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学者姓名：林峰根
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Abstract ：
Separable nonlinear models (SNLMs) adopt a linear combination of nonlinear functions, which is often used in the field of system identification, machine learning and signal processing. In this paper, we studied the performance of gradient-based algorithms in identifying separable nonlinear models. We put forward a gradient descent-based variable projection (GD-VP) algorithm which taking advantage of the particular structure of SNLM. In each iteration, the algorithm eliminates the linear parameters of the model, then updates the nonlinear parameters through the gradient descent (GD) algorithm. To improve the convergence rate of GD algorithm, an accelerated GD-VP algorithm is derived by employing the Aitken acceleration technology. Numerical experiments shows the efficiency of the proposed algorithm. © 2021 IEEE.
Keyword ：
Acceleration Acceleration Gradient methods Gradient methods Nonlinear systems Nonlinear systems Religious buildings Religious buildings Signal processing Signal processing
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| GB/T 7714 | Xu, Min , Lin, Fenggen , Chen, Guangyong et al. Accelerating variable projection algorithm by Aitken technique [C] . 2021 : 596-600 . |
| MLA | Xu, Min et al. "Accelerating variable projection algorithm by Aitken technique" . (2021) : 596-600 . |
| APA | Xu, Min , Lin, Fenggen , Chen, Guangyong , Gan, Min . Accelerating variable projection algorithm by Aitken technique . (2021) : 596-600 . |
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A complex square matrix is a ray pattern matrix if each of its nonzero entries has modulus 1. A ray pattern matrix naturally corresponds to a weighted-digraph. A ray pattern matrix A is ray nonsingular if for each entry-wise positive matrix K, A omicron K is nonsingular. A random model of ray pattern matrices with order n is introduced, where a uniformly random ray pattern matrix B is defined to be the adjacency matrix of a simple random digraph D-n,D- p whose arcs are weighted with i.i.d. random variables uniformly distributed over the unit circle in the complex plane. It is shown that p* (n) = 1/n is a threshold function for the random matrix M = I-B to be ray nonsingular, which is the same as the threshold function of the appearance of giant strong components in D-n,D-p.
Keyword ：
random digraph random digraph ray nonsingular ray nonsingular ray pattern matrix ray pattern matrix Threshold function Threshold function uniformly random uniformly random
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| GB/T 7714 | Liu, Yue , Chen, Ailian , Lin, Fenggen . Threshold function of ray nonsingularity for uniformly random ray pattern matrices [J]. | LINEAR & MULTILINEAR ALGEBRA , 2021 . |
| MLA | Liu, Yue et al. "Threshold function of ray nonsingularity for uniformly random ray pattern matrices" . | LINEAR & MULTILINEAR ALGEBRA (2021) . |
| APA | Liu, Yue , Chen, Ailian , Lin, Fenggen . Threshold function of ray nonsingularity for uniformly random ray pattern matrices . | LINEAR & MULTILINEAR ALGEBRA , 2021 . |
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Let G1 and GI be two connected graphs. The Kronecker product G\ x GI has vertex set V{G1 x G2) = V{G1) x V(G2) and the edge set E(G1 x G2) = {(u1 , v1)(U2,V2) : u1u2 € E(GI),V1V2 €= E(G2)}- Let S ⊆ V be a vertex set, S is called h-extra cut, if G- S is not connected and each component oiG-S has more than h vertices. The h-extra connectivity Kh(G) is the cardinality of the minimum /i-extra cuts. In this paper, we determine the h-ex tra connectivity of Km X Kn, Km x Pn and Km X Cn. © 2018 Charles Babbage Research Centre. All rights reserved.
Keyword ：
Graph theory Graph theory
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| GB/T 7714 | Guo, Litao , Lin, Fenggen . Extra connectivity of Kronecker products of some graphs and complete graphs [J]. | Journal of Combinatorial Mathematics and Combinatorial Computing , 2018 , 105 : 3-10 . |
| MLA | Guo, Litao et al. "Extra connectivity of Kronecker products of some graphs and complete graphs" . | Journal of Combinatorial Mathematics and Combinatorial Computing 105 (2018) : 3-10 . |
| APA | Guo, Litao , Lin, Fenggen . Extra connectivity of Kronecker products of some graphs and complete graphs . | Journal of Combinatorial Mathematics and Combinatorial Computing , 2018 , 105 , 3-10 . |
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The irregularity of a simple graph G = (V, E) is defined as irr(G) = Sigma(uv is an element of E(G)) |d(G)(u) - d(G)(v)|, where dG(u) denotes the degree of a vertex u is an element of V(G). This graph invariant, introduced by Albertson in 1997, is a measure of the defect of regularity of a graph. Recently, it also gains interest in Chemical Graph Theory, where it is named the third Zagreb index. In this paper, by means of the Laplacian eigenvalues and the normalized Laplacian eigenvalues of G, we establish some new spectral upper bounds for irr(G). We then compare these new bounds with a known bound by Goldberg, and it turns out that our bounds are better than the Goldberg bound in most cases. We also present two spectral lower bounds on irr(G). (C) 2017 Elsevier Inc. All rights reserved.
