Search Results (445)

Let ${\mathcal{Z}}_2\left(s\right)$ denote the modified Mellin transforms of the modulus of the fourth power of the Riemann zeta-function. This paper is devoted to the probabilistic properties of generalized discrete shifts ${\mathcal{Z}}_2(s+i\psi \left(k\right))$, $k\in \mathbb{N}$, with a certain differentiable function $\psi \left(\tau \right)$ satisfying some estimate connected to the mean square of the function ${\mathcal{Z}}_2\left(s\right)$ and such that the sequence $\left\{\kappa \psi \right(k):k\in \mathbb{N}\}$ is uniformly distributed modulo 1 with every $\kappa \in \mathbb{R}\setminus \left\{0\right\}$. We propose the condition that ${\mathcal{Z}}_2(s+i\psi \left(k\right))$ in the space of analytic functions has a limit distribution concentrated at the point $g_0\left(s\right)\equiv 0$. Such a limit theorem is applied for the approximation of the function $g_0\left(s\right)$. Full article

Let X be a compact Riemann surface of genus $g\ge 2$. An octonionic bundle over X is a fiber bundle whose fiber is the non-associative algebra of complex octonions, equivalently a principal $G_2\left(\mathbb{C}\right)$-bundle, where $G_2\left(\mathbb{C}\right)$ is the exceptional Lie group of automorphisms of the octonions. We prove that the natural inclusion $G_2\left(\mathbb{C}\right)\hookrightarrow \mathrm{SO}(7,\mathbb{C})$ induces a closed embedding of the moduli space ${\mathcal{M}}_{\mathrm{Oct}}\left(X\right)$ into the moduli space ${\mathcal{M}}_{\mathrm{SO}(7,\mathbb{C})}\left(X\right)$ of $\mathrm{SO}(7,\mathbb{C})$-bundles. We further analyze the normal bundle to this embedding, computing its rank as $7(g-1)$ and providing an explicit cohomological description of its fibers, which enables explicit computations of tangent spaces and provides a foundation for deformation theory. As applications of the embedding, we prove that the image is a closed irreducible subvariety not contained in the singular locus of the ambient space, and we derive the Whitney formula $c\left(T_{\mathrm{amb}}\right)=c\left(T\right)·c\left(N\right)$ relating the Chern classes of the tangent bundle of ${\mathcal{M}}_{\mathrm{Oct}}\left(X\right)$, the pullback of the ambient tangent bundle, and the normal bundle over the smooth locus. Full article

Small noncoding RNAs play critical regulatory roles in development across organisms. This study profiled microRNAs (miRNAs) and tRNA-derived fragments (tRFs) during bovine conceptus elongation. Elongating conceptuses were obtained via superovulation of eight Angus heifers. Twenty samples from ovoid (OV, n = 6; 0.5–3 mm), tubular (TUB, n = 7; 5–15 mm), and filamentous (FIL, n = 7; 20–34 mm) stages underwent small RNA sequencing. Differential expression of miRNAs and tRFs was analyzed using DESeq2, accounting for donor-sire effects. No tRFs showed differential abundance across any pairwise comparisons. For miRNAs, the expressions of six miRNAs were upregulated in OV versus TUB conceptuses (padj < 0.05), including four let-7 family members (bta-let-7g, bta-let-7f, bta-let-7a-5p, and bta-let-7c) and two additional miRNAs (bta-miR-224 and bta-miR-449a). Furthermore, there were 3 miRNAs differently abundant between the ovoid and filamentous transition (padj < 0.04), including two members of the let7 family (bta-let-7g and bta-let-7f) and bta-miR-449a. Predicted targets of these differentially abundant miRNAs were identified using miRanda. Enrichment analyses of the targeted genes included pathways regulating cellular proliferation, pathways in cancer, and immune-related pathways. The let-7 family, along with miR-449a and miR-224, are candidate regulators of the balance between cellular proliferation and differentiation during elongation, based on their differential abundance and in silico target predictions. Full article

