Determination of Dark Matter Halo Mass from Dynamics of Satellite Galaxies

We show that the mass of a dark matter halo can be inferred from the dynamical status of its satellite galaxies. Using 9 dark-matter simulations of halos like the Milky Way (MW), we find that the present-day substructures in each halo follow a characteristic distribution in the phase space of orbital binding energy and angular momentum, and that this distribution is similar from halo to halo but has an intrinsic dependence on the halo formation history. We construct this distribution directly from the simulations for a specific halo and extend the result to halos of similar formation history but different masses by scaling. The mass of an observed halo can then be estimated by maximizing the likelihood in comparing the measured kinematic parameters of its satellite galaxies with these distributions. We test the validity and accuracy of this method with mock samples taken from the simulations. Using the positions, radial velocities, and proper motions of 9 tracers and assuming observational uncertainties comparable to those of MW satellite galaxies, we find that the halo mass can be recovered to within $\sim$40%. The accuracy can be improved to within $\sim$25% if 30 tracers are used. However, the dependence of the phase-space distribution on the halo formation history sets a minimum uncertainty of $\sim$20% that cannot be reduced by using more tracers. We believe that this minimum uncertainty also applies to any mass determination for a halo when the phase space information of other kinematic tracers is used.Comment: Accepted for publication in ApJ, 18 pages, 13 figure

Sequential Recommendation with Diffusion Models

Generative models, such as Variational Auto-Encoder (VAE) and Generative Adversarial Network (GAN), have been successfully applied in sequential recommendation. These methods require sampling from probability distributions and adopt auxiliary loss functions to optimize the model, which can capture the uncertainty of user behaviors and alleviate exposure bias. However, existing generative models still suffer from the posterior collapse problem or the model collapse problem, thus limiting their applications in sequential recommendation. To tackle the challenges mentioned above, we leverage a new paradigm of the generative models, i.e., diffusion models, and present sequential recommendation with diffusion models (DiffRec), which can avoid the issues of VAE- and GAN-based models and show better performance. While diffusion models are originally proposed to process continuous image data, we design an additional transition in the forward process together with a transition in the reverse process to enable the processing of the discrete recommendation data. We also design a different noising strategy that only noises the target item instead of the whole sequence, which is more suitable for sequential recommendation. Based on the modified diffusion process, we derive the objective function of our framework using a simplification technique and design a denoise sequential recommender to fulfill the objective function. As the lengthened diffusion steps substantially increase the time complexity, we propose an efficient training strategy and an efficient inference strategy to reduce training and inference cost and improve recommendation diversity. Extensive experiment results on three public benchmark datasets verify the effectiveness of our approach and show that DiffRec outperforms the state-of-the-art sequential recommendation models

Identification of a potential novel biomarker in intervertebral disk degeneration by bioinformatics analysis and experimental validation

BackgroundIntervertebral disk degeneration (IVDD) is a major cause of low back pain and one of the most common health problems all over the world. However, the early diagnosis of IVDD is still restricted. The purpose of this study is to identify and validate the key characteristic gene of IVDD and analyze its correlation with immune cell infiltration.Methods3 IVDD-related gene expression profiles were downloaded from the Gene Expression Omnibus database to screen for differentially expressed genes (DEGs). Gene Ontology (GO) and gene set enrichment analysis (GSEA) were conducted to explore the biological functions. Two machine learning algorithms were used to identify characteristic genes, which were tested to further find the key characteristic gene. The receiver operating characteristic curve was performed to estimate the clinical diagnostic value of the key characteristic gene. The excised human intervertebral disks were obtained, and the normal nucleus pulposus (NP) and degenerative NP were carefully separated and cultured in vitro. The expression of the key characteristic gene was validated by real-time quantitative PCR (qRT-PCR). The related protein expression in NP cells was detected by Western blot. Finally, the correlation was investigated between the key characteristic gene and immune cell infiltration.ResultsA total of 5 DEGs, including 3 upregulated genes and 2 downregulated genes, were screened between IVDD and control samples. GO enrichment analysis showed that DEGs were enriched to 4 items in BP, 6 items in CC, and 13 items in MF. They mainly included the regulation of ion transmembrane transport, transporter complex, and channel activity. GSEA suggested that the cell cycle, DNA replication, graft versus host disease, and nucleotide excision repair were enriched in control samples, while complement and coagulation cascades, Fc γ R–mediated phagocytosis, neuroactive ligand–receptor interaction, the NOD-like receptor signaling pathway, gap junctions, etc., were enriched in IVDD samples. Furthermore, ZNF542P was identified and tested as key characteristic gene in IVDD samples through machine learning algorithms and showed a good diagnostic value. The results of qRT-PCR showed that compared with normal NP cells, the expression of ZNF542P gene was decreased in degenerated NP cells. The results of Western blot suggested that compared with normal NP cells, the expression of NLRP3 and pro Caspase-1 was increased in degenerated NP cells. Finally, we found that the expression of ZNF542P was positively related to the proportions of T cells gamma delta (γδT cells).ConclusionZNF542P is a potential biomarker in the early diagnosis of IVDD and may be associated with the NOD-like receptor signaling pathway and the infiltration of γδT cells

A Deterministic and Storable Single-Photon Source Based on Quantum Memory

A single photon source is realized with a cold atomic ensemble ($^{87}$Rb atoms). In the experiment, single photons, which is initially stored in an atomic quantum memory generated by Raman scattering of a laser pulse, can be emitted deterministically at a time-delay in control. It is shown that production rate of single photons can be enhanced by a feedback circuit considerably while the single-photon quality is conserved. Thus our present single-photon source is well suitable for future large-scale realization of quantum communication and linear optical quantum computation