arXiv subjects

Jianping Li

Publications and source records attributed to Jianping Li.

At least 73 records · Page 4Linked to original sources

arXiv2022

The maximum $A_α$-spectral radius of $t$-connected graphs with bounded matching number

Let $G$ be a graph with adjacency matrix $A(G)$ and let $D(G)$ be a diagonal matrix of the degrees of $G$. In 2017, Nikiforov defined the $A_α$-matrix of $G$ as \begin{equation*} A_α(G)=αG)+(1-α)A(G), \end{equation*}d where $α\in[0,1]$ is an arbitrary real number. The largest eigenvalue of $A_α(G)$ is called the $A_α$-spectral radius of $G$. Let $n$, $t$, $k$ be positive integers, satisfying $t\geq1$, $k\geq2$, $n\geq k+2$, and $n\equiv k$ (mod $2$). In this paper, for $α\in[0,\frac{1}{2}]$, we determine the extremal graphs with the maximum $A_α$-spectral radius among all $t$-connected graphs on $n$ vertices with matching number $\frac{n-k}{2}$ at most. This generalizes some results of O (2021) and Zhang (2022).

math.CO↗

arXiv2021

Signless Laplacian spectral radius and matching in graphs

The signless Laplacian matrix of a graph $G$ is given by $Q(G)=D(G)+A(G)$, where $D(G)$ is a diagonal matrix of vertex degrees and $A(G)$ is the adjacency matrix. The largest eigenvalue of $Q(G)$ is called the signless Laplacian spectral radius, denoted by $q_1=q_1(G)$. In this paper, some properties between the signless Laplacian spectral radius and perfect matching in graphs are establish. Let $r(n)$ be the largest root of equation $x^3-(3n-7)x^2+n(2n-7)x-2(n^2-7n+12)=0$. We show that $G$ has a perfect matching for $n=4$ or $n\geq10$, if $q_1(G)>r(n)$, and for $n=6$ or $n=8$, if $q_1(G)>4+2\sqrt{3}$ or $q_1(G)>6+2\sqrt{6}$ respectively, where $n$ is a positive even integer number. Moreover, there exists graphs $K_{n-3}\vee K_1 \vee \overline{K_2}$ such that $q_1(K_{n-3}\vee K_1 \vee \overline{K_2})=r(n)$ if $n\geq4$, a graph $K_2\vee\overline{K_4}$ such that $q_1(K_2\vee\overline{K_4})=4+2\sqrt{3}$ and a graph $K_3\vee\overline{K_5}$ such that $q_1(K_3\vee\overline{K_5})=6+2\sqrt{6}$. These graphs all have no prefect matching.

math.CO↗

arXiv2021

Topological quantum phase transition in the magnetic semimetal HoSb

Magnetic topological semimetals, a novel state of quantum matter with nontrivial band topology, have emerged as a new frontier in physics and materials science. An external stimulus like temperature or magnetic field could be expected to alter their spin states and thus the Fermi surface anisotropies and topological features. Here, we perform the angular magnetoresistance measurements and electronic band structure calculations to reveal the evolution of HoSb's Fermi surface anisotropies and topological nature in different magnetic states. The angular magnetoresistance results manifest that its Fermi surface anisotropy is robust in the paramagnetic state but is significantly modulated in the antiferromagnetic and ferromagnetic states. More interestingly, a transition from the trivial (nontrivial) to nontrivial (trivial) topological electronic phase is observed when HoSb undergoes a magnetic transition from the paramagnetic (antiferromagnetic) to antiferromagnetic (ferromagnetic) state induced by temperature (applied magnetic field). Our studying suggests that HoSb provides an archetype platform to study the correlations between magnetism and topological states of matter.

cond-mat.mtrl-sci↗

arXiv2021

Distance signless Laplacian spectral radius and perfect matching in graphs and bipartite graphs

The distance matrix $\mathcal{D}$ of a connected graph $G$ is the matrix indexed by the vertices of $G$ which entry $\mathcal{D}_{i,j}$ equals the distance between the vertices $v_i$ and $v_j$. The distance signless Laplacian matrix $\mathcal{Q}(G)$ of graph $G$ is defined as $\mathcal{Q}(G)=Diag(Tr)+\mathcal{D}(G)$, where $Diag(Tr)$ is the diagonal matrix of the vertex transmissions in $G$. The largest eigenvalue of $\mathcal{Q}(G)$ is called the distance signless Laplacian spectral radius of $G$, written as $η_1(G)$. And a perfect matching in a graph is a set of disadjacent edges covering every vertex of $G$. In this paper, we present two suffcient conditions in terms of the distance signless Laplacian sepectral radius for the exsitence of perfect matchings in graphs and bipatite graphs.