Background: The ORF3 protein of swine hepatitis E virus (HEV-4) is a key virulence factor involved in viral assembly, egress, and host signaling regulation. The mammalian target of rapamycin (mTOR) pathway plays a pivotal role in autophagy, metabolism, and immunity, and is often modulated by viruses to promote replication. However, it remains unknown whether HEV-4 ORF3 modulates the mTOR pathway via circular RNAs (circRNAs). Methods: Using an adenovirus-mediated ORF3 overexpression system in HepG2 cells, we integrated circRNA and transcriptome high-throughput sequencing data, followed by KEGG enrichment analysis to identify mTOR-associated differentially expressed genes. A circRNA–miRNA regulatory network was constructed using bioinformatics tools, and the expression changes of m6A-related genes, including YTHDF3, were evaluated. Results: ORF3 overexpression significantly activated the mTOR pathway (p < 0.05) and led to the identification of 20 mTOR-related circRNAs (e.g., circRNA5142). These circRNAs regulated downstream autophagy and lipid metabolism genes by sponging miRNAs such as hsa-let-7d-5p and hsa-miR-132-3p. Altered YTHDF3 expression indicated possible m6A-dependent epitranscriptomic regulation of the mTOR pathway. Conclusions: Our integrated analysis suggests that HEV-4 ORF3 may modulate the mTOR pathway through a circRNA–miRNA network, perturbing host autophagy and metabolic balance, which may contribute to viral immune evasion. Targeting the ORF3-mediated circRNA-mTOR regulatory axis represents a promising therapeutic approach and provides a theoretical basis for novel anti-HEV-4 strategies. Full article

Ultra-high dose-rate (FLASH) irradiation can transiently deplete oxygen and modulate radical-mediated chemistry in irradiated cells. Cellular antioxidants also contribute to mitigating oxidative damage in a manner dependent on linear energy transfer (LET), as suggested by recent experimental studies. In this work, we employed our multi-track Monte Carlo simulation framework (IONLYS-IRT) to investigate how LET influences transient radiation-induced oxygen depletion (ROD) in a cell-like aqueous environment under FLASH irradiation conditions. FLASH exposures were modeled as single, instantaneous pulses of protons with energies from 300 MeV to 150 keV, corresponding to LET values of ~0.3 to 71 keV/μm. Our simulations revealed a marked decline in oxygen depletion with increasing LET, in agreement with experimental observations. For an intracellular O₂ concentration of 30 μM, the oxygen consumption yield, G(–O₂), decreased from ~4.0 molecules/100 eV at low LET (~0.3 keV/μm) to ~1.6 molecules/100 eV at high LET (~71 keV/μm), representing a ~60% reduction. To assess whether ROD depends solely on LET or is also governed by ion track structure, we systematically compared multiple ion species (protons, ⁴He²⁺, ¹⁰B⁵⁺, ¹²C⁶⁺, ¹⁶O⁸⁺, ²⁰Ne¹⁰⁺, ²⁸Si¹⁴⁺, ³²S¹⁶⁺, and ⁴⁰Ar¹⁸⁺) at comparable LET values. At ~70 keV/μm, heavier ions produced significantly higher G(−O₂) values than protons—though still below those at low LET—suggesting that track structure plays a key role beyond LET alone. These findings highlight the dual importance of LET and ion-specific track structure in modulating ROD under FLASH conditions. Notably, enhanced ROD in surrounding normal tissues (low-LET plateau regions) may contribute to radioprotective effects, whereas reduced ROD in tumor tissues (high-LET Bragg peak regions) would be expected to preserve tumoricidal efficacy. Together, these results provide a mechanistic framework for optimizing proton and heavy-ion approaches in FLASH radiotherapy. Full article

