Deciphering competing interactions of Kitaev-Heisenberg-\texorpdfstring{$\Gamma$} system in clusters: part II - dynamics of Majorana fermions.

We perform a systematic and exact study of Majorana fermion dynamics in the Kitaev-Heisenberg-$\Gamma$ model in a few finite-size clusters increasing in size up to twelve sites. We employ exact Jordan-Wigner transformations to evaluate certain measures of Majorana fermion correlation functions, which effectively capture matter and gauge Majorana fermion dynamics in different parameter regimes. An external magnetic field is shown to produce a profound effect on gauge fermion dynamics. Depending on certain non-zero choices of other non-Kitaev interactions, it can stabilise it to its non-interacting Kitaev limit. For all the parameter regimes, gauge fermions are seen to have slower dynamics, which could help build approximate decoupling schemes for appropriate mean-field theory. The probability of Majorana fermions returning to their original starting site shows that the Kitaev model in small clusters can be used as a test bed for the quantum speed limit.

A review of current practice in the design and analysis of extremely small stepped-wedge cluster randomized trials.

BACKGROUND/AIMS: Stepped-wedge cluster randomized trials tend to require fewer clusters than standard parallel-arm designs due to the switches between control and intervention conditions, but there are no recommendations for the minimum number of clusters. Trials randomizing an extremely small number of clusters are not uncommon, but the justification for small numbers of clusters is often unclear and appropriate analysis is often lacking. In addition, stepped-wedge cluster randomized trials are methodologically more complex due to their longitudinal correlation structure, and ignoring the distinct within- and between-period intracluster correlations can underestimate the sample size in small stepped-wedge cluster randomized trials. We conducted a review of published small stepped-wedge cluster randomized trials to understand how and why they are used, and to characterize approaches used in their design and analysis. METHODS: Electronic searches were used to identify primary reports of full-scale stepped-wedge cluster randomized trials published during the period 2016-2022; the subset that randomized two to six clusters was identified. Two reviewers independently extracted information from each report and any available protocol. Disagreements were resolved through discussion. RESULTS: We identified 61 stepped-wedge cluster randomized trials that randomized two to six clusters: median sample size (Q1-Q3) 1426 (420-7553) participants. Twelve (19.7%) gave some indication that the evaluation was considered a "preliminary" evaluation and 16 (26.2%) recognized the small number of clusters as a limitation. Sixteen (26.2%) provided an explanation for the limited number of clusters: the need to minimize contamination (e.g. by merging adjacent units), limited availability of clusters, and logistical considerations were common explanations. Majority (51, 83.6%) presented sample size or power calculations, but only one assumed distinct within- and between-period intracluster correlations. Few (10, 16.4%) utilized restricted randomization methods; more than half (34, 55.7%) identified baseline imbalances. The most common statistical method for analysis was the generalized linear mixed model (44, 72.1%). Only four trials (6.6%) reported statistical analyses considering small numbers of clusters: one used generalized estimating equations with small-sample correction, two used generalized linear mixed model with small-sample correction, and one used Bayesian analysis. Another eight (13.1%) used fixed-effects regression, the performance of which requires further evaluation under stepped-wedge cluster randomized trials with small numbers of clusters. None used permutation tests or cluster-period level analysis. CONCLUSION: Methods appropriate for the design and analysis of small stepped-wedge cluster randomized trials have not been widely adopted in practice. Greater awareness is required that the use of standard sample size calculation methods can provide spuriously low numbers of required clusters. Methods such as generalized estimating equations or generalized linear mixed models with small-sample corrections, Bayesian approaches, and permutation tests may be more appropriate for the analysis of small stepped-wedge cluster randomized trials. Future research is needed to establish best practices for stepped-wedge cluster randomized trials with a small number of clusters.

Air and Thermally Stable Fluoride Bridged Rare-Earth Clusters Showing Intense Photoluminescence and Potential LED Application.