math.CO↗

arXiv2021

Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number

The zeroth-order general Randić index of graph $G=(V_G,E_G)$, denoted by $^0R_α(G)$, is the sum of items $(d_{v})^α$ over all vertices $v\in V_G$, where $α$ is a pertinently chosen real number. In this paper, we obtain the sharp upper and lower bounds on $^0R_α$ of trees with a domination number $γ$, in intervals $α\in(-\infty,0)\cup(1,\infty)$ and $α\in(0,1)$, respectively. The corresponding extremal graphs of these bounds are also characterized.

math.CO↗

arXiv2021

Burst-Error Propagation Suppression for Decision-Feedback Equalizer in Field-Trial Submarine Fiber-Optic Communications

In this paper, we present a field-trial C-band 72Gbit/s optical on-off keying (OOK) system over 18.8km dispersion-uncompensated submarine optical cable in the South China Sea. Chromatic dispersion (CD) of 18.8km submarine optical cable causes four spectral nulls on the 36GHz bandwidth of 72Gbit/s OOK signal, which is the main obstacle for achieving an acceptable bit-error-rate (BER) performance. Decision feedback equalizer (DFE) is effective to compensate for the spectral nulls. However, DFE has a serious defect of burst-error propagation when the burst errors emerge due to the unstable submarine environment. Weighted DFE (WDFE) can be used to mitigate the burst-error propagation, but it cannot fully compensate for the spectral nulls because only a part of feedback symbols is directly decided. Fortunately, maximum likelihood sequence estimation (MLSE) can be added after the WDFE to simultaneously eliminate the resisting spectral distortions and implement optimal detection. Compared to the joint DFE and MLSE algorithm, the joint WDFE and MLSE algorithm can effectively suppress the burst-error propagation to obtain a maximum 2.9dB improvement of $\boldsymbol{Q}$ factor and eliminate the phenomenon of BER floor. In conclusion, the joint WDFE and MLSE algorithm can solve the burst-error propagation for the field-trial fiber-optic communications.

cs.IT↗

arXiv2019

BGD-based Adam algorithm for time-domain equalizer in PAM-based optical interconnects

To the best of our knowledge, for the first time, we propose adaptive moment estimation (Adam) algorithm based on batch gradient descent (BGD) to design a time-domain equalizer (TDE) for PAM-based optical interconnects. Adam algorithm has been widely applied in the fields of artificial intelligence. For TDE, BGD-based Adam algorithm can obtain globally optimal tap coefficients without being trapped in locally optimal tap coefficients. Therefore, fast and stable convergence can be achieved by BGD-based Adam algorithm with low mean square error. Meanwhile, BGD-based Adam algorithm is implemented by parallel processing, which is more efficient than conventional serial algorithms, such as least mean square and recursive least square algorithms. The experimental results demonstrate that BGD-based Adam feed-forward equalizer works well in 120-Gbit/s PAM8 optical interconnects. In conclusion, BGD-based Adam algorithm shows great potential for converging the tap coefficients of TDE in future optical interconnects.

cs.IT↗

arXiv2019

Resistance distance-based graph invariants and spanning trees of graphs derived from the strong product of $P_2$ and $C_n$

Let $G_n$ be a graph obtained by the strong product of $P_2$ and $C_n$, where $n\geqslant3$. In this paper, explicit expressions for the Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning trees of $G_n$ are determined, respectively. It is surprising to find that the Kirchhoff (resp. multiplicative degree-Kirchhoff) index of $G_n$ is almost one-sixth of its Wiener (resp. Gutman) index. Moreover, let $\mathcal{G}^r_n$ be the set of subgraphs obtained from $G_n$ by deleting any $r$ vertical edges of $G_n$, where $0\leqslant r\leqslant n$. Explicit formulas for the Kirchhoff index and the number of spanning trees for any graph $G^r_n\in \mathcal{G}^r_{n}$ are completely established, respectively. Finally, it is interesting to see that the Kirchhoff index of $G^r_n$ is almost one-sixth of its Wiener index.

