We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on weighted graphs. We first show that, for locally finite graphs and a certain family of metrics, completeness of the graph implies uniqueness of these extensions. Moreover, in the case when the graph is not metrically complete and the Cauchy boundary has finite capacity, we characterize the uniqueness of the Markovian extensions.

We prove the following sufficient condition for stochastic completeness of symmetric jump processes on metric measure spaces: if the volume of the metric balls grows at most exponentially with radius and if the distance function is adapted in a certain sense to the jump kernel then the process is stochastically complete. We use this theorem to prove the following criterion for stochastic completeness of a continuous time random walk on a graph with a counting measure: if the volume growth with respect to the graph distance is at most cubic then the random walk is stochastically complete, where the cubic volume growth is sharp.

The size of microcapsules (MCs) is an important and easily adjustable parameter; however, the function of this parameter in the movement behavior of pesticide MCs had not yet been studied. Phoxim-loaded polyurethane MCs with three various size distributions (average diameters of 1.39 μm, MC-S; 5.78 μm, MC-M; and 23.60 μm, MC-L) were obtained. In the greenhouse experiment, the insecticidal activities of MC-S and MC-M occurred mainly in the first 3 days and that of MC-L was maintained from 3 to 10 days after application. The direct and secondary distributions of a pesticide were defined and used to investigate the effects of particle size on the insecticidal activity of MCs in the field. The results indicated that the reason why MC-S had an excellent initial activity was that it was more widely distributed on the surface of the organism, was more likely to be adhered to by pests, and had greater resistance to rain washing. MC-L had excellent later-stage insecticidal activity, which was mainly because of its outstanding light stability. Then, retained phoxim was released through a crack caused by a light shining onto the shell. The increase in the size of the MCs improved the amount of pesticide swallowed by the insect and the movement distance of the pesticide within the digestive system of the insect. Thus, increasing the size of MCs helps increase the utilization rate of pesticides if a chemical group responding to alkaline conditions can be added into the capsule shell. The transfer and release behavior of pesticide MCs in the field can be regulated by simply adjusting the particle size, which is of great value to the application of pesticide MCs in agriculture and could provide a new approach for the efficient utilization of pesticide MC formulation.

CD99 is a 32-kDa transmembrane glycoprotein that is encoded by the MIC2 gene. Our study was carried out to examine the role of CD99 in tumor progression of classical Hodgkin lymphoma (cHL). Here, we showed that lowly expressed CD99 protein in cHL cell lines and primary cHL cases correlates with the deficient expression of the positive regulatory domain 1 (PRDM1/ BLIMP1). In addition, cHL cell lines showed high levels of miR-9 expression. We determined that the upregulation of CD99 induced expression of transcription factor PRDM1, a master regulator of plasma-cell differentiation, which is also a target for miR-9-mediated downregulation. Indeed, inhibition of miR-9 also triggered upregulation of PRDM1 expression. Furthermore, overexpression of CD99 resulted in changed growth features and reorganization of actin cytoskeleton. As upregulation of CD99 led to a decrease in cHL diagnosis marker CD30 and CD15 and an increase in plasma-cell differentiation marker CD38 and the restoration of B-cell makers PAX5, CD79a and CD19, we suggest that downregulated CD99 leads to the prevention of plasma-cell differentiation in Hodgkin/Reed-Sternberg (H/RS) cells. Furthermore, these data indicate that CD99 may control miR-9 expression, which directly targets PRDM1. Altogether, these results reveal a CD99-miR-9-PRDM1 molecule axis in lymphomagenesis of cHL and suggest that upregulation of CD99 in H/RS cells induces terminal B-cell differentiation, which may provide a novel therapeutic strategies for cHL.The classical Hodgkin lymphoma (cHL) is a malignant lymphoma characterized by the presence of rare Hodgkin and Reed-Sternberg (H/RS) cells residing in a complex admixture of inflammatory cells. Although the nature of H/RS cells is still difficult to interpret, H/RS cells have evidence of abortive plasma-cell differentiation. 1 Recent published data showed that blockage of terminal B-cell differentiation may play a role in the pathogenetic mechanisms of B-cell lymphoma. [2][3][4] The positive regulatory domain 1 (PRDM1), also known as Blimp-1, is a transcriptional repressor that is a master regulator of terminal differentiation of B-cells into plasma cells. 5,6 It also plays a critical role in T FH and CD8 þ T-cell differentiation, 7,8 myeloid differentiation, 9 dendritic cell homeostatic development 10 and NK cell maturation. 11 PRDM1 is found in all plasma cells and in a small proportion of germinal center (GC) cells. 1 In the course of plasmacell differentiation, PRDM1 inhibits GC-B cell repressor BCL6, which can also repress expression of PRDM1. 12 MUM1/IRF4, expressed at high levels in plasma cells, coexpressed with PRDM1, is also critical for plasma-cell differentiation. 13 The consistent expression of MUM1 in H/RS cells demonstrates evidence of initial plasma-cell commitment and proposes a potential plasma-cell differentiation. 1 CD99, encoded by the MIC2 gene, is a human 32-kDa transmembrane glycoprotein, which is highly expressed in Ewing's sarcoma, anaplastic large-cell lymphoma, thymocytes and peripheral T cells. 14-17 CD9...

