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Due to the fuzziness of anomaly definition and the complexity of scenes in real video data, video anomaly detection is still a challenging task. In this work, we explored a novel lightweight dual branch convolution neural architecture that can separate appearance-motion representations to capture spatial and temporal information, respectively, since abnormal events are usually different from normal cases in appearance or motion behavior. Considering the channel redundancy problem in the traditional neural network, and the feature information processed by different branches is different, the corresponding channel attenuation is carried out, which greatly improves the speed of anomaly detection while maintaining the performance of the model. In order to improve the utilization of key features, we exploited a Channel Squeeze and Excitation module and insert it into the encoder part of the network to focus on the channel correlation and adaptively recalibrate the characteristic response of the channel. The importance of each feature channel is automatically acquired through learning, and then according to the importance, the useful channels are promoted and the channels that are not useful for the current task are suppressed. In addition, in order to increase the reconstruction error of the motion encoder and consider the diversity of the normal patterns, we propose to use a memory module to augment the motion U-Net, where the items in the memory record the prototype mode of the normal data. The experiments on three benchmark datasets, UCSD Ped2, CHUK Avenue, and ShanghaiTech, demonstrate that our method achieves AUC scores of 96.3%, 87.4%, and 73.5%, respectively. The experimental speed reaches 55fps, showing a competitive performance relative to the current state of research. [ABSTRACT FROM AUTHOR]

Traumatic brain injury (TBI) is associated with diffuse axonal injury (DAI), a primary pathology linked to progressive neurodegeneration and neuroinflammation, including chronic astrogliosis, which influences long-term post-TBI recovery and morbidity. Sex-based differences in blood-brain barrier (BBB) permeability increases the risk of accelerated brain aging and early-onset neurodegeneration. However, few studies have evaluated chronic time course of astrocytic responses around cerebrovascular in the context of aging after TBI and sex dependence. We observed increased glial fibrillary acidic protein (GFAP)-labeled accessory processes branching near and connecting with GFAP-ensheathed cortical vessels, suggesting a critical nuance in astrocyte-vessel interactions after TBI. To quantify this observation, male and female Sprague Dawley rats (~3 months old, n = 5–6/group) underwent either sham surgery or midline fluid percussion injury. Using immunohistochemical analysis, we quantified GFAP-labeled astrocyte primary and accessory processes that contacted GFAP-ensheathed vessels in the somatosensory barrel cortex at 7, 56, and 168 days post-injury (DPI). TBI significantly increased GFAP-positive primary processes at 7 DPI (P < 0.01) in both sexes. At 56 DPI, these vessel-process interactions remained significantly increased exclusively in males (P < 0.05). At 168 DPI, both sexes showed a significant reduction in vessel-process interactions compared to 7 DPI (P < 0.05); however, a modest but significant injury effect reemerged in females (P < 0.05). A similar sex-dependent pattern in the number of accessory processes provides novel evidence of long-term temporal changes in astrocyte-vessel interactions. TBI-induced changes in astrocyte-vessel interactions may indicate chronic BBB vulnerability and processes responsible for early onset vascular and neurodegenerative pathology. [ABSTRACT FROM AUTHOR]

For two Polish state spaces E X and E Y , and an operator G X , we obtain existence and uniqueness of a G X -martingale problem provided there is a bounded continuous duality function H on E X × E Y together with a dual process Y on E Y which is the unique solution of a G Y -martingale problem. For the corresponding solutions (X t) t ≥ 0 and (Y t) t ≥ 0 , duality with respect to a function H in its simplest form means that the relation E x [ H (X t , y) ] = E y [ H (x , Y t) ] holds for all (x , y) ∈ E X × E Y and t ≥ 0. While duality is well-known to imply uniqueness of the G X -martingale problem, we give here a set of conditions under which duality also implies existence without using approximating sequences of processes of a different kind (e.g. jump processes to approximate diffusions) which is a widespread strategy for proving existence of solutions of martingale problems. Given the process (Y t) t ≥ 0 and a duality function H , to prove existence of (X t) t ≥ 0 one has to show that the r.h.s. of the duality relation defines for each y a measure on E X , i.e. there are transition kernels (μ t) t ≥ 0 from E X to E X such that E y [ H (x , Y t) ] = ∫ μ t (x , d x ′) H (x ′ , y) for all (x , y) ∈ E X × E Y and all t ≥ 0. As examples, we treat resampling and branching models, such as the Fleming–Viot measure-valued diffusion and its spatial counterparts (with both, discrete and continuum space), as well as branching systems, such as Feller's branching diffusion. While our main result as well as all examples come with (locally) compact state spaces, we discuss the strategy to lift our results to genealogy-valued processes or historical processes, leading to non-compact (discrete and continuum) state spaces. Such applications will be tackled in forthcoming work based on the present article. [ABSTRACT FROM AUTHOR]

In this paper we study invasion probabilities and invasion times of cooperative parasites spreading in spatially structured host populations. The spatial structure of the host population is given by a random geometric graph on [ 0 , 1 ] n , n ∈ N , with a Poisson (N) -distributed number of vertices and in which vertices are connected over an edge when they have a distance of at most r N with r N of order N (β − 1) / n for some 0 < β < 1. At a host infection many parasites are generated and parasites move along edges to neighbouring hosts. We assume that parasites have to cooperate to infect hosts, in the sense that at least two parasites need to attack a host simultaneously. We find lower and upper bounds on the invasion probability of the parasites in terms of survival probabilities of branching processes with cooperation. Furthermore, we characterize the asymptotic invasion time. An important ingredient of the proofs is a comparison with infection dynamics of cooperative parasites in host populations structured according to a complete graph, i.e. in well-mixed host populations. For these infection processes we can show that invasion probabilities are asymptotically equal to survival probabilities of branching processes with cooperation. Furthermore, we build on proof techniques developed in Brouard and Pokalyuk (2022), where an analogous invasion process has been studied for host populations structured according to a configuration model. We substantiate our results with simulations. [ABSTRACT FROM AUTHOR]

