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The elevated levels of inflammatory cytokines have attracted much attention during the treatment of COVID-19 patients. The conclusions of current observational studies are often controversial in terms of the causal effects of COVID-19 on various cytokines because of the confounding factors involving underlying diseases. To resolve this problem, we conducted a Mendelian randomization analysis by integrating the GWAS data of COVID-19 and 41 cytokines. As a result, the levels of 2 cytokines were identified to be promoted by COVID-19 and had unsignificant pleiotropy. In comparison, the levels of 10 cytokines were found to be inhibited and had unsignificant pleiotropy. Among down-regulated cytokines, CCL2, CCL3 and CCL7 were members of CC chemokine family. We then explored the potential molecular mechanism for a significant causal association at a single cell resolution based on single-cell RNA data, and discovered the suppression of CCL3 and the inhibition of CCL3-CCR1 interaction in classical monocytes (CMs) of COVID-19 patients. Our findings may indicate that the capability of COVID-19 in decreasing the chemotaxis of lymphocytes by inhibiting the CCL3-CCR1 interaction in CMs.

Since the first report of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in December 2019, over 100 million people have been infected by COVID-19, millions of whom have died. In the latest year, a large number of omics data have sprung up and helped researchers broadly study the sequence, chemical structure and function of SARS-CoV-2, as well as molecular abnormal mechanisms of COVID-19 patients. Though some successes have been achieved in these areas, it is necessary to analyze and mine omics data for comprehensively understanding SARS-CoV-2 and COVID-19. Hence, we reviewed the current advantages and limitations of the integration of omics data herein. Firstly, we sorted out the sequence resources and database resources of SARS-CoV-2, including protein chemical structure, potential drug information and research literature resources. Next, we collected omics data of the COVID-19 hosts, including genomics, transcriptomics, microbiology and potential drug information data. And subsequently, based on the integration of omics data, we summarized the existing data analysis methods and the related research results of COVID-19 multi-omics data in recent years. Finally, we put forward SARS-CoV-2 (COVID-19) multi-omics data integration research direction and gave a case study to mine deeper for the disease mechanisms of COVID-19.

In this note, we prove Gluck’s conjecture and Isaacs-Navarro-Wolf Conjecture are true for the solvable groups with disconnected graphsby using Lewis’ group structure theorem with respect to the disconnectedcharacter degree graphs. 1. IntroductionFor a finite group G, we attach a graph ∆(G) to G, whose vertices are primedivisors of degree of some nonlinear irreducible complex character of G, anddistinct vertices p,q are connected when pq divides degree of some irreduciblecharacter of G.By [8, 9], the number of connected components is at most 3 for any finitegroups and 2 for any solvable group. When the graph ∆(G) is disconnected forthe solvable group G, P. Palfy described in [12] the structure of G; furthermoreM. Lewis characterized in [7] the structure of G as follows:Theorem(Lewis). For a solvable group G, the graph ∆(G) is disconnected ifand only if G is one of the groups as Examples 2.1-2.6 in [7].In [7], Examples 2.1-2.6 along with corresponding Lemmas 3.1-3.6 give de-tailed information of structure and character degrees of G, and even the specificgroup examples in individual cases.In this note, we intend to apply the theorem to two open problems ofcharacter theory of finite solvable groups. We write b(G) for the largest ir-reducible character degree of G. Gluck conjectured [3] that the inequality|G : F(G)| ≤ b(G)

In this paper we prove that a finite group G is isomorphic to the finite simple group L n (q) with n ≥ 3 if and only if they have the same set of order of solvable subgroups. #Communicated by A. Yu Olshanskii.

In this paper, we prove that a finite group G is isomorphic to the alternating group An with n≥5 if and only if they have the same set of the orders of solvable subgroups.

LetG be a finite group. If $$\left| {N_G (R_1 )} \right| = \left| {N_{L_n (q)} (R_2 )} \right|$$ for every primer, whereR 1 e Syl r G andR 2 e Syl r (L n (q)), thenG ≅L n (q).