Triangular Motifs Research Articles

Interplay between Halogen and Hydrogen Bonds in 2D Self-Assembly on the Gold Surface: A First-Principles Investigation

The interplay between halogen bonding and hydrogen bonding has caused recent interest in the formation of 2D self-assembled molecular arrays on solid surfaces. Herein we present a first-principles density functional theory study of the self-assemblies of two brominated anthraquione molecules on Au(111) and Au(110). The possible binding sites of these two compounds on the facets were first explored, and then various self-assembled patterns involving different halogen and hydrogen bonds were examined both in the gas phase and on the gold surface. To visually investigate the nature of lateral adsorbate–adsorbate and vertical adsorbate–substrate interactions, the atoms in molecules, noncovalent interaction index, and electron density difference analyses were undertaken. The molecules tend to be self-assembled by means of triangular binding motifs with simultaneous halogen and hydrogen bonds. Upon the formation of the dimers in the gas phase as well as on the gold surface, significant band shifts around the Fe...

Fractal rules in brain networks: Signatures of self-organization

We study brain network data of three species, namely, C. elegans, cat and macaque monkey within the framework of network theory and Potts Hamiltonian model, and explore rich fractal nature in it, which could be an important signature of self-organization, and a simple rule to be obeyed in complex patterns of brain networks. Further, this fractal behaviors in topological parameters of brain networks at various network levels could be an indicator of systems level organization in complicated brain functionality. Again, Rich-club formation of leading hubs in brain networks becomes unpredictable as one goes down to different levels of organization. The popularity of these leading hubs in main modules or sub-modules also gets changed at different network levels, with varied attitudes at each level. Moreover, distribution of edges, which involves intra- and inter-modular/sub-modular interactions, inherited from one level of organization to another level follows fractal law. In addition to this, the Hamiltonian function at each network level, which may correspond to the energy cost in network organization at that level, shows fractal nature. Significant motifs, which are building blocks of networks and related to basic functionalities, in brain networks is found to be triangular motif, and its probability distribution at various levels as a function of size of modules or sub-modules follows fractal law.

Three-dimensional buckled honeycomb boron lattice with vacancies as an intermediate phase on the transition pathway from \u03b1-B to \u03b3-B

In the phase diagram of elemental boron, an unknown high-pressure form was identified as γ-orthorhombic boron (γ-B28), provoking studies of the extraordinary properties of its main building blocks, B12 icosahedra and B2 dumbbells. Although two low-pressure phases, α- and β-rhombohedral boron (α-B12 and β-B106), are also composed of icosahedra, the detailed kinetics and mechanisms of the structural transition from α-B12 or β-B106 to γ-B28 remain poorly understood. We report on new metastable boron phases formed during the transition in high-pressure high-temperature conditions that were discovered using the crystal structure search method. The metastable phases are understood to be a three-dimensional buckled defective honeycomb lattice in which boron vacancies lead to a dynamically and mechanically stable structure with triangular motifs. We suggest that the metastable phases act as intermediate states on the transition pathway from α-B12 to γ-B28 owing to their structural flexibility and low enthalpies, in the framework of Ostwald’s step rule.

FLOWER: Fusing global and local associations towards personalized social recommendation

In big data era people are dependent on a variety of social media to manage their social circles. Many online social networks employ social recommendation as an increasingly important component. Although global and local recommendation methods have achieved remarkable success, current studies seldom consider to play advantages of both in social networks. To demonstrate the effectiveness of incorporating local methods to global ones, we first investigated associations between triangular motifs and existing social relations and found that potential links are related with common relations. Further, we analyzed correlations of all methods and clustered them and found obvious strong correlations among methods with same type, which demonstrated the necessity of taking advantages of both. Consequently, we proposed a novel method FLOWER which resorts to Fisher’s combined probability test to systematically calibrate statistical significance of global and local associations. FLOWER utilizes information of social relations in both local and global scopes, which are less correlated with each other, and therefore imply possibilities of different aspects for a candidate link. We demonstrated the effectiveness of FLOWER by considering each possible pairwise combination of six global approaches with two local methods and performing 10-fold cross-validation experiments on five real social network datasets (Facebook, Last.fm, Epinions, HEP-PH and Delicious). Results show that FLOWER-based methods significantly outperform either their global or local components in accuracy and retrieval performance.

Synthesis of Enantiopure C3 -Symmetric Triangular Molecules.