We study the representation theory of the Lie superalgebra g l (1 | 1) , constructing two spectral sequences which eventually annihilate precisely the superdimension 0 indecomposable modules in the finite-dimensional category. The pages of these spectral sequences, along with their limits, define symmetric monoidal functors on Rep g l (1 | 1). These two spectral sequences are related by contragredient duality, and from their limits we construct explicit semisimplification functors, which we explicitly prove are isomorphic up to a twist. We use these tools to prove branching results for the restriction of simple modules over Kac-Moody and queer Lie superalgebras to g l (1 | 1) -subalgebras. [ABSTRACT FROM AUTHOR]

The subventricular zone (SVZ) is one of the neurogenic regions of the adult mammalian brain. Neural stem cells (NSCs) in the SVZ have certain key features: they express glial fibrillary acidic protein (GFAP), proliferate slowly, have a radial glia–like (RG‐L) morphology, and are in contact with the cerebrospinal fluid (CSF). NSCs have been isolated by FACS to analyse them, but their morphology has not been systematically examined. To address this knowledge gap, we sparsely labelled RG‐L cells in the SVZ of neonatal mice by introducing via electroporation a plasmid expressing fluorescent protein under the control of the GFAP promoter. We then classified RG‐L cells into three types (RG‐L1, 2, and 3) based on their morphologies. RG‐L1 cells had a basal process with some branches and numerous fine processes. RG‐L2 cells had a basal process, but fewer branches and fine processes than RG‐L1 cells. RG‐L3 cells had one basal process that was almost free of branches and fine processes. Importantly, regardless of the cell type, about half of their somata resided on the basal side of the SVZ. Based on changes in their proportions during postnatal development and their expression of GFAP and cell proliferation markers at the adult stage, we speculated that NSCs change their morphologies during development/maturation and not all NSCs must always be in the apical SVZ or in contact with the CSF. Our results indicate that in addition to expression of markers for NSCs, the morphology is a critical feature to identify NSCs. [ABSTRACT FROM AUTHOR]

The tensile failure of complex branching cracks will cause irreversible damage to the structures. In this paper, the effects of the crack orientations, the local branch lengths, and the different load forms on the crack propagation pattern and the bearing capacity of structures are investigated based on the phase field method and experimental research method. The results show that the bearing capacity and propagation patterns of the specimens change significantly with the change of the orientation of the Y-shaped crack under tensile load. The local branch length of the crack only affects the sequence in which the regional crack reaches the final failure and the bearing capacity of the specimen. Under the dynamic impact load, the bifurcation phenomenon occurs, and with the increase of the dynamic impact load, the number of bifurcations increases. The crack propagation pattern in the numerical simulation is completely consistent with the experiment, and the difference in the maximum reaction force is 2.5%. [ABSTRACT FROM AUTHOR]

Tumours often display invasive behaviours that induce fingering, branching and fragmentation processes. The phenomenon, known as diffusional instability, is driven by differential cell proliferation, migration, and death due to the presence of metabolite and catabolite concentration gradients. An understanding of the intricate dynamics of this spatially heterogeneous process plays a key role in the investigation of tumour growth and invasion. In this study, we developed an in vitro tumour invasion assay to investigate cell invasiveness in tumour spheroids under a chemotactic stimulus. Our method, employing tumour spheroids seeded in a 3D collagen gel within a microfluidic chemotaxis chamber, focuses on the role of diffusive gradients. Using Time-Lapse Microscopy, the dynamic evolution of tumour spheroids was monitored in real-time, providing a comprehensive view of the morphological changes and cell migration patterns under different chemotactic conditions. Specifically, we explored the impact of fetal bovine serum (FBS) gradients on the behaviour of CT26 mouse colon carcinoma cells and compared the effects of varying FBS concentrations to two isotropic control conditions. Furthermore, a finite element in silico model was developed to quantify the diffusive flow of nutrients in the chemotaxis chamber and obtain a detailed understanding of tumour dynamics. Our findings reveal that the presence of a chemotactic gradient significantly influences tumour invasiveness, with higher concentrations of nutrients associated with increased cancer growth and cell migration. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time t is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given. [ABSTRACT FROM AUTHOR]

Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be accurately approximated by including an additional random time-shift to the initial conditions. We present a efficient numerical method to compute this time-shift distribution for a large class of stochastic models. The method relies on differentiation of certain functional equations, which we show can be effectively automated by deriving rules for different types of model rates that arise commonly when mass-action mixing is assumed. Explicit computation of the time-shift distribution can be used to build a practical tool for the efficient generation of macroscopic trajectories of stochastic population models, without the need for costly stochastic simulations. Full code is provided to implement the calculations and we demonstrate the method on an epidemic model and a model of within-host viral dynamics. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer Science & Technology (JOCSTEC) is the property of PT. Padang Tekno Corp and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We continue with the systematic study of the speed of extinction of continuous-state branching processes in Lévy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime under the assumption that the branching mechanism is regularly varying. We extend recent results of Li and Xu (2018) and Palau et al. (2016), where it is assumed that the branching mechanism is stable, and complement the recent articles of Bansaye et al. (2021) and Cardona-Tobón and Pardo (2021), where the critical and the strongly and intermediate subcritical cases were treated, respectively. Our methodology combines a path analysis of the branching process together with its Lévy environment, fluctuation theory for Lévy processes, and the asymptotic behaviour of exponential functionals of Lévy processes. Our approach is inspired by the last two previously cited papers, and by Afanasyev et al. (2012), where the analogue was obtained. [ABSTRACT FROM AUTHOR]

