arXiv subjects

Bing Yao

Publications and source records attributed to Bing Yao.

At least 37 records · Page 2Linked to original sources

arXiv2022

Topological Authentication Technique In Topologically Asymmetric Cryptosystem

Making topological authentication from theory to practical application is an important and challenging task. More and more researchers pay attention on coming quantum computation, privacy data protection, lattices and cryptography. Research show the advantages of topological authentications through graph operations, various matrices, graph colorings and graph labelings are: related with two or more different mathematical areas, be not pictures, there are huge number of colorings and labelings, rooted on modern mathematics, diversity of asymmetric ciphers, simplicity and convenience, easily created, irreversibility, computational security, provable security, and so on. Topological authentications based on various graph homomorphisms, degree-sequence homomorphisms, graph-set homomorphisms. Randomly topological coding and topological authentications are based on Hanzi authentication, randomly adding-edge-removing operation, randomly leaf-adding algorithms, graph random increasing techniques, operation graphic lattice and dynamic networked models and their spanning trees and maximum leaf spanning trees. Realization of topological authentication is an important topic, we study: number-based strings generated from colored graphs, particular graphs (complete graphs, trees, planar graphs), some methods of generating public-keys. some techniques of topologically asymmetric cryptosystem are: W-type matching labelings, dual-type labelings, reciprocal-type labelings, topological homomorphisms, indexed colorings, graphic lattices, degree-sequence lattices, every-zero Cds-matrix groups of degree-sequences, every-zero graphic groups, graphic lattices having coloring closure property, self-similar networked lattices.

cs.CR↗

arXiv2022

Physics-constrained Deep Learning for Robust Inverse ECG Modeling

The rapid developments in advanced sensing and imaging bring about a data-rich environment, facilitating the effective modeling, monitoring, and control of complex systems. For example, the body-sensor network captures multi-channel information pertinent to the electrical activity of the heart (i.e., electrocardiograms (ECG)), which enables medical scientists to monitor and detect abnormal cardiac conditions. However, the high-dimensional sensing data are generally complexly structured and realizing the full data potential depends to a great extent on advanced analytical and predictive methods. This paper presents a physics-constrained deep learning (P-DL) framework for high-dimensional inverse ECG modeling. This method integrates the physical laws of the complex system with the advanced deep learning infrastructure for effective prediction of the system dynamics. The proposed P-DL approach is implemented to solve the inverse ECG model and predict the time-varying distribution of electric potentials in the heart from the ECG data measured by the body-surface sensor network. Experimental results show that the proposed P-DL method significantly outperforms existing methods that are commonly used in current practice.

cs.LG↗

arXiv2022

An extension on neighbor sum distinguishing total coloring of graphs

Let $f: V(G)\cup E(G)\rightarrow \{1,2,\dots,k\}$ be a non-proper total $k$-coloring of $G$. Define a weight function on total coloring as $$ϕ(x)=f(x)+\sum\limits_{e\ni x}f(e)+\sum\limits_{y\in N(x)}f(y),$$ where $N(x)=\{y\in V(G)|xy\in E(G)\}$. If $ϕ(x)\neq ϕ(y)$ for any edge $xy\in E(G)$, then $f$ is called a neighbor full sum distinguishing total $k$-coloring of $G$. The smallest value $k$ for which $G$ has such a coloring is called the neighbor full sum distinguishing total chromatic number of $G$ and denoted by fgndi$_{\sum}(G)$. The coloring is an extension of neighbor sum distinguishing non-proper total coloring. In this paper we conjecture that fgndi$_{\sum}(G)\leq 3$ for any connected graph $G$ of order at least three. We prove that the conjecture is true for (i) paths and cycles; (ii) 3-regular graphs and (iii) stars, complete graphs, trees, hypercubes, bipartite graphs and complete $r$-partite graphs. In particular, complete graphs can achieve the upper bound for the above conjecture.

