Some formulas for determinants of tridiagonal matrices in terms of finite generalized continued fractions: Formulas for determinants of tridiagonal matrices

In the paper, by virtue of induction and properties of determinants, the authors discover explicit and recurrent formulas of evaluations for determinants of general tridiagonal matrices in terms of finite generalized continued fractions and apply these formulas to evaluations for determinants of the Sylvester matrix and two Sylvester type matrices.In the paper, by virtue of induction and properties of determinants, the authors discover explicit and recurrent formulas of evaluations for determinants of general tridiagonal matrices in terms of finite generalized continued fractions and apply these formulas to evaluations for determinants of the Sylvester matrix and two Sylvester type matrices

Integrable Open Spin Chains from Flavored ABJM Theory

We compute the two-loop anomalous dimension matrix in the scalar sector of planar ${\cal N}=3$ flavored ABJM theory. Using coordinate Bethe ansatz, we obtain the reflection matrix and confirm that the boundary Yang-Baxter equations are satisfied. This establishes the integrability of this theory in the scalar sector at the two-loop order.Comment: v2, 25 pages, 2 figures, minor corrections, references adde

Testing the light scalar meson as a non-qqˉq\bar q state in semileptonic DD decays

To distinguish between the normal $q\bar q$ and exotic diquark-antidiqark ($q^2\bar q^2$) contents of the lowest-lying scalar meson ($S_0$), we investigate the semileptonic $D\to S_0 e^+\nu_e, S_0\to M_1 M_2$ decays, where $M_{1(2)}$ represents a pseudoscalar meson. With the form factors extracted from the current data, we calculate ${\cal B}(D_s^+\to \sigma_0 e^+\nu_e,\sigma_0\to\pi^0\pi^0) =(12.9^{+6.3}_{-4.9})\times 10^{-4}$ and $(0.8^{+1.2}_{-0.7})\times 10^{-4}$ for the $q\bar q$ and $q^2\bar q^2$ quark structures, respectively, and compare them to the experimental upper limit: $6.4\times 10^{-4}$. It is clearly seen that $S_0$ prefers to be the $q^2\bar q^2$ bound state. Particularly, ${\cal B}_{q\bar q}(D_s^+\to \sigma_0 e^+\nu_e,\sigma_0\to\pi^+\pi^-) =(25.8^{+12.5}_{-\;\,9.8})\times 10^{-4}$ and ${\cal B}_{q^2\bar q^2}(D_s^+\to \sigma_0 e^+\nu_e,\sigma_0\to\pi^+\pi^-) =(1.5^{+2.4}_{-1.3})\times 10^{-4}$ are predicted to deviate far from each other, useful for a clear experimental investigation.Comment: 10 pages, 1 figure, 1 tabl

Novel biomarkers of inflammation-associated immunity in cervical cancer

BackgroundCervical cancer (CC) is a highly malignant gynecological cancer with a direct causal link to inflammation, primarily resulting from persistent high-risk human papillomavirus (HPV) infection. Given the challenges in early detection and mid to late-stage treatment, our research aims to identify inflammation-associated immune biomarkers in CC.MethodsUsing a bioinformatics approach combined with experimental validation, we integrated two CC datasets (GSE39001 and GSE63514) in the Gene Expression Omnibus (GEO) to eliminate batch effects. Immune-related inflammation differentially expressed genes (DGEs) were obtained by R language identification.ResultsThis analysis identified 37 inflammation-related DEGs. Subsequently, we discussed the different levels of immune infiltration between CC cases and controls. Weighted gene co-expression network analysis (WGCNA) identified seven immune infiltration-related modules in CC. We identified 15 immune DEGs associated with inflammation at the intersection of these findings. In addition, we constructed a protein interaction network using the String database and screened five hub genes using "CytoHubba": CXC chemokine ligand 8 (CXCL8), CXC chemokine ligand 10 (CXCL10), CX3C chemokine receptor 1 (CX3CR1), Fc gamma receptors 3B (FCGR3B), and SELL. The expression of these five genes in CC was determined by PCR experiments. In addition, we assessed their diagnostic value and further analyzed the association of immune cells with them.ConclusionsFive inflammation- and immune-related genes were identified, aiming to provide new directions for early diagnosis and mid to late-stage treatment of CC from multiple perspectives

Repetitive transcranial magnetic stimulation regulates neuroinflammation in neuropathic pain

Neuropathic pain (NP) is a frequent condition caused by a lesion in, or disease of, the central or peripheral somatosensory nervous system and is associated with excessive inflammation in the central and peripheral nervous systems. Repetitive transcranial magnetic stimulation (rTMS) is a supplementary treatment for NP. In clinical research, rTMS of 5–10 Hz is widely placed in the primary motor cortex (M1) area, mostly at 80%–90% RMT, and 5–10 treatment sessions could produce an optimal analgesic effect. The degree of pain relief increases greatly when stimulation duration is greater than 10 days. Analgesia induced by rTMS appears to be related to reestablishing the neuroinflammation system. This article discussed the influences of rTMS on the nervous system inflammatory responses, including the brain, spinal cord, dorsal root ganglia (DRG), and peripheral nerve involved in the maintenance and exacerbation of NP. rTMS has shown an anti-inflammation effect by decreasing pro-inflammatory cytokines, including IL-1β, IL-6, and TNF-α, and increasing anti-inflammatory cytokines, including IL-10 and BDNF, in cortical and subcortical tissues. In addition, rTMS reduces the expression of glutamate receptors (mGluR5 and NMDAR2B) and microglia and astrocyte markers (Iba1 and GFAP). Furthermore, rTMS decreases nNOS expression in ipsilateral DRGs and peripheral nerve metabolism and regulates neuroinflammation

Text-Image Conditioned Diffusion for Consistent Text-to-3D Generation

By lifting the pre-trained 2D diffusion models into Neural Radiance Fields (NeRFs), text-to-3D generation methods have made great progress. Many state-of-the-art approaches usually apply score distillation sampling (SDS) to optimize the NeRF representations, which supervises the NeRF optimization with pre-trained text-conditioned 2D diffusion models such as Imagen. However, the supervision signal provided by such pre-trained diffusion models only depends on text prompts and does not constrain the multi-view consistency. To inject the cross-view consistency into diffusion priors, some recent works finetune the 2D diffusion model with multi-view data, but still lack fine-grained view coherence. To tackle this challenge, we incorporate multi-view image conditions into the supervision signal of NeRF optimization, which explicitly enforces fine-grained view consistency. With such stronger supervision, our proposed text-to-3D method effectively mitigates the generation of floaters (due to excessive densities) and completely empty spaces (due to insufficient densities). Our quantitative evaluations on the T$^3$Bench dataset demonstrate that our method achieves state-of-the-art performance over existing text-to-3D methods. We will make the code publicly available