scholarly journals Allometric Scaling of Mutual Information in Complex Networks: A Conceptual Framework and Empirical Approach

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 206
Author(s):  
Eduardo Viegas ◽  
Hayato Goto ◽  
Yuh Kobayashi ◽  
Misako Takayasu ◽  
Hideki Takayasu ◽  
...  
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Scaling Laws ◽  
Allometric Scaling ◽  
Free Market ◽  
Preferential Attachment ◽  
Building Blocks ◽  
Structural Features ◽  
Network Activity ◽  
Analysis Tool

Complexity and information theory are two very valuable but distinct fields of research, yet sharing the same roots. Here, we develop a complexity framework inspired by the allometric scaling laws of living biological systems in order to evaluate the structural features of networks. This is done by aligning the fundamental building blocks of information theory (entropy and mutual information) with the core concepts in network science such as the preferential attachment and degree correlations. In doing so, we are able to articulate the meaning and significance of mutual information as a comparative analysis tool for network activity. When adapting and applying the framework to the specific context of the business ecosystem of Japanese firms, we are able to highlight the key structural differences and efficiency levels of the economic activities within each prefecture in Japan. Moreover, we propose a method to quantify the distance of an economic system to its efficient free market configuration by distinguishing and quantifying two particular types of mutual information, total and structural.

scholarly journals Generalized Mutual Information

Stats ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 158-165
Author(s):  
Zhiyi Zhang
Keyword(s):  
Information Theory ◽  
Positive Integer ◽  
Mutual Information ◽  
General Class ◽  
Building Blocks ◽  
Potential Utility ◽  
First Order ◽  
The Family ◽  
Random Elements

Mutual information is one of the essential building blocks of information theory. It is however only finitely defined for distributions in a subclass of the general class of all distributions on a joint alphabet. The unboundedness of mutual information prevents its potential utility from being extended to the general class. This is in fact a void in the foundation of information theory that needs to be filled. This article proposes a family of generalized mutual information whose members are indexed by a positive integer n, with the nth member being the mutual information of nth order. The mutual information of the first order coincides with Shannon’s, which may or may not be finite. It is however established (a) that each mutual information of an order greater than 1 is finitely defined for all distributions of two random elements on a joint countable alphabet, and (b) that each and every member of the family enjoys all the utilities of a finite Shannon’s mutual information.

A Pseudo Five-Fold Symmetrical Ligand Drives Geometric Frustration in Porous Metal-Organic and Hydrogen Bonded Frameworks

2020 ◽  
Author(s):  
Frederik Haase ◽  
Gavin Craig ◽  
Mickaele Bonneau ◽  
kunihisa sugimoto ◽  
Shuhei Furukawa
Keyword(s):  
Topological Defects ◽  
Porous Metal ◽  
Building Blocks ◽  
Structural Features ◽  
Equilibrium Structure ◽  
Sorption Behavior ◽  
Building Unit ◽  
Geometric Frustration ◽  
Secondary Building Units ◽  
Hydrogen Bonded

Reticular framework materials thrive on designability, but unexpected reaction outcomes are crucial in exploring new structures and functionalities. By combining “incompatible” building blocks, we employed geometric frustration in reticular materials leading to emergent structural features. The combination of a pseudo C<sub>5</sub> symmetrical organic building unit based on a pyrrole core, with a C<sub>4</sub> symmetrical copper paddlewheel synthon led to three distinct frameworks by tuning the synthetic conditions. The frameworks show structural features typical for geometric frustration: self-limiting assembly, internally stressed equilibrium structures and topological defects in the equilibrium structure, which manifested in the formation of a hydrogen bonded framework, distorted and broken secondary building units and dangling functional groups, respectively. The influence of geometric frustration on the CO<sub>2</sub> sorption behavior and the discovery of a new secondary building unit shows geometric frustration can serve as a strategy to obtain highly complex porous frameworks.

A Pseudo Five-Fold Symmetrical Ligand Drives Geometric Frustration in Porous Metal-Organic and Hydrogen Bonded Frameworks

2020 ◽  
Author(s):  
Frederik Haase ◽  
Gavin Craig ◽  
Mickaele Bonneau ◽  
kunihisa sugimoto ◽  
Shuhei Furukawa
Keyword(s):  
Topological Defects ◽  
Porous Metal ◽  
Building Blocks ◽  
Structural Features ◽  
Equilibrium Structure ◽  
Sorption Behavior ◽  
Building Unit ◽  
Geometric Frustration ◽  
Secondary Building Units ◽  
Hydrogen Bonded

