On the upper bounds for complexities of discrete functions

In this paper, we study two classes of complexity measures induced by new data structures (abstract reduction systems) for representing [Formula: see text]-valued functions (operations), namely subfunction and minor reductions. When assigning values to some variables in a function, the resulting functions are called subfunctions, and when identifying some variables, the resulting functions are called minors. The number of the distinct objects obtained under these reductions of a function [Formula: see text] is a well-defined measure of complexity denoted by [Formula: see text] and [Formula: see text], respectively. We examine the maximums of these complexities and construct functions which reach these upper bounds.

Deep Learning to Ternary Hash Codes by Continuation

Recently, it has been observed that $\{0,\pm1\}$-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform $\{-1, 1\}$-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes.

Deep Learning to Ternary Hash Codes by Continuation

Recently, it has been observed that $\{0,\pm1\}$-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform $\{-1, 1\}$-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes.

Application of Bullseye Diagram in Teaching of “Variance”

Variance and standard deviation, as a kind of discrete function, are an important content in high school teaching, and they are widely used in data statistics. For high school students, they have difficulty understanding abstract concepts such as stability, volatility, and degree of dispersion when they are first exposed to discrete functions. In actual teaching, you can apply “bullseye chart” to “variance” teaching, and use abstract concept diagrams. Demonstration helps high school students to intuitively understand the concept of “variance” and the nature of dispersion.

Characterization of a novel multidomain CE15-GH8 enzyme encoded by a polysaccharide utilization locus in the human gut bacterium Bacteroides eggerthii

Bacteroidetes are efficient degraders of complex carbohydrates, much thanks to their use of polysaccharide utilization loci (PULs). An integral part of PULs are highly specialized carbohydrate-active enzymes, sometimes composed of multiple linked domains with discrete functions—multicatalytic enzymes. We present the biochemical characterization of a multicatalytic enzyme from a large PUL encoded by the gut bacterium Bacteroides eggerthii. The enzyme, BeCE15A-Rex8A, has a rare and novel architecture, with an N-terminal carbohydrate esterase family 15 (CE15) domain and a C-terminal glycoside hydrolase family 8 (GH8) domain. The CE15 domain was identified as a glucuronoyl esterase (GE), though with relatively poor activity on GE model substrates, attributed to key amino acid substitutions in the active site compared to previously studied GEs. The GH8 domain was shown to be a reducing-end xylose-releasing exo-oligoxylanase (Rex), based on having activity on xylooligosaccharides but not on longer xylan chains. The full-length BeCE15A-Rex8A enzyme and the Rex domain were capable of boosting the activity of a commercially available GH11 xylanase on corn cob biomass. Our research adds to the understanding of multicatalytic enzyme architectures and showcases the potential of discovering novel and atypical carbohydrate-active enzymes from mining PULs.

IL-30† (IL-27A): a familiar stranger in immunity, inflammation, and cancer

Over the years, interleukin (IL)-27 has received much attention because of its highly divergent, sometimes even opposing, functions in immunity. IL-30, the p28 subunit that forms IL-27 together with Ebi3 and is also known as IL-27p28 or IL-27A, has been considered a surrogate to represent IL-27. However, it was later discovered that IL-30 can form complexes with other protein subunits, potentially leading to overlapping or discrete functions. Furthermore, there is emerging evidence that IL-30 itself may perform immunomodulatory functions independent of Ebi3 or other binding partners and that IL-30 production is strongly associated with certain cancers in humans. In this review, we will discuss the biology of IL-30 and other IL-30-associated cytokines and their functions in inflammation and cancer.

Perinatal development of innate immune topology

At the transition from intrauterine to postnatal life, drastic alterations are mirrored by changes in cellular immunity. These changes are in part immune cell intrinsic, originate in the replacement of fetal cells, or result from global regulatory mechanisms and adaptation to changes in the tissue microenvironment. Overall, longer developmental trajectories are intersected by events related to mother-infant separation, birth cues, acquisition of microbiota and metabolic factors. Perinatal alterations particularly affect immune niches, where structures with discrete functions meet, the intestinal mucosa, epidermis and lung.

occAssess: An R package for assessing potential biases in species occurrence data

Species occurrence records from a variety of sources are increasingly aggregated into heterogeneous databases and made available to ecologists for immediate analytical use. However, these data are typically biased, i.e. they are not a representative sample of the target population of interest, meaning that the information they provide may not be an accurate reflection of reality. It is therefore crucial that species occurrence data are properly scrutinised before they are used for research. In this article, we introduce occAssess, an R package that enables quick and easy screening of species occurrence data for potential biases. The package contains a number of discrete functions, each of which returns a measure of the potential for bias in one or more of the taxonomic, temporal, spatial and environmental dimensions. The outputs are provided visually (as ggplot2 objects) and do not include a formal recommendation as to whether data are of sufficient quality for any given inferential use. Instead, they should be used as ancillary information and viewed in the context of the question that is being asked, and the methods that are being used to answer it. We demonstrate the utility of occAssess by applying it to data on two key pollinator taxa in South America: leaf-nosed bats (Phyllostomidae) and hoverflies (Syrphidae). In this worked example, we briefly assess the degree to which various aspect of data coverage appear to have changed over time. We then discuss additional ways in which the package could be used, highlight its limitations, and point to where it could be improved in the future. Going forward, we hope that occAssess will help to improve the quality, and transparency, of assessments of species occurrence data as a necessary first step where they are being used for ecological research at large scales.