An asymmetric synthesis of C3 -symmetric triangular macrocycles is reported. 1-Methylsulfonyl-4-(4-vinylphenyl)-1,2,3-triazole undergoes a rhodium(II)-catalyzed cyclotrimerization to establish an enantiopure C3 -symmetric triangular macrocycle motif. This method can be applied to the synthesis of an enantiopure hydrocarbon, which owes its chirality to asymmetric distribution of H/D atoms on the benzene rings.

Synthesis of Enantiopure C3‐Symmetric Triangular Molecules

AbstractAn asymmetric synthesis of C3‐symmetric triangular macrocycles is reported. 1‐Methylsulfonyl‐4‐(4‐vinylphenyl)‐1,2,3‐triazole undergoes a rhodium(II)‐catalyzed cyclotrimerization to establish an enantiopure C3‐symmetric triangular macrocycle motif. This method can be applied to the synthesis of an enantiopure hydrocarbon, which owes its chirality to asymmetric distribution of H/D atoms on the benzene rings.

Switchable Multiple Spin States in the Kondo description of Doped Molecular Magnets

We show that introducing electrons in magnetic clusters and molecular magnets lead to rich phase diagrams with a variety of low-spin and high-spin states allowing for multiple switchability. The analysis is carried out for a quantum spin-fermion model using the exact diagonalization, and the cluster mean-field approach. The model is relevant for a number of molecular magnets with triangular motifs consisting of transition metal ions such as Cr, Cu and V. Re-entrant spin-state behavior and chirality on-off transitions exist over a wide parameter regime. A subtle competition among geometrical frustration effects, electron itinerancy, and Kondo coupling at the molecular level is highlighted. Our results demonstrate that electron doping provides a viable mean to tame the magnetic properties of molecular magnets towards potential technological applications.

Mechanical behavior of planar borophenes: A molecular mechanics study

The aim of the present work is to provide numerical data regarding the in-plane tensile mechanical response of two-dimensional boron sheets known as borophene sheets or borophenes. The proposed theoretical approach is grounded in a molecular mechanics method which utilizes the equilibrium atomistic structure of the nanomaterials under investigation. In addition, it incorporates special spring-like finite elements to approximate the interatomic force field. The computational approach is mainly based on the modified Morse interatomic potential. Some of the relevant force field parameters concerning boron element are estimated according to the universal force field. Four different atomistic configurations of borophene monolayers are analyzed, i.e., an ideal perfect sheet exclusively made from regular triangular motifs, a sheet made from the ideal structure of the B36 molecule, a sheet known as “α” containing uniformly distributed regular hexagonal holes, and a sheet known as “β” having hexagonal holes distributed in lines. The four tested sheets are selected to have an almost square shape of the same size. Based on the computed tensile stress-strain curves, several mechanical properties along the zigzag and armchair directions are estimated. The Young’s modulus, Poisson’s ratio, tensile strength and failure strain of the borophenes are illustrated with respect to the hexagonal hole density. Comparisons are made where possible.

Do halogen bonds dictate the packing preferences in solid solutions?

The isomeric compounds, 4-bromo-2-chloro benzoic acid (4Br) and 2-bromo-4-chlorobenzoic acid (2Br), crystallize in entirely different space groups, P21/n and P1[combining macron] respectively. Both structures are stabilized by a strong O-HO hydrogen bonds generating a carboxylic acid dimer along with an unusual triangular halogen bonded motif in the former and a well-defined halogen bond in the latter. Charge density analysis establishes the nature of halogen bonds by bringing out significant changes in the packing features of the two structures as well as the quantification of the interaction energies involved in the formation of the motifs. Cocrystallization efforts lead to the formation of solid solutions of varied stoichiometric ratios among the two entirely different crystalline forms, a feature which is observed for the first time, and depends on the nature of the halogen bonds. Despite the significant variations in the charge density distribution in intermolecular space, the triangular motif, with two type II BrCl and ClBr and one type I BrBr contact in the structure of 4Br dictates the packing preferences in the solid solution as established by accurate single crystal diffraction studies supported by cognate powder diffraction analysis (PXRD) and differential scanning calorimetric (DSC) studies. A systematic study of the solid solution by varying the stoichiometric ratios establishes the hierarchy in halogen bonded motifs and consequently its directional influence to form the resultant supramolecular assembly.

