Competitive and Weighted Evolving Simplicial Complexes

A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. This paper first proposes a competitive evolving model of higher-order networks. We notice the batch effect of low-dim simplices during the growth of such a network. We obtain an analytical expression for the distribution of higher-order degrees by employing the theory of Poisson processes and the mean field method and use computers to simulate higher-order networks of competitions. The established results indicate that the scale-free behavior for the (d-1)-dim simplex with respect to the d-order degree is controlled by the competitiveness factor. As the competitiveness increases, the d-order degree of the (d-1)-dim simplex is bent under the logarithmic coordinates. Second, by considering the weight changes of the neighboring simplices, as triggered by the selected simplex, a new weighted evolving model in higher-order networks is proposed. The results of the competitive evolving model of higher-order networks are used to analyze the weighted evolving model so that obtained are the analytical expressions of the higher-order degree distribution and higher-order strength density function of weighted higher-order networks. The outcomes of the simulation experiments are consistent with the theoretical analysis. Therefore, the weighted network belongs to the collection of competition networks

Haplotype association analysis of North American Rheumatoid Arthritis Consortium data using a generalized linear model with regularization

The Genetic Analysis Workshop 16 rheumatoid arthritis data include a set of 868 cases and 1194 controls genotyped at 545,080 single-nucleotide polymorphisms (SNPs) from the Illumina 550 k chip. We focus on investigating chromosomes 6 and 18, which have 35,574 and 16,450 SNPs, respectively. Association studies, including single SNP and haplotype-based analyses, were applied to the data on those two chromosomes. Specifically, we conducted a generalized linear model with regularization (rGLM) approach for detecting disease-haplotype association using unphased SNP data. A total of 444 and 43 four-SNP tests were found to be significant at the Bonferroni corrected 5% significance level on chromosome 6 and 18, respectively

Comparing hierarchical black hole mergers in star clusters and active galactic nuclei

Star clusters (SCs) and active galactic nuclei (AGNs) are promising sites for the occurrence of hierarchical black hole (BH) mergers. We use simple models to compare hierarchical BH mergers in two of the dynamical formation channels. We find that the primary mass distribution of hierarchical mergers in AGNs is higher than that in SCs, with the peaks of $\sim$$50\,M_{\odot}$ and $\sim$$13\,M_{\odot}$, respectively. The effective spin ($\chi_{\rm eff}$) distribution of hierarchical mergers in SCs is symmetrical around zero as expected and $\sim$$50\%$ of the mergers have $|\chi_{\rm eff}|>0.2$. The distribution of $\chi_{\rm eff}$ in AGNs is narrow and prefers positive values with the peak of $\chi_{\rm eff}\ge0.3$ due to the assistance of AGN disks. BH hierarchical growth efficiency in AGNs, with at least $\sim$$30\%$ of mergers being hierarchies, is much higher than the efficiency in SCs. Furthermore, there are obvious differences in the mass ratios and effective precession parameters of hierarchical mergers in SCs and AGNs. We argue that the majority of the hierarchical merger candidates detected by LIGO-Virgo may originate from the AGN channel as long as AGNs get half of the hierarchical merger rate.Comment: 12 pages, 5 figures, 2 tables, accepted for publication in PHYS. REV. D; v2. add Figs. 4 and 5, showing mass-ratios and effective precession parameters, respectively; v3. delete an additional free parameter (maximum generation, $N_{\rm max}^{\rm G}$), replot Fig. 3 using the mergers detected by LIGO-Virgo, and add Yong Yuan as the third author of this manuscript; v4. add more details for SN

Large Magnetoresistance over an Extended Temperature Regime in Monophosphides of Tantalum and Niobium

We report extremely large magnetoresistance (MR) in an extended temperature regime from 1.5 K to 300 K in non-magnetic binary compounds TaP and NbP. TaP exhibits linear MR around $1.8\times 10^4$ at 2 K in a magnetic field of 9 Tesla, which further follows its linearity up to $1.4\times 10^5$ in a magnetic field of 56 Tesla at 1.5 K. At room temperature the MR for TaP and NbP follows a power law of the exponent about $1.5$ with the values larger than $300\%$ in a magnetic field of 9 Tesla. Such large MR in a wide temperature regime is not likely only due to a resonance of the electron-hole balance, but indicates a complicated mechanism underneath.Comment: 13 pages, 4 figures; submitted in May 20, 2015; accepted for publicatio

The single parton fragmentation functions of heavy quarkonium in soft gluon factorization

We study the single parton fragmentation functions (FFs) at the input factorization scale $\mu_0\gtrsim 2m_Q$, with heavy quark mass $m_Q$, in the soft gluon factorization (SGF) approach. We express the FFs in terms of perturbatively calculable short distance hard parts for producing a heavy quark-antiquark pair in all possible states, convoluted with corresponding soft gluon distribution for the hadronization of the pair to a heavy quarkonium. We compute the perturbative short distance hard parts for producing a heavy quark pair in all possible $S$-wave and $P$-wave states up to $O(\alpha_s^2)$. With our results, the SGF can be further used to study the heavy quarkonium production at the hadron colliders and heavy quarkonium production within a jet.Comment: 19 pages, 0 figures. arXiv admin note: text overlap with arXiv:2304.0455

RBA-GCN: Relational Bilevel Aggregation Graph Convolutional Network for Emotion Recognition

Emotion recognition in conversation (ERC) has received increasing attention from researchers due to its wide range of applications. As conversation has a natural graph structure, numerous approaches used to model ERC based on graph convolutional networks (GCNs) have yielded significant results. However, the aggregation approach of traditional GCNs suffers from the node information redundancy problem, leading to node discriminant information loss. Additionally, single-layer GCNs lack the capacity to capture long-range contextual information from the graph. Furthermore, the majority of approaches are based on textual modality or stitching together different modalities, resulting in a weak ability to capture interactions between modalities. To address these problems, we present the relational bilevel aggregation graph convolutional network (RBA-GCN), which consists of three modules: the graph generation module (GGM), similarity-based cluster building module (SCBM) and bilevel aggregation module (BiAM). First, GGM constructs a novel graph to reduce the redundancy of target node information. Then, SCBM calculates the node similarity in the target node and its structural neighborhood, where noisy information with low similarity is filtered out to preserve the discriminant information of the node. Meanwhile, BiAM is a novel aggregation method that can preserve the information of nodes during the aggregation process. This module can construct the interaction between different modalities and capture long-range contextual information based on similarity clusters. On both the IEMOCAP and MELD datasets, the weighted average F1 score of RBA-GCN has a 2.17$\sim$5.21\% improvement over that of the most advanced method