Densely connected sub-Gaussian linear structural equation model learning via ℓ1- and ℓ2-regularized regressions

Improved square coloring of planar graphs

Recent experiments have shown ASP solvers to run significantly faster on ground programs of small treewidth. If possible, it may therefore be beneficial to write a non-ground ASP encoding such that grounding it together with an input of small treewidth leads to a propositional program of small treewidth. In this work, we prove that a class of non-ground programs called guarded ASP guarantees this property. Guarded ASP is a subclass of the recently proposed class of connection-guarded ASP, which is known to admit groundings whose treewidth depends on both the treewidth and the maximum degree of the input. Here we show that this dependency on the maximum degree cannot be dropped. Hence, in contrast to connection-guarded ASP, guarded ASP promises good performance even if the input has large maximum degree.

Unsupervised feature selection is one of the key topics in data engineering. Previous studies usually use a score vector which has the same length as the feature number to measure the discriminating power of each feature, and the top ranked features are considered to represent the intrinsic multi-cluster structure of the original data. Among different algorithms, Multi-Cluster Feature Selection(MCFS) is one well designed algorithm for its superior performance in feature selection tasks. However, in practice the score vector of MCFS is often sparse, and it brings a problem that only few features are well evaluated about the discriminating power while most others’ are still ambiguous. In this paper, by simultaneously solving one L1-regularized regression and one L2-regularized regression, we propose a novel Multi-Cluster Feature Selection via Smooth Distributed Score(MCFS-SDS), which combines the two results to clearly evaluate the discriminating power of most features via smooth distributed score vector. It is extremely efficient when cluster number is small. Experimental results over various real-life data demonstrate the effectiveness of the proposed algorithm.KeywordsUnsupervised feature selectionclusteringspectral regression

An adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that any pair of adjacent vertices have distinct sets of colors. The minimum number of colors needed for an adjacent vertex distinguishing total coloring of G is denoted by $\chi''_{a}(G)$ . In this paper, we characterize completely the adjacent vertex distinguishing total chromatic number of planar graphs G with large maximum degree Δ by showing that if Δ?14, then $\varDelta+1\leq \chi''_{a}(G)\leq \varDelta+2$ , and $\chi''_{a}(G)=\varDelta+2$ if and only if G contains two adjacent vertices of maximum degree.

It is proved that a planar graph with maximum degree Δ ≥ 11 has total (vertex-edge) chromatic number $Delta; + 1. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 53–59, 1997

Given a simple graph $G$, denote by $\Delta(G)$, $\delta(G)$, and $\chi'(G)$ the maximum degree, the minimum degree, and the chromatic index of $G$, respectively. We say $G$ is $\Delta$-critical if $\chi'(G)=\Delta(G)+1$ and $\chi'(H)\le \Delta(G)$ for every proper subgraph $H$ of $G$, and $G$ is overfull if $|E(G)|>\Delta(G) \lfloor |V(G)|/2 \rfloor$. Since a maximum matching in $G$ can have size at most $\lfloor |V(G)|/2 \rfloor$, it follows that $\chi'(G) = \Delta(G) +1$ if $G$ is overfull. Conversely, let $G$ be a $\Delta$-critical graph. The well known overfull conjecture of Chetwynd and Hilton asserts that $G$ is overfull provided $\Delta(G) > |V(G)|/3$. In this paper, we show that any $\Delta$-critical graph $G$ is overfull if $\Delta(G) - 7\delta(G)/4\ge (3|V(G)|-17)/4$.

ABSTRACTSurvey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. With typical nonnormally distributed data in practice, a rescaled statistic Trml proposed by Satorra and Bentler was recommended in the literature of SEM. However, Trml has been shown to be problematic when the sample size N is small and/or the number of variables p is large. There does not exist a reliable test statistic for SEM with small N or large p, especially with nonnormally distributed data. Following the principle of Bartlett correction, this article develops empirical corrections to Trml so that the mean of the empirically corrected statistics approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics control type I errors reasonably well even when N is smaller than 2p, where Trml may reject the correct model 100% even for normally distributed data. The application of the empirically corrected statistics is illustrated via a real data example.

Theoretical aspects of equitable partition of networks into sparse modules

It is shown by Luo and Zhao (J Graph Theory 73:469---482, 2013) that an overfull $$\Delta $$Δ-critical graph with n vertices that satisfies $$\Delta \ge \frac{n}{2}$$Δźn2 is Hamiltonian. If Hilton'...

Incidence coloring of Mycielskians with fast algorithm

Minimum training sample size requirements for achieving high prediction accuracy with the BN model: A case study regarding seismic liquefaction

PCG solver and its computational complexity for implicit control-volume finite-element method of RTM mold filling simulation

The importance of sample size, although widely discussed in the literature on structural equation modeling (SEM), has not been widely recognized among applied SEM researchers. To narrow this gap, we focus on second language testing and learning studies and examine the following: (a) Is the sample size sufficient in terms of precision and power of parameters in a model using Monte Carlo analysis? (b) How are the results from Monte Carlo sample size analysis comparable with those from the N ≥ 100 rule and from the N: q ≥ 10 (sample size–free parameter ratio) rule? Regarding (a), parameter bias, standard error bias, coverage, and power were overall satisfactory, suggesting that sample size for SEM models in second language testing and learning studies is generally appropriate. Regarding (b), both rules were often inconsistent with the Monte Carlo analysis, suggesting that they do not serve as guidelines for sample size. We encourage applied SEM researchers to perform Monte Carlo analyses to estimate the requisite sample size of a model.

In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error variances are the same or known. Hence, this work proves the identifiability of Gaussian SEMs with both homogeneous and heterogeneous unknown error variances. Our new identifiability assumption exploits not only error variances, but edge weights; hence, it is strictly milder than prior work on the identifiability result. We further provide a structure learning algorithm that is statistically consistent and computationally feasible, based on our new assumption. The proposed algorithm assumes that all relevant variables are observed, while it does not assume causal minimality and faithfulness. We verify our theoretical findings through simulations and real multivariate data, and compare our algorithm to state-of-the-art PC, GES and GDS algorithms.

In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph G (linear array or mesh in this paper), a graph G′ is called a k-fault-tolerant graph of G if when we remove any k nodes from G′, it still contains a subgraph isomorphic to G. The major quality measures for a fault-tolerant graph are the number of spare nodes it uses and the maximum degree it has. The degree is particularly important in practice as it poses constraints on the scalability of the system. In this paper, we aim at designing fault-tolerant graphs with both small degree and small number of spare nodes. The graphs we obtain have degree O(1) for arrays and O(log3 k) for meshes. The number of spare nodes used are O(k log2 k) and O(k2/log k), respectively. Compared to the previous results, the number of spare nodes used in our construction has one fewer linear factor in k.