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The intensely studied measurement-induced entanglement phase transition has become a hallmark of nonunitary quantum many-body dynamics. Usually, such a transition only appears at the level of each individual quantum trajectory, and is absent for the density matrix averaged over measurement outcomes. In this work, we introduce a class of adaptive random circuit models with feedback that exhibit transitions in both settings. After each measurement, a unitary operation is either applied or not depending on the measurement outcome, which steers the averaged density matrix towards a unique state above a certain measurement threshold. Interestingly, the transition for the density matrix and the entanglement transition in the individual quantum trajectory in general happen at different critical measurement rates. We demonstrate that the former transition belongs to the parity-conserving universality class by explicitly mapping to a classical branching-annihilating random-walk process. 

Study of α-V70I-substituted nitrogenase MoFe protein identified Fe6 of FeMo-cofactor (Fe 7 S 9 MoC-homocitrate) as a critical N 2 binding/reduction site. Freeze-trapping this enzyme during Ar turnover captured the key catalytic intermediate in high occupancy, denoted E 4 (4H), which has accumulated 4[e − /H + ] as two bridging hydrides, Fe2–H–Fe6 and Fe3–H–Fe7, and protons bound to two sulfurs. E 4 (4H) is poised to bind/reduce N 2 as driven by mechanistically-coupled H 2 reductive-elimination of the hydrides. This process must compete with ongoing hydride protonation (HP), which releases H 2 as the enzyme relaxes to state E 2 (2H), containing 2[e − /H + ] as a hydride and sulfur-bound proton; accumulation of E 4 (4H) in α-V70I is enhanced by HP suppression. EPR and 95 Mo ENDOR spectroscopies now show that resting-state α-V70I enzyme exists in two conformational states, both in solution and as crystallized, one with wild type (WT)-like FeMo-co and one with perturbed FeMo-co. These reflect two conformations of the Ile residue, as visualized in a reanalysis of the X-ray diffraction data of α-V70I and confirmed by computations. EPR measurements show delivery of 2[e − /H + ] to the E 0 state of the WT MoFe protein and to both α-V70I conformations generating E 2 (2H) that contains the Fe3–H–Fe7 bridging hydride; accumulation of another 2[e − /H + ] generates E 4 (4H) with Fe2–H–Fe6 as the second hydride. E 4 (4H) in WT enzyme and a minority α-V70I E 4 (4H) conformation as visualized by QM/MM computations relax to resting-state through two HP steps that reverse the formation process: HP of Fe2–H–Fe6 followed by slower HP of Fe3–H–Fe7, which leads to transient accumulation of E 2 (2H) containing Fe3–H–Fe7. In the dominant α-V70I E 4 (4H) conformation, HP of Fe2–H–Fe6 is passively suppressed by the positioning of the Ile sidechain; slow HP of Fe3–H–Fe7 occurs first and the resulting E 2 (2H) contains Fe2–H–Fe6. It is this HP suppression in E 4 (4H) that enables α-V70I MoFe to accumulate E 4 (4H) in high occupancy. In addition, HP suppression in α-V70I E 4 (4H) kinetically unmasks hydride reductive-elimination without N 2 -binding, a process that is precluded in WT enzyme. 

Seed-mediated synthesis strategies, in which small gold nanoparticle precursors are added to a growth solution to initiate heterogeneous nucleation, are among the most prevalent, simple, and productive methodologies for generating well-defined colloidal anisotropic nanostructures. However, the size, structure, and chemical properties of the seeds remain poorly understood, which partially explains the lack of mechanistic understanding of many particle growth reactions. Here, we identify the majority component in the seed solution as an atomically precise gold nanocluster, consisting of a 32-atom Au core with 8 halide ligands and 12 neutral ligands constituting a bound ion pair between a halide and the cationic surfactant: Au₃₂X₈[AQA⁺•X^-]₁₂(X = Cl, Br; AQA = alkyl quaternary ammonium). Ligand exchange is dynamic and versatile, occurring on the order of minutes and allowing for the formation of 48 distinct Au₃₂clusters with AQAX (alkyl quaternary ammonium halide) ligands. Anisotropic nanoparticle syntheses seeded with solutions enriched in Au₃₂X₈[AQA⁺•X^-]₁₂show narrower size distributions and fewer impurity particle shapes, indicating the importance of this cluster as a precursor to the growth of well-defined nanostructures.

 

CandidatusNanohaloarchaeota, an archaeal phylum within the DPANN superphylum, is characterized by limited metabolic capabilities and limited phylogenetic diversity and until recently has been considered to exclusively inhabit hypersaline environments due to an obligate association withHalobacteria. Aside from hypersaline environments,Ca.Nanohaloarchaeota can also have been discovered from deep-subsurface marine sediments.

Three metagenome-assembled genomes (MAGs) representing a new order within theCa.Nanohaloarchaeota were reconstructed from a stratified salt crust and proposed to represent a novel order,Nucleotidisoterales. Genomic features reveal them to be anaerobes capable of catabolizing nucleotides by coupling nucleotide salvage pathways with lower glycolysis to yield free energy. Comparative genomics demonstrated that these and otherCa.Nanohaloarchaeota inhabiting saline habitats use a “salt-in” strategy to maintain osmotic pressure based on the high proportion of acidic amino acids. In contrast, previously describedCa.Nanohaloarchaeota MAGs from geothermal environments were enriched with basic amino acids to counter heat stress. Evolutionary history reconstruction revealed that functional differentiation of energy conservation strategies drove diversification withinCa.Nanohaloarchaeota, further leading to shifts in the catabolic strategy from nucleotide degradation within deeper lineages to polysaccharide degradation within shallow lineages.

This study provides deeper insight into the ecological functions and evolution of the expanded phylumCa.Nanohaloarchaeota and further advances our understanding on the functional and genetic associations between potential symbionts and hosts.

 

Multiplicity code decoders are based on Hermite polynomial interpolation with error correction. In order to have a unique Hermite interpolant one assumes that the field of scalars has characteristic 0 or >= k+1, where k is the maximum order of the derivatives in the list of values of the polynomial and its derivatives which are interpolated. For scalar fields of characteristic k+1, the minimum number of values for interpolating a polynomial of degree <= D is D+1+2E(k+1) when <= E of the values are erroneous. Here we give an error-correcting Hermite interpolation algorithm that can tolerate more errors, assuming that the characteristic of the scalar field is either 0 or >= D+1. Our algorithm requires (k+1)D + 1 - (k+1)k/2 + 2E values. As an example, we consider k = 2. If the error ratio (number of errors)/(number of evaluations) <= 0.16, our new algorithm requires ceiling( (4+7/17) D - (1+8 /17) ) values, while multiplicity decoding requires 25D+25 values. If the error ratio is <= 0.2, our algorithm requires 5D-2 evaluations over characteristic 0 or >= D+1, while multiplicity decoding for an error ratio 0.2 over fields of characteristic 3 is not possible for D >= 3. Our algorithm is based on Reed-Solomon interpolation without multiplicities, which becomes possible for Hermite interpolation because of the high redundancy necessary for error-correction.