Comparing the effects of interparticle friction coefficient and intermediate stress ratio on critical-state DEM simulations using Delaunay triangulations

Strong force chains form when any granular material is subjected to load. A prior study used Delaunay triangulations to investigate the role of interparticle friction coefficient, μ, in stabilising the strong force chains [1]. In this follow-on paper, the effects of μ and the intermediate stress ratio, b , are compared. Numerical samples were sheared triaxially until critical state was attained. The contact networks and Delaunay triangulations of the particle centroids were both obtained at the end of each simulation. As μ is increased, the numbers of contacts in the contact networks decrease consistently. The numbers of edges, faces or tetrahedra in the Delaunay triangulations all increase with increasing μ up to 0.25 and become approximately constant thereafter. Changing b has no significant effect. The percentage of faces in the triangulation comprising three contacts shows a linearly-decreasing trend with increasing angle of shearing resistance. This is because only orthogonal loads are applied. Triangular structures require larger lateral supporting forces to maintain their stability than columnar structures when subjected to an axial load; hence, σ 3 ′ is expected to be larger relative to σ 1 ′ when triangular motifs are more prevalent. An increased proportion of triangular structures therefore leads to a lower ϕ cv ′.

Analysis of an unusual hetero-halogen bonded trimer using charge density analysis: A case of concerted type I Br⋯Br and type II Br⋯Cl interactions

The crystal structure of 4−bromo−2−chlorobenzoic acid generates an unusual triangular motif consisting of a hitherto uncharacterized Type I Br⋯Br contact along with two Type II Br⋯Cl interactions as edges of the triangle. The nature of such bonding is analyzed based on both experimental and theoretical charge density followed by topological analysis. An unusual triangular motif consisting of a hitherto uncharacterized Type I Br⋯×Br contact along with two Type II Br⋯Cl interactions as edges of the triangle is seen in the crystal structure of 4−bromo−2−chlorobenzoic acid. The nature of such bonding is analyzed based on both experimental and theoretical charge density followed by topological analysis.

Identification, analysis, and interpretation of a human serum metabolomics causal network in an observational study

Untargeted metabolomics, measurement of large numbers of metabolites irrespective of their chemical or biologic characteristics, has proven useful for identifying novel biomarkers of health and disease. Of particular importance is the analysis of networks of metabolites, as opposed to the level of an individual metabolite. The aim of this study is to achieve causal inference among serum metabolites in an observational setting. A metabolomics causal network is identified using the genome granularity directed acyclic graph (GDAG) algorithm where information across the genome in a deeper level of granularity is extracted to create strong instrumental variables and identify causal relationships among metabolites in an upper level of granularity.Information from 1,034,945 genetic variants distributed across the genome was used to identify a metabolomics causal network among 122 serum metabolites. We introduce individual properties within the network, such as strength of a metabolite. Based on these properties, hypothesized targets for intervention and prediction are identified. Four nodes corresponding to the metabolites leucine, arichidonoyl-glycerophosphocholine, N-acyelyalanine, and glutarylcarnitine had high impact on the entire network by virtue of having multiple arrows pointing out, which propagated long distances. Five modules, largely corresponding to functional metabolite categories (e.g. amino acids), were identified over the network and module boundaries were determined using directionality and causal effect sizes. Two families, each consists of a triangular motif identified in the network had essential roles in the network by virtue of influencing a large number of other nodes. We discuss causal effect measurement while confounders and mediators are identified graphically.

Molecular geometries and relative stabilities of titanium oxide and gold-titanium oxide clusters

Titanium oxide and gold-titanium oxide clusters of stoichiometry MxOy (Mx=Ti3, Ti4 & AuTi3; y=0−(2x+2)) have been investigated using density functional theory. Geometries of determined global energy minimum structures are reported and other isomers predicted up to 0.5eV higher in energy. The Ti3On geometries build upon a triangular Ti3 motif, while Ti4On stoichiometries template upon a pseudo-tetrahedral Ti4 structure. Addition of a gold atom to the Ti3On series does not significantly alter the cluster geometry, with the gold atom preferentially binding to titanium atoms over oxygen atoms. Adiabatic ionization energies, electron affinities and HOMO/LUMO energies increase in magnitude with increasing oxygenation. The HOMO-LUMO energy gaps reach the bulk anatase band gap energy at stoichiometry (Au)TimO2m−1, and increase above this upon further oxygen addition. The most stable structural moieties are found to be a cage-like, C3v symmetric Ti4O6/7 geometry and a Ti3O6 structure with an η3-bound oxygen atom.

