Fundamental Building Block Research Articles

Virtual Reality Based Executive Function Training in Schools: The Experience of Primary School-Aged Children, Teachers and Training Teaching Assistants

Executive function (EF) is a set of higher order cognitive processes through which learning and everyday goals are realised. They comprise the fundamental building blocks of how we plan, execute, monitor and regulate tasks, and impact our cognitive, socioemotional and behavioural responses. An important question to consider is how we can support children to develop effective EF skills through motivating and age-appropriate training. Virtual reality (VR) offers an interesting avenue to enhance motivation due to the experience of presence and immersion, however, whether children experience presence and immersion similarly to adults is unknown and could impact the educational utility of VR over other media. In order to understand whether VR is suitable for an educational setting we must understand the experience of key stakeholders, such as school-aged children and adults that will be facilitating use in the educational context. Therefore, the current study aims to understand the experience of key stakeholders using EF training delivered in a VR environment, to enable reflection on the feasibility and usability of the technology. This study aimed to explore the qualitative experiences of 8 primary school-aged children, 5 teachers and 13 training teaching assistants, after playing an EF training game, Koji’s Quest, on a VR head mounted display. Firstly we found that most teachers and trainee teachers gave good ratings of usability, but in their subjective descriptions of use focused on hedonic experiences, whereas, children focused on pragmatic experiences. Results also indicate that adults may favour ‘being’ definitions of presence, whereas child participants appear to incorporate both ‘being’ and ‘doing’ definitions into their accounts. This research has implications for how VR based EF training can be maximised within an educational setting.

Highly Responsive Polar Vortices in All-Ferroelectric Heterostructures.

The discovery of polar vortices and skyrmions in ferroelectric-dielectric superlattices [such as (PbTiO3)n/(SrTiO3)n] has ushered in an era of novel dipolar topologies and corresponding emergent phenomena. The key to creating such emergent features has generally been considered to be related to counterpoising strongly polar and non-polar materials thus creating the appropriate boundary conditions. This limits the utility these materials can have, however, by rendering (effectively) half of the structure unresponsive to applied stimuli. Here, using advanced thin-film deposition and an array of characterization and simulation approaches, polar vortices are realized in all-ferroelectric trilayers, multilayers, and superlattices built from the fundamental building block of (PbTiO3)n/(PbxSr1- xTiO3)n wherein in-plane ferroelectric polarization in the PbxSr1- xTiO3 provides the appropriate boundary conditions. These superlattices exhibit substantially enhanced electromechanical and ferroelectric responses in the out-of-plane direction that arise from the ability of the polarization in both layers to rotate to the out-of-plane direction under field. In the in-plane direction, the layers are found to be strongly coupled during switching and when heterostructured with ferroelectric-dielectric building blocks, it is possible to produce multistate switching. This approach expands the realm of systems supporting emergent dipolar texture formation and does so with entirely ferroelectric materials thus greatly improving their responses.

From β-KB3O4F2 to α-KB3O4F2: Phase Transition-Directed Great Changes in Structure and Optical Anisotropy.

Herein, a new fluorooxoborate α-KB3O4F2 is synthesized successfully in a closed system. It crystallizes in the P21/n space group and features the rare one-dimensional (1D) zigzag [B6O8F4]∞ chains built by fundamental building blocks (FBBs) [B6O9F4]. To the best of our knowledge, KB3O4F2 is a unique example of inorganic anhydrous borate whose two polymorphs show 1D B-O/F chains constructed by different FBBs but the same symmetry operation. Different from β-KB3O4F2, the inconsistent arrangement of π-conjugated [B2O5] units in α-KB3O4F2 makes it exhibit a small birefringence (0.011@546 nm). Further, α-KB3O4F2 owns a deep-ultraviolet (DUV) cutoff edge (<200 nm), suggesting that it has a potential application as the zero-order waveplate material in the DUV region.

