The Structure of Minimum Vertex Cuts

In this paper we continue a long line of work on representing the cut structure of graphs. We classify the types of minimum vertex cuts, and the possible relationships between multiple minimum vertex cuts. As a consequence of these investigations, we exhibit a simple O(? n)-space data structure that can quickly answer pairwise (?+1)-connectivity queries in a ?-connected graph. We also show how to compute the "closest" ?-cut to every vertex in near linear O?(m+poly(?)n) time

Non-Mergeable Sketching for Cardinality Estimation

Cardinality estimation is perhaps the simplest non-trivial statistical problem that can be solved via sketching. Industrially-deployed sketches like HyperLogLog, MinHash, and PCSA are mergeable, which means that large data sets can be sketched in a distributed environment, and then merged into a single sketch of the whole data set. In the last decade a variety of sketches have been developed that are non-mergeable, but attractive for other reasons. They are simpler, their cardinality estimates are strictly unbiased, and they have substantially lower variance. We evaluate sketching schemes on a reasonably level playing field, in terms of their memory-variance product (MVP). E.g., a sketch that occupies 5m bits and whose relative variance is 2/m (standard error ?{2/m}) has an MVP of 10. Our contributions are as follows. - Cohen [Edith Cohen, 2015] and Ting [Daniel Ting, 2014] independently discovered what we call the {Martingale transform} for converting a mergeable sketch into a non-mergeable sketch. We present a simpler way to analyze the limiting MVP of Martingale-type sketches. - Pettie and Wang proved that the Fishmonger sketch [Seth Pettie and Dingyu Wang, 2021] has the best MVP, H?/I? ? 1.98, among a class of mergeable sketches called "linearizable" sketches. (H? and I? are precisely defined constants.) We prove that the Martingale transform is optimal in the non-mergeable world, and that Martingale Fishmonger in particular is optimal among linearizable sketches, with an MVP of H?/2 ? 1.63. E.g., this is circumstantial evidence that to achieve 1% standard error, we cannot do better than a 2 kilobyte sketch. - Martingale Fishmonger is neither simple nor practical. We develop a new mergeable sketch called Curtain that strikes a nice balance between simplicity and efficiency, and prove that Martingale Curtain has limiting MVP? 2.31. It can be updated with O(1) memory accesses and it has lower empirical variance than Martingale LogLog, a practical non-mergeable version of HyperLogLog

A Randomized Algorithm for Single-Source Shortest Path on Undirected Real-Weighted Graphs

In undirected graphs with real non-negative weights, we give a new randomized algorithm for the single-source shortest path (SSSP) problem with running time $O(m\sqrt{\log n \cdot \log\log n})$ in the comparison-addition model. This is the first algorithm to break the $O(m+n\log n)$ time bound for real-weighted sparse graphs by Dijkstra's algorithm with Fibonacci heaps. Previous undirected non-negative SSSP algorithms give time bound of $O(m\alpha(m,n)+\min\{n\log n, n\log\log r\})$ in comparison-addition model, where $\alpha$ is the inverse-Ackermann function and $r$ is the ratio of the maximum-to-minimum edge weight [Pettie & Ramachandran 2005], and linear time for integer edge weights in RAM model [Thorup 1999]. Note that there is a proposed complexity lower bound of $\Omega(m+\min\{n\log n, n\log\log r\})$ for hierarchy-based algorithms for undirected real-weighted SSSP [Pettie & Ramachandran 2005], but our algorithm does not obey the properties required for that lower bound. As a non-hierarchy-based approach, our algorithm shows great advantage with much simpler structure, and is much easier to implement.Comment: 17 page

Identifying Intraspecific Variation in Venom Yield of Chinese Cobra (Naja atra) from Ten Populations in Mainland China