Keyword ：
Graph irregularity Graph irregularity Laplacian eigenvalues Laplacian eigenvalues Normalized Laplacian eigenvalues Normalized Laplacian eigenvalues Spectral bound Spectral bound The third Zagreb index The third Zagreb index
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| GB/T 7714 | Chen, Xiaodan , Hou, Yaoping , Lin, Fenggen . Some new spectral bounds for graph irregularity [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2018 , 320 : 331-340 . |
| MLA | Chen, Xiaodan et al. "Some new spectral bounds for graph irregularity" . | APPLIED MATHEMATICS AND COMPUTATION 320 (2018) : 331-340 . |
| APA | Chen, Xiaodan , Hou, Yaoping , Lin, Fenggen . Some new spectral bounds for graph irregularity . | APPLIED MATHEMATICS AND COMPUTATION , 2018 , 320 , 331-340 . |
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Topological indices based on the distances between vertices(atoms) of a molecular graph are widely used for characterizing molecular graphs and their fragments, establishing relationships between structures and properties of molecules, predicting biological activity of chemical compounds, and making other chemical applications. Polyphenyls are a kind of macrocyclic aromatic hydrocarbons and their derivatives are very important organic chemicals, which can be used in organic synthesis, drug synthesis, heat exchanger, etc. In this paper we investigate the relationships between the Wiener index and other distance-based topological indices in the tree-like polyphenyl systems and obtain some exactly formulae on the relationships. (C) 2016 Elsevier Inc. All rights reserved.
Keyword ：
Degree distance Degree distance Polyphenyl chain Polyphenyl chain Szeged index Szeged index Topological index Topological index Wiener index Wiener index
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| GB/T 7714 | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Distance-based topological indices of the tree-like polyphenyl systems [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 281 : 233-242 . |
| MLA | Chen, Ailian et al. "Distance-based topological indices of the tree-like polyphenyl systems" . | APPLIED MATHEMATICS AND COMPUTATION 281 (2016) : 233-242 . |
| APA | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Distance-based topological indices of the tree-like polyphenyl systems . | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 281 , 233-242 . |
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The Wiener index W(G) and the edge-Wiener index W-e(G) of a graph G are defined as the sum of all distances between pairs of vertices in a graph G and the sum of all distances between pairs of edges in G, respectively. The Wiener index, due to its correlation with a large number of physico-chemical properties of organic molecules and its interesting and non-trivial mathematical properties, has been extensively studied in both theoretical and chemical literature. The edge-Wiener index of G is nothing but the Wiener index of the line graph of G. The concept of line graph has been found various applications in chemical research. In this paper, we show that if G is a catacondensed hexagonal system with h hexagons and has t linear segments S-1, S-2, ,S-t of lengths l(S-i) = l(i)(1 <= i <= t), then W-e(G) = 25/16W(G) + 1/16(120h(2) + 94h + 29) - 1/4 Sigma(t)(i=1)(l(i) - 1)(2). Our main result reduces the problems on the edge-Wiener index to those on the Wiener index in the catacondensed hexagonal systems, which makes the former ones easier. (C) 2015 Elsevier Inc. All rights reserved.
Keyword ：
Catacondensed hexagonal system Catacondensed hexagonal system Edge-Wiener index Edge-Wiener index Line graph Line graph Wiener index Wiener index
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| GB/T 7714 | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 273 : 1100-1106 . |
| MLA | Chen, Ailian et al. "Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems" . | APPLIED MATHEMATICS AND COMPUTATION 273 (2016) : 1100-1106 . |
| APA | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems . | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 273 , 1100-1106 . |
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Dimer problem for three dimensional lattice is an unsolved problem in statistical mechanics and solid-state chemistry. In this paper, we obtain asymptotical expressions of the number of close-packed dimers (perfect matchings) for two types of three dimensional lattice graphs. Let M(G) denote the number of perfect matchings of G. Then log(M(K-2 X C-4 X P-n)) approximate to (-1.171. n(-1.1223) + 3.146)n, and log(M(K-2 X P-4 X P-n)) approximate to (-1.164. n(-1.196) + 2.804)n, where log() denotes the natural logarithm. Furthermore, we obtain a sufficient condition under which the lattices with multiple cylindrical and multiple toroidal boundary conditions have the same entropy. (C) 2015 Elsevier B.V. All rights reserved.
