate that MiGDiff outperforms state-of-the-art methods and possesses strong generalization capabilities, particularly on generating previously unseen molecules, revealing the vast untapped potential of combining traditional computational methods with deep generative models for 3D molecular generation.

Aurantiacin A (1), a unique ascorbylated meroditerpenoid composed of an unusual 9-epi-spiro-lactone-type ent-kaurane diterpenoid core, ascorbic acid (vitamin C), and syringic acid, and three new 9-epi-spiro-lactone-type ent-kauranoids, aurantiacins B-D (2-4), were isolated from an untapped species, Isodon aurantiacus. Their structures were determined by spectroscopic data analysis, semisynthesis, floating chirality distance geometry calculations, and quantum chemical calculations. Aurantiacin A (1) was found to induce lysosomal biogenesis, and the potential mechanisms underlying this effect were preliminarily explored.

Distance Geometry offers an alternative approach to analytically studying geometry: it explores a metric space based on distance information between points, rather than their coordinates. Although it is a relatively recent field, DG has already made significant contributions to Mathematics and Computer Science, with various applications in Robotics, Inverse Kinematics, Proteomics, Engineering, and other areas. However, this approach is still absent in basic mathematics education, where teachers generally present content in traditional ways with limited connections to student's real-world experiences or to current innovations. This work investigates the feasibility of incorporating Distance Geometry problems into the curriculum, aiming to modernize basic Mathematics education through new perspectives that foster problem-solving and integrate technologies in developing the skills defined in the Brazilian National Common Core Curriculum (BNCC). Based on a case study with activities conducted at Feliciano Pires School in Brusque, Santa Catarina, this paper suggests activities to enrich teaching practices and enhance student learning through this new perspective.

Two bicyclic pyrazolylpyrimidine compounds, 2-benzylthio-4-(3,5-dimethyl-1H-pyrazol-1-yl)pyrimidine (LH) and 2-benzylthio-4-(3,5-dimethyl-1H-pyrazol-1-yl)-6-methylpyrimidine (LMe), were synthesized and studied as ligands for the preparation of copper(I) halido complexes. In the solid state, LH and LMe demonstrate dual excitation-wavelength dependent emission, i.e. fluorescence at higher excitation energies and phosphorescence at lower excitation energies due to the presence of a heavy sulphur atom. The reactions of LH and LMe with CuBr and CuI afforded a series of centrosymmetric binuclear complexes of the [Cu2L2Hal2] type (L = LH, Hal = Br, I; L = LMe, Hal = I). The possibility of rotation of the benzylthio group relative to the pyrazolylpyrimidine core leads to the isolation of two polymorphic modifications of the copper(I) iodido complex with LH, which differ by the Cu⋯Cu distance by more than 0.2 Å (2.86 Å for [Cu2(LH)2I2] (form I)vs. 2.65 Å for [Cu2(LH)2I2] (form II)). The isolation of the [Cu2(LH)2I2] complex in two different crystalline forms made it possible to reveal the influence of a rarely explored factor, namely the change in the Cu⋯Cu distance in a single molecule, on the photoluminescence quantum efficiency. Two structural indices, τdim, which showcases the degree of merging of CuLHal monomers into the centrosymmetric [Cu2L2Hal2] dimers, and τplan, which characterises the degree of planarization of the N2CuHal2CuN2 unit, were introduced and used for combined experimental and theoretical analyses of the relation between the structure of the complexes and their luminescence. All complexes exhibit phosphorescence of the ligand-to-halide charge transfer (LXCT) character in the orange region. According to TD-DFT calculations, an increase in the Cu⋯Cu distance facilitates structural rearrangement in the T1 state followed by a rapid decrease in the T1-S0 energy gap and subsequent non-radiative decay via electron-phonon coupling, which substantiates the higher photoluminescence quantum yield (PLQY) of [Cu2(LH)2I2] (form II) (Cu⋯Cu 2.65 Å) compared to that of [Cu2(LH)2I2] (form I) (Cu⋯Cu 2.86 Å).

In wireless sensor networks (WSN), sources are usually localized with the help of pre-deployed base stations (BS). Due to the unknown environment, the main challenge in source localization is the non-line-of-sight (NLOS) error. This paper focuses on two approaches, such as triangulation constraints based on the relationships between each BS, and distance geometry constraints of Cayley-Menger determinants (CMD). However, there is no literature using them jointly. Therefore, this study aims to combine triangulation constraints and Distance geometry constraints of CMD to improve localization performance. First, we obtain the weight coefficients for all combinations of BSs by solving the Karush-Kuhn-Tucker (KKT) conditions for the triangular constraints and the distance geometry constraints of CMD. Since various combinations of BSs have different weighting coefficients, leading to uncertainty. Then, based on the uncertainty of the weight coefficients, we formulate the source localization problem as a robust least squares (RLS) problem. Finally, we eliminate the uncertainty by continuously relaxing the constraints through some mathematical methods, such as Cauchy-Schwarz inequality and norm compatibility. In addition, excessively relaxing the constraints may lead to low estimation accuracy, so we add some inherent constraints. Simulations and experiments demonstrate that the proposed method can perform well in different environments.

