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Product of experts (PoE) are layered networks in which the value at each node is an AND (or product) of the values (possibly negated) at its inputs. These were introduced as a neural network architecture that can efficiently learn to generate high-dimensional data which satisfy many low-dimensional constraints---thereby allowing each individual expert to perform a simple task. PoEs have found a variety of applications in learning. We study the problem of identifiability of a product of experts model having a layer of binary latent variables, and a layer of binary observables that are iid conditional on the latents. The previous best upper bound on the number of observables needed to identify the model was exponential in the number of parameters. We show: (a) When the latents are uniformly distributed, the model is identifiable with a number of observables equal to the number of parameters (and hence best possible). (b) In the more general case of arbitrarily distributed latents, the model is identifiable for a number of observables that is still linear in the number of parameters (and within a factor of two of best-possible). The proofs rely on root interlacing phenomena for some special three-term recurrences. 

Ab initio chemical shift prediction plays a central role in nuclear magnetic resonance (NMR) crystallography, and the accuracy with which chemical shifts can be predicted relative to experiment impacts the... 

Abstract Aim and QuestionsSea‐level rise has been responsible for extensive vegetation changes in coastal areas worldwide. The intent of our study was to analyze vegetation dynamics of a South Florida coastal watershed within an explicit spatiotemporal framework that might aid in projecting the landscape's future response to restoration efforts. We also asked whether recent transgression by mangroves and other halophytes has resulted in reduced plant diversity at local or subregional scales. LocationFlorida’'s Southeast Saline Everglades, USA. MethodsWe selected 26 locations, representing a transition zone between sawgrass marsh and mangrove swamp, that was last sampled floristically in 1995. Within this transition zone, leading‐ and trailing‐edge subzones were defined based on plant composition in 1995. Fifty‐two site × time combinations were classified and then ordinated to examine vegetation–environment relationships using 2016 environmental data. We calculated alpha‐diversity using Hill numbers or Shannon–Weiner index species equivalents and compared these across the two surveys. We used a multiplicative diversity partition to determine beta‐diversity from landscape‐scale (gamma) diversity in the entire dataset or in each subzone. ResultsMangrove and mangrove associates became more important in both subzones: through colonization and establishment in the leading edge, and through population growth combined with the decline of freshwater species in the trailing edge. Alpha‐diversity increased significantly in the leading edge and decreased nominally in the trailing edge, while beta‐diversity declined slightly in both subzones as well as across the study area. ConclusionsRecent halophyte encroachment in the Southeast Saline Everglades continues a trend evident for almost a century. While salinity is an important environmental driver, species’ responses suggest that restoration efforts based on supplementing freshwater delivery will not reverse a trend that depends on multiple interacting factors. Sea‐level‐rise‐driven taxonomic homogenization in coastal wetland communities develops slowly, lagging niche‐based changes in community structure and composition. 

The queen caste plays a central role in colony success in eusocial insects, as queens lay eggs and regulate colony behavior and development. Queen failure can cause colonies to collapse, which is one of the major concerns of beekeepers. Thus, understanding the biology behind the queen’s health is a pressing issue. Previous studies have shown that the bee microbiome plays an important role in worker bee health, but little is known about the queen microbiome and its functionin vivo. Here, we characterized the queen microbiome, identifying for the first time the present species and their putative functions. We show that the queen microbiome has predicted nutritional and protective roles in queen association and comprises only four consistently present bacterial species. Additionally, we bring to attention the spread of phages in the queen microbiome, which increased in abundance in failing queens and may impact the fate of the colony. 

Abstract Ribosomes of Bacteroidia (formerly Bacteroidetes) fail to recognize Shine-Dalgarno (SD) sequences even though they harbor the anti-SD (ASD) of 16S rRNA. Inhibition of SD-ASD pairing is due to sequestration of the 3’ tail of 16S rRNA in a pocket formed by bS21, bS18, and bS6 on the 30S platform. Interestingly, in many Flavobacteriales, the gene encoding bS21, rpsU, contains an extended SD sequence. In this work, we present genetic and biochemical evidence that bS21 synthesis in Flavobacterium johnsoniae is autoregulated via a subpopulation of ribosomes that specifically lack bS21. Mutation or depletion of bS21 in the cell increases translation of reporters with strong SD sequences, such as rpsU’-gfp, but has no effect on other reporters. Purified ribosomes lacking bS21 (or its C-terminal region) exhibit higher rates of initiation on rpsU mRNA and lower rates of initiation on other (SD-less) mRNAs than control ribosomes. The mechanism of autoregulation depends on extensive pairing between mRNA and 16S rRNA, and exceptionally strong SD sequences, with predicted pairing free energies of < –13 kcal/mol, are characteristic of rpsU across the Bacteroidota. This work uncovers a clear example of specialized ribosomes in bacteria. 

Photomechanical molecular crystals have garnered attention for their ability to transform light into mechanical work, but difficulties in characterizing the structural changes and mechanical responses experimentally have hindered the development of practical organic crystal engines. This study proposes a new computational framework for predicting the solid-state crystal-to-crystal photochemical transformations entirely from first principles, and it establishes a photomechanical engine cycle that quantifies the anisotropic mechanical performance resulting from the transformation. The approach relies on crystal structure prediction, solid-state topochemical principles, and high-quality electronic structure methods. After validating the framework on the well-studied [4 + 4] cycloadditions in 9-methyl anthracene and 9- tert -butyl anthracene ester, the experimentally-unknown solid-state transformation of 9-carboxylic acid anthracene is predicted for the first time. The results illustrate how the mechanical work is done by relaxation of the crystal lattice to accommodate the photoproduct, rather than by the photochemistry itself. The large ∼10 7 J m −3 work densities computed for all three systems highlight the promise of photomechanical crystal engines. This study demonstrates the importance of crystal packing in determining molecular crystal engine performance and provides tools and insights to design improved materials in silico . 

In the Euclidean k-Means problem we are given a collection of n points D in an Euclidean space and a positive integer k. Our goal is to identify a collection of k points in the same space (centers) so as to minimize the sum of the squared Euclidean distances between each point in D and the closest center. This problem is known to be APX-hard and the current best approximation ratio is a primal-dual 6.357 approximation based on a standard LP for the problem [Ahmadian et al. FOCS'17, SICOMP'20]. In this note we show how a minor modification of Ahmadian et al.'s analysis leads to a slightly improved 6.12903 approximation. As a related result, we also show that the mentioned LP has integrality gap at least (16+Sqrt(5))/15 > 1.2157. .