Plasticity-Driven Self-Organization under Topological Constraints Accounts for Non-random Features of Cortical Synaptic Wiring.

Understanding the structure and dynamics of cortical connectivity is vital to understanding cortical function. Experimental data strongly suggest that local recurrent connectivity in the cortex is significantly non-random, exhibiting, for example, above-chance bidirectionality and an overrepresentation of certain triangular motifs. Additional evidence suggests a significant distance dependency to connectivity over a local scale of a few hundred microns, and particular patterns of synaptic turnover dynamics, including a heavy-tailed distribution of synaptic efficacies, a power law distribution of synaptic lifetimes, and a tendency for stronger synapses to be more stable over time. Understanding how many of these non-random features simultaneously arise would provide valuable insights into the development and function of the cortex. While previous work has modeled some of the individual features of local cortical wiring, there is no model that begins to comprehensively account for all of them. We present a spiking network model of a rodent Layer 5 cortical slice which, via the interactions of a few simple biologically motivated intrinsic, synaptic, and structural plasticity mechanisms, qualitatively reproduces these non-random effects when combined with simple topological constraints. Our model suggests that mechanisms of self-organization arising from a small number of plasticity rules provide a parsimonious explanation for numerous experimentally observed non-random features of recurrent cortical wiring. Interestingly, similar mechanisms have been shown to endow recurrent networks with powerful learning abilities, suggesting that these mechanism are central to understanding both structure and function of cortical synaptic wiring.

Latent space inference of internet-scale networks

The rise of Internet-scale networks, such as web graphs and social media with hundreds of millions to billions of nodes, presents new scientific opportunities, such as overlapping community detection to discover the structure of the Internet, or to analyze trends in online social behavior. However, many existing probabilistic network models are difficult or impossible to deploy at these massive scales. We propose a scalable approach for modeling and inferring latent spaces in Internet-scale networks, with an eye towards overlapping community detection as a key application. By applying a succinct representation of networks as a bag of triangular motifs, developing a parsimonious statistical model, deriving an efficient stochastic variational inference algorithm, and implementing it as a distributed cluster program via the Petuum parameter server system, we demonstrate overlapping community detection on real networks with up to 100 million nodes and 1000 communities on 5 machines in under 40 hours. Compared to other state-of-the-art probabilistic network approaches, our method is several orders of magnitude faster, with competitive or improved accuracy at overlapping community detection.

Self-assembled π-conjugated organic nanoplates: from hexagonal to triangular motifs

The formation of triangular nanoplates of an organic semiconducting compound is discussed by considering enhanced solvent/molecule interactions.

Self-organization of complex cortex-like wiring in a spiking neural network model

Understanding the structure and dynamics of cortical connectivity is vital to understanding cortical function. Experimental data strongly suggest that local recurrent connectivity in the cortex is significantly non-random, exhibiting above-chance bidirectionality, an overrepresentation of certain triangular motifs, and a heavy-tailed distribution of synaptic efficacies [1]. Additional evidence suggests a significant distance dependency to connectivity over a local scale of a few hundred microns [2], and particular patterns of synaptic turnover dynamics [3]. It is currently not understood how many of these non-random features arise. Gaining understanding, then, of the processes that lead to these complexities would provide valuable insights into the development and computational functionality of the cortex. While previous work has attempted to model some of the individual features of local cortical wiring, there is no model that comprehensively begins to account for all of them. Here we present a spiking network model of a Layer V-like cortical slice culture (panel B) that, via the interactions of a few simple biologically motivated plasticity mechanisms, qualitatively reproduces many of these non-random effects, such as synaptic weight (panel A) and triangular motif distribution (panel C) Additionally, it reproduced experimentally observed synaptic growth and efficacy dynamics [3]. These plasticity mechanisms include spike timing dependent plasticity, synaptic normalization, homeostatic firing threshold adaptation, pruning of zero-efficacy synaptic connections, and the distance-dependent generation of new synaptic connections. As a spiking, topographic extension to the previously developed SORN family of models [4,5], there is also evidence suggesting that these plasticity mechanisms endow recurrent networks with powerful learning abilities. Our model suggests that mechanisms of self-organization arising from a small number of plasticity rules provide a parsimonious explanation for numerous experimentally observed non-random features of recurrent cortical wiring. Figure 1 Panel A: Mature synaptic weight distribution (in logarithmic space) for a simulation run with associated Gaussian (lognormal in linear space) fit. Panel B: Topological graph of mature network for a simulation run. Panel C: Triangular motif count (relative ...

