The Existence of Hamilton Cycle in n-Balanced k-Partite Graphs

Let $G_{k,n}$ be the $n$-balanced $k$-partite graph, whose vertex set can be partitioned into $k$ parts, each has $n$ vertices. In this paper, we prove that if $k \geq 2,n \geq 1$, for the edge set $E(G)$ of $G_{k,n}$ $$|E(G)| \geq\left\{\begin{array}{cc} 1 & \text { if } k=2, n=1 n^{2} C_{k}^{2}-(k-1) n+2 & \text { other } \end{array}\right.$$ then $G_{k,n}$ is hamiltonian. And the result may be the best

TWO-STAGE MODEL SELECTION WITH PARAMETERS WEIGHTED HIDDEN MARKOV MODELS AND LIKELIHOOD RATIO FOR PART-OF-SPEECH TAGGING

Abstract: In many natural language processing applications two or more models usually have to be involved for accuracy. But it is difficult for minor models, such as "backoff" taggers in part-of-speech tagging, to cooperate smoothly with the major probabilistic model. We introduce a two-stage approach for model selection between hidden Markov models and other minor models. In the first stage, the major model is extended to give a set of candidates for model selection. Parameters weighted hidden Markov model is presented using weighted ratio to create the candidate set. In the second stage, heuristic rules and features are used as evaluation functions to give extra scores to candidates in the set. Such scores are calculated using a diagnostic likelihood ratio test based on sensitivity and specificity criteria. The selection procedure can be fulfilled using swarm optimization technique. Experiment results on public tagging data sets show the applicability of the proposed approach

Graph Condensation for Graph Neural Networks

Given the prevalence of large-scale graphs in real-world applications, the storage and time for training neural models have raised increasing concerns. To alleviate the concerns, we propose and study the problem of graph condensation for graph neural networks (GNNs). Specifically, we aim to condense the large, original graph into a small, synthetic and highly-informative graph, such that GNNs trained on the small graph and large graph have comparable performance. We approach the condensation problem by imitating the GNN training trajectory on the original graph through the optimization of a gradient matching loss and design a strategy to condense node futures and structural information simultaneously. Extensive experiments have demonstrated the effectiveness of the proposed framework in condensing different graph datasets into informative smaller graphs. In particular, we are able to approximate the original test accuracy by 95.3% on Reddit, 99.8% on Flickr and 99.0% on Citeseer, while reducing their graph size by more than 99.9%, and the condensed graphs can be used to train various GNN architectures.Comment: 16 pages, 4 figure

Comparative genomics of five Valsa species gives insights on their pathogenicity evolution

Valsa is a genus of ascomycetes within the Valsaceae family. This family includes many wood destructive pathogens such as the well known Valsa mali and Valsa pyri which cause canker diseases in fruit trees and threaten the global fruit production. Lack of genomic information of this family is impeding our understandings about their evolution and genetic basis of their pathogenicity divergence. Here, we report genome assemblies of Valsa malicola, Valsa persoonii, and Valsa sordida which represent close relatives of Valsa mali and Valsa pyri with different host preferences. Comparative genomics analysis revealed that segmental rearrangements, inversions, and translocations frequently occurred among Valsa spp. genomes. Gene families that exhibited gene copy expansions tended to be associated with secondary metabolism, transmembrane transport, and pyrophosphatase activities. Orthologous genes in regions lost synteny exhibited significantly higher rate of synonymous substitution (KS) than those in regions retained synteny. Moreover, among these genes, membrane transporter families associated with antidrug (MFS, DHA) activities and nutrient transportation (SP and APCs) activities were significantly over-represented. Lineage specific synonymous substitution (KS) and nonsynonymous substitution (KA) analysis based on the phylogeny constructed from 11 fungal species identified a set of genes with selection signatures in Valsa clade and these genes were significantly enriched in functions associated with fatty acid beta-oxidation, DNA helicase activity, and ATPase activity. Furthermore, unique genes that possessed or retained by each of the five Valsa species are more likely part of the secondary metabolic (SM) gene clusters. SM gene clusters conserved across five Valsa species showed various degrees of diversification in both identity and completeness. All 11 syntenically conserved SM clusters showed differential expression during the infection of apple branch with Valsa mali suggesting involvements of secondary metabolism in the pathogenicity of Valsa species

Linkless Link Prediction via Relational Distillation

Graph Neural Networks (GNNs) have shown exceptional performance in the task of link prediction. Despite their effectiveness, the high latency brought by non-trivial neighborhood data dependency limits GNNs in practical deployments. Conversely, the known efficient MLPs are much less effective than GNNs due to the lack of relational knowledge. In this work, to combine the advantages of GNNs and MLPs, we start with exploring direct knowledge distillation (KD) methods for link prediction, i.e., predicted logit-based matching and node representation-based matching. Upon observing direct KD analogs do not perform well for link prediction, we propose a relational KD framework, Linkless Link Prediction (LLP), to distill knowledge for link prediction with MLPs. Unlike simple KD methods that match independent link logits or node representations, LLP distills relational knowledge that is centered around each (anchor) node to the student MLP. Specifically, we propose rank-based matching and distribution-based matching strategies that complement each other. Extensive experiments demonstrate that LLP boosts the link prediction performance of MLPs with significant margins, and even outperforms the teacher GNNs on 7 out of 8 benchmarks. LLP also achieves a 70.68x speedup in link prediction inference compared to GNNs on the large-scale OGB dataset