At present, it is highly important to develop a simple and compatible nano delivery system for pesticides for foliar application, which can improve their insecticidal efficacy and resistance to adverse climates while reducing the environmental risks. Polyethylene glycol and 4,4-methylenediphenyl diisocyanate are used as hydrophilic soft and hydrophobic hard segments, respectively, for polymer self-assembly and polyurethane gelation in a nanoreactor. The nanocarrier synthesis and the pesticide loading are realized by a one-step integration procedure and suited well for hydrophobic active compounds. Modifying the molecular structure of the soft segment can adjust the flexibility of the nanocarriers and result in viscosity and deformation characteristics. After foliar spray application, the foliar flattening state of the nanogels increases the foliar protection area by 2.21 times and improves both pesticide exposure area and target contact efficiency. Concurrently, the flexibility and viscosity of the nanogels increase the washing resistance and the retention rate of the pesticide by approximately 80 times under continuous washing. The encapsulation of the nanogels reduces the foliar ultraviolet (UV) degradation and aquatic pesticide exposure, which increase the security of λ-cyhalothrine by 9.33 times. Moreover, the degradability of nanogels is beneficial for pesticide exposure and reducing pollution. This system has simple preparation, good properties, and environmental friendliness, making the nanocarriers promising for delivering pesticides.

We generalize the weak Omori-Yau maximum principle to the setting of strongly local Dirichlet forms. As an application, we obtain an analytic approach to compare the stochastic completeness of a weighted graph with that of an associated metric graph. This comparison result played an essential role in the volume growth criterion of Folz [15], who first proved it via a probabilistic approach. We also give an alternative analytic proof based on a criterion in Fukushima, Oshima, and Takeda [19].

Early brain injury (EBI) following subarachnoid hemorrhage (SAH) is closely associated with neuroinflammation. Microglial activation is an early event that leads to neuroinflammation after SAH. Peli1 is an E3 ubiquitin ligase that mediates the induction of pro-inflammatory cytokines in microglia. Here we report Peli1 contributions in SAH mediated brain pathology. An SAH model was induced by endovascular perforation in adult male C57BL/6J mice. Peli1 was markedly induced in mice brains in a time-dependent manner and was predominantly expressed in CD16/32-positive microglia after SAH. Using genetic approaches, we demonstrated that decreased Peli1 significantly improved neurological deficits, attenuated brain edema, reduced over-expression of pro-inflammatory cytokine IL-6 and modified apoptotic/antiapoptotic biomarkers. In addition, Peli1 downregulation suppressed ERK and JNK phosphorylation levels via the downregulation of cIAP1/2 expression, subsequently reducing inducible nitric oxide synthase (iNOS) expression after SAH. Therefore, these findings demonstrate that Peli1 contributes to microglia-mediated neuroinflammation in EBI by mediating cIAP1/2 activation, thus promoting the activation of MyD88-dependent MAPK pathway after experimental SAH. Our findings also showed that Peli1 could promote the expression of M1 microglia polarization biomarker CD16/32 and iNOS after SAH. Targeting Peli1 exerts neuroprotective effects during EBI after SAH, thus could provide potential option for prevention-therapy in high-risk individuals.

We prove an analogue of the weak Omori-Yau maximum principle and Khas'minskii's criterion for graphs in the general setting of Keller and Lenz. Our approach naturally gives the stability of stochastic incompleteness under certain surgeries of graphs. It allows to develop a unified approach to all known criteria of stochastic completeness/incompleteness, as well as to obtain new criteria.