Keyword ：
Dimer Dimer Entropy Entropy Three dimensional lattice Three dimensional lattice
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| GB/T 7714 | Lin, Fenggen , Chen, Ailian , Lai, Jiangzhou . Dimer problem for some three dimensional lattice graphs [J]. | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS , 2016 , 443 : 347-354 . |
| MLA | Lin, Fenggen et al. "Dimer problem for some three dimensional lattice graphs" . | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 443 (2016) : 347-354 . |
| APA | Lin, Fenggen , Chen, Ailian , Lai, Jiangzhou . Dimer problem for some three dimensional lattice graphs . | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS , 2016 , 443 , 347-354 . |
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Let G be a (molecule) graph. A perfect matching, or Kekul, structure of G is a set of independent edges covering every vertex exactly once. Enumeration of Kekul, structures of a graph is interest in chemistry, physics and mathematics. In this paper, we focus on the number of perfect matchings in polyomino chain graphs. Simple exact formulas are given for the expected value of the number of perfect matchings in random polyomino chain graphs and for the asymptotic behavior of this expectation. Moreover, the average value of the number of perfect matchings with respect to the set of all polyomino chain graphs with s square-cells.
Keyword ：
Expected value Expected value Perfect matching Perfect matching Polyomino chain graph Polyomino chain graph Random variable Random variable
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| GB/T 7714 | Wei, Shouliu , Ke, Xiaoling , Lin, Fenggen . Perfect matchings in random polyomino chain graphs [J]. | JOURNAL OF MATHEMATICAL CHEMISTRY , 2016 , 54 (3) : 690-697 . |
| MLA | Wei, Shouliu et al. "Perfect matchings in random polyomino chain graphs" . | JOURNAL OF MATHEMATICAL CHEMISTRY 54 . 3 (2016) : 690-697 . |
| APA | Wei, Shouliu , Ke, Xiaoling , Lin, Fenggen . Perfect matchings in random polyomino chain graphs . | JOURNAL OF MATHEMATICAL CHEMISTRY , 2016 , 54 (3) , 690-697 . |
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A graph is a brick if it is 3-connected and bicritical. A brick is minimal if for every edge, the deletion of it results in a graph that is not a brick. In this article, we prove that every minimal brick has at least four cubic vertices.
Keyword ：
cubic vertex cubic vertex minimal brick minimal brick thin edge thin edge
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| GB/T 7714 | Lin, Fenggen , Zhang, Lianzhu , Lu, Fuliang . The Cubic Vertices of Minimal Bricks [J]. | JOURNAL OF GRAPH THEORY , 2014 , 76 (1) : 20-33 . |
| MLA | Lin, Fenggen et al. "The Cubic Vertices of Minimal Bricks" . | JOURNAL OF GRAPH THEORY 76 . 1 (2014) : 20-33 . |
| APA | Lin, Fenggen , Zhang, Lianzhu , Lu, Fuliang . The Cubic Vertices of Minimal Bricks . | JOURNAL OF GRAPH THEORY , 2014 , 76 (1) , 20-33 . |
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An even cycle C of a graph G is nice if the graph G - V(C) has a perfect matching. An orientation of G is a Pfaffian orientation if every nice cycle of G has an odd number of edges directed in either direction of the cycle. A graph is Pfaffian if it has a Pfaffian orientation. If a graph is Pfaffian, then the number of perfect matchings of it can be computed in polynomial time. In this paper, we focus on a special type of 1-extendable bipartite graph with maximum degree Delta(G) = vertical bar V(G)vertical bar/2. We characterize some properties of Pfaffian graphs in this type. According to the properties, we find an algorithm in time O(vertical bar E(G)vertical bar(2)) to determine whether a graph G in this type is Pfaffian or not. Furthermore, if G is Pfaffian, this algorithm also constructs a Pfaffian orientation of it. (C) 2014 Elsevier B.V. All rights reserved.
Keyword ：
Algorithm Algorithm Bipartite graph Bipartite graph Pfaffian orientation Pfaffian orientation
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| GB/T 7714 | Lin, Fenggen , Zhang, Lianzhu , Lu, Fuliang . Pfaffian orientations for a type of bipartite graph [J]. | THEORETICAL COMPUTER SCIENCE , 2014 , 527 : 97-101 . |
| MLA | Lin, Fenggen et al. "Pfaffian orientations for a type of bipartite graph" . | THEORETICAL COMPUTER SCIENCE 527 (2014) : 97-101 . |
| APA | Lin, Fenggen , Zhang, Lianzhu , Lu, Fuliang . Pfaffian orientations for a type of bipartite graph . | THEORETICAL COMPUTER SCIENCE , 2014 , 527 , 97-101 . |
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