Crystal structure of tris-[μ2-bis-(di-phenyl-phosphan-yl)methane-κ(2) P:P']di-μ3-iodido-tris-ilver(I) iodide-N-phenyl-thio-urea (1/1).

The title complex, [Ag3I2(C25H22P2)3]I·C7H8N2S, comprises a trinuclear [Ag3I2(C25H22P2)3]+ unit, an I− anion and one N,N′-phenyl­thio­urea mol­ecule (ptu). Two μ3-bridging I− anions are linked by three AgI ions, leading to the formation of a dicapped triangular motif with Ag⋯Ag separations in the range 3.0823 (5)–3.2999 (5) Å. Each AgI atom exhibits a distorted tetra­hedral geometry, with coordination to two I atoms and two P atoms from bis­(di­phenyl­phosphan­yl)methane ligands. In the crystal, the I− anion is linked to the ptu mol­ecule through two N—H⋯I hydrogen bonds [graph-set motif R 2 1(6)]. These N—H⋯I hydrogen bonds, in addition to weak C—H⋯S and C—H⋯I hydrogen bonds, form zigzag chains along [010]. Two of the phenyl rings of two dppm ligands are disordered over two sets of sites with refined occupancies of 0.557 (16) and 0.443 (16).

A bulky oxime for the synthesis of Mn(III) clusters

The reaction between Mn(OAc)2·4H2O and Br-saoH2 (=5-Br-salicylaldoxime) in EtOH in the presence of NMe4OH led to the formation of the hexanuclear cluster [Mn6O2(Br-sao)6(OAc)2(H2O)2(EtOH)2]·2.8H2O·2.2EtOH (1). Switching from Mn(OAc)2·4H2O to Mn(ClO4)2·6H2O, the same reaction upon addition of pivH (= trimethyl acetic acid) yielded [Mn6O2(Br-sao)6(piv)2(H2O)2(EtOH)2]·6EtOH (2 6EtOH), and finally upon changing pivH to NaO2CPh, we were able to isolate [Mn6Na2O2(Br-sao)6(O2CPh)4(H2O)2(EtOH)4]·6EtOH (3 6EtOH). Clusters 1 and 2 6EtOH describe “typical” [Mn6/oximate] complexes consisting of two {Mn3} oxo-centered triangular units bridged by oximate groups, while in 3 6EtOH these triangular motifs are separated by two sodium cations. An investigation into the magnetic properties of all three clusters revealed the presence of dominant antiferromagnetic interactions, leading to ground states of S = 4 and 2 for 1 and 3, respectively. Finally, cluster 2 6EtOH functions as a single-molecule magnet with Ueff = 27.54 K.

Spin-glass behavior in single crystals of hetero-metallic magnetic warwickites MgFeBO4, Mg0.5Co0.5FeBO4, and CoFeBO4

Magnetic properties of heterometallic warwickites MgFeBO4, Mg0.5Co0.5FeBO4, and CoFeBO4 are presented, highlighting the effect of Co substitution on the magnetic properties of these compounds. The analysis of magnetization and heat capacity data has shown that these compounds exhibit a spin-glass transition below TSG=10, 20 and 22K, respectively. Using zero field ac susceptibility as entanglement witness we find that the low dimensional magnetic behavior above TSG show quantum entanglement behavior χ(Τ)∝T−α(Τ) up to TE≈130K. The α parameters have been deduced as a function of temperature and Co content, indicating the existence of random singlet phase in this temperature region. Above TE the paramagnetism is interpreted in terms of non-entangled spins giving rise to Curie–Weiss paramagnetism. The different intra- and inter-ribbon exchange interaction pathways have been calculated within a simple indirect coupling model. It is determined that the triangular motifs in the warwickite structure, together with the competing interactions, induce frustration. The spin-glass character is explained in terms of the substitutional disorder of the Mg, Fe and Co atoms at the two available crystallographic sites, and the frustration induced by the competing interactions. The Co substitution induces uniaxial anisotropy, increases the absolute magnetization and increases the spin-glass freezing temperature. The entanglement behavior is supported in the intermediate phase irrespective of the introduction of anisotropy by the Co substitution.