RTPL: A Real-Time Communication Protocol for LoRa Network

The industrial Internet of Things (IIoT) is prominently emerging in applications of large-scale and wide-area applications, such as oilfield management, smart grid management, real-time equipment monitoring, and integration of traffic management systems for smart cities. Relying on short-range wireless technologies (e.g., WirelessHART and ISA100.11a), traditional wireless solutions for industrial automation find it challenging to support the expansive scale of today’s IIoT. To address this limitation, we propose to adopt LoRaWAN, a prominent low-power wide-area network technology, for industrial automation. LoRaWAN for industrial automation poses some unique challenges. The fundamental building blocks of any industrial automation system are feedback control loops that largely rely on real-time communication. LoRaWAN traditionally adopts a simple protocol based on ALOHA with no collision avoidance or Listen Before Talk with Clear Channel Assessment and Random Backoff mechanisms to minimize energy consumption, which are less suitable for real-time communication. Existing real-time protocols for short-range technologies cannot be applied to a LoRaWAN network due to its unique characteristics such as asymmetry between downlink and the uplink spectrum, predefined modes (or classes) of operation, and concurrent reception through orthogonal spreading factors. In this paper, we address these challenges and propose RTPL - a Real-Time communication Protocol for LoRaWAN networks. RTPL is a low-overhead and conflict-free communication protocol allowing autonomous real-time communication of low-energy devices and exploits LoRa’s capability of parallel communication. We implement our approach on LoRa devices and evaluate through both physical experiments and extensive simulations. All results show that RTPL achieves on average 75% improvement in real-time performance without sacrificing throughput or energy compared to traditional LoRaWAN.

Transfer learning enabled transformer-based generative adversarial networks for modeling and generating terahertz channels

Terahertz communications are envisioned as a promising technology for the sixth generation and beyond wireless systems, which can support wireless links with Terabits-per-second (Tbps) data rates. As the foundation of designing terahertz communications, channel modeling and characterization are crucial to scrutinize the potential of this spectrum. However, current channel modeling in the terahertz band heavily relies on time-consuming and costly measurements. Here, we propose a transfer learning enabled transformer based generative adversarial network to mitigate this problem in terahertz channel modeling. Specifically, as a fundamental building block, a generative adversarial network is exploited to generate channel parameters. To improve the accuracy, a transformer structure with a self-attention mechanism is incorporated in generative adversarial network. Still incurring errors compared with ground-truth measurement, a transfer learning is designed to solve the mismatch between the formulated network and measurement. The proposed method can achieve high accuracy in channel modeling, while requiring only rather limited amount of measurement, which is a promising complement of current channel modeling techniques.

Recent Progress for the Synthesis of Pyrrole Derivatives – An Update

Abstract: Pyrrole is a versatile heterocyclic moiety exhibiting a wide range of pharmacological actions with high therapeutic value. The importance of pyrrole in the pharmaceutical field lies in its versatility, selectivity, and biocompatibility, and these properties make it a valuable tool for drug design and development. The pyrrole moiety is a fundamental building block for many biologically active molecules and has gathered significant attention in the fields of medicinal and organic chemistry; hence, its synthesis has been a crucial area for research. There are various conventional as well as modern approaches to acquiring a series of pyrrole scaffolds, with a wide range of attractive features and drawbacks pertaining to each approach. An extensive amount of literature must be studied to compare the best synthetic routes. This article highlights the applications of pyrrole derivatives in various fields, such as drug discovery, material science, and catalysis, and provides an overview of modern synthetic pathways that include metals, nanomaterials, and complex heterogeneous catalysed methods for pyrrole derivatives. Special emphasis is given to the use of green chemistry principles like green solvent-based methods, microwave-aided methods, and solvent-free methods in the synthesis of pyrroles, with the recent developments and prospects in the synthetic and organic chemistry fields. Overall, this review article provides a comprehensive overview of the synthesis of pyrroles and complies with all the possible developments in the synthetic routes for pyrroles within 2015– 2022. Among all, the reactions catalysed by proline, copper oxides, and oxones have been shown to be the most effective synthetic route for pyrrole derivatives at mild reaction conditions and with excellent yields. This information will be helpful for researchers interested in the development of new pyrrole-based compounds. The categorization in this review provides an easy means for the reader to rationally select the best possible synthetic method for pyrrole derivatives.

