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Min Feng

Publications and source records attributed to Min Feng.

36 records · Page 2Linked to original sources
arXiv2017

On the Fractional fixing number of graphs

An automorphism group of a graph $G$ is the set of all permutations of the vertex set of $G$ that preserve adjacency and non adjacency of vertices in a graph. A fixing set of a graph $G$ is a subset of vertices of $G$ such that only the trivial automorphism fixes every vertex in $S$. Minimum cardinality of a fixing set of $G$ is called the fixing number of $G$. In this article, we define a fractional version of the fixing number of a graph. We formulate the problem of finding the fixing number of a graph as an integer programming problem. It is shown that a relaxation of this problem leads to a linear programming problem and hence to a fractional version of the fixing number of a graph. We also characterize the graphs $G$ with the fractional fixing number $\frac{|V(G)|}{2}$ and the fractional fixing number of some families of graphs is also obtained.

math.CO↗
arXiv2016

Optimizing Memory Efficiency for Deep Convolutional Neural Networks on GPUs

Leveraging large data sets, deep Convolutional Neural Networks (CNNs) achieve state-of-the-art recognition accuracy. Due to the substantial compute and memory operations, however, they require significant execution time. The massive parallel computing capability of GPUs make them as one of the ideal platforms to accelerate CNNs and a number of GPU-based CNN libraries have been developed. While existing works mainly focus on the computational efficiency of CNNs, the memory efficiency of CNNs have been largely overlooked. Yet CNNs have intricate data structures and their memory behavior can have significant impact on the performance. In this work, we study the memory efficiency of various CNN layers and reveal the performance implication from both data layouts and memory access patterns. Experiments show the universal effect of our proposed optimizations on both single layers and various networks, with up to 27.9x for a single layer and up to 5.6x on the whole networks.

cs.DC↗
arXiv2015

The rainbow connection number of the power graph of a finite group

This paper studies the rainbow connection number of the power graph $Γ_G$ of a finite group $G$. We determine the rainbow connection number of $Γ_G$ if $G$ has maximal involutions or is nilpotent, and show that the rainbow connection number of $Γ_G$ is at most three if $G$ has no maximal involutions. The rainbow connection numbers of power graphs of some nonnilpotent groups are also given.

math.CO↗
arXiv2014

Identifying codes of Cartesian product of two cliques

An identifying code in a graph $G$ is a dominating set $C$ such that the closed neighborhood of each vertex in $G$ has a distinct intersection with $C$. In 2008, Gravier et al. determined the minimum cardinality of an identifying code of the Cartesian product of two cliques with the same size. In this note, we generalize this result to the Cartesian product of any two nontrivial cliques.

math.CO↗
arXiv2014

On the power graph of a finite group

The power graph $\mathcal P_G$ of a finite group $G$ is the graph with the vertex set $G$, where two elements are adjacent if one is a power of the other. We first show that $\mathcal P_G$ has an transitive orientation, so it is a perfect graph and its core is a complete graph. Then we use the poset on all cyclic subgroups (under usual inclusion) to characterise the structure of $\mathcal P_G$. Finally, the closed formula for the metric dimension of $\mathcal P_G$ is established. As an application, we compute the metric dimension of the power graph of a cyclic group.

math.CO↗
arXiv2013

Manipulating the magnetic anisotropy of cobalt doped titanium dioxide by carrier accumulation

Based on first-principles calculations, we predict that the magnetic anisotropy energy (MAE) of Co-doped TiO$_2$ sensitively depends on carrier accumulation. This magnetoelectric phenomenon provides a promising route to directly manipulate the magnetization direction of diluted magnetic semiconductor by external electric-fields. We calculate the band structures and reveal the origin of carrier-dependent MAE in k-space. In fact, the carrier accumulation shifts the Fermi energy and regulates the competing contributions to MAE. The first-principles calculations provide a straightforward way to design spintronics materials with electrically controllable spin direction.