We study a variant of the color-avoiding percolation model introduced by Krause et al. , namely we investigate the color-avoiding bond percolation setup on (not necessarily properly) edge-colored Erdős–Rényi random graphs. We say that two vertices are color-avoiding connected in an edge-colored graph if, after the removal of the edges of any color, they are in the same component in the remaining graph. The color-avoiding connected components of an edge-colored graph are maximal sets of vertices such that any two of them are color-avoiding connected. We consider the fraction of vertices contained in color-avoiding connected components of a given size, as well as the fraction of vertices contained in the giant color-avoidin g connected component. It is known that these quantities converge, and the limits can be expressed in terms of probabilities associated to edge-colored branching process trees. We provide explicit formulas for the limit of the fraction of vertices contained in the giant color-avoiding connected component, and we give a simpler asymptotic expression for it in the barely supercritical regime. In addition, in the two-colored case we also provide explicit formulas for the limit of the fraction of vertices contained in color-avoiding connected components of a given size. [ABSTRACT FROM AUTHOR]

We study in a general graph-theoretic formulation a long-range percolation model introduced by Lamperti [27]. For various underlying digraphs, we discuss connections between this model and random exchange processes. We clarify, for all $n \in \mathbb{N}$ , under which conditions the lattices $\mathbb{N}_0^n$ and $\mathbb{Z}^n$ are essentially covered in this model. Moreover, for all $n \geq 2$ , we establish that it is impossible to cover the directed n -ary tree in our model. [ABSTRACT FROM AUTHOR]

We consider a discrete-time population growth system called the Bienaymé–Galton–Watson stochastic branching system. We deal with a noncritical case, in which the per capita offspring mean $m\neq1$. The famous Kolmogorov theorem asserts that the expectation of the population size in the subcritical case $m on positive trajectories of the system asymptotically stabilizes and approaches ${1}/\mathcal{K}$ , where $\mathcal{K}$ is called the Kolmogorov constant. The paper is devoted to the search for an explicit expression of this constant depending on the structural parameters of the system. Our argumentation is essentially based on the basic lemma describing the asymptotic expansion of the probability-generating function of the number of individuals. We state this lemma for the noncritical case. Subsequently, we find an extended analogue of the Kolmogorov constant in the noncritical case. An important role in our discussion is also played by the asymptotic properties of transition probabilities of the Q-process and their convergence to invariant measures. Obtaining the explicit form of the extended Kolmogorov constant, we refine several limit theorems of the theory of noncritical branching systems, showing explicit leading terms in the asymptotic expansions. [ABSTRACT FROM AUTHOR]

We show joint convergence of the Łukasiewicz path and height process for slightly supercritical Galton–Watson forests. This shows that the height processes for supercritical continuous-state branching processes as constructed by Lambert (2002) are the limit under rescaling of their discrete counterparts. Unlike for (sub-)critical Galton–Watson forests, the height process does not encode the entire metric structure of a supercritical Galton–Watson forest. We demonstrate that this result is nonetheless useful, by applying it to the configuration model with an independent and identically distributed power-law degree sequence in the critical window, of which we obtain the metric space scaling limit in the product Gromov–Hausdorff–Prokhorov topology, which is of independent interest. [ABSTRACT FROM AUTHOR]

This research explores the legitimation processes underpinning the implementation of specific urban policies in cities grappling with socio-economic challenges, such as in a post-industrial context. Focusing on Europe, where public authorities are seeking to enhance the socio-economic dynamics of post-industrial cities through cultural initiatives like branch museums, our research is based on a historical study of media relating to the establishment in 2012 of the Louvre-Lens museum in northern France. Within this framework, we reveal how institutional actors have performed strategies of legitimation to develop the Louvre-Lens. Our findings underscore the confluence of two primary strategies – economic and cultural –in an effort to navigate the complexities and tensions inherent in establishing a cultural offer in a disadvantaged post-industrial region. We conclude with a discussion about the broader implications of these strategies within the realm of macromarketing. We provide practical recommendations for practitioners and policy makers involved in the development of branch museums. [ABSTRACT FROM AUTHOR]