The p.D417N variant of TUBB4A as a possible cause of hereditary spastic paraplegia: a case report

BackgroundTubulins are dimeric proteins expressed in all eukaryotic cells, serving as the fundamental building blocks of microtubule filaments. The TUBB4A gene encodes the protein β-tubulin. Mutations of TUBB4A have been associated with two neurodegenerative diseases with very different clinical characteristics: dystonia type 4 (DYT4) and Hypomyelination with Atrophy of the Basal Ganglia and Cerebellum (H-ABC). Several cases of patients with H-ABC or unclassified leukoencephalopathy show spastic ataxia with or without leukodystrophy in association with mutations in exon 5 of TUBB4A gene.Case presentationWe report the case of a 65-year-old woman who has been complaining of progressive difficulty in walking since childhood. The neurological examination revealed, among all, a spastic gait, difficulties in standing on the toes and heels, brisk deep tendon reflexes at upper limbs, clonic patellar reflexes, brisk ankle reflexes, as well as bilateral Babinski and Hoffmann sign, brisk jaw jerk and severe lower limb spasticity. NGS studies for inherited cases of spastic paraplegia revealed a novel variant of unknown significance (VUS) (c.1249A > G, p.D417N), in TUBB4A. To the best of our knowledge, this variant has not been reported in the literature or any databases in association with these diseases.ConclusionWe report the case of a patient carrying a variant of uncertain significance (VUS) of the TUBB4A gene, showing a progressive, spastic paraparesis, supporting the extension of the phenotypic spectrum up to include spastic paraplegia.

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In radial quantization, the ground states of a gauge theory on ADE singularities ℝ4/Γ are characterized by flat connections that are maps from Γ to the gauge group. We study Class S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S} $$\\end{document} theory of type a1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathfrak{a}}_1 $$\\end{document} = su2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{su}(2) $$\\end{document} on a Riemann surface of genus g > 1, without punctures. The fundamental building block of Class S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S} $$\\end{document} theory is the trifundamental Trinion theory — a low energy limit of two M5 branes compactified on the three-punctured Riemann sphere. We show, through the superconformal index, that the supersymmetric Casimir energy of the trifundamental theory imposes a constraint on the set of allowed flat connections, which agrees with the prediction of a duality relating the ground state Hilbert space of Class S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S} $$\\end{document} on ADE singularities to the Hilbert space of a certain dual Chern-Simons theory whose gauge group is given by the McKay correspondence. The conjecture is shown to hold for Γ = ℤk, agreeing with the previous results of Benini et al. and Alday et al. A non-abelian generalization of this duality is analyzed by considering the example of the dicyclic group Γ = Dic2, corresponding to Chern-Simons gauge group SO(8).

Investigation of PNN Inverter-Based Low PDP 12T GNRFET Full Adder for VLSI Signal Processing Applications

When an adder circuit, which uses less power and operates at a higher speed, is introduced as a fundamental building block, the multiplier, arithmetic and logic unit (ALU), and digital system’s power delay product (PDP) performance can be easily improved. The graphene nanoribbon field effect transistor (GNRFET) used in very large-scale integrated (VLSI) circuits was developed in the submicron regime and offers superior electrical properties to the MOS transistor. This research paper introduces a full-adder circuit containing twelve GNRFETs (12T GF-FA). Calculations have been made about the introduced 12T GF-FA’s power usage, speed, PDP and leakage power. A few of the existing full adders with 8–32 transistors are compared to the performance of the newly proposed 12T GF-FA in terms of power and delay. For this comparison, some conventional full adders with 8–32 transistors have been implemented using 16[Formula: see text]nm technology GNRFETs. The pull-down network of the suggested adder has two stacked GNRFETs. The proposed adder’s current conduction and power consumption are reduced by the use of stacked transistors. According to the simulation results, the PDP of the suggested 12T GF-FA is 73.2–99% lower when compared to other full adders considered state-of-the-art. Additionally, it has been researched and documented how variations in the PVT and GNRFET parameters affect the performance of full-adder circuits. The proposed adder, with its low PDP, is especially suitable for VLSI signal processing applications. The simulation was carried out using the HSPICE simulation tool and the 16[Formula: see text]nm MOS-GNRFET model.

Engineering of tnaC-Based Tryptophan Biosensors for Dynamic Control of Violacein Production.

