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In times of such public health crisis as the COVID-19, staying well-informed can not only help people get prepared and make wise decisions, but also relieve anxiety. Students with disabilities, however, face great difficulty in keeping up-to-date on the pandemic. Using a qualitative research method, this study explored the experiences and perceived difficulties of special education teachers in trying to keep their students informed amid the COVID-19 pandemic. Semistructured focus group interviews were conducted with a total of 24 teachers from seven special education schools in China. The results showed that teachers adopted various measures to improve students’ information access, such as holding weekly class meetings, making use of posters and LED displays, working with families and collaborating with local health institutions. Despite these efforts, teachers reported facing multiple challenges and much remains to be desired. This research highlights the need for a holistic approach to providing information for students with disabilities, one that is tailored to their special needs and that involves other players in addition to teachers.

Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture of Gaussians, and we add edge $(i,j)$ if and only if the feature vectors are sufficiently similar, in that $\langle u_i,u_j \rangle \ge \tau$ for a pre-specified threshold $\tau$. The different components of the Gaussian mixture represent the fact that there may be different types of nodes with different distributions over features -- for example, in a social network each component represents the different attributes of a distinct community. Natural algorithmic tasks associated with these networks are embedding (recovering the latent feature vectors) and clustering (grouping nodes by their mixture component). In this paper we initiate the study of clustering and embedding graphs sampled from high-dimensional Gaussian mixture block models, where the dimension of the latent feature vectors $d\to \infty$ as the size of the network $n \to \infty$. This high-dimensional setting is most appropriate in the context of modern networks, in which we think of the latent feature space as being high-dimensional. We analyze the performance of canonical spectral clustering and embedding algorithms for such graphs in the case of 2-component spherical Gaussian mixtures, and begin to sketch out the information-computation landscape for clustering and embedding in these models., Comment: 41 pages

Introduction: Epidermolysis bullosa (EB) is a skin fragility disorder that is caused by molecular aberrations in the epidermal basement membrane zone. Based primarily on the cleavage plane within the skin, EB is classified into four major subtypes: EB simplex; junctional EB (JEB); dystrophic EB; and Kindler EB. The junctional form (JEB) can lead to blistering and a variety of extracutaneous complications, including genitourinary tract involvement. Despite therapeutic progress, treatment modalities for urological complications of JEB are currently limited.Results: We present the case of a Chinese male with intermediate JEB and profound urinary tract stenosis. Due to the progression of the urinary tract stenosis, he presented with repeated urological symptoms, such as high frequency of urination, painful urination, and difficult voiding. After birth, multiple blisters on the fingers, feet, and limbs, as well as nail dystrophies and spare hair were noted. Mutation analysis revealed that the patient carried a homozygous frameshift mutation in the LAMB3 gene [c.1172_1179delinsTGTGTGTGCAAGGAG/p. (P391Lfs*23)]. After receiving treatment for urethral dilatation, lingual mucosa for anterior urethroplasty, and repair of urethral stricture using a ventral onlay penile skin flap, the patient still experienced a relapse of urinary tract stenosis. Finally, the patient underwent perineal urethrostomy. In contrast, his older brother with similar urological symptoms received regular urethral dilatation, and the curative effect was positive.Conclusion: Here we report on a case with a novel LAMB3 mutation that led to JEB with profound urinary tract stenosis, which has expanded our experience in the treatment of EB urological complications.

It was recently shown that almost all solutions in the symmetric binary perceptron are isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In contrast, some algorithms have been shown empirically to succeed in finding solutions at low density. This phenomenon has been justified numerically by the existence of subdominant and dense connected regions of solutions, which are accessible by simple learning algorithms. In this paper, we establish formally such a phenomenon for both the symmetric and asymmetric binary perceptrons. We show that at low constraint density (equivalently for overparametrized perceptrons), there exists indeed a subdominant connected cluster of solutions with almost maximal diameter, and that an efficient multiscale majority algorithm can find solutions in such a cluster with high probability, settling in particular an open problem posed by Perkins-Xu '21. In addition, even close to the critical threshold, we show that there exist clusters of linear diameter for the symmetric perceptron, as well as for the asymmetric perceptron under additional assumptions.