Aiming at the problem of the low rate of resource utilization of large amounts of grape branch pruning and the high cost of leaving the garden, we design a kind of grape branch picking and crushing collection machine that integrates the collection of strips, the picking up, crushing, and collecting operations. The crushing and collecting parts of the machine are simulated, analyzed, and tested. Using the method of numerical simulation, combined with the results of the pre-branch material properties measurement, the branch crushing process is simulated based on LS-DYNA software. Our analysis found that in the branch destruction process, not only does knife cutting exist, but the bending fracture of the opposite side of the cutting place also exists. With the increase in the knife roller speed, the cutting resistance of the tool increases, reaching 2690 N at 2500 r/min. In the cutting simulation under different tool edge angles, the cutting resistance of the tool is the smallest when the edge angle is 55°, which is 1860 N, and this edge angle is more suitable for branch crushing and cutting. In the cutting simulation under different cutting edge angles, the cutting resistance of the tool is the smallest when the edge angle is 55°, which is 1860 N, and this edge angle is more suitable for branch crushing and cutting. Using Fluent software to analyze the characteristics of the airflow field of the pulverizing device, it was found that with the increase in the knife roller speed, the inlet flow and negative pressure of the pulverizing chamber increase. When the knife roller speed is 2500 r/min, the inlet flow rate and negative pressure are 1.92 kg/s and 37.16 Pa, respectively, which will be favorable to the feeding of the branches, but the speed is too high and will also lead to the enhancement of the vortex in some areas within the pulverizing device, which will in turn affect the feeding of the branches as well as the throwing out of pulverized materials. Therefore, the speed range of the pulverizing knife roller was finally determined to be 1800~2220 r/min. Based on the ANSYS/Model module modal analysis of the crushing knife roller, the knife roller of the first six orders of the intrinsic frequency and vibration pattern, the crushing knife roller of the lowest order had a modal intrinsic frequency of 137.42 Hz, much larger than the crushing knife roller operating frequency of 37 Hz, above which the machine will not resonate during operation. The research results can provide a theoretical basis and technical support for other similar crops to be crushed and collected. [ABSTRACT FROM AUTHOR]

In order to explore the influence of microorganisms from different sources on the composting process of grape branch and pig manure, 3 treatments were set including no external microorganisms (CK), inoculated biogas slurry (T1), and inoculated microbial inoculum (T2) . The temperature, moisture content, pH, electrical conductivity (EC), total nitrogen (TN), total phosphorus (TP), total potassium (TK), seed germination index (GI), bacterial and fungal communities were analyzed during the composting process to determine the key microbial in the composting process. The results showed that the temperature of T1 was higher than that of T2 treatment in the early stage of composting with over 45 °C at the 3rd day, and the maximum temperature all reached 60 °C in 3 treatments. The changes of moisture, pH, EC and nutrient content of compost in each treatment were consistent, and the contents of TN, TP and TK were 3.43%~3.59%, 1.46%~1.56% and 1.87%~2.02%, respectively. The moisture content, pH and EC of compost in T2 were higher than those in other treatments after composted. The germination indexes of CK and T1 treatment exceeded 70% on the 30th day, and reached the organic fertilizer standard faster than T2 treatment. The results of microbial community analysis showed that the relative abundance of Proteobacteria and Firmicutes exceeded 75% in the early stage, Firmicutes was the dominant phylum in the middle stage, and the relative abundances of Bacteroides and Deinococcus-Thermus increased in the middle and final stages, and their final proportions exceeded 20%. There were significant correlations between Firmicutes, Bacteroides, Deinococcus-Thermus and indicators of composting. The analysis of contribution degree showed that the total contribution degree of microbial community to composting was 33.90%, and the contribution degree of Gemmatimonadetes was 80.80%. Above results provided a reference for further research and screening of special antioxidant resistant microorganism inoculants. [ABSTRACT FROM AUTHOR]

Copyright of Environmental & Social Management Journal / Revista de Gestão Social e Ambiental is the property of Environmental & Social Management Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

It is shown that the features of chain processes are determined mainly by the fact that most of the internal energy of the initial reagents is converted into the energy of free valences of atoms and radicals. This results in high concentrations of active particles, which react with the initial reagents at higher rates, providing intensive self-heating, which additionally accelerates the process. It is noted that, without considering the chain nature of reactions, it is impossible to explain ignition upon heating, since the high activation energies of reactions of only molecular reagents exclude an increase in the rate during heating. Taking into account the chain nature of combustion reactions made it possible to explain ignition upon heating and develop a theory of the phenomenon. An explanation is given to the most important characteristic of gas combustion: the length of reaction chains, which determines the role of the chain mechanism in combustion, and the dependence of kinetics on temperature. A solution to the problems of the third flammability limit, confirmed by kinetic and spectroscopic experiments, was obtained, as well as the evidence of the presence of HO2 radicals in the flame, their active role in the heterogeneous development of reaction chains and in combustion in general. The possibility of replacing the solution of diffusion differential equations by effective kinetic parameters when describing combustion has been experimentally proven. [ABSTRACT FROM AUTHOR]

In his famous letter to A. N. Prior dated 3 September 1958, Saul Kripke suggested the use of branching time in temporal logic. In this paper, however, it is argued that Prior worked with an idea close to the notion of branching time ('the big Y') already the year before he received Kripke's letter. It is likely that Prior's findings based on this early study can explain why Prior so quickly accepted the idea of branching time when he received Kripke's letter. [ABSTRACT FROM AUTHOR]

The nonparametric bootstrap has been used in cluster analysis for various purposes. One of those purposes is to account for sampling variability. This can be achieved by obtaining a bootstrap approximation of the sampling distribution function of the estimator of interest and then clustering those distribution functions. Although the consistency of the nonparametric bootstrap in estimating transformations of the sample mean has been known for decades, little is known about how it carries over to clustering. Here, we investigated this problem with a simulation study. We considered single-linkage agglomerative hierarchical clustering and a three-type branching process for parametrized transformations of random vectors of relative frequencies of possible types of the index case of each process. In total, there were nine factors and 216 simulation scenarios in a fully-factorial design. The ability of the bootstrap-based clustering to recover the ground truth clusterings was quantified by the adjusted transfer distance between partitions. The results showed that in the best 18 scenarios, the average value of the distance was less than 20 percent of the maximum possible distance value. We noticed that the results most notably depended on the number of retained clusters, the distribution for sampling the prevalence of types, and the sample size appearing in the denominators of relative frequency types. The comparison of the bootstrap-based clustering results with so-called uninformed random partitioning results showed that in the vast majority of scenarios considered, the bootstrap-based approach led, on average, to remarkably lower classification errors than the random partitioning. [ABSTRACT FROM AUTHOR]

