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1. Coil–Helix Block Copolymers Can Exhibit Divergent Thermodynamics in the Disordered Phase

   https://doi.org/10.1021/acs.jctc.3c00680  

   Grant, Michael J; Fingler, Brennan J; Buchanan, Natalie; Padmanabhan, Poornima (September 2023, Journal of Chemical Theory and Computation)

   Chiral building blocks have the ability to self-assemble and transfer chirality to larger hierarchical length scales, which can be leveraged for the development of novel nanomaterials. Chiral block copolymers, where one block is made completely chiral, are prime candidates for studying this phenomenon, but fundamental questions regarding the self-assembly are still unanswered. For one, experimental studies using different chemistries have shown unexplained diverging shifts in the order–disorder transition temperature. In this study, particle-based molecular simulations of chiral block copolymers in the disordered melt were performed to uncover the thermodynamic behavior of these systems. A wide range of helical models were selected, and several free energy calculations were performed. Specifically, we aimed to understand (1) the thermodynamic impact of changing the conformation of one block in chemically identical block copolymers and (2) the effect of the conformation on the Flory–Huggins interaction parameter, χ, when chemical disparity was introduced. We found that the effective block repulsion exhibits diverging behavior, depending on the specific conformational details of the helical block. Commonly used conformational metrics for flexible or stiff block copolymers do not capture the effective block repulsion because helical blocks are semiflexible and aspherical. Instead, pitch can quantitatively capture the effective block repulsion. Quite remarkably, the shift in χ for chemically dissimilar block copolymers can switch sign with small changes in the pitch of the helix. 

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2. Sparse Popularity Adjusted Stochastic Block Model

   Majid Noroozi, Marianna Pensky (October 2021, Journal of machine learning research)

   null (Ed.)

   In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes only the behavior of network as a whole, without distinguishing between the block-dependent sparsity patterns. To the best of our knowledge, the recently introduced Popularity Adjusted Block Model (PABM) is the only block model that allows to introduce a structural sparsity where some probabilities of connections are identically equal to zero while the rest of them remain above a certain threshold. The latter presents a more nuanced view of the network. 

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3. Poly(Piloty's acid): a slow releasing macromolecular HNO donor

   https://doi.org/10.1039/d2py01339h  

   Swilley, Sarah N.; Zajkowski, Evan M.; Matson, John B. (May 2023, Polymer Chemistry)

   We report a polymeric version of Piloty's acid where the release rate of HNO can be tuned by changing the block ratios of PEG- b -poly(Piloty's acid) in a block copolymer system. The poly(Piloty's acid) block was derived from poly(styrene sulfonate), and HNO release from the block copolymers varied by as much as an order of magnitude via increasing the length of the poly(Piloty's acid) block. We anticipate this study will guide the development of HNO-releasing polymers to measure the effects of sustained HNO delivery in biological systems. 

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4. Block bootstrap optimality and empirical block selection for sample quantiles with dependent data

   https://doi.org/10.1093/biomet/asaa075  

   Kuffner, T A; Lee, S M; Young, G A (September 2020, Biometrika)

   Summary We establish a general theory of optimality for block bootstrap distribution estimation for sample quantiles under mild strong mixing conditions. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the sub- sampling bootstrap and the moving block bootstrap, in which the number of blocks is between 1 and the ratio of sample size to block length. The hybrid block bootstrap is shown to give theoretical benefits, and startling improvements in accuracy in distribution estimation in important practical settings. The conclusion that bootstrap samples should be of smaller size than the original sample has significant implications for computational efficiency and scalability of bootstrap methodologies with dependent data. Our main theorem determines the optimal number of blocks and block length to achieve the best possible convergence rate for the block bootstrap distribution estimator for sample quantiles. We propose an intuitive method for empirical selection of the optimal number and length of blocks, and demonstrate its value in a nontrivial example. 

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5. Transaction Fee Mechanism Design in a Post-MEV World

   https://doi.org/10.4230/LIPIcs.AFT.2024.29  

   Bahrani, Maryam; Garimidi, Pranav; Roughgarden, Tim (January 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Böhme, Rainer; Kiffer, Lucianna (Ed.)

   The incentive-compatibility properties of blockchain transaction fee mechanisms have been investigated with passive block producers that are motivated purely by the net rewards earned at the consensus layer. This paper introduces a model of active block producers that have their own private valuations for blocks (representing, for example, additional value derived from the application layer). The block producer surplus in our model can be interpreted as one of the more common colloquial meanings of the phrase "maximal extractable value (MEV)." We first prove that transaction fee mechanism design is fundamentally more difficult with active block producers than with passive ones: With active block producers, no non-trivial or approximately welfare-maximizing transaction fee mechanism can be incentive-compatible for both users and block producers. These results can be interpreted as a mathematical justification for augmenting transaction fee mechanisms with additional components such as order flow auctions, block producer competition, trusted hardware, or cryptographic techniques. We then consider a more fine-grained model of block production that more accurately reflects current practice, in which we distinguish the roles of "searchers" (who actively identify opportunities for value extraction from the application layer and compete for the right to take advantage of them) and "proposers" (who participate directly in the blockchain protocol and make the final choice of the published block). Searchers can effectively act as an "MEV oracle" for a transaction fee mechanism, thereby enlarging the design space. Here, we first consider a TFM that is inspired by how searchers have traditionally been incorporated into the block production process, with each transaction effectively sold off to a searcher through a first-price auction. We then explore the TFM design space with searchers more generally, and design a mechanism that circumvents our impossibility results for TFMs without searchers. Our mechanism (the "SAKA" mechanism) is incentive-compatible (for users, searchers, and the block producer), sybil-proof, and guarantees roughly 50% of the maximum-possible welfare when transaction sizes are small relative to block sizes. We conclude with a matching negative result: even when transaction sizes are small, no DSIC and sybil-proof deterministic TFM can guarantee more than 50% of the maximum-possible welfare. 

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