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Personne# Jian Li

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Understanding patterns of spontaneous mutations is of fundamental interest in studies of human genome evolution and genetic disease. Here, we used extremely rare variants in humans to model the molecular spectrum of single-nucleotide mutations. Compared to common variants in humans and human-chimpanzee fixed differences (substitutions), rare variants, on average, arose more recently in the human lineage and are less affected by the potentially confounding effects of natural selection, population demographic history, and biased gene conversion. We analyzed variants obtained from a population-based sequencing study of 202 genes in >14,000 individuals. We observed considerable variability in the per-gene mutation rate, which was correlated with local GC content, but not recombination rate. Using >20,000 variants with a derived allele frequency >= 10(-4), we examined the effect of local GC content and recombination rate on individual variant subtypes and performed comparisons with common variants and substitutions. The influence of local GC content on rare variants differed from that on common variants or substitutions, and the differences varied by variant subtype. Furthermore, recombination rate and recombination hotspots have little effect on rare variants of any subtype, yet both have a relatively strong impact on multiple variant subtypes in common variants and substitutions. This observation is consistent with the effect of biased gene conversion or selection-dependent processes. Our results highlight the distinct biases inherent in the initial mutation patterns and subsequent evolutionary processes that affect segregating variants.

Graphdiyne (GDY) with a direct bandgap, high charge carrier mobility, and ordered pore structure, is considered an excellent matrix for the construction of heterojunction photocatalysts. However, the traditional fabrication methods for GDY-based heterojunctions require a complicated deprotection of hexakis-[(trimethylsilyl)ethynyl]benzene (HEB-TMS) and usually result in localized heterojunctions. Herein, we developed a facile deprotection-free method to in situ grow GDY on the surface of C3N4 by directly using HEB-TMS as the precursor. Such a method enabled the formation of an integral GDY@C3N4 heterojunction, resulting in a significantly enhanced photocatalytic activity in the visible region. The optimized GDY@C3N4 showed 15.6-fold hydrogen production efficiency compared to pristine C3N4, and outperformed the GDY/C3N4 samples synthesized by other approaches (e.g. physical mixing, hydrothermal treatment and calcination treatment). This study provides a universal and efficient strategy for the design of GDY-based heterojunction photocatalysts for solar-to-hydrogen energy conversion.

We study the problem of constructing epsilon-coresets for the (k, z)-clustering problem in a doubling metric M(X, d). An epsilon-coreset is a weighted subset S subset of X with weight function w : S -> R->= 0, such that for any k-subset C is an element of X, it holds that Sigma(x is an element of S) w(x).d(z) (x, C) is an element of (1 +/- epsilon) . Sigma(x is an element of X) d(z) (x, C). We present an efficient algorithm that constructs an epsilon-coreset for the (k, z)-clustering problem in M(X, d), where the size of the coreset only depends on the parameters k, z, epsilon and the doubling dimension ddim(M). To the best of our knowledge, this is the first efficient epsilon-coreset construction of size independent of vertical bar X vertical bar for general clustering problems in doubling metrics. To this end, we establish the first relation between the doubling dimension of M(X, d) and the shattering dimension (or VC-dimension) of the range space induced by the distance d. Such a relation is not known before, since one can easily construct instances in which neither one can be bounded by (some function of) the other. Surprisingly, we show that if we allow a small (1 +/- epsilon)-distortion of the distance function d (the distorted distance is called the smoothed distance function), the shattering dimension can be upper bounded by O(epsilon(-O(ddim(M)))). For the purpose of coreset construction, the above bound does not suffice as it only works for unweighted spaces. Therefore, we introduce the notion of tau-error probabilistic shattering dimension, and prove a (drastically better) upper bound of O(ddim(M).log(1/epsilon)+log log 1/tau) for the probabilistic shattering dimension for weighted doubling metrics. As it turns out, an upper bound for the probabilistic shattering dimension is enough for constructing a small coreset. We believe the new relation between doubling and shattering dimensions is of independent interest and may find other applications. Furthermore, we study robust coresets for (k, z)-clustering with outliers in a doubling metric. We show an improved connection between alpha-approximation and robust coresets. This also leads to improvement upon the previous best known bound of the size of robust coreset for Euclidean space [Feldman and Langberg, STOC 11]. The new bound entails a few new results in clustering and property testing. As another application, we show constant-sized (epsilon, k, z)-centroid sets in doubling metrics can be constructed by extending our coreset construction. Prior to our result, constant-sized centroid sets for general clustering problems were only known for Euclidean spaces. We can apply our centroid set to accelerate the local search algorithm (studied in [Friggstad et al., FOCS 2016]) for the (k, z)-clustering problem in doubling metrics.