We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and three-region geographic-state speciation-extinction (GeoSSE) models. We show that the species range state dynamics simulated under tree-based and diffusion-based processes are comparable. We derive a method to infer rate parameters that are compatible with given observed stationary state frequencies and obtain an analytical result to compute stationary state frequencies for a given set of rate parameters. We also describe a procedure to find the time to reach the stationary frequencies of a ClaSSE model using our diffusion-based approach, which we demonstrate using a worked example for a two-region GeoSSE model. Finally, we discuss how the diffusion framework can be applied to formalize relationships between evolutionary patterns and processes under state-dependent diversification scenarios. [ABSTRACT FROM AUTHOR]

Galton-Watson forests consisting of N rooted trees and n non-root vertices are considered. The distribution of the forest is determined by that of critical branching process with infinite variance and regularly varying tail of the progeny distribution. We prove limit theorem for the maximal size of a tree in a forest as N, n → ∞ in such a way that n/N → ∞. Our conditions are significantly wider than was previously known. [ABSTRACT FROM AUTHOR]

We consider local probabilities of lower deviations for branching process Zn = Xn,1 + ⋯ + Xn,Zn−1 in random environment η. We assume that η is a sequence of independent identically distributed variables and for fixed η the variables Xi,j are independent and have geometric distributions. We suppose that steps ξi of the associated random walk Sn = ξ1 + ⋯ + ξn has positive mean and satisfies left-side Cramér condition: E exp(hξi) < ∞ if h− < h < 0 for some h− < − 1. Under these assumptions we find the asymptotic of the local probabilities P(Zn = ⌊exp(θn)⌋), n → ∞, for θ ∈ (max(m−, 0); m(− 1)) and for θ in a neighbourhood of m(− 1), where m− and m(− 1) are some constants. [ABSTRACT FROM AUTHOR]

The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup, which is defined by the backward differential equation. We provide a proof of the assertion of Rhyzhov and Skorokhod (Theory Probab. Appl., 1970) on the uniqueness of the solutions to the equation, which is based on a characterization of the process as the pathwise unique solution to a system of stochastic equations. [ABSTRACT FROM AUTHOR]

By generalizing a criterion of Mufa Chen for Markov jump processes, we establish the necessary and sufficient conditions for the extinction, explosion and coming down from infinity of a continuous-state nonlinear Neveu's branching process. [ABSTRACT FROM AUTHOR]

Let (Zn) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm. By similar approach and with the help of a change of measure, we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering (17264073) is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A numerical simulation of the detonation propagation process of acetylene-air under fuel-rich conditions is carried out using a reduced acetylene reaction model. The loose coupling method is used to solve the conservation equations with source terms. The flow is solved explicitly using a gas kinetic scheme, and the chemical reactions are solved implicitly. The numerical results show that the oxidation reaction is the chain initiation in the self-sustained detonation propagation process in rich acetylene. The self-decomposition reaction of acetylene provides the energy to maintain the coupling between the shock wave and the chemical reaction zone. The results show that the initial induced reaction is still an oxidation reaction due to the low activation energy of the oxidation reaction under the condition of low oxygen content. The intensity of the transverse wave is affected by the acetylene concentration. The post-detonation disturbance of temperature is mainly affected by the strength of the tail of transverse wave and the area of the unreacted pocket. With the increase of acetylene concentration, the self-decomposition process of acetylene increases the intensity of the transverse wave tail and improves the degree of temperature homogenization. This creates a formation-fragmentation-regeneration cycle of polycyclic aromatic hydrocarbons. This process changed the branching ratio of polycyclic aromatic hydrocarbons with different structures and delayed the formation of polycyclic aromatic hydrocarbons. When the acetylene concentration is low, the region where the dominant temperature after detonation is 1500 ~ 2500 K provides a favorable environment for the growth of polycyclic aromatic hydrocarbons. [ABSTRACT FROM AUTHOR]

Abstract: Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this article, we extend the multi-type branching process method developed in Keating et al., (2022), which relies on networks having homogenous node properties, to a more general class of clustered networks. Using a model of socially inspired complex contagion we obtain results, not just for the average behaviour of the cascades but for full distributions of the cascade properties. We introduce a new method for the inversion of probability generating functions to recover their underlying probability distributions; this derivation naturally extends to higher dimensions. This inversion technique is used along with the multi-type branching process to obtain univariate and bivariate distributions of cascade properties. Finally, using clique-cover methods, we apply the methodology to synthetic and real-world networks and compare the theoretical distribution of cascade sizes with the results of extensive numerical simulations.