In this paper we consider coalescing random walks on a general connected graph $G=(V,E)$. We set up a unified framework to study the leading order of the decay rate of $P_t$, the expectation of the fraction of occupied sites at time $t$, particularly for the `Big Bang' regime where $t\ll t_{\text{coal}}:=\mathbb{E}[\inf\{s:\text{There is only one particle at time }s\}]$. Our results show that $P_t$ satisfies certain mean field behavior, if the graphs satisfy certain transience-like conditions. We apply this framework to two families of graphs: (1) graphs given by the configuration model with a degree distribution supported in $[3,\bar d]$ for some $\bar d\geq 3$, and (2) finite and infinite vertex-transitive graphs. In the first case, we show that for $1 \ll t \ll |V|$, $P_t$ decays in the order of $t^{-1}$, and $(tP_t)^{-1}$ is approximately the probability that two particles starting from the root of the corresponding unimodular Galton-Watson tree never collide after one of them leaves the root, which is also roughly $|V|/(2t_{\text{meet}})$, where $t_{\text{meet}}$ is the mean meeting time of two walkers. By taking the local weak limit, for the unimodular Galton-Watson tree we prove the convergence of $tP_t$ as $t\to\infty$. For the second family of graphs, if we take a sequence of finite graphs $G_n=(V_n, E_n)$, such that $t_{\text{meet}}=O(|V_n|)$ and the inverse of the spectral gap $t_{\text{rel}}$ is $o(|V_n|)$, then for $t_{\text{rel}}\ll t\ll t_{\text{coal}}$, $(tP_t)^{-1}$ is approximately the probability that two random walks never meet before time $t$, and also $|V|/(2t_{\text{meet}})$. In addition, we define a natural uniform transience condition, and show that it implies the above for all $1\ll t\ll t_{\text{coal}}$. Such estimates of $tP_t$ are also obtained for all infinite transient transitive unimodular graphs, in particular, all transient transitive amenable graphs., 72 pages

YY We consider the symmetric binary perceptron model, a simple model of neural networks that has gathered significant attention in the statistical physics, information theory and probability theory communities, with recent connections made to the performance of learning algorithms in Baldassi et al. '15., We establish that the partition function of this model, normalized by its expected value, converges to a lognormal distribution. As a consequence, this allows us to establish several conjectures for this model: (i) it proves the contiguity conjecture of Aubin et al. '19 between the planted and unplanted models in the satisfiable regime; (ii) it establishes the sharp threshold conjecture; (iii) it proves the frozen 1-RSB conjecture in the symmetric case, conjectured first by Krauth-Mezard '89 in the asymmetric case., In a recent work of Perkins-Xu '21, the last two conjectures were also established by proving that the partition function concentrates on an exponential scale, under an analytical assumption on a real-valued function. This left open the contiguity conjecture and the lognormal limit characterization, which are established here unconditionally, with the analytical assumption verified. In particular, our proof technique relies on a dense counterpart of the small graph conditioning method, which was developed for sparse models in the celebrated work of Robinson and Wormald.

The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in order to succeed with efficient algorithms in the challenging cases where the local structure of the graph is homogeneous. This paper provides an efficient algorithm to learn graphons in the constant expected degree regime. The algorithm is shown to succeed in estimating the rank-$k$ projection of a graphon in the $L_2$ metric if the top $k$ eigenvalues of the graphon satisfy a generalized Kesten-Stigum condition., 32 pages

In order to promote the application of big data analysis technology in the safety management in operation of basin’s hydro-junctions, the concept of big data and the “5V” characteristics are briefly described in this paper, which explains all the basic characteristics of monitoring data with big data. At the first time, it is proposed that the big data for safety monitoring in operation of basin’s hydro-junctions is composed of four dimensions: monitoring data of survey, design and construction, real-time monitoring data during operation and maintenance period, management data in operation and maintenance of dams and social resource data. The general relationship between the various factors of monitoring data, and the classification, process and mining method of correlation analysis for monitoring big data are analyzed. The method of analyzing the safety monitoring data in operation of basin’s hydro-junctions has been broadened, which meets the needs of the information and intelligence in management and operation of basin’s hydro-junctions.

This paper used PS-InSAR method to monitor the landslide along Qing river. Several typical landslides area were selected as the experimental areas. 61 ASAR data have been processed, which were acquired from 2003 to 2010. The obtained preliminary deformation rate map not only included the experimental areas, but also showed several new landslides areas. The results showed that the deformation rate distribute between −8.4 to 8.18 mm/y in typical landslides area. Meanwhile an new landslide area in ShuangGuMu was detected with the subsidence rate for 5.3mm/y. As for PS-InSAR results were not consistent with the traditional surveying results, this paper analyzed the possible reasons which affected the landslide monitoring in Qing river reservoir area.

It was recently shown that almost all solutions in the symmetric binary perceptron are isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In contrast, some algorithms have been shown empirically to succeed in finding solutions at low density. This phenomenon has been justified numerically by the existence of subdominant and dense connected regions of solutions, which are accessible by simple learning algorithms. In this paper, we establish formally such a phenomenon for both the symmetric and asymmetric binary perceptrons. We show that at low constraint density (equivalently for overparametrized perceptrons), there exists indeed a subdominant connected cluster of solutions with almost maximal diameter, and that an efficient multiscale majority algorithm can find solutions in such a cluster with high probability, settling in particular an open problem posed by Perkins-Xu in STOC'21. In addition, even close to the critical threshold, we show that there exist clusters of linear diameter for the symmetric perceptron, as well as for the asymmetric perceptron under additional assumptions.