Fluoride based lattice is attractive for reducing phonon-induced quenching in rare-earth (RE) based luminescent materials. However, due to the strong affinity between RE and oxygen, the synthesis of fluoride-based complexes has to be protected under anhydrous conditions, and many known fluoride bridged RE clusters are unstable in air. Here, by using the "mixed-ligand" strategy a family of fluoride bridged RE clusters is synthesized, namely RE16(µ4-F)6(µ3-F)12(tBuCOO)18[N(CH2CH2O)3]4 (RE = Eu, EuFC-16; RE = Tb, TbFC-16), which are highly stable in air and decomposed thermally only when heating above 435 °C. Moreover, both clusters exhibit high photoluminescence quantum yields (PLQYEuFC-16 = 87.7%, PLQYTbFC-16 = 99.0%). Upon warming, EuFC-16 and TbFC-16 display excellent structural, thermal, and chroma stability. Thus, EuFC-16 and TbFC-16 have the potential to be used in light-emitting diode (LED) devices, offering many advantages over commercial phosphors. First, both clusters are soluble in UV-curable resin at any mixing rate, and the emission colors can be tuned from magenta, turquoise, willow green, and ivory to pure white if mixing blue phosphor BAM:Eu2+. Second, the clusters are hydrophobic, and the LEDs work well after soaking in water, indicating a good quality for outdoor lighting.

Factors Determining the Selectivity of NO Reduction Catalyzed by Copper-Vanadium Oxide Cluster Anions Cu2VO3‒5.

Catalytic NO reduction by CO is imperative to satisfy the increasingly rigorous emission regulations. Identifying the structural characteristic of crucial intermediate that governs the selectivity of NO reduction is pivotal to having a fundamental understanding on real-life catalysis. Herein, benefiting from the state-of-the-art mass spectrometry, we demonstrated experimentally that the Cu2VO3-5- clusters can mediate the catalysis of NO reduction by CO, and two competitive channels to generate N2O and N2 can co-exist. Quantum-chemical calculations were performed to rationalize this selectivity. The formation of the ONNO unit on the Cu2 dimer was demonstrated to be a precursor from which two pathways of NO reduction start to emerge. In the pathway of N2O generation, only the Cu2 dimer was oxidized and the VO3 moiety  functions as a "support", while both moieties have to contribute to anchor oxygen atoms from the ONNO unit and then N2 can be generated. This finding displays a clear picture to elucidate how and why the involvement of VO3 "support" can regulate the selectivity of NO reduction.

Introducing KICK-MEP: exploring potential energy surfaces in systems with significant non-covalent interactions.

CONTEXT: Exploring potential energy surfaces (PES) is fundamental in computational chemistry, as it provides insights into the relationship between molecular energy, geometry, and chemical reactivity. We introduce Kick-MEP, a hybrid method for exploring the PES of atomic and molecular clusters, particularly those dominated by non-covalent interactions. Kick-MEP computes the Coulomb integral between the maximum and minimum electrostatic potential values on a 0.001 a.u. electron density isosurface for two interacting fragments. This approach efficiently estimates interaction energies and selects low-energy configurations at reduced computational cost. Kick-MEP was evaluated on silicon-lithium clusters, water clusters, and thymol encapsulated within Cucurbit[7]uril, consistently identifying the lowest energy structures, including global minima and relevant local minima. METHODS: Kick-MEP generates an initial population of molecular structures using the stochastic Kick algorithm, which combines two molecular fragments (A and B). The molecular electrostatic potential (MEP) values on a 0.001 a.u. electron density isosurface for each fragment are used to compute the Coulomb integral between them. Structures with the lowest Coulomb integral are selected and refined through gradient-based optimization and DFT calculations at the PBE0-D3/Def2-TZVP level. Molecular docking simulations for the thymol-Cucurbit[7]uril complex using AutoDock Vina were performed for benchmarking. Kick-MEP was validated across different molecular systems, demonstrating its effectiveness in identifying the lowest energy structures, including global minima and relevant local minima, while maintaining a low computational cost.

Affecting Charges and Structures of {Bi6} Architectures by 12-Electron Transition Metal Fragments.