Let G be a finite group. The vertex set of the prime-power graph of G is defined as $V\left(G\right)=\left\{p^{e_p\left(G\right)}|p\in \rho \left(G\right)\right\}$, where $\rho \left(G\right)$ is the set of all prime divisors of the degrees of all irreducible characters of G and $p^{e_p\left(G\right)}=max\left\{\psi {\left(1\right)}_p\mid \psi \in Irr\left(G\right)\right\}$. It has been proved that the simple groups $L_3\left(p\right)$ can be characterized by its orders and vertex set of prime-power graphs. In this paper, we continue this topic and prove that $L_3\left(p^2\right)$ can be uniquely characterized by its orders and degree prime-power graphs, where p is a prime. Full article

The second immanantal polynomial is one of the important directions in algebraic theory. Let $M=\left[m_{ij}\right]$ be an $n\times n$ matrix. The second immanant of matrix M is defined as $d_2\left(M\right)={\sum }_{\sigma \in S_n}\chi \left(\sigma \right){\prod }_{i=1}^n{m}_{i\sigma \left(i\right)}$, where $\chi$ is the irreducible character of the symmetric group $S_n$ of degree n, corresponding to the partition $(2^1,1^{n-2})$. Let G be a graph with n vertices. Denote by $Q\left(G\right)$ the signless Laplacian matrix of G. The second signless Laplacian immanantal polynomial of G is defined as $d_2(xI-Q\left(G\right))={\sum }_{k=0}^n{(-1)}^k{c}_k\left(G\right)x^{n-k}$, where $c_k\left(G\right)$ is the coefficient of this polynomial. This paper investigates fundamental properties of this polynomial. First, we give combinatorial expressions for the first few coefficients of the second signless Laplacian immanantal polynomial. Next, we prove that the polynomial has no zero or negative real roots for connected graphs. Furthermore, we show that there is an equivalence relation among three polynomials for regular graphs, which implies that if two regular graphs share the same characteristic polynomial, then they also share the same second signless Laplacian immanantal polynomial. Finally, we prove that paths and almost complete graphs are determined by their second signless Laplacian immanantal polynomials. Full article

Background/Objectives: We performed a systematic review of preclinical literature on the use of high-LET particle therapy, DDRi, and/or immunotherapy specifically in pMMR colorectal cancer. Methods: A systematic review of the literature published between 2014 and 2025 was conducted across major databases. Studies were included if they examined particle radiotherapy (e.g., proton, alpha, and carbon) or X-ray radiation either alone or in combination with DDRi and/or immune checkpoint inhibitors (ICIs) in pMMR colorectal cancer models. Results: In total, 131 studies met the inclusion criteria, including 70 preclinical studies. These studies consistently demonstrate that high-LET radiation amplifies immunogenic cell death, increases cGAS-STING pathway activation, and enhances tumor antigen presentation, thereby fostering greater immune infiltration and systemic antitumor responses. Concurrent irradiation with DDRi enhances persistent DNA damage and cytosolic DNA accumulation. In murine models, high-LET therapies show excellent local control, with manageable toxicity profiles. Combination regimens with ICIs exhibit improved local control and elicit systemic antitumor immune responses. Conclusions: High-LET particle radiation and/or the use of concurrent DDRi with ICI have significant preclinical evidence of immunostimulatory effects in pMMR rectal adenocarcinoma and increased response rates to immunotherapy. The clinical evidence will be reviewed in the companion manuscript. Full article

Let G be a connected graph in which the distance between any two distinct vertices of degree of at least three is at least three. We find the structure of G. It turns out that G decomposes into a tree and a matching. Full article