math.CO↗

arXiv2019

Signless Laplacian spectral radius and fractional matchings in graphs

A fractional matching of a graph $G$ is a function $f$ giving each edge a number in $[0,1]$ such that $\sum_{e\inΓ(v)}f(e)\leq1$ for each vertex $v\in V(G)$, where $Γ(v)$ is the set of edges incident to $v$. The fractional matching number of $G$, written $α^{\prime}_*(G)$, is the maximum value of $\sum_{e\in E(G)}f(e)$ over all fractional matchings. In this paper, we investigate the relations between the fractional matching number and the signless Laplacian spectral radius of a graph. Moreover, we give some sufficient spectral conditions for the existence of a fractional perfect matching.

math.CO↗

arXiv2019

Kirchhoff index, multiplicative degree-Kirchhoff index and spanning trees of the linear crossed polyomino chains

Let $G_n$ be a linear crossed polyomino chain with $n$ four-order complete graphs. In this paper, explicit formulas for the Kirchhoff index, the multiplicative degree-Kirchhoff index and the number of spanning trees of $G_n$ are determined, respectively. It is interesting to find that the Kirchhoff (resp. multiplicative degree-Kirchhoff) index of $G_n$ is approximately one quarter of its Wiener (resp. Gutman) index. More generally, let $\mathcal{G}^r_n$ be the set of subgraphs obtained by deleting $r$ vertical edges of $G_n$, where $0\leqslant r\leqslant n+1$. For any graph $G^r_n\in \mathcal{G}^r_{n}$, its Kirchhoff index and number of spanning trees are completely determined, respectively. Finally, we show that the Kirchhoff index of $G^r_n$ is approximately one quarter of its Wiener index.

math.CO↗

arXiv2018

Exploring cooperative game mechanisms of scientific coauthorship networks

Scientific coauthorship, generated by collaborations and competitions among researchers, reflects effective organizations of human resources. Researchers, their expected benefits through collaborations, and their cooperative costs constitute the elements of a game. Hence we propose a cooperative game model to explore the evolution mechanisms of scientific coauthorship networks. The model generates geometric hypergraphs, where the costs are modelled by space distances, and the benefits are expressed by node reputations, i. e. geometric zones that depend on node position in space and time. Modelled cooperative strategies conditioned on positive benefit-minus-cost reflect the spatial reciprocity principle in collaborations, and generate high clustering and degree assortativity, two typical features of coauthorship networks. Modelled reputations generate the generalized Poisson parts and fat tails appeared in specific distributions of empirical data, e. g. paper team size distribution. The combined effect of modelled costs and reputations reproduces the transitions emerged in degree distribution, in the correlation between degree and local clustering coefficient, etc. The model provides an example of how individual strategies induce network complexity, as well as an application of game theory to social affiliation networks.

physics.soc-ph↗

arXiv2018

Uniform hypergraphs with the first two smallest spectral radii

The spectral radius of a uniform hypergraph $G$ is the the maximum modulus of the eigenvalues of the adjacency tensor of $G$. For $k\ge 2$, among connected $k$-uniform hypergraphs with $m\ge 1$ edges, we show that the $k$-uniform loose path with $m$ edges is the unique one with minimum spectral radius, and we also determine the unique ones with second minimum spectral radius when $m\ge 2$.

math.SP↗

arXiv2018

Modelling transition phenomena of scientific coauthorship networks

In a range of scientific coauthorship networks, transitions emerge in degree distributions, correlations between degrees and local clustering coefficients, etc. The existence of those transitions could be regarded as a result of the diversity in collaboration behaviours of scientific fields. A growing geometric hypergraph built on a cluster of concentric circles is proposed to model two specific collaboration behaviours, namely the behaviour of leaders and that of other members in research teams. The model successfully predicts the transitions, as well as many common features of coauthorship networks. Particulary, it realizes a process of deriving the complex "scale-free" property from the simple "yes/no" experiments. Moreover, it gives a reasonable explanation for the emergence of transitions with the difference of collaboration behaviours between leaders and other members. The difference emerges in the evolution of research teams, which synthetically addresses several specific factors of generating collaborations, namely the communications between research teams, the academic impacts and homophily of authors.

