Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update

The combinatorics of the Baer-Specker group

Denote the integers by Z and the positive integers by N. The groups Z^k (k a natural number) are discrete, and the classification up to isomorphism of their (topological) subgroups is trivial. But already for the countably infinite power Z^N of Z, the situation is different. Here the product topology is nontrivial, and the subgroups of Z^N make a rich source of examples of non-isomorphic topological groups. Z^N is the Baer-Specker group. We study subgroups of the Baer-Specker group which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Ko\v{c}inac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and Scheepers.Comment: To appear in IJ

Structural basis for UFM1 transfer from UBA5 to UFC1

This is the final version. Available on open access from Nature Research via the DOI in this recordData availability: Atomic coordinates and structure factors were deposited in the RCSB PDB (https://www.rcsb.org/) with the accession codes 7NW1, 7NVK, and 7NVJ for UFC1-UBA5 (389–404), UBA5(347-404)-UFC1, and UFC1(Y110A and F121A), respectively. NMR assignments for UFC1 were taken from the BMRB entry 6546. Previously published crystal structures used in this study are available from the RCSB PDB under the accession codes: 3TGD; 1J7D; 1U9A; 1×23; 1Y6L; 4Q5E; 4YII; 1Y8X; 1WZW; 6CYO; 1FZY; 1YLA; 2YBF; 2C4P; 5LBN; 3FN1; 2CYX; 2Z5D; 2F4W; 5BNB; 1YH2; 1YRV; 2Z6P; 2Z6O; 1JBB; 4Q5H; 1WZV; 3RZ3; 2DYT; 6H77. The coordinates of the structural models generated by in silico docking are provided as Supplementary Data 1–3. Source data are provided with this paper.Ufmylation is a post-translational modification essential for regulating key cellular processes. A three-enzyme cascade involving E1, E2 and E3 is required for UFM1 attachment to target proteins. How UBA5 (E1) and UFC1 (E2) cooperatively activate and transfer UFM1 is still unclear. Here, we present the crystal structure of UFC1 bound to the C-terminus of UBA5, revealing how UBA5 interacts with UFC1 via a short linear sequence, not observed in other E1-E2 complexes. We find that UBA5 has a region outside the adenylation domain that is dispensable for UFC1 binding but critical for UFM1 transfer. This region moves next to UFC1’s active site Cys and compensates for a missing loop in UFC1, which exists in other E2s and is needed for the transfer. Overall, our findings advance the understanding of UFM1’s conjugation machinery and may serve as a basis for the development of ufmylation inhibitors.Israel Science FoundationIsrael Cancer Research FundUS-Israel Binational Science Foundatio

The effect of a high-polyphenol Mediterranean diet (Green-MED) combined with physical activity on age-related brain atrophy: The Dietary Intervention Randomized Controlled Trial Polyphenols Unprocessed Study (DIRECT PLUS)

Background: The effect of diet on age-related brain atrophy is largely unproven. Objectives: We aimed to explore the effect of a Mediterranean diet (MED) higher in polyphenols and lower in red/processed meat (Green-MED diet) on age-related brain atrophy. Methods: This 18-mo clinical trial longitudinally measured brain structure volumes by MRI using hippocampal occupancy score (HOC) and lateral ventricle volume (LVV) expansion score as neurodegeneration markers. Abdominally obese/dyslipidemic participants were randomly assigned to follow 1) healthy dietary guidelines (HDG), 2) MED, or 3) Green-MED diet. All subjects received free gym memberships and physical activity guidance. Both MED groups consumed 28 g walnuts/d (+440 mg/d polyphenols). The Green-MED group consumed green tea (3-4 cups/d) and Mankai (Wolffia-globosa strain, 100 g frozen cubes/d) green shake (+800 mg/d polyphenols). Results: Among 284 participants (88% men; mean age: 51 y; BMI: 31.2 kg/m2; APOE-ε4 genotype = 15.7%), 224 (79%) completed the trial with eligible whole-brain MRIs. The pallidum (-4.2%), third ventricle (+3.9%), and LVV (+2.2%) disclosed the largest volume changes. Compared with younger participants, atrophy was accelerated among those ≥50 y old (HOC change: -1.0% ± 1.4% compared with -0.06% ± 1.1%; 95% CI: 0.6%, 1.3%; P Conclusions: A Green-MED (high-polyphenol) diet, rich in Mankai, green tea, and walnuts and low in red/processed meat, is potentially neuroprotective for age-related brain atrophy.This trial was registered at clinicaltrials.gov as NCT03020186

The Software Performance of Authenticated-Encryption Modes

We study the software performance of authenticated-encryption modes CCM, GCM, and OCB. Across a variety of platforms, we find OCB to be substantially faster than either alternative. For example, on an Intel i5 (“Clarkdale”) processor, good implementations of CCM, GCM, and OCB encrypt at around 4.2 cpb, 3.7 cpb, and 1.5 cpb, while CTR mode requires about 1.3 cpb. Still we find room for algorithmic improvements to OCB, showing how to trim one blockcipher call (most of the time, assuming a counter-based nonce) and reduce latency. Our findings contrast with those of McGrew and Viega (2004), who claimed similar performance for GCM and OCB. Key words: authenticated encryption, cryptographic standards, encryption speed, modes o