Tryptophan not only serves as a fundamental building block for protein synthesis but also acts as a metabolic precursor for a diverse array of high-value chemicals. Although a few tryptophan-responsive biosensors are currently available, there is a growing interest in developing high-performance biosensors. In this study, we create a miniature toolkit of tryptophan biosensors based upon the leader regulatory region of the tnaCAB operon, which is responsible for tryptophan catabolism in Escherichia coli. Four variants are generated by engineering the tnaC leader sequence, which encodes a leader peptide composed of 24 amino acid residues. Subsequently, the performance of both the natural tnaC sequence and its engineered variants is assessed in a reporter strain based on the MazEF toxin-antitoxin system. The results demonstrate that two engineered variants exhibit increased sensitivity to low levels of tryptophan. Moreover, the engineered biosensors are further optimized by replacing the native promoter of tnaC with a phage-derived constitutive promoter. Intriguingly, the engineered biosensors can be reconstructed for extended application in Pseudomonas putida, a robust microbial chassis for metabolic engineering. In summary, our study expands the toolkit of tryptophan biosensors that can be broadly used for the bioproduction of many other high-value tryptophan-derived products.

Amino acids could sustain fungal life in the energy-limited anaerobic sediments below the seafloor.

In the depths beneath the ocean floor, where darkness, anaerobic conditions, and energy scarcity prevail, life persists against all odds. This study illuminates the pivotal role of amino acids, the fundamental building blocks of life, as a vital energy for deep subseafloor fungi. Our research uncovers how these fungi not only rely on amino acids for survival but also utilize them to reproduce, forming fruit bodies in environments deprived of oxygen and energy. This revelation not only elucidates the mechanisms enabling fungal survival in extreme conditions but also hints at the essentiality of amino acids as nutrients for other deep-sea microbes. By unraveling these mysteries of the hidden biosphere, our study opens new frontiers in understanding the resilience and adaptation of life in the most inhospitable environments on our planet.

BIMSA: Accelerating Long Sequence Alignment Using Processing-In-Memory.

Recent advances in sequencing technologies have stressed the critical role of sequence analysis algorithms and tools in genomics and healthcare research. In particular, sequence alignment is a fundamental building block in many sequence analysis pipelines and is frequently a performance bottleneck both in terms of execution time and memory usage. Classical sequence alignment algorithms are based on dynamic programming and often require quadratic time and memory with respect to the sequence length. As a result, classical sequence alignment algorithms fail to scale with increasing sequence lengths and quickly become memory-bound due to data-movement penalties. Processing-In-Memory (PIM) is an emerging architectural paradigm that seeks to accelerate memory-bound algorithms by bringing computation closer to the data to mitigate data-movement penalties. This work presents BIMSA (Bidirectional In-Memory Sequence Alignment), a PIM design and implementation for the state-of-the-art sequence alignment algorithm BiWFA (Bidirectional Wavefront Alignment), incorporating new hardware-aware optimizations for a production-ready PIM architecture (UPMEM). BIMSA supports aligning sequences up to 100K bases, exceeding the limitations of state-of-the-art PIM implementations. First, BIMSA achieves speedups up to 22.24 × (11.95× on average) compared to state-of-the-art PIM-enabled implementations of sequence alignment algorithms. Second, achieves speedups up to 5.84 × (2.83× on average) compared to the highest-performance multicore CPU implementation of BiWFA. Third, BIMSA exhibits linear scalability with the number of compute units in memory, enabling further performance improvements with upcoming PIM architectures equipped with more compute units and achieving speedups up to 9.56 × (4.7× on average). Code and documentation are publicly available at https://github.com/AlejandroAMarin/BIMSA.

Decoding Bennu: Understanding the solar system and life’s origins

The OSIRIS-REx mission to an asteroid named Bennu collected a sample of its regolith—loose material on the surface of an asteroid—and returned to Earth in September 2023. The successful return and initial research on the sample revealed much data about the elemental composition of Bennu’s regolith. The findings offer new insights into the fundamental building blocks of life, potentially revolutionizing our understanding of life and our solar system. The sample contained organic compounds, key to the origin of life, and also elements like iron and magnesium in abundance. Mineral analysis showed the presence of water-rich minerals, a key factor in understanding the origins of our oceans. Analysis of the data helps further the understanding of the origin of our oceans. By understanding the composition of asteroids like Bennu that trace their origins to the early solar system, we can understand the conditions prevalent in those times. And most importantly, understanding the composition of Bennu also gives us key insights into the origin of life because of the discovery of organic compounds in the regolith. Gathering asteroid samples holds much importance in expanding our knowledge in multiple fields and in shedding on many unanswered questions regarding the origin of life, origin of oceans and understanding of the early solar system.

