Growth Rules Research Articles

A clustering coefficient structural entropy of complex networks

The structural entropy is a quantification of the topological structural complexity of the static complex networks, which is defined based on the structural characteristics and the Shannon entropy. For instance, the ’degree structural entropy’ is based on the network’s ’first-order’ topological properties: the degree of each node. The ’betweenness structural entropy’ is based on the betweenness centrality of nodes, which is a global topological structural property of static complex networks. The two different structural entropy give two completely different views of the network’s topological structural complexity. However, a ’mesoscopic’ structural entropy is still missing in the network theory. In this work, a clustering coefficient structural entropy of complex networks is proposed to quantify the structural complexity of static networks on the mesoscopic scale. The effectivity of the proposed ’mesoscopic’ structural entropy is verified in a series of networks that grow from two different seed networks under the Barabási–Albert and Erdős–Rényi rules. We also find that the quantification of structural entropy effectively reflects the impact of structural heterogeneity on the growth rule in the early stages of seed network growth. Finally, we observe that the structural ratio of the clustering coefficient structural entropy and degree structural entropy remains stable and unchanged when network growth reaches maturity. We also note that the convergence rate of the network’s structural entropy ratio varies under different guiding rules. These findings suggest that the differences in structural entropy can serve as a novel tool for measuring the stability of complex networks and provide fresh insights into achieving a ’balanced’ state in the dynamic evolution of complex networks.

RETRACTED: Wang et al. Power Cable Status Evaluation Method Based on Electrical Tree Growth and Data Association Rules. Processes 2023, 11, 2900

The journal retracts the article titled “Power Cable Status Evaluation Method Based on Electrical Tree Growth and Data Association Rules” [...]

Early treatment of Class Ⅲ malocclusion based on craniomaxillofacial growth and development

More and more attention has been paid to the early treatment of malocclusion, especially the early treatment of class Ⅲ malocclusion. Class Ⅲ malocclusion not only affects maxillofacial growth and development, occlusal function and facial beauty, but also leads to serious physical and mental problems. Focusing on class Ⅲ malocclusion, the definition, classification, etiological mechanism, craniofacial growth and development rule, and the influence of early treatment on craniofacial growth and development were reviewed. In class Ⅲ patients, the craniofacial growth and development should be evaluated and analyzed when the early intervention carried out. The purpose of treatment of class Ⅲ malocclusion is achieved by using the appliance to affect the craniomaxillofacial growth.

Gamma-protocadherins regulate dendrite self-recognition and dynamics to drive self-avoidance

Neurons form cell-type-specific morphologies that are shaped by cell-surface molecules and their cellular events governing dendrite growth. One growth rule is dendrite self-avoidance, whereby dendrites distribute uniformly within a neuron's territory by avoiding sibling branches. In mammalian neurons, dendrite self-avoidance is regulated by a large family of cell-recognition molecules called the clustered protocadherins (cPcdhs). Genetic and molecular studies suggest that the cPcdhs mediate homophilic recognition and repulsion between self-dendrites. However, this model has not been tested through direct investigation of self-avoidance during development. Here, we performed live imaging and four-dimensional (4D) quantifications of dendrite morphogenesis to define the dynamics and cPcdh-dependent mechanisms of self-avoidance. We focused on the mouse retinal starburst amacrine cell (SAC), which requires the gamma-Pcdhs (Pcdhgs) and self/non-self-recognition to establish a stereotypic radial morphology while permitting dendritic interactions with neighboring SACs. Through morphogenesis, SACs extend dendritic protrusions that iteratively fill the growing arbor and contact and retract from nearby self-dendrites. Compared to non-self-contacting protrusions, self-contacting events have longer lifetimes, and a subset persists as loops. In the absence of the Pcdhgs, non-self-contacting dynamics are unaffected but self-contacting retractions are significantly diminished. Self-contacting bridges accumulate, leading to the bundling of dendritic processes and disruption to the arbor shape. By tracking dendrite self-avoidance in real time, our findings establish that the γ-Pcdhs mediate self-recognition and retraction between contacting sibling dendrites. Our results also illustrate how self-avoidance shapes stochastic and space-filling dendritic outgrowth for robust pattern formation in mammalian neurons.