We study the problem of determining the configuration of n points by using their distances to m nodes, referred to as anchor nodes. One sampling scheme is Nyström sampling, which assumes known distances between the anchors and between the anchors and the n points, while the distances among the n points are unknown. For this scheme, a simple adaptation of the Nyström method, which is often used for kernel approximation, is a viable technique to estimate the configuration of the anchors and the n points. In this manuscript, we propose a modified version of Nyström sampling, where the distances from every node to one central node are known, but all other distances are incomplete. In this setting, the standard Nyström approach is not applicable, necessitating an alternative technique to estimate the configuration of the anchors and the n points. We show that this problem can be framed as the recovery of a low-rank submatrix of a Gram matrix. Using synthetic and real data, we demonstrate that the proposed approach can exactly recover configurations of points given sufficient distance samples. This underscores that, in contrast to methods that rely on global sampling of distance matrices, the task of estimating the configuration of points can be done efficiently via structured sampling with well-chosen reliable anchors. Finally, our main analysis is grounded in a specific centering of the points. With this in mind, we extend previous work in Euclidean distance geometry by providing a general dual basis approach for points centered anywhere.

Realizability of free spaces of curves

The discovery of the three-dimensional shape of protein molecules using interatomic distance information from nuclear magnetic resonance (NMR) can be modeled as a discretizable molecular distance geometry problem (DMDGP). Due to its combinatorial characteristics, the problem is conventionally solved in the literature as a depth-first search in a binary tree. In this work, we introduce a new search strategy, which we call frequency-based search (FBS), that for the first time utilizes geometric information contained in the protein data bank (PDB). We encode the geometric configurations of 14,382 molecules derived from NMR experiments present in the PDB into binary strings. The obtained results show that the sample space of the binary strings extracted from the PDB does not follow a uniform distribution. Furthermore, we compare the runtime of the symmetry-based build-Up (SBBU) algorithm (the most efficient method in the literature to solve the DMDGP) combined with FBS and the depth-first search (DFS) in finding a solution, ascertaining that FBS performs better in about 70% of the cases.

Future missions to the Moon and beyond are likely to involve low-thrust propulsion technologies due to their propellant efficiency. However, these still present a difficult trajectory design problem, owing to the near continuous thrust, lack of control authority and chaotic dynamics. Lyapunov control laws can generate sub-optimal trajectories for such missions with minimal computational cost and are suitable for feasibility studies and as initial guesses for optimisation methods. In this work a Reinforced Lyapunov Controller is used to design optimal low-thrust transfers from geostationary transfer orbit towards lunar polar orbit. Within the reinforcement learning (RL) framework, a dual-actor network setup is used, one in each of the Earth- and Moon-centred inertial frames respectively. A key contribution of this paper is the demonstration of a forwards propagated trajectory, removing the need to define a patch point a priori. This is enabled by an adaptive patch distance and extensive initial geometry exploration during the RL training. Results for both time- and fuel-optimal transfers are presented, along with a Monte Carlo analysis of the robustness to disturbances for such transfers. Phasing is introduced where necessary to aid rendezvous with the Moon. The results demonstrate the potential for such techniques to provide a basis for the design and guidance of low-thrust lunar transfers.

Assuming that the subject of each scientific publication can be identified by one or more classification entities, we address the problem of determining a similarity function (distance) between classification entities based on how often two classification entities are used in the same publication. This similarity function is then used to obtain a representation of the classification entities as points of an Euclidean space of a suitable dimension by means of optimization and dimensionality reduction algorithms. This procedure allows us also to represent the researchers as points in the same Euclidean space and to determine the distance between researchers according to their scientific production. As a case study, we consider as classification entities the codes of the American Mathematical Society Classification System.

Abstract Let $${{\mathbb {K}}}$$ K be any field, let $$X\subset {\mathbb P}^{k-1}$$ X ⊂ P k - 1 be a set of $$n$$ n distinct $${{\mathbb {K}}}$$ K -rational points, and let $$a\ge 1$$ a ≥ 1 be an integer. In this paper we find lower bounds for the minimum distance $$d(X)_a$$ d ( X ) a of the evaluation code of order $$a$$ a associated to $$X$$ X . The first results use $$\alpha (X)$$ α ( X ) , the initial degree of the defining ideal of $$X$$ X , and the bounds are true for any set $$X$$ X . In another result we use $$s(X)$$ s ( X ) , the minimum socle degree, to find a lower bound for the case when $$X$$ X is in general linear position. In both situations we improve and generalize known results.