math.CO↗

arXiv2021

A note on 1-2-3 and 1-2 Conjectures for 3-regular graphs

The 1-2-3 Conjecture, posed by Karoński, Łuczak and Thomason, asked whether every connected graph $G$ different from $K_2$ can be 3-edge-weighted so that every two adjacent vertices of $G$ get distinct sums of incident weights. The 1-2 Conjecture states that if vertices also receive colors and the vertex color is added to the sum of its incident edges, then adjacent vertices can be distinguished using only $\{ 1,2\}$. In this paper we confirm 1-2 Conjecture for 3-regular graphs. Meanwhile, we show that every 3-regular graph can achieve a neighbor sum distinguishing edge coloring by using 4 colors, which answers 1-2-3 Conjecture positively.

math.CO↗

arXiv2021

Recent Colorings And Labelings In Topological Coding

Topological Coding consists of two different kinds of mathematics: topological structure and mathematical relation. The colorings and labelings of graph theory are main techniques in topological coding applied in asymmetric encryption system. Topsnut-gpws (also, colored graphs) have the following advantages: (1) Run fast in communication networks because they are saved in computer by popular matrices rather than pictures. (2) Produce easily text-based (number-based) strings for encrypt files. (3) Diversity of asymmetric ciphers, one public-key corresponds to more private-keys, or more public-keys correspond more private-keys. (4) Irreversibility, Topsnut-gpws can generate quickly text-based (number-based) strings with bytes as long as desired, but these strings can not reconstruct the original Topsnut-gpws. (5) Computational security, since there are many non-polynomial (NP-complete, NP-hard) algorithms in creating Topsnut-gpws. (6) Provable security, since there are many mathematical conjectures (open problems) in graph labelings and graph colorings. We are committed to create more kinds of new Topsnut-gpws to approximate practical applications and antiquantum computation, and try to use algebraic method and Topsnut-gpws to establish graphic group, graphic lattice, graph homomorphism etc.

cs.IT↗

arXiv2020

Two Cumulative Distributions For Scale-freeness of Dynamic Networks

It is well-known that the scale-free networks are ubiquitous in nature and society and have been one of the hotspot topic in complex networks. Recently, scholars presented a large quantity of scale-free networks by calculating cumulative distribution. The purpose of this paper is to discuss the relationship between two cumulative distributions, namely, cumulative distribution, edge-cumulative distribution. Here, firstly, we introduce a relationship between degree distribution and cumulative distribution. Secondly, we introduce the definition of cumulative distribution and edge-cumulative distribution, and compare the relationship between them. Thirdly, we apply algorithmic techniques to construct three deterministic networks, calculate their cumulative distribution and edge-cumulative distribution, and analyze the relationship between cumulative distribution and edge-cumulative distribution. Finally, we offer some open problems for future research in order to understand the interplay between the degree distribution, cumulative distribution and edge-cumulative distribution.

cs.SI↗

arXiv2020

Graphic Lattices and Matrix Lattices Of Topological Coding

Lattice-based Cryptography is considered to have the characteristics of classical computers and quantum attack resistance. We will design various graphic lattices and matrix lattices based on knowledge of graph theory and topological coding, since many problems of graph theory can be expressed or illustrated by (colored) star-graphic lattices. A new pair of the leaf-splitting operation and the leaf-coinciding operation will be introduced, and we combine graph colorings and graph labellings to design particular proper total colorings as tools to build up various graphic lattices, graph homomorphism lattice, graphic group lattices and Topcode-matrix lattices. Graphic group lattices and (directed) Topcode-matrix lattices enable us to build up connections between traditional lattices and graphic lattices. We present mathematical problems encountered in researching graphic lattices, some problems are: Tree topological authentication, Decompose graphs into Hanzi-graphs, Number String Decomposition Problem, $(p,s)$-gracefully total numbers.

cs.IT↗

arXiv2020

Ice-Flower Systems And Star-graphic Lattices

Lattice theory has been believed to resist classical computers and quantum computers. Since there are connections between traditional lattices and graphic lattices, it is meaningful to research graphic lattices. We define the so-called ice-flower systems by our uncolored or colored leaf-splitting and leaf-coinciding operations. These ice-flower systems enable us to construct several star-graphic lattices. We use our star-graphic lattices to express some well-known results of graph theory and compute the number of elements of a particular star-graphic lattice. For more researching ice-flower systems and star-graphic lattices we propose Decomposition Number String Problem, finding strongly colored uniform ice-flower systems and connecting our star-graphic lattices with traditional lattices.