cond-mat.mtrl-sci↗
arXiv2013

Identifying codes of corona product graphs

For a vertex $x$ of a graph $G$, let $N_G[x]$ be the set of $x$ with all of its neighbors in $G$. A set $C$ of vertices is an {\em identifying code} of $G$ if the sets $N_G[x]\cap C$ are nonempty and distinct for all vertices $x$. If $G$ admits an identifying code, we say that $G$ is identifiable and denote by $γ^{ID}(G)$ the minimum cardinality of an identifying code of $G$. In this paper, we study the identifying code of the corona product $H\odot G$ of graphs $H$ and $G$. We first give a necessary and sufficient condition for the identifiable corona product $H\odot G$, and then express $γ^{ID}(H\odot G)$ in terms of $γ^{ID}(G)$ and the (total) domination number of $H$. Finally, we compute $γ^{ID}(H\odot G)$ for some special graphs $G$.

math.CO↗
arXiv2013

Ab initio study of magnetic anisotropy in cobalt doped zinc oxide with electron-filling

Based on first-principles calculation, it has been predicted that the magnetic anisotropy energy (MAE) in Co-doped ZnO (Co:ZnO) depends on electron-filling. Results show that the charge neutral Co:ZnO presents a "easy plane" magnetic state. While modifying the total number of electrons, the easy axis rotates from in-plane to out-of-plane. The alternation of the MAE is considered to be the change of the ground state of Co ion, resulting from the relocating of electrons on Co d-orbitals with electron-filling.

cond-mat.mtrl-sci↗
arXiv2012

On the metric dimension and fractional metric dimension for hierarchical product of graphs

A set of vertices $W$ {\em resolves} a graph $G$ if every vertex of $G$ is uniquely determined by its vector of distances to the vertices in $W$. The {\em metric dimension} for $G$, denoted by $\dim(G)$, is the minimum cardinality of a resolving set of $G$. In order to study the metric dimension for the hierarchical product $G_2^{u_2}\sqcap G_1^{u_1}$ of two rooted graphs $G_2^{u_2}$ and $G_1^{u_1}$, we first introduce a new parameter, the {\em rooted metric dimension} $\rdim(G_1^{u_1})$ for a rooted graph $G_1^{u_1}$. If $G_1$ is not a path with an end-vertex $u_1$, we show that $\dim(G_2^{u_2}\sqcap G_1^{u_1})=|V(G_2)|\cdot\rdim(G_1^{u_1})$, where $|V(G_2)|$ is the order of $G_2$. If $G_1$ is a path with an end-vertex $u_1$, we obtain some tight inequalities for $\dim(G_2^{u_2}\sqcap G_1^{u_1})$. Finally, we show that similar results hold for the fractional metric dimension.

math.CO↗
arXiv2012

On the fractional metric dimension of corona product graphs and lexicographic product graphs

A vertex $x$ in a graph $G$ resolves two vertices $u$, $v$ of $G$ if the distance between $u$ and $x$ is not equal to the distance between $v$ and $x$. A function $g$ from the vertex set of $G$ to $[0,1]$ is a resolving function of $G$ if $g(R_G\{u,v\})\geq 1$ for any two distinct vertices $u$ and $v$, where $R_G\{u,v\}$ is the set of vertices resolving $u$ and $v$. The real number $\sum_{v\in V(G)}g(v)$ is the weight of $g$. The minimum weight of all resolving functions for $G$ is called the fractional metric dimension of $G$, denoted by $\dim_f(G)$. In this paper we reduce the problem of computing the fractional metric dimension of corona product graphs and lexicographic product graphs, to the problem of computing some parameters of the factor graphs.

math.CO↗
arXiv2012

On the fractional metric dimension of graphs

In [S. Arumugam, V. Mathew and J. Shen, On fractional metric dimension of graphs, preprint], Arumugam et al. studied the fractional metric dimension of the cartesian product of two graphs, and proposed four open problems. In this paper, we determine the fractional metric dimension of vertex-transitive graphs, in particular, the fractional metric dimension of a vertex-transitive distance-regular graph is expressed in terms of its intersection numbers. As an application, we calculate the fractional metric dimension of Hamming graphs and Johnson graphs, respectively. Moreover, we give an inequality for metric dimension and fractional metric dimension of an arbitrary graph, and determine all graphs when the equality holds. Finally, we establish bounds on the fractional metric dimension of the cartesian product of graphs. As a result, we completely solve the four open problems.

