A Splitting Augmented Lagrangian Method for Low Multilinear-Rank Tensor Recovery

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low multilinear-rank tensor recovery problem. The variable splitting technique and convex relaxation technique are used to transform this problem into a tractable constrained optimization problem. Considering the favorable structure of the problem, we develop a splitting augmented Lagrangian method to solve the resulting problem. The proposed algorithm is easily implemented and its convergence can be proved under some conditions. Some preliminary numerical results on randomly generated and real completion problems show that the proposed algorithm is very effective and robust for tackling the low multilinear-rank tensor completion problem

Mobile Conductance in Sparse Networks and Mobility-Connectivity Tradeoff

In this paper, our recently proposed mobile-conductance based analytical framework is extended to the sparse settings, thus offering a unified tool for analyzing information spreading in mobile networks. A penalty factor is identified for information spreading in sparse networks as compared to the connected scenario, which is then intuitively interpreted and verified by simulations. With the analytical results obtained, the mobility-connectivity tradeoff is quantitatively analyzed to determine how much mobility may be exploited to make up for network connectivity deficiency.Comment: Accepted to ISIT 201

A Multi-robot Coverage Path Planning Algorithm Based on Improved DARP Algorithm

The research on multi-robot coverage path planning (CPP) has been attracting more and more attention. In order to achieve efficient coverage, this paper proposes an improved DARP coverage algorithm. The improved DARP algorithm based on A* algorithm is used to assign tasks to robots and then combined with STC algorithm based on Up-First algorithm to achieve full coverage of the task area. Compared with the initial DARP algorithm, this algorithm has higher efficiency and higher coverage rate

Densest Subhypergraph: Negative Supermodular Functions and Strongly Localized Methods

Dense subgraph discovery is a fundamental primitive in graph and hypergraph analysis which among other applications has been used for real-time story detection on social media and improving access to data stores of social networking systems. We present several contributions for localized densest subgraph discovery, which seeks dense subgraphs located nearby a given seed sets of nodes. We first introduce a generalization of a recent $\textit{anchored densest subgraph}$ problem, extending this previous objective to hypergraphs and also adding a tunable locality parameter that controls the extent to which the output set overlaps with seed nodes. Our primary technical contribution is to prove when it is possible to obtain a strongly-local algorithm for solving this problem, meaning that the runtime depends only on the size of the input set. We provide a strongly-local algorithm that applies whenever the locality parameter is at least 1, and show why via counterexample that strongly-local algorithms are impossible below this threshold. Along the way to proving our results for localized densest subgraph discovery, we also provide several advances in solving global dense subgraph discovery objectives. This includes the first strongly polynomial time algorithm for the densest supermodular set problem and a flow-based exact algorithm for a densest subgraph discovery problem in graphs with arbitrary node weights. We demonstrate the utility of our algorithms on several web-based data analysis tasks

Trichlorophenyl-benzoxime induces apoptosis in human colon carcinoma cells via activation of mitochondria dependent pathway

Purpose: To determine the apoptotic effect of trichlorophenyl-benzoxime (TCPB) on colorectal cancer (CRC) cells, and to elucidate the mechanism of action. Methods: Colon carcinoma cell lines (DLD-1 and HT-29) were used in this study. The cells were cultured in Dulbecco's modified Eagle's medium (DMEM) supplemented with 10 % fetal bovine serum (FBS) and 1 % penicillin/streptomycin at 37 ˚C in an atmosphere of 5 % CO2 and 95 % air. When the cells attained 60 - 70 % confluency, they were treated with serum-free medium and graded concentrations of TCPB (1.0 – 6.0 μM) for 24 h. Cell viability and apoptosis were assessed using 3-(4, 5-dimethylthiazol-2-yl) 2, 5-diphenyltetrazolium bromide (MTT) and flow cytometric assays, respectively. Western blotting and 2', 7' dichlorofluorescein diacetate (DCFH DA) assays were used for the determination of expression levels of apoptotic proteins, and levels of reactive oxygen species (ROS), respectively. Results: Treatment of DLD-1 and HT-29 cells with TCPB led to significant and dose-dependent reductions in their viability, as well as significant and dose-dependent increases in the number of apoptotic cells (p < 0.05). Treatment of HT-29 cells with TCPB led to significant increases in the population of cells in the G0/G1 phase, but significant reduction of cell proportion in S and G2/M phases (p < 0.05). It also significantly and dose-dependently upregulated the expressions of caspase-3 and bax, down-regulation of the expression of bcl-2 (p < 0.05). TCPB treatment upregulated the expressions of p53, cytochrome c (cyt c), procaspase-3, and procaspase-9, but down-regulated the expression of pAkt dose-dependently (p < 0.05). The expression of Akt in HT-29 cells was not significantly affected by TCPB (p > 0.05). However, TCPB significantly enhanced the cleavage of PARP1, and significantly and dose-dependently increased the levels of ROS in HT-29 cells (p < 0.05). Conclusion: These results suggest that TCPB exerts apoptotic effect on CRC cells via activation of mitochondria-dependent pathway, and thus can be suitably developed for the management of colon cancer

Hardness of Graph-Structured Algebraic and Symbolic Problems

In this paper, we study the hardness of solving graph-structured linear systems with coefficients over a finite field $\mathbb{Z}_p$ and over a polynomial ring $\mathbb{F}[x_1,\ldots,x_t]$. We reduce solving general linear systems in $\mathbb{Z}_p$ to solving unit-weight low-degree graph Laplacians over $\mathbb{Z}_p$ with a polylogarithmic overhead on the number of non-zeros. Given the hardness of solving general linear systems in $\mathbb{Z}_p$ [Casacuberta-Kyng 2022], this result shows that it is unlikely that we can generalize Laplacian solvers over $\mathbb{R}$, or finite-element based methods over $\mathbb{R}$ in general, to a finite-field setting. We also reduce solving general linear systems over $\mathbb{Z}_p$ to solving linear systems whose coefficient matrices are walk matrices (matrices with all ones on the diagonal) and normalized Laplacians (Laplacians that are also walk matrices) over $\mathbb{Z}_p$. We often need to apply linear system solvers to random linear systems, in which case the worst case analysis above might be less relevant. For example, we often need to substitute variables in a symbolic matrix with random values. Here, a symbolic matrix is simply a matrix whose entries are in a polynomial ring $\mathbb{F}[x_1, \ldots, x_t]$. We formally define the reducibility between symbolic matrix classes, which are classified in terms of the degrees of the entries and the number of occurrences of the variables. We show that the determinant identity testing problem for symbolic matrices with polynomial degree $1$ and variable multiplicity at most $3$ is at least as hard as the same problem for general matrices over $\mathbb{R}$.Comment: 57 pages, submitted version to STOC2