Critical Branching Research Articles

Diffusion approximation of critical controlled multi-type branching processes

Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion approximation is derived for some critical CMBPs. Namely, we consider a sequence of appropriately scaled random step functions formed from a critical CMBP with control distributions having expectations that satisfy a kind of linearity assumption. It is proved that such a sequence converges weakly toward a squared Bessel process supported by a ray determined by an eigenvector of a matrix related to the offspring mean matrix and the control distributions of the branching process in question. As applications, among others, we derive Feller-type diffusion approximations of critical, primitive multi-type branching processes with immigration and some two-sex branching processes. We also describe the asymptotic behaviour of the relative frequencies of distinct types of individuals for critical CMBPs.

Market zone configuration under collusive bidding among the conventional generators and renewable energy sources in the day-ahead electricity market

The European cross-zonal day-ahead (DA) electricity market is transitioning to the flow-based market coupling model for market clearing. With the increasing integration of renewable energy sources (RESs), market participants have opportunities for collusive bidding, resulting in decreased social welfare (SW). Thus, this paper is the first to propose an approach to configure the market zone (MZ) considering collusive bidding among conventional generators (CGs) and RESs in the DA market. Specifically, a bi-level model is developed to analyze collusive bidding among the CGs and RESs. Then, multi-dimensional market performance indices are used to determine the critical branches (CBs), on which the configuration of MZs is based. Finally, test 6-bus and simplified European systems are used to demonstrate the validity and merit of the proposed approach. Our simulation on the 6-bus system shows that when compared with the initial zonal market (ZM), the SW of the optimized ZM increased by 18 %, while the re-dispatch surrogate cost decreased to 0. Also, the penetration of RESs improved by 12 %, which guarantees the development of RESs.

A joint image encryption based on a memristive Rulkov neuron with controllable multistability and compressive sensing

Image encryption, as a critical branch, has attracted increasing attention to the demand for information security specifically in the era of artificial intelligence (AI). A chaotic sequence is regarded as an important encryption source, and compressive sensing provides an effective technology for obtaining and reconstructing sparse or compressible signals in applied electronic engineering. In this work, the detouring matching pursuit algorithm and DNA coding are utilized to increase the performance based on a newly developed chaotic firing neuron. A memristor as the electromagnetic component is proven to enhance synaptic plasticity and emulate the synaptic connections in the brain. A unique discrete memristive neuron is derived for exploring the dynamics of neuron firing. By modifying the feedback from the memristor various coexisting neuronal chaotic firing are possessed. Because of the periodic evolution of the resistor from the memristor, the derived memristive Rulkov neuron exhibits coexisting homogeneous and heterogeneous multistability, which enables amplitude controllability and different types of coexisting chaotic firings. Circuit implementation based on CH32 is built to verify the controllability of the coexisting dynamics.

A Flow Graph–Based Scalable Critical Branch Identification Approach for AC State Estimation Under Load Redistribution Attacks

A Flow Graph–Based Scalable Critical Branch Identification Approach for AC State Estimation Under Load Redistribution Attacks

Transient angle stability analysis of maximum Lyapunov exponent based on the key branch response information

Based on real-time access to response information on wide-area tributaries, in order to assess the system stability more quickly, this paper combines the simplified branch transient transmission capability (sBTTC) index and the largest Lyapunov exponent (MLE). An online identification method for transient power angle stability is proposed. Firstly, the method is based on a two-machine system to study the consistency of the power angle difference between the two ends of the critical branch and the change of the phase difference of the fleet. Secondly, the transient power angle stability problem is transformed into the MLE analysis problem according to the change rule of sBTTC index of the key branch. Then, by combining the characteristics of MLE curve and sBTTC index curve, the transient power angle stability criterion is given. Finally, the proposed method is verified and analysed by simulation examples. The method has strong industrial applicability because it does not need system model, the information source is easy to measure, it has strong anti-noise ability, and it overcomes the defect of the traditional method that needs to set a fixed symbolic observation window.

Critical branching dynamics in excitable network without refractory periods

Critical state plays an important role in emerged behavior of neural networks. Excitable networks are widely used in simulation studies. However, the simulation of critical state is sophisticated because the state sensitively depends on dynamical and topological features. We study the effect of refractory period of dynamical units and connection symmetry on the excitable network with critical branching ratio. In bidirectional random networks with refractory period, the critical branching ratio is well known. Here, we show that the collective behavior changes from critical state into ceaseless activity, when refractory period vanishes. Instead of mean degree of all nodes, we show that the control parameter is determined by the mean degree of active nodes which is larger than the average degree and induces the transition. When refractory period is present, the number of effective links connected to resting nodes is equal to average degree. The mechanism ensures the critical branching ratio is unity. In directed networks, collective behavior keeps the critical state when refractory period vanished. However, a few reciprocal links make the network without refractory period becoming ceaseless.

On deterministic approximation for nearly critical branching processes with dependent immigration

In this paper, we investigate the asymptotic behavior of a triangular array of branching processes with non-stationary immigration. In the nearly critical case, we prove weak convergence of properly normalized and scaled branching processes with immigration to a deterministic function when the immigration process is generated by dependent random variables.

