Focal adhesion disassembly requires clathrin-dependent endocytosis of integrins

AbstractCell migration requires the controlled disassembly of focal adhesions, but the underlying mechanisms remain poorly understood. Here, we show that adhesion turnover is mediated through dynamin- and clathrin-dependent endocytosis of activated β1 integrins. Consistent with this, clathrin and the clathrin adaptors AP-2 and disabled-2 (DAB2) distribute along with dynamin 2 to adhesion sites prior to adhesion disassembly. Moreover, knockdown of either dynamin 2 or both clathrin adaptors blocks β1 integrin internalization, leading to impaired focal adhesion disassembly and cell migration. Together, these results provide important insight into the mechanisms underlying adhesion disassembly and identify novel components of the disassembly pathway

Digital almost nets

Digital nets (in base $2$) are the subsets of $[0,1]^d$ that contain the expected number of points in every not-too-small dyadic box. We construct sets that contain almost the expected number of points in every such box, but which are exponentially smaller than the digital nets. We also establish a lower bound on the size of such almost nets.Comment: 8 page

Learning Multi-Level Information for Dialogue Response Selection by Highway Recurrent Transformer

With the increasing research interest in dialogue response generation, there is an emerging branch formulating this task as selecting next sentences, where given the partial dialogue contexts, the goal is to determine the most probable next sentence. Following the recent success of the Transformer model, this paper proposes (1) a new variant of attention mechanism based on multi-head attention, called highway attention, and (2) a recurrent model based on transformer and the proposed highway attention, so-called Highway Recurrent Transformer. Experiments on the response selection task in the seventh Dialog System Technology Challenge (DSTC7) show the capability of the proposed model of modeling both utterance-level and dialogue-level information; the effectiveness of each module is further analyzed as well

Kruskal--Katona-Type Problems via Entropy Method

In this paper, we investigate several extremal combinatorics problems that ask for the maximum number of copies of a fixed subgraph given the number of edges. We call this type of problems Kruskal--Katona-type problems. Most of the problems that will be discussed in this paper are related to the joints problem. There are two main results in this paper. First, we prove that, in a $3$-colored graph with $R$ red, $G$ green, $B$ blue edges, the number of rainbow triangles is at most $\sqrt{2RGB}$, which is sharp. Second, we give a generalization of the Kruskal--Katona theorem that implies many other previous generalizations. Both arguments use the entropy method, and the main innovation lies in a more clever argument that improves bounds given by Shearer's inequality.Comment: 18 page

Tight Bound and Structural Theorem for Joints

A joint of a set of lines $\mathcal{L}$ in $\mathbb{F}^d$ is a point that is contained in $d$ lines with linearly independent directions. The joints problem asks for the maximum number of joints that are formed by $L$ lines. Guth and Katz showed that the number of joints is at most $O(L^{3/2})$ in $\mathbb{R}^3$ using polynomial method. This upper bound is met by the construction given by taking the joints and the lines to be all the $d$-wise intersections and all the $(d-1)$-wise intersections of $M$ hyperplanes in general position. Furthermore, this construction is conjectured to be optimal. In this paper, we verify the conjecture and show that this is the only optimal construction by using a more sophisticated polynomial method argument. This is the first tight bound and structural theorem obtained using this method. We also give a new definition of multiplicity that strengthens the main result of a previous work by Tidor, Zhao and the second author. Lastly, we include some discussion on the constants for the joints of varieties problem.Comment: 39 page

Well-posedness and averaging principle for L\'evy-type McKean-Vlasov stochastic differential equations under local Lipschitz conditions

In this paper, we investigate a class of McKean-Vlasov stochastic differential equations under L\'evy-type perturbations. We first establish the existence and uniqueness theorem for solutions of the McKean-Vlasov stochastic differential equations by utilizing the Euler-like approximation. Then under some suitable conditions, we show that the solutions of McKean-Vlasov stochastic differential equations can be approximated by the solutions of the associated averaged McKean-Vlasov stochastic differential equations in the sense of mean square convergence. In contrast to the existing work, a novel feature is the use of a much weaker condition -- local Lipschitzian in the state variables, allowing for possibly super-linearly growing drift, but linearly growing diffusion and jump coefficients. Therefore, our results are suitable for a wider class of McKean-Vlasov stochastic differential equations.Comment: 29 pages, 7 figure

When Classical Chinese Meets Machine Learning: Explaining the Relative Performances of Word and Sentence Segmentation Tasks

We consider three major text sources about the Tang Dynasty of China in our experiments that aim to segment text written in classical Chinese. These corpora include a collection of Tang Tomb Biographies, the New Tang Book, and the Old Tang Book. We show that it is possible to achieve satisfactory segmentation results with the deep learning approach. More interestingly, we found that some of the relative superiority that we observed among different designs of experiments may be explainable. The relative relevance among the training corpora provides hints/explanation for the observed differences in segmentation results that were achieved when we employed different combinations of corpora to train the classifiers.Comment: 4 pages, 1 figure, 2 tables, 2020 International Conference on Digital Humanities (Alliance of Digital Humanities Organizations, ADHO