Detailed information on venom yield is helpful in preparing antivenoms and treating snakebites, but such information is lacking for many species of venomous snakes. The Chinese cobra (Naja atra) is a large sized, venomous snake commonly found in southeastern China, where it causes a heavy burden of snakebites. To examine the effects of various factors (morphology, sex, age, season, and geographical origin) on the venom yield in this snake, we collected venom samples of 446 individuals (426 adults and 20 neonates) from 10 populations of N. atra over an eight-year period. We used two variables, lyophilized venom mass (venom yield) and solid content of venom (% solids), to quantify the venom yield. We used linear regression analysis to check if venom yield was related to morphological factors, one-way ANOVA and one-way ANCOVA to detect the sexual, ontogenetic, and geographic variation in venom yield, and repeated-measures ANOVA to examine seasonal shifts in venom yield. Our results indicate that venom yield of N. atra is positively related to the morphological traits examined, with male snakes expelling more venom than females. Venom yield in N. atra was age-related, with elder snakes always expelling more venom than younger ones. Geographic variation in venom yield was also observed, while seasonal variation was not. The solid content of venom was lower in males than in females, but this was not related to morphology, season, age, or geography. Our findings suggest that venom yield in N. atra is influenced by multiple factors, as well as by the interactions among these factors

The Bi-Functional Paxilline Enriched in Skin Secretion of Tree Frogs (<i>Hyla japonica</i>) Targets the KCNK18 and BK_Ca Channels

The skin secretion of tree frogs contains a vast array of bioactive chemicals for repelling predators, but their structural and functional diversity is not fully understood. Paxilline (PAX), a compound synthesized by Penicillium paxilli, has been known as a specific antagonist of large conductance Ca2+-activated K+ Channels (BKCa). Here, we report the presence of PAX in the secretions of tree frogs (Hyla japonica) and that this compound has a novel function of inhibiting the potassium channel subfamily K member 18 (KCNK18) channels of their predators. The PAX-induced KCNK18 inhibition is sufficient to evoke Ca2+ influx in charybdotoxin-insensitive DRG neurons of rats. By forming π-π stacking interactions, four phenylalanines located in the central pore of KCNK18 stabilize PAX to block the ion permeation. For PAX-mediated toxicity, our results from animal assays suggest that the inhibition of KCNK18 likely acts synergistically with that of BKCa to elicit tingling and buzzing sensations in predators or competitors. These results not only show the molecular mechanism of PAX-KCNK18 interaction, but also provide insights into the defensive effects of the enriched PAX

天山北坡不同海拔梯度山地草原生态系统地上净初级生产力对气候变化及放牧的响应/Impacts of grazing and climate change on the aboveground net primary productivity of mountainous grassland ecosystems along altitudinal gradients over the Northern Tianshan Mountains, China[J]

以天山北坡三工河流域为例,利用改进后的Biome-BGC模型分别模拟了仅气候变化和气候变化与放牧联合作用下研究区不同海拔梯度3种山地草原生态系统(低山干旱草原(Lower\mountain arid grassland,LAG),森林草甸草原(Forest meadow grassland,FMG),高寒草甸草原(Alpine meadow grassland,AMG)) 1959-2009年地上净初级生产力(Aboveground net primary production,ANPP)的动态,并通过假设27种放牧强度情景(0-8羊/hm2)模拟了其ANPP随放牧强度增加的变化趋势.近50a气候变化致使研究区各海拔梯度草原生态系统ANPP整体均呈上升趋势,但在放牧联合作用下,不同草原类型ANPP变化趋势差异显著;放牧导致FMG和AMG的ANPP呈下降态势,分别减少30.0％和33.2％,对比之下,由于1980年前较低放牧强度促进了LAG的ANPP,放牧导致其ANPP整体增加1.3％.随着放牧强度增加,LAG的ANPP呈先增后减趋势,且在干旱年份最为显著;而FMG和AMG的ANPP呈显著非线性递减趋势.这些结果表明,近50a气候波动可能有利于中亚干旱区山地草原生态系统生产力的提高,但日益增强的放牧活动导致其净初级生产力显著降低;放牧对FMG与AMG生产力的负面效应随放牧强度增加而增强,但适度放牧可能促进LAG净初级生产力,尤其在干旱年份