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Abstract-We show that circuit lower bound proofs based on the method of random restrictions yield non-trivial compression algorithms for "easy" Boolean functions from the corresponding circuit classes. The compression problem is defined as follows: given the truth table of an n-variate Boolean function f computable by some unknown small circuit from a known class of circuits, find in deterministic time poly(2 n ) a circuit C (no restriction on the type of C) computing f so that the size of C is less than the trivial circuit size 2 n /n. We get nontrivial compression for functions computable by AC 0 circuits, (de Morgan) formulas, and (read-once) branching programs of the size for which the lower bounds for the corresponding circuit class are known.These compression algorithms rely on the structural characterizations of "easy" functions, which are useful both for proving circuit lower bounds and for designing "meta-algorithms" (such as Circuit-SAT). For (de Morgan) formulas, such structural characterization is provided by the "shrinkage under random restrictions" results [52], [21], strengthened to the "high-probability" version by [48], [26], [33]. We give a new, simple proof of the "high-probability" version of the shrinkage result for (de Morgan) formulas, with improved parameters. We use this shrinkage result to get both compression and #SAT algorithms for (de Morgan) formulas of size about n 2 . We also use this shrinkage result to get an alternative proof of the recent result by Komargodski and Raz [33] of the average-case lower bound against small (de Morgan) formulas.Finally, we show that the existence of any non-trivial compression algorithm for a circuit class C ⊆ P/poly would imply the circuit lower bound NEXP ⊆ C. This complements Williams's result [55] that any non-trivial Circuit-SAT algorithm for a circuit class C would imply a superpolynomial lower bound against C for a language in NEXP 1 .

Single-chain nanoparticles (SCNP) are a class of polymeric nanoparticles obtained from the intramolecular crosslinking of polymers bearing reactive pendant groups. The development of SCNP has drawn tremendous attention since the fabrication of SCNP mimics the self-folding behavior in natural biomacromolecules and is highly desirable for a variety of applications ranging from catalysis, nanomedicine, nanoreactors, and sensors. The versatility of novel chemistries available for SCNP synthesis has greatly expanded over the past decade. Significant progress was also made in the understanding of a structure− property relationship in the single-chain folding process. In this Viewpoint, we discuss the effect of precursor polymer topology on single polymer folding. We summarize the progress in SCNP of complex architectures and highlight unresolved issues in the field, such as scalability and topological purity of SCNP.

We present a scalable route to single-chain nanoparticles (SCNP) under mild conditions using intramolecular atom transfer radical coupling (ATRC). Typical methods to SCNP, a class of soft nanomaterials in the sub-10 nm size regime, rely on complicated synthetic techniques, high temperatures unsuitable to fragile functional groups, or ultradilute conditions (solutions less than 1 wt %), all of which greatly complicate scale-up. Our method uses a minimal number of synthetic steps and mild reaction conditions amenable to a wide array of solvents and tolerant to a variety of functional groups. Using this scalable method, gram quantities of nanoparticles in the 5−10 nm size regime are accessible.

N95 respirator face masks serve as effective physical barriers against airborne virus transmission, especially in a hospital setting. However, conventional filtration materials, such as nonwoven polypropylene fibers, have no inherent virucidal activity, and thus, the risk of surface contamination increases with wear time. The ability of face masks to protect against infection can be likely improved by incorporating components that deactivate viruses on contact. We present a facile method for covalently attaching antiviral quaternary ammonium polymers to the fiber surfaces of nonwoven polypropylene fabrics that are commonly used as filtration materials in N95 respirators via ultraviolet (UV)-initiated grafting of biocidal agents. Here, C 12 -quaternized benzophenone is simultaneously polymerized and grafted onto melt-blown or spunbond polypropylene fabric using 254 nm UV light. This grafting method generated ultrathin polymer coatings which imparted a permanent cationic charge without grossly changing fiber morphology or air resistance across the filter. For melt-blown polypropylene, which comprises the active filtration layer of N95 respirator masks, filtration efficiency was negatively impacted from 72.5 to 51.3% for uncoated and coated single-ply samples, respectively. Similarly, directly applying the antiviral polymer to full N95 masks decreased the filtration efficiency from 90.4 to 79.8%. This effect was due to the exposure of melt-blown polypropylene to organic solvents used in the coating process. However, N95-level filtration efficiency could be achieved by wearing coated spunbond polypropylene over an N95 mask or by fabricating N95 masks with coated spunbond as the exterior layer. Coated materials demonstrated broad-spectrum antimicrobial activity against several lipid-enveloped viruses, as well as Staphylococcus aureus and Escherichia coli bacteria. For example, a 4.3-log reduction in infectious MHV-A59 virus and a 3.3-log reduction in infectious SuHV-1 virus after contact with coated filters were observed, although the level of viral deactivation varied significantly depending on the virus strain and protocol for assaying infectivity.