Occupation time fluctuations of an age-dependent critical binary branching particle system

Occupation time fluctuations of an age-dependent critical binary branching particle system

Conditional central limit theorem for critical branching random walk

Conditional central limit theorem for critical branching random walk

Asymptotic behaviour of the survival probability of almost critical branching processes in a random environment

A generalization of the well-known result concerning the survival probability of a critical branching process in random environment $Z_k$ is considered. The triangular array scheme of branching processes in random environment $Z_{k,n}$ that are close to $Z_k$ for large $n$ is studied. The equivalence of the survival probabilities for the processes $Z_{n,n}$ and $Z_n$ is obtained under rather natural assumptions on the closeness of $Z_{k,n}$ and $Z_k$. Bibliography: 7 titles.

Thermal Mixing and Flow Characteristics Study in a T-Junction

The objective of the current paper is to investigate the turbulent flow characteristics, thermal mixing behavior, and backflow features of coolant fluid in a T-junction using three-dimensional numerical simulations. The impact of critical flow parameters and different branch pipe axial and transverse incident angles on thermal mixing performance are explored as a function of momentum ratio. The investigation identifies the impact of jet flow, deflection flow, and wall jet flow patterns. The results reveal that the upside backflow of T-junction is more significant for a lower momentum ratio (<0.32) and decreases with higher momentum ratio (0.32 < momentum ratio < 2.7). The efficiency of thermal mixing is considerably improved by changing the incident angle and momentum ratio. Thermal mixing length decreases by ∼39%, 28%, and 21% as compared to the reference case. The current findings will help researchers to understand flow behavior and thermal mixing in a T-junction. It is also useful in high-temperature engineering applications for the evaluation of thermal cracking and safety management.

[Chinese expert consensus on the prevention and treatment of postoperative delirium of cardiovascular surgery].

Postoperative delirium of cardiovascular surgery occurs in up to 26%-52% of patients after cardiovascular surgery and is associated with adverse outcomes, including increased hospital length of stay, higher cost of care, higher rates of readmission. The combination of multiple factors leads to postoperative delirium of cardiovascular surgery, including preoperative (previous psychiatric conditions and cognitive disfunction, cerebrovascular disease, age, cardiac insufficiency, and so on), intraoperative (duration of surgery>5 h, emergency surgery, anesthetic drugs, direct myocardial injury, and so on) and postoperative (pain, sleep disturbance, Deep sedation, duration of mechanical ventilation>72 h) risk factors. On the basis of the latest literature at home and abroad and the clinical experience of many experts, the Cardiac Critical Care Branch of China International Exchange and Promotive Association for Medical and Health sought to develop a consensus document"Chinese expert consensus on the prevention and treatment of postoperative delirium of cardiovascular surgery", in order to standardize the management of postoperative delirium of cardiovascular surgery and improve the prognosis of patients.

Convergence in law for the capacity of the range of a critical branching random walk

Convergence in law for the capacity of the range of a critical branching random walk

A Novel Blockchain-Reinforcement Learning Framework for Securing Wireless Sensor Networks with Energy Efficiency

This paper introduces a novel approach to Reinforcement Learning (RL), focusing on the development and implementation of a Q-learning based algorithm. Reinforcement Learning, a critical branch of machine learning, enables agents to make decisions by interacting with their environment and learning from the consequences of their actions. Our study emphasizes the Q-learning model, a popular, model-free, off-policy algorithm that offers a robust framework for agents to learn optimal strategies in diverse settings. By iteratively updating the action-value function (Q-function) based on observed rewards and future reward estimations, our algorithm aims to achieve efficient learning and decision-making. This work contributes to the field by providing a detailed algorithmic structure, complete with mathematical formulations, that facilitates a deeper understanding of the Q-learning process and its practical applications in various domains.

Population Size of a Critical Branching Process Evolving in an Unfavorable Environment

Population Size of a Critical Branching Process Evolving in an Unfavorable Environment

Architectural Criticism in the Soviet Lithuania 1958-1988: Vision of the New Architecture in the Specialized Periodicals

Architecture criticism of Soviet Lithuania has not been properly addressed in scientific research. The novelty of the work relates to the branch of architecture criticism as part of the history of arts, particularly in the context of the historiography of 20th- century modern architecture. This paper is to uncover the various forms of architectural criticism and its agents among the vocational and scientific publications aimed at other architects of the Lithuanian SSR. Using a systematic approach and qualitative research methods, a database of 100 critical articles is constructed. The phenomena of architecture criticism are explored using the theoretical framework of W. Attoe from his book “Architecture and Critical Imagination” (1978). The results of the research brought several understandings. Despite the common belief among professionals that architects should be predominantly the creators of architecture criticism, architects by profession make up only half or less of the total number of texts in the specialized press. The dominating types of architectural criticism are normative and descriptive (excluding the texts that would describe the context of an architectural idea or particular building). There are very few examples of interpretative criticism encountered (except in the thematic group of criticism around interior design). Further discussion of prevalent thematic groups led to the conclusion that architectural criticism in Soviet Lithuania alongside the official “politically allowed criticism” has been using disguised forms of texts. There has been an underlying narrative to promote modernist or simply, new architecture principles using photography with little to no text, indirect speech, and other forms of non-explicit communication. One of the wider goals of this paper is to initiate wider research into the subject of architectural criticism of Soviet Lithuania and also validate the existence of the neglected phenomena using the specific material of professional and academic architectural publications.

