Conditioning the logistic branching process on non-extinction

We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as a model for numbers of individuals in populations competing for some resource, or for numbers of species. However, because of the quadratic death rate, even if the intrinsic growth rate is positive, the population will, with probability one, die out in finite time. There is considerable interest in understanding the process conditioned on non-extinction. In this paper, we exploit a connection with the ancestral selection graph of population genetics to find expressions for the transition rates in the logistic branching process conditioned on survival until some fixed time $T$, in terms of the distribution of a certain one-dimensional diffusion process at time $T$. We also find the probability generating function of the Yaglom distribution of the process and rather explicit expressions for the transition rates for the so-called Q-process, that is the logistic branching process conditioned to stay alive into the indefinite future. For this process, one can write down the joint generator of the (time-reversed) total population size and what in population genetics would be called the `genealogy' and in phylogenetics would be called the `reconstructed tree' of a sample from the population. We explore some ramifications of these calculations numerically

Air pollution control or economic development? Empirical evidence from enterprises with production restrictions

Production restriction is an environmental regulation adopted in China to curb the air pollution of industrial enterprises. Frequent production restrictions may cause economic losses for enterprises and further hinder their green transformation. Polluting enterprises are faced with the dilemma of choosing environmental protection or economic development. Using panel data on industrial enterprises in China from 2016 to 2019, this paper evaluates the impact of production restrictions on both enterprises' environmental and economic performance with regression models. The results show that production restrictions significantly drop the concentrations of SO2 and NOx emitted from polluting enterprises. Meanwhile, production restrictions have significant negative effects on operating income, financial expenses, net profit, and environmental protection investment. The mechanism analysis reveals that production restrictions mitigate air pollutant concentrations by increasing the number of green patents and improving total factor productivity, which also verifies the Porter hypothesis. However, there is a masking mediating effect of environmental investment, which indicates that the reduction of environmental investment hinders the enterprise's efforts to control air pollution. In addition, heterogeneous analysis shows that the economic shock on microenterprises is larger than that on small enterprises. Implementing production restrictions for microenterprises may be a way to eliminate their backwards production capacity

Related Structure Characters and Stability of Structural Defects in a Metallic Glass

Structural defects were investigated by a recently proposed structural parameter, quasi-nearest atom (QNA), in a modeled Zr50Cu50 metallic glass through molecular dynamics simulations. More QNAs around an atom usually means that more defects are located near the atom. Structural analysis reveals that the spatial distribution of the numbers of QNAs displays to be clearly heterogeneous. Furthermore, QNA is closely correlated with cluster connections, especially four-atom cluster connections. Atoms with larger coordination numbers usually have less QNAs. When two atoms have the same coordination number, the atom with larger five-fold symmetry has less QNAs. The number of QNAs around an atom changes rather frequently and the change of QNAs might be correlated with the fast relaxation metallic glasses

Molecular Characteristics of Cell Pyroptosis and Its Inhibitors: A Review of Activation, Regulation, and Inhibitors

Pyroptosis is an active and ordered form of programmed cell death. The signaling pathways of pyroptosis are mainly divided into canonical pathways mediated by caspase-1 and noncanonical pathways mediated by caspase-11. Cell pyroptosis is characterized by the activation of inflammatory caspases (mainly caspase-1, 4, 5, 11) and cleavage of various members of the Gasdermin family to form membrane perforation components, leading to cell membrane rupture, inflammatory mediators release, and cell death. Moderate pyroptosis is an innate immune response that fights against infection and plays an important role in the occurrence and development of the normal function of the immune system. However, excessive pyroptosis occurs and leads to immune disorders in many pathological conditions. Based on canonical pathways, research on pyroptosis regulation has demonstrated several pyroptotic inhibitors, including small-molecule drugs, natural products, and formulations of traditional Chinese medicines. In this paper, we review the characteristics and molecular mechanisms of pyroptosis, summarize inhibitors of pyroptosis, and propound that herbal medicines should be a focus on the research and development for pyroptosis blockers

Anti-Inflammation and Anti-Pyroptosis Activities of Mangiferin via Suppressing NF-κB/NLRP3/GSDMD Signaling Cascades

Mangiferin (MF), a xanthone that extensively exists in many herbal medicines, processes significant activities of anti-inflammation and immunomodulation. The potential regulatory effect and mechanism of mangiferin on cell pyroptosis remain unclear. In this study, mouse bone-marrow-derived macrophages (BMDMs) were stimulated with 1 μg/mL LPS to induce cell pyroptosis and were treated with 10, 50, or 100 μg/mL MF for regulating pyroptosis. The cell supernatants TNF-α, IL-1β, IL-6, and IL-18 were detected by enzyme-linked immunosorbent assay (ELISA); gene expression of TNF-α, IL-1β, IL-6, IL-18, Caspase-1, Caspase-11, and gasdermin D (GSDMD) was tested by real-time polymerase chain reaction (RT-PCR), and protein expression levels of apoptosis-associated speck-like protein containing a caspase-recruitment domain (ASC), nod-like receptor protein-3 (NLRP3), caspase-1, caspase-11, GSDMD, and NF-κB were detected by Western blot. The results showed that MF significantly inhibited the secretion and gene expression of TNF-α, IL-6, IL-1β, and IL-18 that were elevated by LPS. Moreover, MF significantly suppressed the gene expression of Caspase-1, Caspase-11, and GSDMD, and decreased the protein levels of NLRP3, caspase-1, caspase-11, full-length GSDMD (GSDMD-FL), GSDMD N-terminal (GSDMD-N), and NF-κB. In conclusion, mangiferin has a multi-target regulating effect on inflammation and pyroptosis by inhibiting the NF-κB pathway, suppressing inflammatory caspase-mediated pyroptosis cascades, and reducing GSDMD cleavage in LPS-induced BMDMs

Molecular Dynamics Simulation of Structural Characterization of Elastic and Inelastic Deformation in ZrCu Metallic Glasses

The nanoscopic deformation behaviors in a ZrCu metallic glass model during loading-unloading process under uniaxial compression have been analyzed on the basis of the molecular dynamics (MD). The reversible degree of shear origin zones (SOZs) is used as the structural indicator to distinguish the elastic deformation and inelastic deformation of ZrCu metallic glass at the atomic level. We find that the formation of SOZs is reversible at the elastic stage but irreversible at the inelastic stage during the loading and unloading processes. At the inelastic stage, the full-icosahedra fraction in SOZs is quickly reduced with increased strain and the decreasing process is also irreversible during the unloading processes

Identification of atomic rearrangements in amorphous alloys based on machine learning

The disordered structure inherent in amorphous alloys precludes the existence of well-defined structural defects analogous to crystals. In this investigation, a novel machine-learning parameter termed Structural Atomic Rearrangement (SAR) is formulated. SAR integrates structural parameters, thermodynamic vibrational entropy, and kinetic activation energy. This departure from the conventional reliance solely on microstructure for macroscopic property characterization enables SAR to comprehensively and accurately identify atomic rearrangements. In the context of deformation, SAR proves effective in pinpointing local regions undergoing plastic rearrangement, offering a distinctive signal preceding the formation of shear bands. This innovative approach challenges the conventional notion and underscores the capability of SAR in capturing rearranged atoms in a more nuanced manner than conventional structural parameters alone