math.CO↗

arXiv2020

Graph Homomorphisms Based On Particular Total Colorings of Graphs and Graphic Lattices

Lattice-based cryptography is not only for thwarting future quantum computers, and is also the basis of Fully Homomorphic Encryption. Motivated from the advantage of graph homomorphisms we combine graph homomorphisms with graph total colorings together for designing new types of graph homomorphisms: totally-colored graph homomorphisms, graphic-lattice homomorphisms from sets to sets, every-zero graphic group homomorphisms from sets to sets. Our graph-homomorphism lattices are made up by graph homomorphisms. These new homomorphisms induce some problems of graph theory, for example, Number String Decomposition and Graph Homomorphism Problem.

math.CO↗

arXiv2019

An extremal problem: How small scale-free graph can be

The bloom of complex network study, in particular, with respect to scale-free ones, is considerably triggering the research of scale-free graph itself. Therefore, a great number of interesting results have been reported in the past, including bounds of diameter. In this paper, we focus mainly on a problem of how to analytically estimate the lower bound of diameter of scale-free graph, i.e., how small scale-free graph can be. Unlike some pre-existing methods for determining the lower bound of diameter, we make use of a constructive manner in which one candidate model $\mathcal{G^*} (\mathcal{V^*}, \mathcal{E^*})$ with ultra-small diameter can be generated. In addition, with a rigorous proof, we certainly demonstrate that the diameter of graph $\mathcal{G^{*}}(\mathcal{V^{*}},\mathcal{E^{*}})$ must be the smallest in comparison with that of any scale-free graph. This should be regarded as the tight lower bound.

math.CO↗

arXiv2019

Random walks on Fibonacci treelike models: emergence of power law

In this paper, we propose a class of growth models, named Fibonacci trees $F(t)$, with respect to the intrinsic advantage of Fibonacci sequence $\{F_{t}\}$. First, we turn out model $F(t)$ to have power-law degree distribution with exponent $γ$ greater than $3$. And then, we study analytically two significant indices correlated to random walks on networks, namely, both the optimal mean first-passage time ($OMFPT$) and the mean first-passage time ($MFPT$). We obtain a closed-form expression of $OMFPT$ using algorithm 1. Meanwhile, algorithm 2 and algorithm 3 are introduced, respectively, to capture a valid solution to $MFPT$. We demonstrate that our algorithms are able to be widely applied to many network models with self-similar structure to derive desired solution to $OMFPT$ or $MFPT$. Especially, we capture a nontrivial result that the $MFPT$ reported by algorithm 3 is no longer correlated linearly with the order of model $F(t)$.

physics.soc-ph↗

arXiv2019

Topological Graphic Passwords And Their Matchings Towards Cryptography

Graphical passwords (GPWs) are convenient for mobile equipments with touch screen. Topological graphic passwords (Topsnut-gpws) can be saved in computer by classical matrices and run quickly than the existing GPWs. We research Topsnut-gpws by the matching of view, since they have many advantages. We discuss: configuration matching partition, coloring/labelling matching partition, set matching partition, matching chain, etc. And, we introduce new graph labellings for enriching Topsnut-matchings and show that these labellings can be realized for trees or spanning trees of networks. In theoretical works we explore Graph Labelling Analysis, and show that every graph admits our extremal labellings and set-type labellings in graph theory. Many of the graph labellings mentioned are related with problems of set matching partitions to number theory, and yield new objects and new problems to graph theory.

