Computing Persistent Homology by Spanning Trees and Critical Simplices.

Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the dataset, that is, establishing the integrated taxonomic relation among points, lines, and simplices.

Ranking cliques in higher-order complex networks.

Traditional network analysis focuses on the representation of complex systems with only pairwise interactions between nodes. However, the higher-order structure, which is beyond pairwise interactions, has a great influence on both network dynamics and function. Ranking cliques could help understand more emergent dynamical phenomena in large-scale complex networks with higher-order structures, regarding important issues, such as behavioral synchronization, dynamical evolution, and epidemic spreading.

[Effect of procalcitonin on lipopolysaccharide-induced expression of nucleotide-binding oligomerization domain-like receptor protein 3 and caspase-1 in human umbilical vein endothelial cells].

Objectives: To study the effect of procalcitonin (PCT) on lipopolysaccharide (LPS)-induced expression of the pyroptosis-related proteins nucleotide-binding oligomerization domain-like receptor protein 3 (NLRP3) and caspase-1 in human umbilical vein endothelial cells (HUVECs).

Methods: HUVECs were induced by LPS to establish a model of sepsis-induced inflammatory endothelial cell injury. The experiment was divided into two parts.

Totally homogeneous networks.

In network science, the non-homogeneity of node degrees has been a concerning issue for study. Yet, with today's modern web technologies, the traditional social communication topologies have evolved from node-central structures into online cycle-based communities, urgently requiring new network theories and tools. Switching the focus from node degrees to network cycles could reveal many interesting properties from the perspective of totally homogenous networks or sub-networks in a complex network, especially basic simplexes (cliques) such as links and triangles.

Multiplex congruence network of natural numbers.

Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers.

Markovian iterative method for degree distributions of growing networks.

Currently, simulation is usually used to estimate network degree distribution P(k) and to examine if a network model predicts a scale-free network when an analytical formula does not exist. An alternative Markovian chain-based numerical method was proposed by Shi [Phys. Rev.

Markov chain-based numerical method for degree distributions of growing networks.

In this paper, we establish a relation between growing networks and Markov chains, and propose a computational approach for network degree distributions. Using the Barabási-Albert model as an example, we first show that the degree evolution of a node in a growing network follows a nonhomogeneous Markov chain. Exploring the special structure of these Markov chains, we develop an efficient algorithm to compute the degree distribution numerically with a computation complexity of O (t(2)), where t is the number of time steps.

Multiple sequence alignment of the M protein in SARS-associated and other known coronaviruses.

In this paper, we report a multiple sequence alignment result on the basis of 10 amino acid sequences of the M protein, which come from different coronaviruses (4 SARS-associated and 6 others known). The alignment model was based on the profile HMM (Hidden Markov Model), and the model training was implemented through the SAHMM (Self-Adapting Hidden Markov Model) software developed by the authors.