math.CO↗
arXiv2011

On the metric dimension of line graphs

Let $G$ be a (di)graph. A set $W$ of vertices in $G$ is a \emph{resolving set} of $G$ if every vertex $u$ of $G$ is uniquely determined by its vector of distances to all the vertices in $W$. The \emph{metric dimension} $μ(G)$ of $G$ is the minimum cardinality of all the resolving sets of $G$. Cáceres et al. \cite{Ca2} computed the metric dimension of the line graphs of complete bipartite graphs. Recently, Bailey and Cameron \cite{Ba} computed the metric dimension of the line graphs of complete graphs. In this paper we study the metric dimension of the line graph $L(G)$ of $G$. In particular, we show that $μ(L(G))=|E(G)|-|V(G)|$ for a strongly connected digraph $G$ except for directed cycles, where $V(G)$ is the vertex set and $E(G)$ is the edge set of $G$. As a corollary, the metric dimension of de Brujin digraphs and Kautz digraphs is given. Moreover, we prove that $\lceil\log_2Δ(G)\rceil\leqμ(L(G))\leq |V(G)|-2$ for a simple connected graph $G$ with at least five vertices, where $Δ(G)$ is the maximum degree of $G$. Finally, we obtain the metric dimension of the line graph of a tree in terms of its parameters.

math.CO↗
arXiv2011

Identifying codes of lexicographic product of graphs

Gravier et al. investigated the identifying codes of Cartesian product of two graphs. In this paper we consider the identifying codes of lexicographic product G[H] of a connected graph G and an arbitrary graph H, and obtain the minimum cardinality of identifying codes of G[H] in terms of some parameters of G and H.

math.CO↗
arXiv2011

On the metric dimension of bilinear forms graphs

The metric dimension of a graph is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. Bailey and Meagher obtained an upper bound on the metric dimension of Grassmann graphs. In this paper we obtain an upper bound on the metric dimension of bilinear forms graphs.

math.CO↗
arXiv2009

Kinesin Is an Evolutionarily Fine-Tuned Molecular Ratchet-and-Pawl Device of Decisively Locked Direction

Conventional kinesin is a dimeric motor protein that transports membranous organelles toward the plus-end of microtubules (MTs). Individual kinesin dimers show steadfast directionality and hundreds of consecutive steps, yetthe detailed physical mechanism remains unclear. Here we compute free energies for the entire dimer-MT system for all possible interacting configurations by taking full account of molecular details. Employing merely first principles and several measured binding and barrier energies, the system-level analysis reveals insurmountable energy gaps between configurations, asymmetric ground state caused by mechanically lifted configurational degeneracy, and forbidden transitions ensuring coordination between both motor domains for alternating catalysis. This wealth of physical effects converts a kinesin dimer into a molecular ratchet-and-pawl device, which determinedly locks the dimer's movement into the MT plus-end and ensures consecutive steps in hand-over-hand gait.Under a certain range of extreme loads, however, the ratchet-and-pawl device becomes defective but not entirely abolished to allow consecutive back-steps. This study yielded quantitative evidence that kinesin's multiple molecular properties have been evolutionarily adapted to fine-tune the ratchet-and-pawl device so as to ensure the motor's distinguished performance.

physics.bio-ph↗
arXiv2009

The intrinsic load-resisting capacity of kinesin

Conventional kinesin is a homodimeric motor protein that is capable of walking unidirectionally along a cytoskeletal filament. While previous experiments indicated unyielding unidirectionality against an opposing load up to the so-called stall force, recent experiments also observed limited processive backwalking under superstall loads. This theoretical study seeks to elucidate the molecular mechanical basis for kinesin's steps over the full range of external loads that can possibly be applied to the dimer. We found that kinesin's load-resisting capacity is largely determined by a synergic ratchet-and-pawl mechanism inherent in the dimer. Load susceptibility of this inner molecular mechanical mechanism underlies kinesin's response to various levels of external loads. Computational implementation of the mechanism enabled us to rationalize major trends observed experimentally in kinesin's stalemate and consecutive back steps. The study also predicts several distinct features of kinesin's load-affected motility, which are seemingly counterintuitive but readily verifiable by future experiment.

physics.bio-ph↗