arXiv subjects

Jin Xu

Publications and source records attributed to Jin Xu.

At least 199 records · Page 11Linked to original sources

arXiv2018

Graph Theory Towards New Graphical Passwords In Information Networks

Graphical passwords (GPWs) have been studied over 20 years. We are motivated from QR codes that can be considered GPWs, are successfully applied in today's world. However, one need such GPWs that can be use conveniently and have higher level security in information networks. We aim to GPWs for mobile devices with touch screen. No more researching papers of GPWs by means of techniques of graph theory that are already used in a wide range of scientific areas, especially, dynamic networks. Our investigation is devoted to designing new type of graphical passwords by methods of graph theory, such as various topological structures and colorings (labellings). We develop the idea of "topological structure plus number theory" in maximal planar graphs, and provide new techniques for designing new type of GPWs, and furthermore we do theoretical analysis on these new type of GPWs.

cs.CR↗

arXiv2018

On Spectral Graph Embedding: A Non-Backtracking Perspective and Graph Approximation

Graph embedding has been proven to be efficient and effective in facilitating graph analysis. In this paper, we present a novel spectral framework called NOn-Backtracking Embedding (NOBE), which offers a new perspective that organizes graph data at a deep level by tracking the flow traversing on the edges with backtracking prohibited. Further, by analyzing the non-backtracking process, a technique called graph approximation is devised, which provides a channel to transform the spectral decomposition on an edge-to-edge matrix to that on a node-to-node matrix. Theoretical guarantees are provided by bounding the difference between the corresponding eigenvalues of the original graph and its graph approximation. Extensive experiments conducted on various real-world networks demonstrate the efficacy of our methods on both macroscopic and microscopic levels, including clustering and structural hole spanner detection.

cs.SI↗

arXiv2017

Optical Observations of LIGO Source GW 170817 by the Antarctic Survey Telescopes at Dome A, Antarctica

The LIGO detection of gravitational waves (GW) from merging black holes in 2015 marked the beginning of a new era in observational astronomy. The detection of an electromagnetic signal from a GW source is the critical next step to explore in detail the physics involved. The Antarctic Survey Telescopes (AST3), located at Dome A, Antarctica, is uniquely situated for rapid response time-domain astronomy with its continuous night-time coverage during the austral winter. We report optical observations of the GW source (GW~170817) in the nearby galaxy NGC 4993 using AST3. The data show a rapidly fading transient at around 1 day after the GW trigger, with the $i$-band magnitude declining from $17.23\pm0.13$ magnitude to $17.72\pm0.09$ magnitude in $\sim 1.8$ hour. The brightness and time evolution of the optical transient associated with GW~170817 are broadly consistent with the predictions of models involving merging binary neutron stars. We infer from our data that the merging process ejected about $\sim 10^{-2}$ solar mass of radioactive material at a speed of up to $30\%$ the speed of light.

astro-ph.HE↗

arXiv2017

The Join of Scale-free Network Models

We focus on constructing the domi-join model by doing the join operation based on two smallest dominating sets of two network models and analysis the properties of domi-join model, such as power law distribution, small world. Besides, we will import two class of edge-bound growing network models to explain the process of domi-join model. Then we compute the average degree, clustering coefficient, power law distribution of the domi-join model. Finally, we discuss an impressive method for cutting down redundant operation of domi-join model.

cs.SI↗

arXiv2017

A Bayesian Stochastic Approximation Method

Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and nonrecursive iteration. Strong consistency of the Bayes estimator is obtained. Simulation studies show that our method is superior in finite-sample performance to Robbins--Monro type procedures. Extensions to searching for extrema and a version of generalized multivariate quantile are presented.

stat.ME↗

arXiv2016

Theory on the Structure and Coloring of Maximal Planar Graphs (1)Recursion Formulae of Chromatic Polynomial and Four-Color Conjecture

In this paper, two recursion formulae of chromatic polynomial of a maximal planar graph G are obtained. Moreover, the application of these formulaes to the proof of Four-Color Conjecture is investigated. By using these formulae, the proof of Four-Color Conjecture boils down to the study on a special class of graphs, viz., 4-chromatic-funnel pseudo uniquely-4-colorable maximal planar graphs.

math.GM↗

arXiv2016

Probe Machine

A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather than sequentially process every pair of linearly-adjacent data. In this paper, we establish the mathematical model of Probe Machine as a 9-tuple consisting of data library, probe library, data controller, probe controller, probe operation, computing platform, detector, true solution storage, and residue collector. We analyze the computation capability of the Probe Machine model, and in particular we show that Turing Machine is a special case of Probe Machine. We revisit two NP-complete problems---i.e., the Graph Coloring and Hamilton Cycle problems, and devise two algorithms on basis of the established Probe Machine model, which can enumerate all solutions to each of these problems by only one probe operation. Furthermore, we show that Probe Machine can be implemented by leveraging the nano-DNA probe technologies. The computational power of an electronic computer based on Turing Machine is known far more than that of the human brain. A question naturally arises: will a future computer based on Probe Machine outperform the human brain in more ways beyond the computational power?