Excited states are the key species in photocatalysis, while the critical parameters that govern their applications are (i) excitation energy, (ii) accessibility, and (iii) lifetime. However, in molecular transition metal-based photosensitizers, there is a design tension between the creation of long-lived excited (triplet), e.g., metal-to-ligand charge transfer (3MLCT) states and the population of such states. Long-lived triplet states have low spin–orbit coupling (SOC) and hence their population is low. Thus, a long-lived triplet state can be populated but inefficiently. If the SOC is increased, the triplet state population efficiency is improved—coming at the cost of decreasing the lifetime. A promising strategy to isolate the triplet excited state away from the metal after intersystem crossing (ISC) involves the combination of transition metal complex and an organic donor/acceptor group. Here, we elucidate the excited state branching processes in a series of Ru(II)-terpyridyl push–pull triads by quantum chemical simulations. Scalar-relativistic time-dependent density theory simulations reveal that efficient ISC takes place along 1/3MLCT gateway states. Subsequently, competitive electron transfer (ET) pathways involving the organic chromophore, i.e., 10-methylphenothiazinyl and the terpyridyl ligands are available. The kinetics of the underlying ET processes were investigated within the semiclassical Marcus picture and along efficient internal reaction coordinates that connect the respective photoredox intermediates. The key parameter that governs the population transfer away from the metal toward the organic chromophore either by means of ligand-to-ligand (3LLCT; weakly coupled) or intra-ligand charge transfer (3ILCT; strongly coupled) states was determined to be the magnitude of the involved electronic coupling. [ABSTRACT FROM AUTHOR]

Let {Zn} be a supercritical branching process with immigration in an independent, identically distributed(i.i.d.) environment ξ. The Berry-Esseen bound for log⁡Zn has been established by Wang et al. (2021). To refine that, under the less restrictive moment conditions, we calculate the exact convergence rate in the central limit theorem for log⁡Zn under the annealed law. [ABSTRACT FROM AUTHOR]

When initially introduced into a susceptible population, a disease may die out or result in a major outbreak. We present a Continuous- Time Markov Chain model for enzootic WNV transmission between two avian host species and a single vector, and use multitype branching process theory to determine the probability of disease extinction based upon the type of infected individual initially introducing the disease into the population -- an exposed vector, infectious vector, or infectious host of either species. We explore how the likelihood of disease extinction depends on the ability of each host species to transmit WNV, vector biting rates on host species, and the relative abundance of host species, as well as vector abundance. Theoretical predictions are compared to the outcome of stochastic simulations. We find the community composition of hosts and vectors, as well as the means of disease introduction, can greatly affect the probability of disease extinction. [ABSTRACT FROM AUTHOR]

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise interactions, and captures a number of important nonlinear models from various fields, including chemical reaction networks, Boltzmann's model of an ideal gas, recombination in population genetics and genetic algorithms. In the context of spin systems, it is a natural generalization of linear dynamics based on Markov chains, such as Glauber dynamics and block dynamics, which are by now well understood. However, the inherent nonlinearity makes the dynamics much harder to analyze, and rigorous quantitative results so far are limited to processes which converge to essentially trivial stationary distributions that are product measures. In this paper we provide the first quantitative convergence analysis for natural nonlinear dynamics in a combinatorial setting where the stationary distribution contains non-trivial correlations, namely spin systems at high temperatures. We prove that nonlinear versions of both the Glauber dynamics and the block dynamics converge to the Gibbs distribution of the Ising model (with given external fields) in times O (n log n) and O (log n) respectively, where n is the size of the underlying graph (number of spins). Given the lack of general analytical methods for such nonlinear systems, our analysis is unconventional, and combines tools such as information percolation (due in the linear setting to Lubetzky and Sly), a novel coupling of the Ising model with Erdős-Rényi random graphs, and non-traditional branching processes augmented by a "fragmentation" process. Our results extend immediately to any spin system with a finite number of spins and bounded interactions. [ABSTRACT FROM AUTHOR]

This research focused its interest on the mathematical modeling of the demographic dynamics of semelparous biological species through branching processes. We continued the research line started in previous papers, providing new methodological contributions of biological and ecological interest. We determined the probability distribution associated with the number of generations elapsed before the possible extinction of the population in its natural habitat. We mathematically modeled the phenomenon of populating or repopulating habitats with semelparous species. We also proposed estimates for the offspring parameters governing the reproductive strategies of the species. To this purpose, we used the maximum likelihood and Bayesian estimation methodologies. The statistical results are illustrated through a simulated example contextualized with Labord chameleon (Furcifer labordi) species.

Peripheral nerve damage often leads to the onset of neuropathic pain (NeuP). This condition afflicts millions of people, significantly burdening healthcare systems and putting strain on families' financial well-being. Here, we will focus on the role of peripheral sensory neurons, specifically the Dorsal Root Ganglia neurons (DRG neurons) in the development of NeuP. After axotomy, DRG neurons activate regenerative signals of axons-soma communication to promote a gene program that activates an axonal branching and elongation processes. The results of a neuronal morphological cytoskeleton change are not always associated with functional recovery. Moreover, any axonal misstargeting may contribute to NeuP development. In this review, we will explore the epidemiology of NeuP and its molecular causes at the level of the peripheral nervous system and the target organs, with major focus on the neuronal crosstalk between intrinsic and extrinsic factors. Specifically, we will describe how failures in the neuronal regenerative program can exacerbate NeuP. [ABSTRACT FROM AUTHOR]

Aiming to address the issues of excessive parameters and inadequate recovery of facial details in certain existing face super-resolution networks, we propose a U-shaped face super resolution reconstruction network based on wavelet transform. Firstly, a novel Refined Feature Extraction Block (RFEB) is proposed in the Down-sampling Unit, which uses two depth-separable convolution blocks as the main branch and introduces a feature calibration path branch and a residual branch to perform refined feature extraction of the original face images. Secondly, in order to further reduce the number of network parameters, a novel Double Branch Distillation Fusion Block (DBDFB) is designed, which uses two branches to process the features extracted in the down-sampling stage respectively. Finally, Discrete Wavelet Transform (DWT) and Inverse Discrete Wavelet Transform (IDWT) are used to extract and retain high-frequency detail information of face images. Quantitative and qualitative experiments show that our method outperforms state-of-the-art face super-resolution algorithms using only a few parameters. The source codes of the proposed method are available at https://github.com/Aichiniuroumian/UFSRNet. [ABSTRACT FROM AUTHOR]