‘Rhythmite’, Ca29(SiO4)8Cl26, an Anthropogenic Phase from the Chelyabinsk Coal Basin (Ural, Russia) with a Complex Modular Structure Related to α-Ca3SiO4Cl2 (‘Albovite’): Crystal Structure, Raman Spectra, and Thermal Expansion

‘Rhythmite’, Ca29(SiO4)8Cl26, an anthropogenic calcium chloride silicate from the Chelyabinsk coal basin (South Ural, Russia), was investigated using chemical microprobe analysis, in situ single-crystal X-ray diffraction analysis (27–727 °C), and Raman spectroscopy. ‘Rhythmite’ is orthorhombic, Pnma: a = 17.0749(6), b = 15.1029(5), c = 13.2907(4) Å, and V = 3427.42(18) Å3 (R1 = 0.045). The crystal structure of ‘rhythmite’ consists of a porous framework formed by Ca-O bonds and SiO4 tetrahedra with additional Ca2+ cations and Cl− anions in the structure interstices. The framework is built up from multinuclear [Ca15(SiO4)4]14+ fundamental building blocks (FBBs) cut from the crystal structure of α-Ca3SiO4Cl2 (‘albovite’). The FBBs are linked by sharing common Ca atoms to form a network with an overall pcu topology. The empirical chemical formula was calculated as Ca29.02(Si7.89Al0.05P0.05)Ʃ7.99O32Cl26 (on the basis of Cl + O = 58). ‘Rhythmite’ is stable up to 627 °C and expands slightly anisotropically (αmax/αmin = 1.40) in the ab and bc planes and almost isotropically in the ac plane (α33/α11 = 1.02) with the following thermal expansion coefficients (×106 °C−1): α11 = 14.6(1), α22 = 20.5(4), α33 = 15.0(3), and αV = 50.1(6) (room temperature). During expansion, the silicate tetrahedra remain relatively rigid with average bond length changes of less than 0.5%. A structural complexity analysis indicates that ‘rhythmite’ is complex, with IG,total = 920.313 (bits/u.c.), which significantly exceeds the average value of structural complexity for silicates and is caused by the modular framework construction and the presence of a large number of independent positions in the crystal structure.

Towards a Pedagogy of Ancient Egyptian Language and Hieroglyphs

This paper discusses the challenges of teaching the Middle Egyptian language and Egyptian hieroglyphs to adult anglophone learners outside university settings. These challenges include the lack of L1 speakers; the large volume of signs in the script; the difficulty in reconstructing pronunciation due to the paucity of written vowels; and the lack of accessible learning tools such as readers and textbooks for the intermediate stage. As spoken proficiency in this extinct language is not a feasible goal, it is argued here that teaching should revolve around achieving reading competence. The paper advocates for a pedagogical approach that centres on using vocabulary, including variant spellings, as the fundamental building blocks of learning. This entails reading words, sentences and paragraphs of increasing complexity, which over time aids memorisation of vocabulary and builds confidence. Grammar and syntax can be gradually introduced and contextualised by reading practice sentences. It is also argued here that producing digitised versions of ancient Egyptian texts using hieroglyphic font software such as JSesh allows for the creation of practice texts in a standardised and legible format. This, in turn, makes it possible to use pedagogical aids such as adding spaces between words and adding signs omitted by the ancient scribes. Finally, it is argued that learning vocabulary and grammar is enhanced by discussions of the wider semantic and cultural meaning(s) of the ancient text in question.

Interactive Segmentation for Medical Images Using Spatial Modeling Mamba

Interactive segmentation methods utilize user-provided positive and negative clicks to guide the model in accurately segmenting target objects. Compared to fully automatic medical image segmentation, these methods can achieve higher segmentation accuracy with limited image data, demonstrating significant potential in clinical applications. Typically, for each new click provided by the user, conventional interactive segmentation methods reprocess the entire network by re-inputting the click into the segmentation model, which greatly increases the user’s interaction burden and deviates from the intended goal of interactive segmentation tasks. To address this issue, we propose an efficient segmentation network, ESM-Net, for interactive medical image segmentation. It obtains high-quality segmentation masks based on the user’s initial clicks, reducing the complexity of subsequent refinement steps. Recent studies have demonstrated the strong performance of the Mamba model in various vision tasks; however, its application in interactive segmentation remains unexplored. In our study, we incorporate the Mamba module into our framework for the first time and enhance its spatial representation capabilities by developing a Spatial Augmented Convolution (SAC) module. These components are combined as the fundamental building blocks of our network. Furthermore, we designed a novel and efficient segmentation head to fuse multi-scale features extracted from the encoder, optimizing the generation of the predicted segmentation masks. Through comprehensive experiments, our method achieved state-of-the-art performance on three medical image datasets. Specifically, we achieved 1.43 NoC@90 on the Kvasir-SEG dataset, 1.57 NoC@90 on the CVC-ClinicDB polyp segmentation dataset, and 1.03 NoC@90 on the ADAM retinal disk segmentation dataset. The assessments on these three medical image datasets highlight the effectiveness of our approach in interactive medical image segmentation.