Milton Friedman and nominal income targeting

AbstractFor much of his career, Milton Friedman advocated a constant monetary growth rule to limit central bank discretion and to achieve long‐term price stability. By contrast, Friedman wrote little on nominal income stabilization as an alternative goal for monetary policy. Nevertheless, a careful examination of Friedman's work shows that in his view the desirability of a constant monetary growth rule depended on its ability to stabilize nominal income. Friedman's preference for simple rules, requiring minimal knowledge on the part of central banks, would have given him strong reason to support nominal income targeting over central banks' standard practice of inflation targeting. Several strategies for achieving a nominal income target are considered, including a modified Taylor rule and several monetary base rules.

Cellular gradient algorithm for solving complex mechanical optimization design problems

In mechanical optimization design problems, there are often some non-continuous or non-differentiable objective functions. For these non-continuous and non-differentiable optimization objectives, it is often difficult for existing optimal design algorithms to find the desired optimal solutions. In this paper, we incorporate the idea of gradient descent into cellular automata and propose a Cellular Gradient (CG) method. First, we have given the basic rules and algorithmic framework of CG and designed three kinds of growth and extinction rules respectively. Then, the three evolutionary rules for cellular within a single cycle are analyzed separately for form and ordering. The best expressions for the cellular jealous neighbor rule and the solitary regeneration rule are given, and the most appropriate order in which the rules are run is selected. Finally, the solution results of the cellular gradient algorithm and other classical optimization design algorithms are compared with a multi-objective multi-parameter mechanical optimization design problem as an example. The computational results show that the cellular gradient algorithm has an advantage over other algorithms in solving global and dynamic mechanical optimal design problems. The novelty of CG is to provide a new way of thinking for solving optimization problems with global discontinuities.

Structural analysis and the sum of nodes’ betweenness centrality in complex networks

Structural analysis in the field of network science aims to uncover the hidden information embedded within the topological structure of complex networks. Betweenness centrality is a measure that quantifies a node’s influence on the overall network, based on the shortest paths between different pairs of nodes. This unique property of betweenness centrality allows it to capture more structural information than the commonly employed degree centrality, which is a fundamental characteristic of network structure. In this study, we demonstrate that the sum of nodes’ betweenness centralities (SBC) can be utilized as a novel structural index to reveal the underlying rules governing the growth of a network. Additionally, we have developed a method that combines K-shell decomposition and SBC analysis to investigate the growth rules that have shaped the evolution of static networks in the past. Our findings indicate that the Barabási–Albert model guides the network’s SBC to grow in a logarithmic fashion, whereas the Erdős–Rényi model leads to the convergence of SBC values. Interestingly, we also discover that the convergence or divergence of SBC within the k-shell-like decomposition of a static network can be used to distinguish between developed networks (where growth rules have reached saturation) and developing networks (still undergoing expansion). These results highlight the utility of SBC as a reasonable and effective index for the structural analysis of complex networks, providing insights into the rules governing their evolution.

Economic voting behavior: The peak‐end growth rule

AbstractThis paper introduces the peak‐end rule to economic voting, finding that voters focus on peak and end economic growth when evaluating incumbents. Cross‐national data from 595 elections in 70 countries (1960–2020) shows that the average of the highest GDP growth rate during the term and the growth rate in the election year positively impacts incumbent vote share, with peak growth having a stronger effect. Instrumental variable analysis addresses endogeneity. Heterogeneity analysis reveals that less‐educated voters rely more on the peak‐end rule. The findings contribute to understanding voters' behavioral patterns and improving democratic accountability.

Pinning-depinning transitions in two classes of discrete elastic-string models in (2+1)-dimensions

The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to the growth rule, and compare the estimated values with the previous numerical and experimental results. For the (2+1)-dimensional case, we perform extensive simulations on pinning-depinning transitions in these discrete models with quenched disorder. For full comparisons in the physically relevant spatial dimensions, we also perform numerically two distinct universality classes, including the quenched Edwards–Wilkinson, and the quenched Kardar–Parisi–Zhang equations with and without external driving forces. The critical exponents of these systems in the presence of quenched disorder are numerically estimated. Our results show that the critical exponents satisfy scaling relations well, and these two discrete elastic-string models do not fall into the existing universality classes. In order to visually comparisons of these discrete systems with quenched disorder in the (2+1)-dimensional cases, we present surface morphologies with various external driving forces during the saturated time regimes. The relationships between surface morphologies, scaling exponents and correlation length are also revealed.