Mechanisms underlying the beneficial effects of physical exercise on multiple sclerosis: focus on immune cells

Multiple sclerosis (MS) is a prevalent neuroimmunological illness that leads to neurological disability in young adults. Although the etiology of MS is heterogeneous, it is well established that aberrant activity of adaptive and innate immune cells plays a crucial role in its pathogenesis. Several immune cell abnormalities have been described in MS and its animal models, including T lymphocytes, B lymphocytes, dendritic cells, neutrophils, microglia/macrophages, and astrocytes, among others. Physical exercise offers a valuable alternative or adjunctive disease-modifying therapy for MS. A growing body of evidence indicates that exercise may reduce the autoimmune responses triggered by immune cells in MS. This is partially accomplished by restricting the infiltration of peripheral immune cells into the central nervous system (CNS) parenchyma, curbing hyperactivation of immune cells, and facilitating a transition in the balance of immune cells from a pro-inflammatory to an anti-inflammatory state. This review provides a succinct overview of the correlation between physical exercise, immune cells, and MS pathology, and highlights the potential benefits of exercise as a strategy for the prevention and treatment of MS

Deep interest shifting network with meta embeddings for fresh item recommendation

Nowadays, people have an increasing interest in fresh products such as new shoes and cosmetics. To this end, an E-commerce platform Taobao launched a fresh-item hub page on the recommender system, with which customers can freely and exclusively explore and purchase fresh items, namely, the New Tendency page. In this work, we make a first attempt to tackle the fresh-item recommendation task with two major challenges. First, a fresh-item recommendation scenario usually faces the challenge that the training data are highly deficient due to low page views. In this paper, we propose a deep interest-shifting network (DisNet), which transfers knowledge from a huge number of auxiliary data and then shifts user interests with contextual information. Furthermore, three interpretable interest-shifting operators are introduced. Second, since the items are fresh, many of them have never been exposed to users, leading to a severe cold-start problem. Though this problem can be alleviated by knowledge transfer, we further babysit these fully cold-start items by a relational meta-Id-embedding generator (RM-IdEG). Specifically, it trains the item id embeddings in a learning-to-learn manner and integrates relational information for better embedding performance. We conducted comprehensive experiments on both synthetic datasets as well as a real-world dataset. Both DisNet and RM-IdEG significantly outperform state-of-the-art approaches, respectively. Empirical results clearly verify the effectiveness of the proposed techniques, which are arguably promising and scalable in real-world applications

A Role for a Dioxygenase in Auxin Metabolism and Reproductive Development in Rice

SummaryIndole-3-acetic acid (IAA), the natural auxin in plants, regulates many aspects of plant growth and development. Extensive analyses have elucidated the components of auxin biosynthesis, transport, and signaling, but the physiological roles and molecular mechanisms of auxin degradation remain elusive. Here, we demonstrate that the dioxygenase for auxin oxidation (DAO) gene, encoding a putative 2-oxoglutarate-dependent-Fe (II) dioxygenase, is essential for anther dehiscence, pollen fertility, and seed initiation in rice. Rice mutant lines lacking a functional DAO display increased levels of free IAA in anthers and ovaries. Furthermore, exogenous application of IAA or overexpression of the auxin biosynthesis gene OsYUCCA1 phenocopies the dao mutants. We show that recombinant DAO converts the active IAA into biologically inactive 2-oxoindole-3-acetic acid (OxIAA) in vitro. Collectively, these data support a key role of DAO in auxin catabolism and maintenance of auxin homeostasis central to plant reproductive development

Climate change : strategies for mitigation and adaptation

The sustainability of life on Earth is under increasing threat due to humaninduced climate change. This perilous change in the Earth's climate is caused by increases in carbon dioxide and other greenhouse gases in the atmosphere, primarily due to emissions associated with burning fossil fuels. Over the next two to three decades, the effects of climate change, such as heatwaves, wildfires, droughts, storms, and floods, are expected to worsen, posing greater risks to human health and global stability. These trends call for the implementation of mitigation and adaptation strategies. Pollution and environmental degradation exacerbate existing problems and make people and nature more susceptible to the effects of climate change. In this review, we examine the current state of global climate change from different perspectives. We summarize evidence of climate change in Earth’s spheres, discuss emission pathways and drivers of climate change, and analyze the impact of climate change on environmental and human health. We also explore strategies for climate change mitigation and adaptation and highlight key challenges for reversing and adapting to global climate change