Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.     

Automorphism subgroups for designs with $$\lambda =1$$ λ = 1

Designs, Codes and Cryptography - Given an integer $$k\ge 3$$ and a group G of odd order,  if there exists a 2-(v, k, 1)-design and if v is sufficiently large then there...     

Semi-invariants of binary forms and Sylvester’s theorem

The Ramanujan Journal - We obtain a combinatorial formula related to the shear transformation for semi-invariants of binary forms, which implies the classical characterization of semi-invariants in...     

Solidifying framework nucleic acids

正Living organisms have developed their unique strategies during the natural evolution for building hard tissues with minerals, including silica, calcium carbonate, calcium phosphate, and ferric oxide [1]. Such biomineralized materials generally have complex hierarchical structures with excellent mechanical properties. Although bioinspired approaches have led to the creation of well-defined synthetic structural materials ranging from micro to macro scales, the rational design of discrete biomimetic structures at the nanoscale remains a grand challenge.     

Effects of multiple delays on dynamics of a five-neuron network model

A five-neuron network model with multiple delays is proposed. This paper presents the combined effect of different delays on the dynamics of the proposed network. Pitchfork bifurcation is discussed in detail with the variation of the value of coupled weight or attenuation rate of internal neurons. By analyzing the corresponding characteristic equation, some stable criteria on delay-dependence and delay-independence are derived including multiple delays and coupled weights and the periodic oscillation arises bifurcated from the trivial equilibrium after the network loses its stability. Stable regions on delay-dependence are displayed in the two delayed parameter plane. It is shown that multiple delays can produce stability switching between resting state and periodic activity. Finally, theoretical results are justified by providing two illustrative examples.     

Infinitely many reducts of homogeneous structures

It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.     

Molecularly Engineered 6FDA-Based Polyimide Membranes for Sour Natural Gas Separation

Glassy polyimide membranes are attractive for industrial applications in sour natural gas purification. Unfortunately, the lack of fundamental understanding of relationships between polyimide chemical structures and their gas transport properties in the presence of H₂S constrains the design and engineering of advanced membranes for such challenging applications. Herein, 6FDA-based polyimide membranes with engineered structures were synthesized to tune their CO₂/CH₄ and H₂S/CH₄ separation performances and plasticization properties. Under ternary mixed sour gas feeds, controlling polymer chain packing and plasticization tendency of such polyimide membranes via tuning the chemical structures were found to offer better combined H₂S and CO₂ removal efficiency compared to conventional polymers. Fundamental insights into structure–property relationships of 6FDA-based polyimide membranes observed in this study offer guidance for next generation membranes for sour natural gas separation.     

Single-Molecule Observation of Intermediates in Bioorthogonal 2-Cyanobenzothiazole Chemistry

We report a single-molecule mechanistic investigation into 2-cyanobenzothiazole (CBT) chemistry within a protein nanoreactor. When simple thiols reacted reversibly with CBT, the thioimidate monoadduct was approximately 80-fold longer-lived than the tetrahedral bisadduct, with important implications for the design of molecular walkers. Irreversible condensation between CBT derivatives and N-terminal cysteine residues has been established as a biocompatible reaction for site-selective biomolecular labeling and imaging. During the reaction between CBT and aminothiols, we resolved two transient intermediates, the thioimidate and the cyclic precursor of the thiazoline product, and determined the rate constants associated with the stepwise condensation, thereby providing critical information for a variety of applications, including the covalent inhibition of protein targets and dynamic combinatorial chemistry.     

Computational and dynamic NMR investigation of 2,2-dimesityl-1,1,1,3,3,3-hexamethyltrisilane

The structure and rotational barrier for the mesityl-silicon bond of 2,2-dimesityl-1,1,1,3,3,3-hexamethyltrisilane have been investigated by ¹H- and ¹³C-variable temperature nuclear magnetic resonance (NMR) as well as by density functional theory structural calculations. The calculations show that the lowest energy structure has C₂ symmetry with nonequivalent ortho methyl groups, consistent with the crystal structure and solution NMR. The nonequivalent ortho methyl groups exchange through a C_s transition state with a calculated relative free energy of 11.0 kcal mol⁻¹. The barrier for this rotation found by dynamic NMR is 13.4 ± 0.2 kcal mol⁻¹ at 298 K.