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1. Manufacturing silica aerogel and cryogel through ambient pressure and freeze drying

   https://doi.org/10.1039/D2RA03325A  

   Di Luigi, Massimigliano; Guo, Zipeng; An, Lu; Armstrong, Jason N.; Zhou, Chi; Ren, Shenqiang (July 2022, RSC Advances)

   Achieving a mesoporous structure in superinsulation materials is pivotal for guaranteeing a harmonious relationship between low thermal conductivity, high porosity, and low density. Herein, we report silica-based cryogel and aerogel materials by implementing freeze-drying and ambient-pressure-drying processes respectively. The obtained freeze-dried cryogels yield thermal conductivity of 23 mW m −1 K −1 , with specific surface area of 369.4 m 2 g −1 , and porosity of 96.7%, whereas ambient-pressure-dried aerogels exhibit thermal conductivity of 23.6 mW m −1 K −1 , specific surface area of 473.8 m 2 g −1 , and porosity of 97.4%. In addition, the fiber-reinforced nanocomposites obtained via freeze-drying feature a low thermal conductivity (28.0 mW m −1 K −1 ) and high mechanical properties (∼620 kPa maximum compressive stress and Young's modulus of 715 kPa), coupled with advanced flame-retardant capabilities, while the composite materials from the ambient pressure drying process have thermal conductivity of 28.8 mW m −1 K −1 , ∼200 kPa maximum compressive stress and Young's modulus of 612 kPa respectively. The aforementioned results highlight the capabilities of both drying processes for the development of thermal insulation materials for energy-efficient applications. 

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2. Development and use of DJ-1 affinity microcolumns to screen and study small drug candidates for Parkinson's disease

   https://doi.org/10.1016/j.aca.2024.343520  

   Jones, Jacob C; Lin, Jiusheng; Sharmeen, Sadia; Rahman, Md Masudur; Truong, Ha H; Chern, Ting-Rong; Wilson, Mark A; Hage, David S (January 2025, Analytica Chimica Acta)

   Background: DJ-1 is a protein whose mutation causes rare heritable forms of Parkinson’s disease (PD) and is of interest as a target for treating PD and other disorders. This work used high performance affinity microcolumns to screen and examine the binding of small molecules to DJ-1, as could be used to develop new therapeutics or to study the role of DJ-1 in PD. Non-covalent entrapment was used to place microgram quantities of DJ-1 in an unmodified form within microcolumns, which were then used in multiple studies to analyze binding by model compounds and possible drug candidates to DJ-1. Results: Several factors were examined in optimizing the entrapment method, including the addition of a reducing agent to maintain a reduced active site cysteine residue in DJ-1, the concentration of DJ-1 employed, and the entrapment times. Isatin was used as a known binding agent (dissociation constant, ~2.0 µM) and probe for DJ-1 activity. This compound gave good retention on 2.0 cm × 2.1 mm inner diameter DJ-1 microcolumns made under the final entrapment conditions, with a typical retention factor of 14 and elution in ~8 min at 0.50 mL/min. These DJ-1 microcolumns were used to evaluate the binding of small molecules that were selected in silico to bind or not to bind DJ-1. A compound predicted to have good binding with DJ-1 gave a retention factor of 122, an elution time of ~15 min at 0.50 mL/min, and an estimated dissociation constant for this protein of 0.5 µM. Significance: These chromatographic tools can be used in future work to screen additional possible binding agents for DJ-1 or adapted for examining drug candidates for other proteins. This work represents the first time protein entrapment has been deployed with DJ-1, and it is the first experimental confirmation of binding to DJ-1 by a small lead compound selected in silico. 

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3. Log-rank and lifting for AND-functions

   https://doi.org/10.1145/3406325.3450999  

   Knop, Alexander; Lovett, Shachar; McGuire, Sam; Yuan, Weiqiang (June 2021, Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing)

   Let f: {0, 1}n → {0, 1} be a boolean function, and let f∧(x, y) = f(x ∧ y) denote the AND-function of f, where x ∧ y denotes bit-wise AND. We study the deterministic communication complexity of f∧ and show that, up to a logn factor, it is bounded by a polynomial in the logarithm of the real rank of the communication matrix of f∧. This comes within a logn factor of establishing the log-rank conjecture for AND-functions with no assumptions on f. Our result stands in contrast with previous results on special cases of the log-rank conjecture, which needed significant restrictions on f such as monotonicity or low F2-degree. Our techniques can also be used to prove (within a logn factor) a lifting theorem for AND-functions, stating that the deterministic communication complexity of f∧ is polynomially related to the AND-decision tree complexity of f. The results rely on a new structural result regarding boolean functions f: {0, 1}n → {0, 1} with a sparse polynomial representation, which may be of independent interest. We show that if the polynomial computing f has few monomials then the set system of the monomials has a small hitting set, of size poly-logarithmic in its sparsity. We also establish extensions of this result to multi-linear polynomials f: {0, 1}n → with a larger range. 

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4. Optimal Document Exchange and New Codes for Small Number of Insertions and Deletions

   Haeupler, Bernhard (October 2019, IEEE Symposium on Foundations of Computer Science)

   We give the first communication-optimal document exchange protocol. For any n and k 

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5. Triforce and corners

   https://doi.org/10.1017/s0305004119000173  

   FOX, JACOB; SAH, ASHWIN; SAWHNEY, MEHTAAB; STONER, DAVID; ZHAO, YUFEI (July 2020, Mathematical Proceedings of the Cambridge Philosophical Society)

   Abstract May the triforce be the 3-uniform hypergraph on six vertices with edges {123′, 12′3, 1′23}. We show that the minimum triforce density in a 3-uniform hypergraph of edge density δ is δ 4– o (1) but not O ( δ 4 ). Let M ( δ ) be the maximum number such that the following holds: for every ∊ > 0 and $$G = {\mathbb{F}}_2^n$$ with n sufficiently large, if A ⊆ G × G with A ≥ δ | G | 2 , then there exists a nonzero “popular difference” d ∈ G such that the number of “corners” ( x , y ), ( x + d , y ), ( x , y + d ) ∈ A is at least ( M ( δ )–∊)| G | 2 . As a corollary via a recent result of Mandache, we conclude that M ( δ ) = δ 4– o (1) and M ( δ ) = ω ( δ 4 ). On the other hand, for 0 < δ < 1/2 and sufficiently large N , there exists A ⊆ [ N ] 3 with | A | ≥ δN 3 such that for every d ≠ 0, the number of corners ( x , y , z ), ( x + d , y , z ), ( x , y + d , z ), ( x , y , z + d ) ∈ A is at most δ c log(1/ δ ) N 3 . A similar bound holds in higher dimensions, or for any configuration with at least 5 points or affine dimension at least 3. 

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