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...     

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.     

Maximum of the Characteristic Polynomial for a Random Permutation Matrix

Let P_N be a uniform random N × N permutation matrix and let χ_N(z) = det(zI_N − P_N) denote its characteristic polynomial. We prove a law of large numbers for the maximum modulus of χ_N on the unit circle, specifically, with probability tending to 1 as N → ∞ , for a numerical constant x₀ ≈ 0.652 . The main idea of the proof is to uncover a logarithmic correlation structure for the distribution of (the logarithm of) χ_N , viewed as a random field on the circle, and to adapt a well-known second-moment argument for the maximum of the branching random walk. Unlike the well-studied CUE field in which P_N is replaced with a Haar unitary, the distribution of χ_N(e^2πit) is sensitive to Diophantine properties of the point t . To deal with this we borrow tools from the Hardy-Littlewood circle method. © 2020 Wiley Periodicals LLC     

Physical aging in amorphous poly(ethylene furanoate): Enthalpic recovery,density, and oxygen transport considerations

The current work utilizes three separate techniques to study the physical aging process in amorphous poly(ethylene furanoate) (PEF), which is a recently introduced engineering thermoplastic with enhanced properties compared to petroleum‐sourced poly(ethylene terephthalate). Differential scanning calorimetry aging experiments were conducted at multiple aging temperatures and times, and the resultant enthalpic recovery values compared to the theoretical maximum enthalpy loss evaluated from calculations involving extrapolation of the equilibrium liquid line. Density measurements reveal densification of the matrix for the aged versus unaged samples, and provide an estimate for the reduction in free volume for the aged samples. Complementary oxygen permeation and pressure‐decay sorption experiments provide independent verification of the free volume reduction mechanism for physical aging in glassy polymers. The current work provides the first detailed aging study for PEF. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 389–399