Molecules based on polyatomic bismuth substructures are currently attracting a lot of attention owing to this heavy and essentially non-toxic element's uncommon chemical and physical properties, which include unprecedented bonding properties. Hexaatomic {Bi6} substructures that underly more complex cluster structures were recently reported to adopt different structures or exhibit different structural details as a consequence of the charge of the {Bi6} unit. This leads to either crown-shaped cycles for a nominal Bi66- or differently distorted trigonal prisms for compositions close to Bi62-. It was predicted by quantum chemistry that Bi64- should adopt a distinctly distorted boat-like shape, yet a corresponding compound has remained elusive. Here, we report a proof of this assumption by the synthesis and isolation of [K(crypt-222)]2[Bi6{Zn(hmds)}2]∙1.5THF (1), comprising a bimetallic [Bi6{Zn(hmds)}2]2- cluster that fulfils the prediction for the geometric and electronic structure of the missing link (crypt-222 = 4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo-[8.8.8]hexa-cosane, hmds = hexamethyldisilazanid). A detailed quantum chemical study shows how the nature of Lewis-acidic transition metal complexes - in particular, 12-electron fragments - control and fine-tune the resulting {Bi6} architectures in accordance with the degree of electron-withdrawal from the polybismuthide core.

Octahedral vs Tiara-like Pd6(SR)12 Clusters.

Atomically precise Pd-thiolate clusters are well-known for their well-defined structures and diverse applications involving catalysis, sensors, and biomedicine. While many of these clusters have been studied, their molecular structures typically feature a tiara-like arrangement. In this study, we present the first example of a non-tiara-like Pd-thiolate cluster: the octahedral Pd6(SC6H11)12 (denoted as Pd6-Oct). The composition and geometric structure of the cluster were characterized using electrospray ionization mass spectrometry (ESI-MS) together with single-crystal X-ray diffraction (SXRD). Despite having a similar chemical composition to tiara-like Pd6(SC2H4Ph)12 (denoted as Pd6-Tia), Pd6-Oct exhibits a distinctly different geometric structure. Additionally, UV-vis-NIR absorption spectroscopy combined with quantum chemical calculations provided valuable insights into the electronic structures of these clusters. The excited-state dynamics, host-guest chemistry, and the catalytic properties of Pd6-Oct and Pd6-Tia were examined to compare their structure-property relationships. This research represents significant advances in the synthesis and understanding of structure-property correlations in Pd-thiolate clusters.

Spatiotemporal coupling analysis between green total factor productivity and urban e-commerce development in China's eight urban clusters.

The coordinated development of urban e-commerce and green total factor productivity (GTFP) plays a crucial role in achieving high-quality development. This paper selects relevant data from the eight major urban agglomerations in China for research. A model that described the coupling coordination between the regions' GTFP and urban e-commerce was presented. Then, unfold the spatiotemporal evolution characteristics of their coupling coordination from the "dynamic and static", "overall and regional" dimensions. The results indicate: (1) The coupling coordination degree between two systems within China's eight urban agglomerations exhibits an upward trend with fluctuations, transitioning from a state of near dysfunction to good coordination. (2) The spatial heterogeneity in the coupling coordination degree between the two systems in China's eight major urban agglomerations is evident, with an overall downward trend and exhibiting a "V-shaped" pattern of "decline-rise".(3) The coupling coordination degree between two systems across China's eight urban agglomerations exhibits a trend toward centralization, with an amelioration of bipolar differentiation, and a progressive attenuation of spatial heterogeneity.

The expanding antimicrobial diversity of the genus Pantoea.

With the rise of antimicrobial resistance, there is high demand for novel antimicrobials to combat multi-drug resistant pathogens. The bacterial genus Pantoea produces a diversity of antimicrobial natural products effective against a wide range of bacterial and fungal targets. These antimicrobials are synthesized by specialized biosynthetic gene clusters that have unique distributions across Pantoea as well as several other genera outside of the Erwiniaceae. Phylogenetic and genomic evidence shows that these clusters can mobilize within and between species and potentially between genera. Pantoea antimicrobials belong to unique structural classes with diverse mechanisms of action, but despite their potential in antagonizing a wide variety of plant, human, and animal pathogens, little is known about many of these metabolites and how they function. This review will explore the known antimicrobials produced by Pantoea: agglomerins, andrimid, D-alanylgriseoluteic acid, dapdiamide, herbicolins, pantocins, and the various Pantoea Natural Products (PNPs). It will include information on the structure of each compound, their genetic basis, biosynthesis, mechanism of action, spectrum of activity, and distribution, highlighting the significance of Pantoea antimicrobials as potential therapeutics and for applications in biocontrol.