cs.CR↗

arXiv2019

Topological Coding and Topological Matrices Toward Network Overall Security

A mathematical topology with matrix is a natural representation of a coding relational structure that is found in many fields of the world. Matrices are very important in computation of real applications, s ce matrices are easy saved in computer and run quickly, as well as matrices are convenient to deal with communities of current networks, such as Laplacian matrices, adjacent matrices in graph theory. Motivated from convenient, useful and powerful matrices used in computation and investigation of today's networks, we have introduced Topcode-matrices, which are matrices of order $3\times q$ and differ from popular matrices applied in linear algebra and computer science. Topcode-matrices can use numbers, letters, Chinese characters, sets, graphs, algebraic groups \emph{etc.} as their elements. One important thing is that Topcode-matrices of numbers can derive easily number strings, since number strings are text-based passwords used in information security. Topcode-matrices can be used to describe topological graphic passwords (Topsnut-gpws) used in information security and graph connected properties for solving some problems coming in the investigation of Graph Networks and Graph Neural Networks proposed by GoogleBrain and DeepMind. Our topics, in this article, are: Topsnut-matrices, Topcode-matrices, Hanzi-matrices, adjacency ve-value matrices and pan-Topcode-matrices, and some connections between these Topcode-matrices will be proven. We will discuss algebraic groups obtained from the above matrices, graph groups, graph networking groups and number string groups for encrypting different communities of dynamic networks. The operations and results on our matrices help us to set up our overall security mechanism to protect networks.

cs.IT↗

arXiv2019

Using Chinese Characters To Generate Text-Based Passwords For Information Security

Graphical passwords (GPWs) are in many areas of the current world. Topological graphic passwords (Topsnut-gpws) are a new type of cryptography, and they differ from the existing GPWs. A Topsnut-gpw consists of two parts: one is a topological structure (graph), and one is a set of discrete elements (a graph labelling, or coloring), the topological structure connects these discrete elements together to form an interesting "story". Our idea is to transform Chinese characters into computer and electronic equipments with touch screen by speaking, writing and keyboard for forming Hanzi-graphs and Hanzi-gpws. We will use Hanzigpws to produce text-based passwords (TB-paws). We will introduce flawed graph labellings on disconnected Hanzi-graphs.

cs.IT↗

arXiv2019

Handshake between Fibonacci series and pure preferential attachment mechanism on a graph-model

In order to better understand dynamical functions on amounts of natural and man-made complex systems, lots of researchers from a wide range of disciplines, covering statistic physics, mathematics, theoretical computer science, and so on, have spent much time in doing this intriguing study. In this paper, the discussed popularly topic, how to construct reasonable graph-model and then to explain many features of realistic networks using previously presented theoretical models, is still our main work. Compared with many pre-existing deterministic graph-model in single evolution way, our new graph-model can be constructed using three types of growth ways to meet preferential attachment mechanism. Meanwhile several typical indices associated with network research will be reported. In addition, some interesting findings will be shown, including the first handshake between Fibonacci series and "pure" preferential attachment mechanism, an obvious relationship connecting two well-known rules, power-law and Zipf-law, and a common but useful equation on the basis of both spanning trees number and the number of spanning trees with maximum leaves. Based on these foregoing discussions, we can demonstrate that our graph-model obeys power-law and small-world property. For the future research directions, we present some unknown problems to be studied at the end of this paper.

cs.SI↗

arXiv2018

Text-based Passwords Generated From Topological Graphic Passwords

Topological graphic passwords (Topsnut-gpws) are one of graph-type passwords, but differ from the existing graphical passwords, since Topsnut-gpws are saved in computer by algebraic matrices. We focus on the transformation between text-based passwords (TB-paws) and Topsnut-gpws in this article. Several methods for generating TB-paws from Topsnut-gpws are introduced; these methods are based on topological structures and graph coloring/labellings, such that authentications must have two steps: one is topological structure authentication, and another is text-based authentication. Four basic topological structure authentications are introduced and many text-based authentications follow Topsnut-gpws. Our methods are based on algebraic, number theory and graph theory, many of them can be transformed into polynomial algorithms. A new type of matrices for describing Topsnut-gpws is created here, and such matrices can produce TB-paws in complex forms and longer bytes. Estimating the space of TB-paws made by Topsnut-gpws is very important for application. We propose to encrypt dynamic networks and try to face: (1) thousands of nodes and links of dynamic networks; (2) large numbers of Topsnut-gpws generated by machines rather than human's hands. As a try, we apply spanning trees of dynamic networks and graphic groups (Topsnut-groups) to approximate the solutions of these two problems. We present some unknown problems in the end of the article for further research.

cs.IT↗

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↗

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↗