physics.soc-ph↗

arXiv2018

Profiling MOOCs from viewing perspective

We profiled three aspects of MOOCs from the perspective of viewing behaviors, the most prominent and common ones of MOOC learning. They were learner classification, course attraction, teaching order and learning order. Based on viewing behavior data, we provided a non-parametric algorithm to categorize learners, which helped to narrow the scope of finding potential all-rounders, and a method to measure the correlations between teaching order and learning order, which helped to assign teaching contents. Using information entropy, we provided an index to measure course attraction, which integrated the viewing time invested on courses and the number of viewed course videos. This index describes the diminishing marginal utility of repeated viewing and the increasing information of viewing new videos. It has potential to be an auxiliary method of assessing course achievements.

physics.ed-ph↗

arXiv2018

Feature analysis of multidisciplinary scientific collaboration patterns based on PNAS

The features of collaboration patterns are often considered to be different from discipline to discipline. Meanwhile, collaborating among disciplines is an obvious feature emerged in modern scientific research, which incubates several interdisciplines. The features of collaborations in and among the disciplines of biological, physical and social sciences are analyzed based on 52,803 papers published in a multidisciplinary journal PNAS during 1999 to 2013. From those data, we found similar transitivity and assortativity of collaboration patterns as well as the identical distribution type of collaborators per author and that of papers per author, namely a mixture of generalized Poisson and power-law distributions. In addition, we found that interdisciplinary research is undertaken by a considerable fraction of authors, not just those with many collaborators or those with many papers. This case study provides a window for understanding aspects of multidisciplinary and interdisciplinary collaboration patterns.

physics.soc-ph↗

arXiv2017

Modeling the coevolution between citations and coauthorships in scientific papers

Collaborations and citations within scientific research grow simultaneously and interact dynamically. Modelling the coevolution between them helps to study many phenomena that can be approached only through combining citation and coauthorship data. A geometric graph for the coevolution is proposed, the mechanism of which synthetically expresses the interactive impacts of authors and papers in a geometrical way. The model is validated against a data set of papers published on PNAS during 2007-2015. The validation shows the ability to reproduce a range of features observed with citation and coauthorship data combined and separately. Particularly, in the empirical distribution of citations per author there exist two limits, in which the distribution appears as a generalized Poisson and a power-law respectively. Our model successfully reproduces the shape of the distribution, and provides an explanation for how the shape emerges via the decisions of authors. The model also captures the empirically positive correlations between the numbers of authors' papers, citations and collaborators.

physics.soc-ph↗

arXiv2016

Modeling the time-periodicity of in-degree distributions in scientific citation networks

In a range of citation networks, the in-degree distributions boast time-periodicity---the distributions of citations per article published each year present similar scale-free tails. This phenomenon can be regarded as a consequence of the emergence of hot topics and the existence of the "burst" phenomenon. With this inference considered, a geometric model based on our previous study is established, in which the sizes of the influence zones of nodes follow the same power-law distribution and decrease with their ages. The model successfully reproduces the time-periodicity of the in-degree distributions of the empirical data, and accounts for the presence of citation burst as well. Moreover, a reasonable explanation for the emergence of the scale-free tails by regarding the citation behavior between articles as a "yes/no" experiment is presented. The model can also predict the time-periodicity of the local clustering coefficients, which indicates that the model is a good tool in researches on the evolutionary mechanism of citation networks.

physics.soc-ph↗

arXiv2016

A geometric graph model of citation networks with linearly growing node-increment

Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic influence scopes of the papers are denoted through specific geometric areas related to time and space. In the model, nodes (papers) are uniformly and randomly sprinkled onto a cluster of circles of the Minkowski space whose centers are on the time axis. Edges (citations) are linked according to an influence mechanism which indicates that an existing paper will be cited by a new paper located in its influence zone. Considering the citations among papers in different disciplines, an interdisciplinary citation mechanism is added to the model in which some papers with a small probability of being chosen will cite some existing papers randomly and uniformly. Different from most existing models that only study the power-law tail of the in-degree distribution, this model also characterizes the overall in-degree distribution. Moreover, it presents the description of some other important statistical characteristics of real networks, such as in- and out-assortativity, giant component and clear community structure. Therefore, it is reasonable to believe that a good example is provided in the paper to study real networks by geometric graphs.

physics.soc-ph↗