Both let-7a and miR-34a have been repeatedly studied as pivotal suppressors for Hepatocellular carcinoma; however, their combined regulations remain to be fully elucidated. In the present study, we performed a comprehensive in silico analysis for let-7a and miR-34a using a wealth of updated tools: miRWalk, Genetrail and miRnet. In addition, our study is the first to quantify both miRs and their three predicted yet not experimentally validated oncogenic targets: FNDC3B, IGF2 and SOX4. This was assessed in HepG2 cell model following treatment by PEGP-vector expressing the miRs by MTT assay, florescence microscopy, qPCR and immune-florescence. Our bioinformatics analysis revealed a pool of common predicted hepatocarcinogenic targets shared by both let-7a and miR-34a. Importantly, three targets were identified as co-regulated through multiple canonical binding sites for each miR, and these had not been experimentally validated before. Furthermore, functional enrichment of these putative targets demonstrated their significant involvement in major and emerging HCC hallmarks, such as reprogramming of energy metabolism and evading immune destruction. These findings support our concept of simultaneous co-regulation of these oncogenes through the signaling networks and GO terms associated with both miRs. Consistently, our experimental results verified the significant overexpression of both miRs in HepG2 cells, leading to reduced tumor cell proliferation and decreased levels of the three oncogenic transcripts. Interestingly, miR-34a exhibited a superior suppression effect, reaching 38.7%, and SOX4 was identified as the most significantly downregulated target at both transcriptional and translational levels. Our findings provide new insights into the interconnected anti-HCC effects of let-7a and miR-34a and highlight the potential of applying their combined use to achieve the best therapeutic outcomes for this invasive tumor. Full article

Let $\eta :X\to \mathbb{R}$ be a Morse function on a connected closed manifold X. We denote by $C\left(\eta \right)$ the fiber product of two copies of $\eta$. For Morse functions $f:M\to \mathbb{R}$ and $g:N\to \mathbb{R}$, we define the function $f\ast g:M\times N\to \mathbb{R}$ by $(f\ast g)(p,q):=f\left(p\right)·g\left(q\right)$. The purpose of this paper is twofold: Firstly, we study the sufficient condition for which $\chi \left(C\right(f\ast g\left)\right)=\chi \left(C\right(f\left)\right)·\chi \left(C\right(g\left)\right)$ holds, where $\chi$ denotes the Euler characteristic. Secondly, for the case that f is the well-known Morse function on $\mathbb{C}{P}^n$, we determine $\chi \left(C\right(f\ast f\left)\right)$. Full article

Let G be a graph with n vertices and m edges. A vertex magic total labeling of G is a bijection $f:V\left(G\right)\cup E\left(G\right)\to \{1,2,\dots ,n+m\}$ such that, for each vertex $u\in V\left(G\right)$, the sum of the label of u and the labels of all edges incident to u is equal to a fixed constant, referred to as the magic constant. A vertex magic total labeling is said to be even if the labels assigned to the vertices are exactly even numbers $\{2,4,6,\dots ,2n\}$. These labelings, along with related variations, have theoretical significance and practical applications, such as resource allocation, fault tolerance, and network design. Structured labelings aid channel assignment, address computation, and reduce collisions in networks. In this paper, we investigate wheel-related graphs that either admit or do not admit an even vertex magic total labeling. Furthermore, we introduce a new class of wheel-related graph, referred to as the plus wheel $W_n+r$, that can have such labelings, and we also establish a necessary and sufficient condition for such graphs to possess this property. Full article

Background: Zika virus (ZIKV), a mosquito-borne flavivirus, is associated with congenital malformations and neuroinflammatory disorders, highlighting the need to identify host factors that shape infection outcomes. Macrophages, key targets and reservoirs of ZIKV, orchestrate both antiviral and inflammatory responses. Methods: Vitamin D (VitD) has emerged as a potent immunomodulator that enhances macrophage antimicrobial activity and regulates inflammation. To investigate how VitD shapes macrophage responses to ZIKV, we reanalyzed publicly available RNA-seq and miRNA-seq datasets from monocyte-derived macrophages (MDMs) of four donors, differentiated with or without VitD and subsequently infected with ZIKV. Results: Differential expression analysis identified long non-coding RNAs (lncRNAs), microRNAs (miRNAs), and mRNAs integrated into competing endogenous RNA (ceRNA) networks. In VitD-conditioned and ZIKV-infected MDMs, 65 lncRNAs and 23 miRNAs were significantly modulated. Notably, lncRNAs such as HSD11B1-AS1, Lnc-FOSL2, SPIRE-AS1, and PCAT7 were predicted to regulate immune and metabolic genes, including G0S2, FOSL2, PRELID3A, and FBP1. Among the miRNAs, let-7a and miR-494 were downregulated, while miR-146a, miR-708, and miR-378 were upregulated, all of which have been previously implicated in antiviral immunity. Functional enrichment analysis revealed pathways linked to metabolism, stress responses, and cell migration. ceRNA network analysis suggested that SOX2-OT and SLC9A3-AS1 may act as molecular sponges, modulating regulatory axes relevant to immune control and viral response. Conclusions: Despite limitations in sample size and experimental validation, this study provides an exploratory map of ncRNA–mRNA networks shaped by VitD during ZIKV infection, highlighting candidate molecules and pathways for further studies on host–virus interactions and VitD-mediated immune regulation. Full article