Reticular framework materials thrive on designability, but unexpected reaction outcomes are crucial in exploring new structures and functionalities. By combining “incompatible” building blocks, we employed geometric frustration in reticular materials leading to emergent structural features. The combination of a pseudo C<sub>5</sub> symmetrical organic building unit based on a pyrrole core, with a C<sub>4</sub> symmetrical copper paddlewheel synthon led to three distinct frameworks by tuning the synthetic conditions. The frameworks show structural features typical for geometric frustration: self-limiting assembly, internally stressed equilibrium structures and topological defects in the equilibrium structure, which manifested in the formation of a hydrogen bonded framework, distorted and broken secondary building units and dangling functional groups, respectively. The influence of geometric frustration on the CO<sub>2</sub> sorption behavior and the discovery of a new secondary building unit shows geometric frustration can serve as a strategy to obtain highly complex porous frameworks.

Application of Nitrogen Heterocyclic Carbenes in Organocatalysis

2020 ◽  
Vol 09 ◽  
Author(s):  
Minita Ojha ◽  
R. K. Bansal
Keyword(s):  
Asymmetric Catalysis ◽  
Building Blocks ◽  
Structural Features ◽  
Heterocyclic Carbenes ◽  
Stetter Reaction ◽  
Metal Pollutants ◽  
Synthetic Strategy ◽  
Wide Range ◽  
Benzoin Condensation ◽  
Nitrogen Heterocyclic

Background: During the last two decades, horizon of research in the field of Nitrogen Heterocyclic Carbenes (NHC) has widened remarkably. NHCs have emerged as ubiquitous species having applications in a broad range of fields, including organocatalysis and organometallic chemistry. The NHC-induced non-asymmetric catalysis has turned out to be a really fruitful area of research in recent years. Methods: By manipulating structural features and selecting appropriate substituent groups, it has been possible to control the kinetic and thermodynamic stability of a wide range of NHCs, which can be tolerant to a variety of functional groups and can be used under mild conditions. NHCs are produced by different methods, such as deprotonation of Nalkylhetrocyclic salt, transmetallation, decarboxylation and electrochemical reduction. Results: The NHCs have been used successfully as catalysts for a wide range of reactions making a large number of building blocks and other useful compounds accessible. Some of these reactions are: benzoin condensation, Stetter reaction, Michael reaction, esterification, activation of esters, activation of isocyanides, polymerization, different cycloaddition reactions, isomerization, etc. The present review includes all these examples published during the last 10 years, i.e. from 2010 till date. Conclusion: The NHCs have emerged as versatile and powerful organocatalysts in synthetic organic chemistry. They provide the synthetic strategy which does not burden the environment with metal pollutants and thus fit in the Green Chemistry.

scholarly journals 1,3-Diketone Calix[4]arene Derivatives—A New Type of Versatile Ligands for Metal Complexes and Nanoparticles

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1214
Author(s):  
Sergey N. Podyachev ◽  
Rustem R. Zairov ◽  
Asiya R. Mustafina
Keyword(s):  
Structural Diversity ◽  
Building Blocks ◽  
Structural Features ◽  
Structure Property ◽  
One Pot ◽  
Arene Ligands ◽  
Structure Property Relationships ◽  
New Type ◽  
Synthetic Routes ◽  
Magnetic Resonance Imaging Mri

The present review is aimed at highlighting outlooks for cyclophanic 1,3-diketones as a new type of versatile ligands and building blocks of the nanomaterial for sensing and bioimaging. Thus, the main synthetic routes for achieving the structural diversity of cyclophanic 1,3-diketones are discussed. The structural diversity is demonstrated by variation of both cyclophanic backbones (calix[4]arene, calix[4]resorcinarene and thiacalix[4]arene) and embedding of different substituents onto lower or upper macrocyclic rims. The structural features of the cyclophanic 1,3-diketones are correlated with their ability to form lanthanide complexes exhibiting both lanthanide-centered luminescence and magnetic relaxivity parameters convenient for contrast effect in magnetic resonance imaging (MRI). The revealed structure–property relationships and the applicability of facile one-pot transformation of the complexes to hydrophilic nanoparticles demonstrates the advantages of 1,3-diketone calix[4]arene ligands and their complexes in developing of nanomaterials for sensing and bioimaging.