Improving the Lithography Sensitivity of Atomically Precise Tin-Oxo Nanoclusters via Heterometal Strategy.

Tin-oxo clusters are increasingly recognized as promising materials for nanolithography technology due to their unique properties, yet their structural impacts on lithography performance remain underexplored. This work explores the structural impacts of heterometal strategies on the performance of tin-oxo clusters in nanolithography, focusing on various metal dopants and their coordination geometries. Specifically, SnOC-1(In), SnOC-1(Al), SnOC-1(Fe), and SnOC-2 were synthesized and characterized. These clusters demonstrate excellent solubility, dispersibility, and stability, facilitating the preparation of high-quality films via spin-coating for lithographic applications. Notably, this work innovatively employs nano-infrared (nano-IR), neutron reflectivity (NR), and X-ray reflectivity (XRR) measurements to confirm film homogeneity. Upon electron beam lithography (EBL), all four materials achieve 50 nm line patterns, with SnOC-1(In) demonstrating the highest lithography sensitivity. This enhanced sensitivity is attributed to indium dopants, which possess superior EUV absorption capabilities and unsaturated coordination environments. Further studies on exposure mechanisms indicated that Sn-C bond cleavage generates butyl free radicals, promoting network formations that induce solubility-switching behaviors for lithography. These findings underscore the efficacy of tailored structural design and modulation of cluster materials through heterometal strategies in enhancing lithography performance, offering valuable insights for future material design and applications.

CIDACC: Chlorella vulgaris image dataset for automated cell counting.

This CIDACC dataset was created to determine the cell population of Chlorella vulgaris microalga during cultivation. Chlorella vulgaris has diverse applications, including use as food supplement, biofuel production, and pollutant removal. High resolution images were collected using a microscope and annotated, focusing on computer vision and machine learning models creation for automatic Chlorella cell detection, counting, size and geometry estimation. The dataset comprises 628 images, organized into hierarchical folders for easy access. Detailed segmentation masks and bounding boxes were generated using external tools enhancing the dataset's utility. The dataset's efficacy was demonstrated through preliminary experiments using deep learning architecture such as object detection and localization algorithms, as well as image segmentation algorithms, achieving high precision and accuracy. This dataset is a valuable tool for advancing computer vision applications in microalgae research and other related fields. The dataset is particularly challenging due to its dynamic nature and the complex correlations it presents across various application domains, including cell analysis in medical research. Its intricacies not only push the boundaries of current computer vision algorithms but also offer significant potential for advancements in diverse fields such as biomedical imaging, environmental monitoring, and biotechnological innovations.

Bjerrum defects in s-II gas hydrate.

The energy and structure of Bjerrum defects in structure II gas hydrates were investigated by using first-principle calculations for finite-size clusters and periodic 3D lattice systems. The formation energies of these defects were calculated for the first time when the cages of the structure II structure were completely empty and the large cage was filled with a THF molecule. Analogous to findings in ice structures, one of the hydrogen atoms forming the D defect was noted to orient toward the cage. If the excess proton resides in the large cage, it acts as an attraction center for the polar guest molecule, i.e., THF. Therefore, the large cage guest THF molecule stabilizes the D/L defect pair and isolated D/L defect formation energies by forming hydrogen bonds with the D defect. In such cases, the defect structure representing a D/L defect pair containing a THF molecule interacting with one of the hydrogen atoms of the D defect mirrors the guest-induced ones. Notably, the classical Bjerrum defect and the guest-induced Bjerrum defect exhibit a similar phenomenon in defective structures. Contrary to existing literature, it is evident that guest-induced Bjerrum defects involve both the L and D components. The insights gained from this study could potentially offer an alternative perspective to understand various experimental observations, such as those related to dielectric and NMR properties.

Clinical Grade Fibroin Sutures with Bioactive Gold Clusters Enhance Surgical Wound Healing via Inflammation Modulation.

