The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy

The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the rest of the elements in the distribution. Because classical entropy-based Maxent collapses cases confounding all distinct degrees of randomness and pseudo-randomness, here we take into consideration the generative mechanism of the systems considered in the ensemble to separate objects that may comply with the principle under some restriction and whose entropy is maximal but may be generated recursively from those that are actually algorithmically random offering a refinement to classical Maxent. We take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code. Using the distinction between computable and algorithmic randomness we quantify the cost in information loss associated with reprogramming. To illustrate this we apply the algorithmic refinement to Maxent on graphs and introduce a Maximal Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a generalisation over previous approaches. We discuss practical implications of evaluation of network randomness. Our analysis provides insight in that the reprogrammability asymmetry appears to originate from a non-monotonic relationship to algorithmic probability. Our analysis motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation.Comment: 30 page

From Local Atomic Environments to Molecular Information Entropy

The similarity of local atomic environments is an important concept in many machine-learning techniques which find applications in computational chemistry and material science. Here, we present and discuss a connection between the information entropy and the similarity matrix of a molecule. The resulting entropy can be used as a measure of the complexity of a molecule. Exemplarily, we introduce and evaluate two specific choices for defining the similarity: one is based on a SMILES representation of local substructures and the other is based on the SOAP kernel. By tuning the sensitivity of the latter, we can achieve a good agreement between the respective entropies. Finally, we consider the entropy of two molecules in a mixture. The gain of entropy due to the mixing can be used as a similarity measure of the molecules. We compare this measure to the average and the best-match kernel. The results indicate a connection between the different approaches and demonstrate the usefulness and broad applicability of the similarity-based entropy approach.Comment: 20 pages, 6 figure

Chemoinformatic Expedition of the Chemical Space of Fungal Products

Aim: Fungi are valuable resources for bioactive secondary metabolites. However, the chemical space of fungal secondary metabolites has been studied only on a limited basis. Herein, we report a comprehensive chemoinformatic analysis of a unique set of 207 fungal metabolites isolated and characterized in a USA National Cancer Institute funded drug discovery project. Results: Comparison of the molecular complexity of the 207 fungal metabolites with approved anticancer and nonanticancer drugs, compounds in clinical studies, general screening compounds and molecules Generally Recognized as Safe revealed that fungal metabolites have high degree of complexity. Molecular fingerprints showed that fungal metabolites are as structurally diverse as other natural products and have, in general, drug-like physicochemical properties. Conclusion: Fungal products represent promising candidates to expand the medicinally relevant chemical space. This work is a significant expansion of an analysis reported years ago for a smaller set of compounds (less than half of the ones included in the present work) from filamentous fungi using different structural properties

Synthesis of Cycloheptatriene-Containing Azetidine Lactones

This document is the Accepted Manuscript version of a Published Work that appeared in final form in The Journal of Organic Chemistry, copyright © 2022 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acs.joc.2c00367.We prepared a collection of complex cycloheptatriene-containing azetidine lactones by applying two key photochemical reactions: “aza-Yang” cyclization and Buchner carbene insertion into aromatic rings. While photolysis of phenacyl amines leads to a rapid charge transfer and elimination, we found that a simple protonation of the amine enables the formation of azetidinols as single diastereomers. We provide evidence, through ultrafast spectroscopy, for the electron transfer from free amines in the excited state. Further, we characterize the aza-Yang reaction by establishing the dependence of the initial reaction rates on the rates of photon absorption. An unanticipated change in reactivity in morpholine analogues is explained through interactions with the tosylate anion. The Buchner reaction proceeds with a slight preference for one diastereomer over the other, and successful reaction requires electron-donating carbene-stabilizing substituents. Overall, 16 compounds were prepared over seven steps. Guided by an increase in structural complexity, efforts such as this one extend the reach of chemists into unexplored chemical space and provide useful quantities of new compounds for studies focused on their properties

Complexity, Disorder, and Functionality of Nanoscale Materials

Nature hosts a wealth of materials showcasing intricate structures intertwining order, disorder, and hierarchy, delivering resilient multifunctionality surpassing perfect crystals or simplistic disordered materials. The engineering of such materials through nanoparticle assembly represents a burgeoning field, poised with potential to yield sustainable material systems rivaling or exceeding biological functionalities. This review delineates the fundamental concept of complexity in the context of nanoscale materials. It examines methodologies for characterizing complexity and functionality, explores pragmatic approaches to create complex nanomaterials, and offers a perspective on their potential applications, guiding the trajectory of future research endeavors.Comment: 31 pages, 9 figure