Zeolates: A Coordination Chemistry View of Metal-Ligand Bonding in Intrazeolite MOCVD Type Precursors and Semiconductor Nanoclusters

1992 ◽  
Vol 277 ◽  
Author(s):  
Geoffrey A. Ozin ◽  
Carol L. Bowes ◽  
Mark R. Steele
Keyword(s):  
Self Assembly ◽  
Materials Science ◽  
Zeolite Y ◽  
Chemical Vapour ◽  
Internal Surface ◽  
Building Blocks ◽  
Structural Features ◽  
Organic Chemical ◽  
Wide Range ◽  
Shape Selective

ABSTRACTVarious MOCVD (metal-organic chemical vapour deposition) type precursors and their self-assembled semiconductor nanocluster products [1] have been investigated in zeolite Y hosts. From analysis of in situ observations (FTIR, UV-vis reflectance, Mössbauer, MAS-NMR) of the reaction sequences and structural features of the precursors and products (EXAFS and Rietveld refinement of powder XRD data) the zeolite is viewed as providing a macrospheroidal, multidendate coordination environment towards encapsulated guests. By thinking about the α- and β-cages of the zeolite Y host effectively as a zeolate ligand composed of interconnected aluminosilicate “crown ether-like” building blocks, the materials chemist is able to better understand and exploit the reactivity and coordination properties of the zeolite internal surface for the anchoring and self-assembly of a wide range of encapsulated guests. This approach helps with the design of synthetic strategies for creating novel guest-host inclusion compounds having possible applications in areas of materials science such as nonlinear optics, quantum electronics, and size/shape selective catalysis.

scholarly journals Inverse Design of Nanoporous Crystalline Reticular Materials with Deep Generative Models

2020 ◽  
Author(s):  
Zhenpeng Yao ◽  
Benjamin Sanchez-Lengeling ◽  
N. Scott Bobbitt ◽  
Benjamin J. Bucior ◽  
Sai Govind Hari Kumar ◽  
...  
Keyword(s):  
Self Assembly ◽  
Metal Organic Framework ◽  
Internal Surface ◽  
Building Blocks ◽  
Structural Features ◽  
Generative Models ◽  
Combinatorial Design ◽  
Surface Areas ◽  
Molecular Building Blocks ◽  
Metal Organic

Reticular frameworks are crystalline porous materials that form <i>via</i> the self-assembly of molecular building blocks (<i>i.e.</i>, nodes and linkers) in different topologies. Many of them have high internal surface areas and other desirable properties for gas storage, separation, and other applications. The notable variety of the possible building blocks and the diverse ways they can be assembled endow reticular frameworks with a near-infinite combinatorial design space, making reticular chemistry both promising and challenging for prospective materials design. Here, we propose an automated nanoporous materials discovery platform powered by a supramolecular variational autoencoder (SmVAE) for the generative design of reticular materials with desired functions. We demonstrate the automated design process with a class of metal-organic framework (MOF) structures and the goal of separating CO<sub>2</sub> from natural gas or flue gas. Our model exhibits high fidelity in capturing structural features and reconstructing MOF structures. We show that the autoencoder has a promising optimization capability when jointly trained with multiple top adsorbent candidates identified for superior gas separation. MOFs discovered here are strongly competitive against some of the best-performing MOFs/zeolites ever reported. This platform lays the groundwork for the design of reticular frameworks for desired applications.

scholarly journals Inverse Design of Nanoporous Crystalline Reticular Materials with Deep Generative Models

2020 ◽  
Author(s):  
Zhenpeng Yao ◽  
Benjamin Sanchez-Lengeling ◽  
N. Scott Bobbitt ◽  
Benjamin J. Bucior ◽  
Sai Govind Hari Kumar ◽  
...  
Keyword(s):  
Self Assembly ◽  
Metal Organic Framework ◽  
Internal Surface ◽  
Building Blocks ◽  
Structural Features ◽  
Generative Models ◽  
Combinatorial Design ◽  
Surface Areas ◽  
Molecular Building Blocks ◽  
Metal Organic

Reticular frameworks are crystalline porous materials that form <i>via</i> the self-assembly of molecular building blocks (<i>i.e.</i>, nodes and linkers) in different topologies. Many of them have high internal surface areas and other desirable properties for gas storage, separation, and other applications. The notable variety of the possible building blocks and the diverse ways they can be assembled endow reticular frameworks with a near-infinite combinatorial design space, making reticular chemistry both promising and challenging for prospective materials design. Here, we propose an automated nanoporous materials discovery platform powered by a supramolecular variational autoencoder (SmVAE) for the generative design of reticular materials with desired functions. We demonstrate the automated design process with a class of metal-organic framework (MOF) structures and the goal of separating CO<sub>2</sub> from natural gas or flue gas. Our model exhibits high fidelity in capturing structural features and reconstructing MOF structures. We show that the autoencoder has a promising optimization capability when jointly trained with multiple top adsorbent candidates identified for superior gas separation. MOFs discovered here are strongly competitive against some of the best-performing MOFs/zeolites ever reported. This platform lays the groundwork for the design of reticular frameworks for desired applications.

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