cs.CC↗

arXiv2016

Maximum Leaf Spanning Trees of Growing Sierpinski Networks Models

The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic parameters of a large network having thousand and thousand nodes. We design several recursive algorithms for finding spanning trees having maximal leaves (MLS-trees) in investigation of topological structures of Sierpinski growing network models, and use MLS-trees to determine the kernels, dominating and balanced sets of the models. We propose a new stochastic method for the models, called the edge-cumulative distribution, and show that it obeys a power law distribution.

cs.DS↗

arXiv2015

Improper Graceful and Odd-graceful Labellings of Graph Theory

In this paper we define some new labellings for trees, called the in-improper and out-improper odd-graceful labellings such that some trees labelled with the new labellings can induce graceful graphs having at least a cycle. We, next, apply the new labellings to construct large scale of graphs having improper graceful/odd-graceful labellings or having graceful/odd-graceful labellings.

cs.DM↗

arXiv2015

Growing Network Models Having Part Edges Removed/added Randomly

Since network motifs are an important property of networks and some networks have the behaviors of rewiring or reducing or adding edges between old vertices before new vertices entering the networks, we construct our non-randomized model N(t) and randomized model N'(t) that have the predicated fixed subgraphs like motifs and satisfy both properties of growth and preferential attachment by means of the recursive algorithm from the lower levels of the so-called bound growing network models. To show the scale-free property of the randomized model N'(t), we design a new method, called edge-cumulative distribution, and democrat two edge-cumulative distributions of N(t) and N'(t) are equivalent to each other.

cs.SI↗

arXiv2015

On uniquely 3-colorable plane graphs without prescribed adjacent faces

A graph $G$ is \emph{uniquely k-colorable} if the chromatic number of $G$ is $k$ and $G$ has only one $k$-coloring up to permutation of the colors. For a plane graph $G$, two faces $f_1$ and $f_2$ of $G$ are \emph{adjacent $(i,j)$-faces} if $d(f_1)=i$, $d(f_2)=j$ and $f_1$ and $f_2$ have a common edge, where $d(f)$ is the degree of a face $f$. In this paper, we prove that every uniquely 3-colorable plane graph has adjacent $(3,k)$-faces, where $k\leq 5$. The bound 5 for $k$ is best possible. Furthermore, we prove that there exist a class of uniquely 3-colorable plane graphs having neither adjacent $(3,i)$-faces nor adjacent $(3,j)$-faces, where $i,j\in \{3,4,5\}$ and $i \neq j$. One of our constructions implies that there exist an infinite family of edge-critical uniquely 3-colorable plane graphs with $n$ vertices and $\frac{7}{3}n-\frac{14}{3}$ edges, where $n(\geq 11)$ is odd and $n\equiv 2\pmod{3}$.

math.CO↗

arXiv2015

Time-Resolved Mass Sensing of a Molecular Adsorbate Nonuniformly Distributed Along a Nanomechnical String

We show that the particular distribution of mass deposited on the surface of a nanomechanical resonator can be estimated by tracking the evolution of the device's resonance frequencies during the process of desorption. The technique, which relies on analytical models we have developed for the multimodal response of the system, enables mass sensing at much higher levels of accuracy than is typically achieved with a single frequency-shift measurement and no rigorous knowledge of the mass profile. We report on a series of demonstration experiments, in which the explosive molecule 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) is vapor deposited along the length of a silicon nitride nanostring to create a dense, random covering of RDX crystallites on the surface. In some cases, the deposition is biased to produce distributions with a slight excess or deficit of mass at the string midpoint. The added mass is then allowed to sublimate away under vacuum conditions, with the device returning to its original state over about 4 h (and the resonance frequencies, measured via optical interferometry, relaxing back to their pre-mass-deposition values). Our claim is that the detailed time trace of observed frequency shifts is rich in information---not only about the quantity of RDX initially deposited but also about its spatial arrangement along the nanostring. The data also reveal that sublimation in this case follows a nontrivial rate law, consistent with mass loss occurring at the exposed surface area of the RDX crystallites.

cond-mat.mes-hall↗

arXiv2014

Active Dictionary Learning in Sparse Representation Based Classification

Sparse representation, which uses dictionary atoms to reconstruct input vectors, has been studied intensively in recent years. A proper dictionary is a key for the success of sparse representation. In this paper, an active dictionary learning (ADL) method is introduced, in which classification error and reconstruction error are considered as the active learning criteria in selection of the atoms for dictionary construction. The learned dictionaries are caculated in sparse representation based classification (SRC). The classification accuracy and reconstruction error are used to evaluate the proposed dictionary learning method. The performance of the proposed dictionary learning method is compared with other methods, including unsupervised dictionary learning and whole-training-data dictionary. The experimental results based on the UCI data sets and face data set demonstrate the efficiency of the proposed method.

cs.CV↗

arXiv2014

Tree-colorable maximal planar graphs

A tree-coloring of a maximal planar graph is a proper vertex $4$-coloring such that every bichromatic subgraph, induced by this coloring, is a tree. A maximal planar graph $G$ is tree-colorable if $G$ has a tree-coloring. In this article, we prove that a tree-colorable maximal planar graph $G$ with $δ(G)\geq 4$ contains at least four odd-vertices. Moreover, for a tree-colorable maximal planar graph of minimum degree 4 that contains exactly four odd-vertices, we show that the subgraph induced by its four odd-vertices is not a claw and contains no triangles.

