Disproof of a conjecture on the minimum spectral radius and the domination number

Let $G_{n,\gamma}$ be the set of all connected graphs on $n$ vertices with domination number $\gamma$. A graph is called a minimizer graph if it attains the minimum spectral radius among $G_{n,\gamma}$. Very recently, Liu, Li and Xie [Linear Algebra and its Applications 673 (2023) 233--258] proved that the minimizer graph over all graphs in $\mathbb{G}_{n,\gamma}$ must be a tree. Moreover, they determined the minimizer graph among $G_{n,\lfloor\frac{n}{2}\rfloor}$ for even $n$, and posed the conjecture on the minimizer graph among $G_{n,\lfloor\frac{n}{2}\rfloor}$ for odd $n$. In this paper, we disprove the conjecture and completely determine the unique minimizer graph among $G_{n,\lfloor\frac{n}{2}\rfloor}$ for odd $n$

Quadratic Embedding Constants of Graph Joins

The quadratic embedding constant (QE constant) of a graph is a new characteristic value of a graph defined through the distance matrix. We derive formulae for the QE constants of the join of two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite graphs, wheel graphs, friendship graphs, completely split graph, and some graphs associated to strongly regular graphs.Comment: 20 page

Numerical and experimental evaluation of nasopharyngeal aerosol administration methods in children with adenoid hypertrophy

Article no 12390

A meaningful exploration of ofatumumab in refractory NMOSD: a case report

ObjectiveTo report the case of a patient with refractory neuromyelitis optica spectrum disorder (NMOSD), who, despite showing poor response or intolerance to multiple immunosuppressants, was successfully treated with Ofatumumab.Case presentationA 42-year-old female was diagnosed with NMOSD in the first episode of the disease. Despite treatment with intravenous methylprednisolone, immunoglobulin, rituximab and immunoadsorption, together with oral steroids, azathioprine, mycophenolate mofetil and tacrolimus, she underwent various adverse events, such as abnormal liver function, repeated infections, fever, rashes, hemorrhagic shock, etc., and experienced five relapses over the ensuing four years. Finally, clinicians decided to initiate Ofatumumab to control the disease. The patient received 9 doses of Ofatumumab over the next 10 months at customized intervals. Her symptoms were stable and there was no recurrence or any adverse events.ConclusionOfatumumab might serve as an effective and safe alternative for NMOSD patients who are resistant to other current immunotherapies

MicroRNAs Up-Regulated by CagA of Helicobacter pylori Induce Intestinal Metaplasia of Gastric Epithelial Cells

CagA of Helicobacter pylori is a bacterium-derived oncogenic protein closely associated with the development of gastric cancers. MicroRNAs (miRNAs) are a class of widespread non-coding RNAs, many of which are involved in cell growth, cell differentiation and tumorigenesis. The relationship between CagA protein and miRNAs is unclear. Using mammalian miRNA profile microarrays, we found that miRNA-584 and miRNA-1290 expression was up-regulated in CagA-transformed cells, miRNA-1290 was up-regulated in an Erk1/2-dependent manner, and miRNA-584 was activated by NF-κB. miRNA-584 sustained Erk1/2 activities through inhibition of PPP2a activities, and miRNA-1290 activated NF-κB by knockdown of NKRF. Foxa1 was revealed to be an important target of miRNA-584 and miRNA-1290. Knockdown of Foxa1 promoted the epithelial-mesenchymal transition significantly. Overexpression of miRNA-584 and miRNA-1290 induced intestinal metaplasia of gastric epithelial cells in knock-in mice. These results indicate that miRNA-584 and miRNA-1290 interfere with cell differentiation and remodel the tissues. Thus, the miRNA pathway is a new pathogenic mechanism of CagA

Study on Multi-Depot Collaborative Transportation Problem of Milk-Run Pattern

Analyze the relevance between Milk Run mode and collaborative transportation problem, put forward collaborative transportation problem of multiple-depot on Milk Run mode under the supply and demand separate nodes, consider the value of transport and transport costs, introduce the concept of node - arc flow, by comparing the size of traffic flow determine nodes collection, and then constructed multi-transport model of the problem. Considering one-way pickup and delivery closed, construct two-stage algorithm model, use dynamic programming recursive solution to determine the best route to pick up, and then solving delivery routing problem with different start and return point based on geometric method of Cosine. Finally use a numerical example illustrates the effectiveness of the algorithm and reasonable model

Study on Multi-Depot Collaborative Transportation Problem of Milk-Run Pattern

Analyze the relevance between Milk Run mode and collaborative transportation problem, put forward collaborative transportation problem of multiple-depot on Milk Run mode under the supply and demand separate nodes, consider the value of transport and transport costs, introduce the concept of node - arc flow, by comparing the size of traffic flow determine nodes collection, and then constructed multi-transport model of the problem. Considering one-way pickup and delivery closed, construct two-stage algorithm model, use dynamic programming recursive solution to determine the best route to pick up, and then solving delivery routing problem with different start and return point based on geometric method of Cosine. Finally use a numerical example illustrates the effectiveness of the algorithm and reasonable model

A Systematic Review of Phytochemistry, Pharmacology and Pharmacokinetics on <i>Astragali</i> Radix: Implications for <i>Astragali</i> Radix as a Personalized Medicine

Astragali radix (AR) is one of the most widely used traditional Chinese herbal medicines. Modern pharmacological studies and clinical practices indicate that AR possesses various biological functions, including potent immunomodulation, antioxidant, anti-inflammation and antitumor activities. To date, more than 200 chemical constituents have been isolated and identified from AR. Among them, isoflavonoids, saponins and polysaccharides are the three main types of beneficial compounds responsible for its pharmacological activities and therapeutic efficacy. After ingestion of AR, the metabolism and biotransformation of the bioactive compounds were extensive in vivo. The isoflavonoids and saponins and their metabolites are the major type of constituents absorbed in plasma. The bioavailability barrier (BB), which is mainly composed of efflux transporters and conjugating enzymes, is expected to have a significant impact on the bioavailability of AR. This review summarizes studies on the phytochemistry, pharmacology and pharmacokinetics on AR. Additionally, the use of AR as a personalized medicine based on the BB is also discussed, which may provide beneficial information to achieve a better and more accurate therapeutic response of AR in clinical practice