Norms of commutators of self-adjoint operators

AbstractIn this note, the estimate of norms of commutators of self-adjoint operators is established

The intersection of the spectra of operator completions

AbstractLet A∈B(H), B∈B(K), C∈B(K,H), X∈B(H,K) and MX=ACXB be an operator completion of the partial operator matrix Q=AC?B. In this note, we consider the intersection of the spectra of MX when X runs over B(H,K). Denote by ∑(A,B,C) the set of scalar λ∈C such that either (A−λ,C) or (B∗−λ̄,C∗) is not right invertible. We prove that⋂X∈B(H,K)σ(MX)=∑(A,B,C)ifdimR(C)=∞,∑(A,B,C)∪Δ(A,B,C)ifdimR(C)<∞,where Δ(A,B,C) is the set of scalars λ∈C such that R((A−λ,C))=H, R((B∗−λ̄,C∗))=K, and ind(A−λ)+ind(B−λ)≠0. We also prove that the intersection is empty if and only if (A,C) and (B∗,C∗) are controllable

Differential analysis of aqueous humor cytokine levels in patients with macular edema secondary to diabetic retinopathy or retinal vein occlusion

AIM: To evaluate the difference and the correlation between the concentrations of cytokines in the aqueous humor of eyes with macular edema secondary to diabetic retinopathy (DR) or retinal vein occlusion (RVO). METHODS: This is a retrospective case control study. The aqueous humor samples were collected during intravitreal injection of anti-vascular endothelial growth factor (VEGF) for patients diagnosed with macular edema secondary to DR (DME) or RVO (RVO-ME) at Xijing Hospital from August 2021 to July 2022. Meanwhile, aqueous humor samples during vitrectomy from patients with idiopathic macular hole (IMH) were also collected and served as controls. The aqueous humor concentrations of VEGF, platelet-derived factor (PDGF), interleukin (IL)-6, IL-8, IL-18, tumor necrosis factor-α (TNF-α) and monocyte chemoattractant protein 1 (MCP-1) were measured with Human Premixed Multi-Analyte Kit (Luminex). The difference of the aqueous cytokines and the correlation between the two diseases were analyzed. RESULTS: A total of 40 eyes of 38 patients were enrolled in the study, including 13 eyes of 11 DME patients (DME group), 16 eyes of 16 RVO-ME patients (RVO-ME group) and 11 eyes of 11 IMH patients (control group). The VEGF, PDGF, IL-6, IL-8, and MCP-1 levels of the aqueous humor were higher in both DME and RVO-ME groups compared with the control group (all P<0.05), the levels of TNF-α was higher in the DME group than in the control group (P<0.05). The VEGF, IL-6, MCP-1, and TNF-α levels in the aqueous humor were significantly higher in the DR group than those in the RVO group (all P<0.05). Correlation analyses revealed that there were complex positive correlations between IL-6, IL-8, IL-18, MCP-1, and TNF-α levels in the aqueous humor of eyes with two diseases. CONCLUSION: Although ischemic and inflammatory factors are similarly involved in the pathogenesis of DME and RVO-ME, the roles of these factors are more significant or more likely to be activated in DR patients, suggesting different treatment strategies should be considered for the two diseases

The Novel Protein Cj0371 Inhibits Chemotaxis of Campylobacter jejuni

cj0371 is a novel gene that is associated with Campylobacter jejuni virulence, and an isogenic mutant of cj0371 showed hyper chemotaxis and motility. Chemotactic motility is an important virulence factor and is involved in C. jejuni pathogenesis. Campylobacter sp. has specific variations of the common chemotaxis components, including histidine autokinase CheA, coupling scaffold protein CheV, chemotaxis response regulator protein CheY and several chemoreceptor proteins. In this study, we used immunoprecipitation combined with LC-MS/MS analyses to screen six chemotaxis pathway proteins that potentially interact with the putative protein Cj0371. qRT-PCR was used to quantitatively analyze the expression of these chemotaxis genes and basic flagella genes. The results showed that the expression of cheV, cj1110c, and cj0262c was significantly up-regulated, and four flagella genes also had up-regulated expression in the cj0371 mutant. GST pull-down analyses found that Cj0371 interacted with the receiver domain of the CheV protein. Enzyme-coupled spectrophotometric assays showed that the ATPase activity of CheA was higher when Cj0371 was not present in the chemotaxis reaction medium. Therefore, we concludes that cj0371 has a negative influence on C. jejuni chemotaxis, which may occur by adjusting the receiver domain of CheV to influence chemotaxis. This paper provides a new component in the chemotaxis pathway of C. jejuni for the first time and highlight the complexity of this remarkable pathway

Inverse design of artificial skins

Mimicking the perceptual functions of human cutaneous mechanoreceptors, artificial skins or flexible pressure sensors can transduce tactile stimuli to quantitative electrical signals. Conventional methods to design such devices follow a forward structure-to-property routine based on trial-and-error experiments/simulations, which take months or longer to determine one solution valid for one specific material. Target-oriented inverse design that shows far higher output efficiency has proven effective in other fields, but is still absent for artificial skins because of the difficulties in acquiring big data. Here, we report a property-to-structure inverse design of artificial skins based on small dataset machine learning, exhibiting a comprehensive efficiency at least four orders of magnitude higher than the conventional routine. The inverse routine can predict hundreds of solutions that overcome the intrinsic signal saturation problem for linear response in hours, and the solutions are valid to a variety of materials. Our results demonstrate that the inverse design allowed by small dataset is an efficient and powerful tool to target multifarious applications of artificial skins, which can potentially advance the fields of intelligent robots, advanced healthcare, and human-machine interfaces

Micro Processes Study on Structure Change in N-Pentadecane Thin Film Adsorbed on Substrate: A Molecular Dynamics Simulation

It is experimentally found that adsorbed thin film consists of chain molecules changes its structure when it is heated at temperature lower than the melting point; but the molecular micro processes are remaining unknown; here we investigated the micro processes of structure change in n-pentadecane thin film adsorbed on substrate by use of molecular dynamics simulation. We found that, at temperature 200K (lower than the melting point), the isotropic amorphous thin film becomes a crystalline thin film in which molecule chains parallel to the substrate with relaxation time of about 12000ps; however, at temperature 290K (also lower than the melting point), the thin film structure changed essentially, the molecule chains changed their orientation from parallel to the substrate becomes nearly perpendicular to the substrate with relaxation time of about 5000ps

Reply to: Mobility overestimation in MoS2_2 transistors due to invasive voltage probes

In this reply, we include new experimental results and verify that the observed non-linearity in rippled-MoS$_2$ (leading to mobility kink) is an intrinsic property of a disordered system, rather than contact effects (invasive probes) or other device issues. Noting that Peng Wu's hypothesis is based on a highly ordered ideal system, transfer curves are expected to be linear, and the carrier density is assumed be constant. Wu's model is therefore oversimplified for disordered systems and neglects carrier-density dependent scattering physics. Thus, it is fundamentally incompatible with our rippled-MoS$_2$, and leads to the wrong conclusion