math.CO↗

arXiv2013

Size of edge-critical uniquely 3-colorable planar graphs

A graph $G$ is \emph{uniquely k-colorable} if the chromatic number of $G$ is $k$ and $G$ has only one $k$-coloring up to permutation of the colors. A uniquely $k$-colorable graph $G$ is edge-critical if $G-e$ is not a uniquely $k$-colorable graph for any edge $e\in E(G)$. Mel'nikov and Steinberg [L. S. Mel'nikov, R. Steinberg, One counterexample for two conjectures on three coloring, Discrete Math. 20 (1977) 203-206] asked to find an exact upper bound for the number of edges in a edge-critical 3-colorable planar graph with $n$ vertices. In this paper, we give some properties of edge-critical uniquely 3-colorable planar graphs and prove that if $G$ is such a graph with $n(\geq6)$ vertices, then $|E(G)|\leq \frac{5}{2}n-6 $, which improves the upper bound $\frac{8}{3}n-\frac{17}{3}$ given by Matsumoto [N. Matsumoto, The size of edge-critical uniquely 3-colorable planar graphs, Electron. J. Combin. 20 (3) (2013) $\#$P49]. Furthermore, we find some edge-critical 3-colorable planar graphs which have $n(=10,12, 14)$ vertices and $\frac{5}{2}n-7$ edges.

math.CO↗

arXiv2013

Two distinct spin liquid states in a layered cubic lattice

We construct a family of short-range resonating-valence-bond wave functions on a layered cubic lattice, allowing for a tunable anisotropy in the amplitudes assigned to nearest-neighbour valence bonds along one axis. Monte Carlo simulations reveal that four phases are stabilized over the full range of the anisotropy parameter. They are separated from one another by a sequence of continuous quantum phase transitions. An antiferromagnetic phase, centred on the perfect isotropy point, intervenes between two distinct quantum spin liquid states. One of them is continuously deformable to the two-dimensional U(1) spin liquid, which is known to exhibit critical bond correlations. The other has both spin and bond correlations that decay exponentially. The existence of this second phase is proof that, contrary to expectations, neither a bipartite lattice structure nor a conventional Marshall sign rule is an impediment to realizing a fully gapped quantum spin liquid.

cond-mat.str-el↗

arXiv2013

Frustrating antiferromagnetic exchange interactions enhance specific valence-bond-pair motifs

We present variational results for the ground state of the antiferromagnetic quantum Heisenberg model with frustrating next-nearest-neighbour interactions. The trial wave functions employed are of resonating-valence-bond type, elaborated to account for various geometric motifs of adjacent bond pairs. The calculation is specialized to a square-lattice cluster consisting of just sixteen sites, large enough that the system can accommodate nontrivial singlet dimer correlations but small enough that exhaustive enumeration of states in the total spin zero sector is still feasible. A symbolic computation approach allows us to generate an algebraic expression for the expectation value of any observable and hence to carry out the energy optimization exactly. While we have no measurements that could unambiguously identify a spin liquid state in the controversial region at intermediate frustration, we can say that the bond-bond correlation factors that emerge do not appear to be consistent with the existence of a columnar valence bond crystal. Furthermore, our results suggest that the magnetically disordered region may accommodate two distinct phases.

cond-mat.str-el↗

arXiv2012

Theory on Structure and Coloring of Maximal Planar Graphs (I): Relationship between Structure and Coloring

Maximal planar graph refers to the planar graph with the most edges, which means no more edges can be added so that the resulting graph is still planar. The Four-Color Conjecture says that every planar graph without loops is 4-colorable. Indeed, in order to prove Four-Color Conjecture, it clearly suffices to show that all maximal planar graphs are 4-colorable. Since this conjecture was proposed in 1852, no mathematical proofs have been invented up until now. Maybe the main reasons lie in the following three aspects in terms of maximal planar graphs: not clearing up the structures, not figuring out the coloring types, and not straightening out the relation between structure and coloring. For this, we will write a series of articles to study the structure and coloring theory of maximal planar graphs systematically. This is our first article, which focuses mainly on the structure and coloring relations. First, we introduce a new way to construct maximal planar graphs. The advantage of this method is that it establishes an immediate relation with 4-colorings, and reveals how a given maximal planar graph is generated. Second, a special class of maximal planar graphs--recursive maximal planar graphs is researched in depth, which lays a foundation for solving the uniquely 4-colorable planar graphs conjecture(see subsequent articles). Third, we discover an important mode for classifying 4-colorings: tree-coloring and cycle-coloring, which runs through the whole series of articles. Furthermore, this mode is applied to the research on an arbitrary 4-coloring and its corresponding structure of unions of two and three bicolored subgraphs. Finally, we introduce the concepts of black-white coloring and stamen phenomenon, and find out a necessary and sufficient condition for an even cycle to be a 2-colorable cycle.

math.GM↗