We investigate multitype subcritical Markov branching processes with immigration driven by Poisson random measures. Limiting distributions are established for various rates of the Poisson measures when they are asymptotically equivalent to exponential or regularly varying functions. Results analogous to a strong LLN are proved, and limiting normal distributions are obtained when the local intensity of the Poisson measure increases with time. When it decreases, conditional limiting distributions are established. When the intensity converges to a constant, a stationary limiting distribution is obtained. The asymptotic behavior of the first and second moments of the processes is also investigated. [ABSTRACT FROM AUTHOR]

Vehicle re-identification employs computer vision to determine the presence of specific vehicles in images or video sequences, often using vehicle appearance for identification due to the challenge of capturing complete license plate information. Addressing the performance issues caused by fog, such as image blur and loss of key positional information, this paper introduces a multi-task learning framework incorporating a multi-scale fusion defogging method (MsF). This method effectively mitigates image blur to produce clearer images, which are then processed by the re-identification branch. Additionally, a phase attention mechanism is introduced to adaptively preserve crucial details. Utilizing advanced artificial intelligence techniques and deep learning algorithms, the framework is evaluated on both synthetic and real datasets, showing significant improvements in mean average precision (mAP)—an increase of 2.5% to 87.8% on the synthetic dataset and 1.4% to 84.1% on the real dataset. These enhancements demonstrate the method's superior performance over the semi-supervised joint defogging learning (SJDL) model, particularly under challenging foggy conditions, thus enhancing vehicle re-identification accuracy and deepening the understanding of applying multi-task learning frameworks in adverse visual environments. [ABSTRACT FROM AUTHOR]

The multicomponent coagulation equation is a generalization of the Smoluchowski coagulation equation, where the size of a particle is described by a vector. Similar to the original Smoluchowski equation, the multicomponent coagulation equation exhibits gelation behavior when supplied with a multiplicative kernel. Additionally, a new type of behaviour called localization is observed due to the multivariate nature of the particle size distribution. Here we extend the branching process representation technique, which we introduced to study differential equations in our previous work, and apply it to find a concise probabilistic solution of the multicomponent coagulation equation supplied with monodisperse initial conditions. We also provide short proofs for the gelation time and characterisation the localization phenomenon. [ABSTRACT FROM AUTHOR]

The article studies a single-type critical Markov branching process with infinite variance of the offspring distribution. The process admits also an immigration component at the time points of a non-homogeneous Poisson process. If additionally the mean number of immigrants is infinite, then proper limit distributions are obtained, under suitable normalization of the sample paths, depending on the rate of change of the intensity of the Poisson process. [ABSTRACT FROM AUTHOR]

Cheek and Johnston (JMB 86:70, 2023) consider a continuous-time Bienaymé-Galton-Watson tree conditioned on being alive at time T. They study the reproduction events along the ancestral lineage of an individual randomly sampled from all those alive at time T. We give a short proof of an extension of their main results (Cheek and Johnston in JMB 86:70, 2023, Theorems 2.3 and 2.4) to the more general case of Bellman-Harris processes. Our proof also sheds light onto the probabilistic structure of the rate of the reproduction events. A similar method will be applied to explain (i) the different ancestral reproduction bias appearing in work by Geiger (JAP 36:301–309, 1999) and (ii) the fact that the sampling rule considered by Chauvin et al. (SPA 39:117–130, 1991), (Theorem 1) leads to a time homogeneous process along the ancestral lineage. [ABSTRACT FROM AUTHOR]

Over the last years, bio-based and biodegradable alternatives have gained considerable attention both of academic and of packaging industrial communities, driven by recent legislation and increasing awareness concerning environmental issues related to traditional plastic. However, it is often observed that packaging products made from bioplastics do not exhibit comparable performance to those produced using common non-biodegradable ones. The presence of long chain branching improves the processing behavior under elongational flow and, then, the filmability of low viscosity polymers such as polyesters. In this work it has been demonstrated that the presence of long chain branching in a bio-co-polyester, induced by the use of pentaerythritol in the synthesis a of poly(butylene adipate-co-butylene terephthalate), is able to dramatically change the rheological behavior of the linear chain polyester improving its filmability. The addition of branching lead to an increase of the elastic modulus and the tensile strength in branched polyester films if compared to the linear ones, while the elongation at break decreased. This is due to the answer of the branched polyester to the non-isothermal elongational flow that allows a better orientation of the macromolecules of the branched polyester. The film obtained with the branched polyester showed a decrease in clarity and a slight increase in haze if compared to linear one due to differences in the morphology of the two samples. [ABSTRACT FROM AUTHOR]