Silk sutures are common in surgeries, and silk-based textiles are widely used in clinical medicine on account of their great mechanical properties and biodegradability. However, due to the lack of biocatalytic activity, silk sutures show unsatisfactory anti-inflammatory properties and healing speed. To address this constraint, we construct clinical grade bioactive gold cluster-sutures through a heterojunction. The antioxidant activity of bioactive gold cluster-sutures is ∼160 times more than that of clinical sutures. Meanwhile, the suture displays superb reactive oxygen species (ROS) scavenging, superoxide dismutase-like (SOD-like, 5 times more than the silk suture), and catalase-like (CAT-like) activities. The clusters assemble on the surface of silk through hydrogen bonding, leading to a durable catalytic and structural stability for 15 months without decay. Subsequently, the suture significantly accelerates wound healing by exerting excellent anti-inflammatory effects, improving neovascularization and collagen deposition. Clinical grade bioactive gold clusters with high bioactivity, stability, and biocompatibility hold promise for clinical translation and pave the way for other implanted biomaterials from wound healing to intelligent textiles.

Mo-Induced Surface Reconstruction in Ni/Co-OOH Prickly Flower Clusters for Improving the Hydrogen Production in Alkaline Seawater Splitting.

Seawater electrolysis is the most promising technology for hydrogen production, in which surface reconstruction on the interface of electrode/electrolyte plays a crucial role in activating the catalytic reactions with a low activation energy barrier. Herein, an efficient Mo modifying NiCoMo prickly flower clusters electrocatalyst supported on nickel foam (Mo-doped Ni/Co-OOH prickly flower clusters) is obtained, which serves as an eminently active and durable catalyst for both hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) due to the surface reconstruction during the alkaline seawater electrolysis with ultralow overpotentials. It just requires a cell voltage of 1.52 V to achieve the current density of 10 mA cm-2 for water electrolysis along with robust durability over 30 h. Mo doping effectively regulates the surface reconstruction of Ni/Co-OOH, which facilitates the adsorption of oxygen-containing intermediates on the active center, and the nonhomogeneous interface induces charge rearrangement for the catalytic process to improve efficiency, providing a new strategy for revealing the seawater electrolytic mechanism.

Research on Synthesis, Structure, and Catalytic Performance of Tetranuclear Copper(I) Clusters Supported by 2-Mercaptobenz-zole-Type Ligands.

Tetrahedral copper(I) clusters [Cu4(MBIZ)4(PPh3)2] (2), [Cu4(MBOZ)4(PPh3)4] (6) (MBIZ = 2-mercaptobenzimidazole, MBOZ = 2-mercaptobenzoxazole) were prepared by regulation of the copper-thiolate clusters [Cu6(MBIZ)6] (1) and [Cu8(MBOZ)8I]- (5) with PPh3. With the presence of iodide anion, the regulation provided the iodide-containing clusters [CuI4(MBIZ)3(PPh3)3I] (3) and [CuI4(MBOZ)3(PPh3)3I] (7). The cyclic voltammogram of 3 in MeCN (0.1 M nBu4NPF6, 298 K) at a scan rate of 100 mV s-1 shows two oxidation processes at Epa = +0.11 and +0.45 V with return waves observed at Epc = +0.25 V (vs. Fc+/Fc). Complex 3 has a higher capability to lose and gain electrons in the redox processes than complexes 2, 4, 4', 6, and 7. Its thermal stability was confirmed by thermogravimetric analysis. The catalytic performance of 3 was demonstrated by the catalytic transformation of iodobenzenes to benzonitriles using AIBN as the cyanide source. The nitrile products show potential applications in the preparation of 1,3,5-triazine compounds for organic fluorescence materials.

Cross-Linked Polyvinylimidazole Complexed with Heteropolyacid Clusters for Deep Oxidative Desulfurization.

The combustion of fuel with high sulfur concentrations produces a large number of sulfur oxides (SOx), which have a range of negative effects on human health and life. The preparation of catalysts with excellent performance in the oxidative desulfurization (ODS) process is highly effective for reducing SOx production. In this paper, cross-linked polyvinylimidazole (VE) was successfully created using a simple ontology aggregation method, after which a catalyst of polyvinylimidazolyl heteropolyacid clusters (VE-HPA) was prepared by adding heteropolyacid clusters. Polyvinylimidazolyl-phosphotungstic acid (VE-HPW) showed an outstanding desulfurization performance, and the desulfurization efficiency reached 99.68% in 60 min at 50 °C with H2O2 as an oxidant. Additionally, the catalyst exhibited recyclability nine consecutive times and remained stable, with a removal rate of 98.60%. The reaction mechanism was eventually proposed with the assistance of the free radical capture experiment and GC-MS analysis.