Umpolung Phosphorylation of Tyrosine via 1,2-Phospha-Brook Rearrangement.

Phosphorylated tyrosine is a fundamental building block of bioactive peptides and proteins. However, the chemoselective phosphorylation of tyrosine over other nucleophilic amino acid residues in unprotected peptides remains a significant challenge. Here we report an umpolung strategy that converts the C-terminal tyrosine into an electrophilic spirolactone cyclohexadienone motif through hypervalent iodine oxidation, followed by a 1,2-phospha-Brook rearrangement using phosphite diesters as nucleophilic phosphoryl donors. This reaction proceeds chemoselectively at the tyrosine phenol and is applicable to a wide range of peptide substrates containing various nucleophilic amino acid residues, including serine and threonine.

Plasmonic devices – equivalent circuit representations

An equivalent circuit model for plasmonic slot waveguide-based devices is presented. Taking advantage of the high mode confinement provided by this waveguide geometry, we express plasmonic waveguide geometries using transmission line parameters and express T-junctions using lumped equivalent circuit elements. By combining these fundamental building blocks, we subsequently introduce equivalent circuit models for stub filters and branch-line couplers. We show that plasmonic circuits, if designed with sharp discontinuities, feature low losses that are comparable to losses from RF circuits and even the corresponding photonic circuits. The framework presented here gives insight into the design of novel microwave-inspired plasmonic devices and circuits and significantly speeds up the design time, as a large part of the geometry optimization can be performed in the equivalent circuit domain. For instance, we use this framework in a follow-up paper to design ultra-compact plasmonic hybrids, such as those needed for coherent detection.

Basilica: New canonical decomposition in matching theory

AbstractIn matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are limited because they are only applicable to particular classes of graphs, such as bipartite graphs, or they are too sparse to provide sufficient information. To overcome these limitations, we introduce a new canonical decomposition that is applicable to all graphs and provides much finer information. This decomposition also provides the answer to the longstanding absence of a canonical decomposition that is nontrivially applicable to general graphs with perfect matchings. We focus on the notion of factor‐components as the fundamental building blocks of a graph; through the factor‐components, our new canonical decomposition states how a graph is organized and how it contains all the maximum matchings. The main results that constitute our new theory are the following: (i) a canonical partial order over the set of factor‐components, which describes how a graph is constructed from its factor‐components; (ii) a generalization of the Kotzig–Lovász decomposition, which shows the inner structure of each factor‐component in the context of the entire graph; and (iii) a canonically described interrelationship between (i) and (ii), which integrates these two results into a unified theory of a canonical decomposition. These results are obtained in a self‐contained way, and our proof of the generalized Kotzig–Lovász decomposition contains a shortened and self‐contained proof of the classical counterpart.

N18 ring: A building block for constructing 1D and 2D polymeric nitrogen frameworks

Exploring the fundamental building block is essential for constructing functional materials with extended topological configurations. In the polymeric nitrogen system, no fundamental building blocks have been reported so far. Here, we successfully synthesize the buckled 1-dimensional (1D) band-shaped and 2-dimensional (2D) layered polymeric nitrogen frameworks with N18 ring as a fundamental building block for the first time. Furthermore, the dimensions of the polymeric nitrogen frameworks can be regulated by pressure conditions. Bader charge analyses indicate that the charge transfer from the La atom to the low-order bonded nitrogen atom plays a crucial role in stabilizing these two low-dimensional polymeric frameworks. Both LaN16 and LaN8 are promising high-energy-density materials (HEDMs). This study reveals that the N18 ring can serve as a fundamental building block, analogous to thesix-membered ring in carbon-based materials, enabling the construction of novel polymeric nitrogen materials with extended frameworks.