Google Earth Engine (GEE) has revolutionised remote sensing. The GEE cloud platform lets users quickly analyse large satellite imagery datasets with custom programmes, enhancing global-scale analysis. Crop condition monitoring using GEE would greatly help in decision-making and precision agriculture. Estimating canopy chlorophyll content (CCC) is an effective way to monitor crops using remote sensing because leaf chlorophyll is a key indicator. A hybrid model that combines radiative transfer models (RTMs), such as PROSAIL, with Gaussian Process Regression (GPR) can effectively estimate crop biophysical parameters using remote sensing images. GPR has proven to be one of the best methods for this purpose. This study aimed to develop a hybrid model to estimate CCC from S2 imagery and transfer it to the GEE platform for efficient data processing. In this work, the CCC (g/cm²) data from the S2 biophysical processor toolbox for the S2 imagery of the ICAR-Indian Agricultural Research Institute (IARI) on 23 February 2023 were used as observation data to train the hybrid algorithm. The hybrid model was successfully validated against the 155 input data with an R2 of 0.94, RMSE of 10.02, and NRMSE of 5.04%. The model was integrated into GEE to successfully generate a CCC-estimated map of IARI using S2 imagery from 23 February 2023. An R2 value of 0.96 was observed when GEE-estimated CCC values were compared against CCC values estimated locally. This establishes that the GEE-based CCC estimation with the PROSAIL + GPR hybrid model is an effective and accurate method for monitoring vegetation and crop conditions over large areas and extended periods. Full article

Background/Objectives: The KRAS rs61764370 T>G single-nucleotide polymorphism (SNP), located in a let-7 microRNA binding site within the 3′ untranslated region (3′UTR) of the KRAS gene, may modulate tumor aggressiveness by altering post-transcriptional gene regulation. This study evaluated its association with adverse histopathological features in colorectal cancer (CRC). Methods: A preliminary study on 83 CRC patients carrying either the TT (wild-type, n = 64) or TG (heterozygous, n = 19) genotype was analyzed. Clinicopathological variables included patient sex, tumor location, American Joint Committee on Cancer (AJCC) staging system, histological grade, perineural invasion (PNI), and lymphovascular invasion (LVI). A composite “tumor aggressiveness” score was defined based on the presence of Grade 3 differentiation, LVI, and/or PNI. Group comparisons were performed using the Chi-square test or Fisher’s exact test, as appropriate. Results: No statistically significant differences were observed in sex (p = 0.689), tumor location (p = 0.781), or stage at diagnosis (p = 0.812). Poorly differentiated tumors (Grade 3) were present in 20.3% of TT patients and absent in TG carriers (p = 0.06), while low-grade tumors (Grade 1) were more prevalent among TG patients (47.4%) compared to TT (29.7%). The composite high-aggressiveness score was lower in TG (36.8%) than in TT (48.4%), while co-occurrence of PNI and LVI was similar in both groups (~26%). Conclusions: Although no significant associations were identified, TG carriers showed a tendency toward lower-grade, less aggressive tumors. Given the limited sample size, these findings should be interpreted with caution, necessitating larger cohorts in order to validate results. Full article