The Reactivity of Ptn + Clusters With N2O Facilitated by Dual Lewis-Acid Sites.

The size dependence of metal cluster reactions frequently reveals valuable information on the mechanism of nanometal catalysis. Here, the reactivity of the Ptn + (n = 1-40) clusters with N2O is studied and a significant dependence on the size of these clusters is noticed. Interestingly, the small Ptn + clusters like Pt3 + and Pt4 + are inclined to form N2O complexes; some larger clusters, such as Pt19 +, Pt21 +, and Pt23 +, appear to be unreactive; however, the others such as Pt3 , 9,15 + and Pt18 + are capable of decomposing N2O. While Pt9 + rapidly reacts with N2O to form a stable quasitetrahedron Pt9O+ product, Pt18 + experiences a series of N2O decompositions to produce Pt18O1-7 +. Utilizing high-precision theoretical calculations, it is shown how the atomic structures and active sites of Ptn + clusters play a vital role in determining their reactivity. Cooperative dual Lewis-acid sites (CDLAS) can be achieved on specific metal clusters like Pt18 +, rendering accelerated N2O decomposition via both N- and O-bonding on the neighboring Pt atoms. The influence of CDLAS on the size-dependent reaction of Pt clusters with N2O is illustrated, offering insights into cluster catalysis in reactions that include the donation of electron pairs.

Unveiling Ionized Interfacial Water-Induced Localized H* Enrichment for Electrocatalytic Nitrate Reduction.

Electrocatalytic nitrate reduction reaction (NO3RR) is a process that requires the participation of eight electrons and nine protons. The regulation of active hydrogen (H*) supply and a deep understanding of related processes are necessary for improving the ammonia yield rate and Faradaic efficiency (FE). Herein, we synthesized a series of atomically precise copper-halide clusters Cu2X2(BINAP)2 (X = Cl, Br, I), among which the Cu2Cl2(BINAP)2 cluster shows the optimal ammonia FE of 94.0% and an ammonia yield rate of 373 µmol h-1 cm-2. In situ experiments and theoretical calculations reveal that halogen atoms, especially Cl in Cu2Cl2(BIANP)2, can significantly affect the distance of alkali metal-ionized water on the catalyst surface, which can promote the water dissociation to enhance the localized H* enrichment for the continues hydrogenation of nitrate to ammonia. This work explains the role of H* in the hydrogenation process of NO3RR and the importance of localized H* enrichment strategy for improving the FEs.

Creating and leveraging bespoke large-scale knowledge graphs for comparative genomics and multi-omics drug discovery with SocialGene.

The rapid expansion of multi-omics data has transformed biological research, offering unprecedented opportunities to explore complex genomic relationships across diverse organisms. However, the vast volume and heterogeneity of these datasets presents significant challenges for analyses. Here we introduce SocialGene, a comprehensive software suite designed to collect, analyze, and organize multi-omics data into structured knowledge graphs, with the ability to handle small projects to repository-scale analyses. Originally developed to enhance genome mining for natural product drug discovery, SocialGene has been effective across various applications, including functional genomics, evolutionary studies, and systems biology. SocialGene's concerted Python and Nextflow libraries streamline data ingestion, manipulation, aggregation, and analysis, culminating in a custom Neo4j database. The software not only facilitates the exploration of genomic synteny but also provides a foundational knowledge graph supporting the integration of additional diverse datasets and the development of advanced search engines and analyses. This manuscript introduces some of SocialGene's capabilities through brief case studies including targeted genome mining for drug discovery, accelerated searches for similar and distantly related biosynthetic gene clusters in biobank-available organisms, integration of chemical and analytical data, and more. SocialGene is free, open-source, MIT-licensed, designed for adaptability and extension, and available from github.com/socialgene.