Positive leaders branch less frequently than negative counterpart, and the physical processes and properties of positive leader branching remain a mystery. We investigated 10 m laboratory discharges under four positive voltages using a high‐speed video camera. Positive leaders differ from negative leaders by either directly splitting or connecting with floating bidirectional leaders to form branching, and the number of leader branches shows a positive correlation with the applied voltage, that is, the branched channels increased from 1 to 4 when the voltage increased by a factor of 1.5. Grounding points are positioned beneath the electrode and are more concentrated with lower voltage. During the stable progression of the leader, there is a slight increase in its development speed as the applied voltage rises. When the voltage is increased by 70%, the average breakdown time decreases by 40%. These characteristics provide insights into the branching mechanism of positive leaders. Plain Language Summary: The discharge mechanisms in natural and laboratory discharges are highly complex. This study aims to unravel the branching mechanism of positive leaders through laboratory experiments. A specific 10 m rod‐to‐plate discharge gap was designed to vary the maximum applied voltage, making it possible to examine the effects of applied voltage on the leader discharging trunk and branched channels. The statistical results indicate that as the peak voltage increases, the number of leader channels during the discharging process also increases. In natural lightning, positive leader channels generally exhibit low bifurcation rates, whereas in our study, the maximum number of discharging channels reached four with a sufficiently high applied voltage. The strike ground points of the trunk channel tend to be more dispersed when the applied voltage increases. Additionally, as the voltage rises, the average propagation speed of the leader trunk channel also increases. Our study presents the first systematic findings in this field, with crucial implications for a comprehensive understanding on the leader branching process and the development of discharge models. Key Points: The positive correlation between the number of positive leader branches and applied voltage is demonstrated for the first timeAs the applied voltage increased, the strike ground points of the discharge channel became more dispersedThe average 3‐D speed of the positive leader trunk channel exhibits a slight increase with the rising applied voltage [ABSTRACT FROM AUTHOR]

The invasion of Mikania micrantha by climbing and covering trees has rapidly caused the death of many shrubs and trees, seriously endangering forest biodiversity. In this study, M. micrantha seedlings were planted together with local tree species (Cryptocarya concinna) to simulate the process of M. micrantha climbing under the forest. We found that the upper part of the M. micrantha stem lost its support after climbing to the top of the tree, grew in a turning and creeping manner, and then grew branches rapidly to cover the tree canopy. Then, we simulated the branching process through turning treatment. We found that a large number of branches had been formed near the turning part of the M. micrantha stem (TP). Compared with the upper part of the main stem (UP), the contents of plant hormones (auxin, cytokinin, gibberellin), soluble sugars (sucrose, glucose, fructose) and trehalose-6-phosphate (T6P) were significantly accumulated at TP. Further combining the transcriptome data of different parts of the main stem under erect or turning treatment, a hypothetical regulation model to illustrate how M. micrantha can quickly cover trees was proposed based on the regulation of sugars and hormones on plant branching; that is, the lack of support after ascending the top of the tree led to turning growth of the main stem, and the enhancement of sugars and T6P levels in the TP may first drive the release of nearby dormant buds. Plant hormone accumulation may regulate the entrance of buds into sustained growth and maintain the elongation of branches together with sugars to successfully covering trees. [ABSTRACT FROM AUTHOR]

In this paper a continuous-time evolving random graph model is defined and examined. The main units of the model are complete graphs on N vertices, where $ N \geq ~3 $ N ≥ 3 is a fixed integer. At each birth event a new vertex and random number of edges are added to the graph. The asymptotic behaviour of the number of vertices and the asymptotic behaviour of the number of m-cliques ( $ 2\leq m\leq N $ 2 ≤ m ≤ N) are studied. The proofs are based on general results of the theory of branching processes. [ABSTRACT FROM AUTHOR]

Co-evolving network models, wherein dynamics such as random walks on the network influence the evolution of the network structure, which in turn influences the dynamics, are of interest in a range of domains. While much of the literature in this area is currently supported by numerics, providing evidence for fascinating conjectures and phase transitions, proving rigorous results has been quite challenging. We propose a general class of co-evolving tree network models driven by local exploration, started from a single vertex called the root. New vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the direction of the root, connecting to the terminal vertex. Specific choices of the exploration step distribution lead to the well-studied affine preferential attachment and uniform attachment models, as well as less well understood dynamic network models with global attachment functionals such as PageRank scores (Chebolu and Melsted, in: SODA, 2008). We obtain local weak limits for such networks and use them to derive asymptotics for the limiting empirical degree and PageRank distribution. We also quantify asymptotics for the degree and PageRank of fixed vertices, including the root, and the height of the network. Two distinct regimes are seen to emerge, based on the expected exploration distance of incoming vertices, which we call the 'fringe' and 'non-fringe' regimes. These regimes are shown to exhibit different qualitative and quantitative properties. In particular, networks in the non-fringe regime undergo 'condensation' where the root degree grows at the same rate as the network size. Networks in the fringe regime do not exhibit condensation. Further, non-trivial phase transition phenomena are shown to arise for: (a) height asymptotics in the non-fringe regime, driven by the subtle competition between the condensation at the root and network growth; (b) PageRank distribution in the fringe regime, connecting to the well known power-law hypothesis. In the process, we develop a general set of techniques involving local limits, infinite-dimensional urn models, related multitype branching processes and corresponding Perron–Frobenius theory, branching random walks, and in particular relating tail exponents of various functionals to the scaling exponents of quasi-stationary distributions of associated random walks. These techniques are expected to shed light on a variety of other co-evolving network models. [ABSTRACT FROM AUTHOR]

We construct an additive functional playing the role of the local time—at a fixed point x—for Markov processes indexed by Lévy trees. We start by proving that Markov processes indexed by Lévy trees satisfy a special Markov property which can be thought as a spatial version of the classical Markov property. Then, we construct our additive functional by an approximation procedure and we characterize the support of its Lebesgue-Stieltjes measure. We also give an equivalent construction in terms of a special family of exit local times. Finally, combining these results, we show that the points at which the Markov process takes the value x encode a new Lévy tree and we construct explicitly its height process. In particular, we recover a recent result of Le Gall concerning the subordinate tree of the Brownian tree where the subordination function is given by the past maximum process of Brownian motion indexed by the Brownian tree. [ABSTRACT FROM AUTHOR]