How far are the sources of IceCube neutrinos? Constraints from the diffuse TeV gamma-ray background

The nearly isotropic distribution of the TeV-PeV neutrinos recently detected by IceCube suggests that they come from sources at distance beyond our Galaxy, but how far they are is largely unknown due to lack of any associations with known sources. In this paper, we propose that the cumulative TeV gamma-ray emission accompanying the production of neutrinos can be used to constrain the distance of these neutrino sources, since the opacity of TeV gamma rays due to absorption by the extragalactic background light (EBL) depends on the distance that these TeV gamma rays have travelled. As the diffuse extragalactic TeV background measured by \emph{Fermi} is much weaker than the expected cumulative flux associated with IceCube neutrinos, the majority of IceCube neutrinos, if their sources are transparent to TeV gamma rays, must come from distances larger than the horizon of TeV gamma rays. We find that above 80\% of the IceCube neutrinos should come from sources at redshift $z>0.5$. Thus, the chance for finding nearby sources correlated with IceCube neutrinos would be small. We also find that, to explain the flux of neutrinos under the TeV gamma-ray emission constraint, the redshift evolution of neutrino source density must be at least as fast as the the cosmic star-formation rate.Comment: Accepted by ApJ, some minor changes made, 8 pages, 5 figure

More on Rainbow Cliques in Edge-Colored Graphs

In an edge-colored graph $G$, a rainbow clique $K_k$ is a $k$-complete subgraph in which all the edges have distinct colors. Let $e(G)$ and $c(G)$ be the number of edges and colors in $G$, respectively. In this paper, we show that for any $\varepsilon>0$, if $e(G)+c(G) \geq (1+\frac{k-3}{k-2}+2\varepsilon) {n\choose 2}$ and $k\geq 3$, then for sufficiently large $n$, the number of rainbow cliques $K_k$ in $G$ is $\Omega(n^k)$. We also characterize the extremal graphs $G$ without a rainbow clique $K_k$, for $k=4,5$, when $e(G)+c(G)$ is maximum. Our results not only address existing questions but also complete the findings of Ehard and Mohr (Ehard and Mohr, Rainbow triangles and cliques in edge-colored graphs. {\it European Journal of Combinatorics, 84:103037,2020}).Comment: 16page

Short-Term Truckload Spot Rates\u27 Prediction in Consideration of Temporal and Between-Route Correlations

Truckload spot rate (TSR), defined as a price offered on the spot to transport a certain cargo by using an entire truck on a target transportation line, usually price per kilometer-ton, is a key factor in shaping the freight market. In particular, the prediction of short-term TSR is of great importance to the daily operations of the trucking industry. However, existing predictive practices have been limited largely by the availability of multilateral information, such as detailed intraday TSR information. Fortunately, the emerging online freight exchange (OFEX) platforms provide unique opportunities to access and fuse more data for probing the trucking industry. As such, this paper aims to leverage the high-resolution trucking data from an OFEX platform to forecast short-term TSR. Specifically, a lagged coefficient weighted matrix-based multiple linear regression modeling (Lag-WMR) is proposed, and exogenous variables are selected by the light gradient boosting (LGB) method. This model simultaneously incorporates the dependency between historical and current TSR (temporal correlation) and correlations between the rates on alternative routes (between-route correlation). In addition, the effects of incorporating temporal and between-route correlations, time-lagged correlation and exogenous variable selection in modeling are emphasized and assessed through a case study on short-term TSR in Southwest China. The comparative results show that the proposed Lag-WMR model outperforms autoregressive integrated moving average (ARIMA) model and LGB in terms of model fitting and the quality and stability of predictions. Further research could focus on rates\u27 standardization, to define a practical freight index for the trucking industry. Although our results are specific to the Chinese trucking market, the method of analysis serves as a general model for similar international studies

Hierarchical Contrastive Learning Enhanced Heterogeneous Graph Neural Network

Heterogeneous graph neural networks (HGNNs) as an emerging technique have shown superior capacity of dealing with heterogeneous information network (HIN). However, most HGNNs follow a semi-supervised learning manner, which notably limits their wide use in reality since labels are usually scarce in real applications. Recently, contrastive learning, a self-supervised method, becomes one of the most exciting learning paradigms and shows great potential when there are no labels. In this paper, we study the problem of self-supervised HGNNs and propose a novel co-contrastive learning mechanism for HGNNs, named HeCo. Different from traditional contrastive learning which only focuses on contrasting positive and negative samples, HeCo employs cross-view contrastive mechanism. Specifically, two views of a HIN (network schema and meta-path views) are proposed to learn node embeddings, so as to capture both of local and high-order structures simultaneously. Then the cross-view contrastive learning, as well as a view mask mechanism, is proposed, which is able to extract the positive and negative embeddings from two views. This enables the two views to collaboratively supervise each other and finally learn high-level node embeddings. Moreover, to further boost the performance of HeCo, two additional methods are designed to generate harder negative samples with high quality. Besides the invariant factors, view-specific factors complementally provide the diverse structure information between different nodes, which also should be contained into the final embeddings. Therefore, we need to further explore each view independently and propose a modified model, called HeCo++. Specifically, HeCo++ conducts hierarchical contrastive learning, including cross-view and intra-view contrasts, which aims to enhance the mining of respective structures.Comment: This paper has been accepted by TKDE as a regular paper. arXiv admin note: substantial text overlap with arXiv:2105.0911