A novel causative role of imbalanced kynurenine pathway in ulcerative colitis: Upregulation of KMO and KYNU promotes intestinal inflammation

The kynurenine pathway (KP) is the principal metabolic route for the essential amino acid tryptophan (TRP). Recent advances have highlighted a pivotal role for several KP metabolites in inflammatory diseases, including ulcerative colitis (UC). However, the alterations of KP enzymes and their functional impact in UC remain poorly defined. Here, we focused on kynurenine 3-monooxygenase (KMO) and kynureninase (KYNU), which serve as critical branching enzymes in the KP. We observed that dextran sodium sulfate (DSS)-induced colitis mice exhibited disturbed TRP metabolism along with KMO and KYNU upregulated. In patients with active UC, both the expression of KMO and KYNU were positively correlated with inflammatory factors TNF-α and IL-1β. Pharmacological blockade of KMO or genetic silencing of KYNU suppressed IL-1β-triggered proinflammatory cytokines expression in intestinal epithelial cells. Furthermore, blockage of KMO by selective inhibitor Ro 61-8048 alleviated the symptoms of DSS-induced colitis in mice, accompanied by an expanded NAD+ pool and redox balance restoration. The protective role of Ro 61-8048 may be partly due to its effect on KP regulation, particularly in enhancing kynurenic acid production. In summary, our study provides new evidence for the proinflammatory property of KMO and KYNU in intestinal inflammation, hinting at a promising therapeutic approach in UC through targeting these enzymes.

Stabilisation of Hydrodynamic Instabilities by Critical Layers in Acoustic Lining Boundary Layers

Acoustics are considered in a straight cylindrical lined duct with an axial mean flow that is uniform apart from a boundary layer near the wall. Within the boundary layer, which may or may not be thin, the flow profile is quadratic and satisfies no-slip at the wall. Time-harmonic modal solutions to the linearized Euler equations are found by solving the Pridmore-Brown equation using Frobenius series. The Briggs–Bers criterion is used to ascertain the spatial stability of the modes, without considering absolute instabilities. The modes usually identified as hydrodynamic instabilities are found to interact with the critical layer branch cut, also known as the continuous spectrum. By varying the boundary-layer thickness, flow speed, frequency, and wall impedance, it is found that these spatial instabilities can be stabilized behind the critical layer branch cut. In particular, spatial instabilities are only found for a boundary layer thinner than a critical boundary-layer thickness . The behaviors observed for the uniform-quadratic sheared flow considered here are further compared to a uniform-linear sheared flow, and a uniform slipping flow under the Ingard–Myers boundary condition, where this process of stabilization is not observed. It is therefore argued that modeling a sufficiently smooth mean flow boundary layer is necessary to predict the correct stability of flow over a lined wall.

Dynamics of cascades in spatial interdependent networks.

The dynamics of cascading failures in spatial interdependent networks significantly depends on the interaction range of dependency couplings between layers. In particular, for an increasing range of dependency couplings, different types of phase transition accompanied by various cascade kinetics can be observed, including mixed-order transition characterized by critical branching phenomena, first-order transition with nucleation cascades, and continuous second-order transition with weak cascades. We also describe the dynamics of cascades at the mutual mixed-order resistive transition in interdependent superconductors and show its similarity to that of percolation of interdependent abstract networks. Finally, we lay out our perspectives for the experimental observation of these phenomena, their phase diagrams, and the underlying kinetics, in the context of physical interdependent networks. Our studies of interdependent networks shed light on the possible mechanisms of three known types of phase transitions, second order, first order, and mixed order as well as predicting a novel fourth type where a microscopic intervention will yield a macroscopic phase transition.

Online evaluation of the distribution system resiliency criteria using Choquet‐based graph technique

AbstractNowadays, due to network expansions, system operators are dealing with natural events including system failures. Evaluating the system readiness to maintain the network interconnections during severe faults are known as an important challenge of today's distribution networks. To do this, this paper presents an online non‐model‐based scheme of evaluating the system resiliency and supplying critical loads within severe natural conditions. In this case, by developing system resiliency as multi‐metric decision making problem and proposing the Choquet integral and graph theoretic methodology, the system resiliency is evaluated. The proposed resiliency scheme is an online non‐model‐based approach can be used for all distribution system configurations with the potential of natural event failures. In this case, by proposing online resiliency criteria based on the system critical loads and branches and developing the proposed criteria on Choquet integral scheme in the form of optimization procedure, the system resiliency is evaluated. The validity of the proposed approach is carried out on two different systems including the IEEE 123‐bus test system and the Consortium for Electric Reliability Technology Solutions (CERTS) microgrid. Simulation results present effectiveness of the proposed scheme to provide proper protective switching strategy and design the system resiliency criteria for future distribution systems.