Crossover effects and dynamic scaling properties from Eden growth to diffusion-limited aggregation

The diffusion-limited aggregation (DLA) model is a classical fractal aggregation model that describes numerous fractal phenomena, and the Eden model is a typical discrete growth model for investigating cell clusters, such as bacteria or tissue cultures. There is a significant difference between these two discrete models in their growth rules and dynamic scaling properties. In this paper, we introduce a generalized growth theory to describe effectively these two distinct growth classes based on the competitive growth rules. By controlling the adhesion coefficient, a continuous transition exists from dense polymerization to finger growth, i.e., the evolution from Eden growth to DLA in both two-dimensional and three-dimensional cases. To simulate effectively the generalized growth system in the most physically relevant case of three-dimensions, we employ a proper technique named the Marsaglia method for correctly obtaining distributed points to avoid the inappropriate simulation schemes commonly used. Furthermore, the crossover of these competitive growth exhibits non-trivial scaling behavior, and the quantitative relation between the corresponding critical exponents and the adhesion parameter is also investigated. Concurrently, the porosities of the generalized growth system are calculated, which exhibit obviously nontrivial dynamic properties depending on the growth dimensions.

Effect of surface radiation on the stability of hypersonic flat plate boundary layer

Transition of hypersonic boundary layer flow is an important problem in aerodynamic research. To obtain the natural transition position using the flow stability analysis method, it is necessary to analysis the neutral curve and the perturbation growth rule. Accurate calculation of the basic flow is the basis and prerequisite for stability analysis. This paper proposes that surface radiation should be considered in the analysis of hypersonic boundary layer flow stability due to the high temperatures at the vehicle surface caused by aerodynamic heating. In order to obtain the influence of surface radiation on the flow stability, we assume that the surface satisfies the energy balance and the gas satisfies calorimetrically perfect gas properties. To simplify the analysis, gas radiation has been neglected. The boundary layer analysis of a hypersonic flat plate with and without radiation has been performed by a combination of flow stability theory and direct numerical simulation. It is found that high temperature radiation on the surface causes energy to transfer outwards. The results showed that surface temperature decreases along the streamwise direction and is no longer an adiabatic surface temperature. Instability interval decreases and the maximum growth rate increases. The range of the instability region expressed in dimensionless frequency values moves to lower frequency as the Mach number increases. Maximum growth rate shows a tendency to increase and then decrease as the Mach number increases.

WPS:A whole phenology-based spectral feature selection method for mapping winter crop from time-series images

Accurately obtaining the spatial distribution and planting patterns of crops is very important for agricultural planning and food security. At present, time-series images have been proved to be an effective tool to characterize crop seasonal growth patterns, and identifying crop information by measuring the time-series similarity between unknown classes and known crop phenology curves is also considered to be a useful way. However, the existing methods of selecting feature ignore the connection between each phenological stage of crops and the unique growth rules of the whole phenology, which makes it difficult to select time-series spectral features that are potentially important for crop mapping. In order to make up for this problem, a Whole Phenology-based Spectral Feature Selection (WPS) method was proposed. The aim was to select the time-series feature sets with great differences among winter crops from a large number of spectral features, so as to improve the mapping accuracy of winter rapeseed and winter wheat. Firstly, spectral separability between all classes is calculated. Secondly, the key phenological periods of winter crops were selected according to the importance of temporal features, and the spectral feature sets with high separability were selected according to the key phenological periods. Finally, a Time-weighted Dynamic Time Warping (TWDTW) algorithm was used to generate the winter rapeseed and winter wheat maps of two cities in the middle and lower reaches of the Yangtze River. The mapping accuracy of the two crops is more than 92%, which matches the crop planting area well. The research shows that combining the WPS method with the TWDTW mapping method has great potential to accurately map crop types based on satellite time-series images.

Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson (EW) and Kardar–Parisi–Zhang (KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation (RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition (BD), etching, and restricted solid on solid (RSOS). The scaling exponents are obtained in both the (1 + 1)- and (2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1 – p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

Terrain-Shape-Adaptive Coverage Path Planning With Traversability Analysis

Coverage path planning (CPP) is in great demand with applications in agriculture, mining, manufacturing, etc. Most research in this area focused on 2D CPP problems solving the coverage problem with irregular 2D maps. Comparatively, CPP on uneven terrains is not fully solved. When there are many slopy areas in the working field, it is necessary to adjust the path shape and make it adapt to the 3D terrain surface to save energy consumption. This article proposes a terrain-shape-adaptive CPP method with three significant features. First, the paths grow by themselves according to the local terrain surface shapes. Second, the growth rule utilizes the 3D terrain traversability analysis, which makes them automatically avoid entering hazardous zones. Third, the irregularly distributed paths are connected under an optimal sequence with an improved genetic algorithm. As a result, the method can provide an autonomously growing terrain-adaptive coverage path with high energy efficiency and coverage rate compared to previous research works. It is demonstrated on various maps and is proven to be robust to terrain conditions.

A biologically inspired repair mechanism for neuronal reconstructions with a focus on human dendrites.

Investigating and modelling the functionality of human neurons remains challenging due to the technical limitations, resulting in scarce and incomplete 3D anatomical reconstructions. Here we used a morphological modelling approach based on optimal wiring to repair the parts of a dendritic morphology that were lost due to incomplete tissue samples. In Drosophila, where dendritic regrowth has been studied experimentally using laser ablation, we found that modelling the regrowth reproduced a bimodal distribution between regeneration of cut branches and invasion by neighbouring branches. Interestingly, our repair model followed growth rules similar to those for the generation of a new dendritic tree. To generalise the repair algorithm from Drosophila to mammalian neurons, we artificially sectioned reconstructed dendrites from mouse and human hippocampal pyramidal cell morphologies, and showed that the regrown dendrites were morphologically similar to the original ones. Furthermore, we were able to restore their electrophysiological functionality, as evidenced by the recovery of their firing behaviour. Importantly, we show that such repairs also apply to other neuron types including hippocampal granule cells and cerebellar Purkinje cells. We then extrapolated the repair to incomplete human CA1 pyramidal neurons, where the anatomical boundaries of the particular brain areas innervated by the neurons in question were known. Interestingly, the repair of incomplete human dendrites helped to simulate the recently observed increased synaptic thresholds for dendritic NMDA spikes in human versus mouse dendrites. To make the repair tool available to the neuroscience community, we have developed an intuitive and simple graphical user interface (GUI), which is available in the TREES toolbox (www.treestoolbox.org).

Long-term day-by-day tracking of microvascular networks sprouting in fibrin gels: From detailed morphological analyses to general growth rules.

Understanding and controlling of the evolution of sprouting vascular networks remains one of the basic challenges in tissue engineering. Previous studies on the vascularization dynamics have typically focused only on the phase of intense growth and often lacked spatial control over the initial cell arrangement. Here, we perform long-term day-by-day analysis of tens of isolated microvasculatures sprouting from endothelial cell-coated spherical beads embedded in an external fibrin gel. We systematically study the topological evolution of the sprouting networks over their whole lifespan, i.e., for at least 14 days. We develop a custom image analysis toolkit and quantify (i) the overall length and area of the sprouts, (ii) the distributions of segment lengths and branching angles, and (iii) the average number of branch generations-a measure of network complexity. We show that higher concentrations of vascular endothelial growth factor (VEGF) lead to earlier sprouting and more branched networks, yet without significantly affecting the speed of growth of individual sprouts. We find that the mean branching angle is weakly dependent on VEGF and typically in the range of 60°-75°, suggesting that, by comparison with the available diffusion-limited growth models, the bifurcating tips tend to follow local VEGF gradients. At high VEGF concentrations, we observe exponential distributions of segment lengths, which signify purely stochastic branching. Our results-due to their high statistical relevance-may serve as a benchmark for predictive models, while our new image analysis toolkit, offering unique features and high speed of operation, could be exploited in future angiogenic drug tests.

Incorporating spatial heterogeneity to model spontaneous and self-organized urban growth

Contemporary investigations into cellular automata (CA) modeling often neglect the considerable influence of spatial heterogeneity on both spontaneous and self-organized processes of urban growth. In this research, we combined a partitioned quantity control strategy, the geographically weighted artificial neural network (GWANN), and a neighborhood size-adaptive approach to formulate a CA framework for simulating spatially heterogeneous spontaneous and self-organized urban growth (SHSS-CA). We examined the simulation performance of SHSS-CA in Beijing, Shanghai, and the Pearl River Delta during 2000–2010 for calibration and 2010–2020 for validation. The findings demonstrate that incorporating spatial heterogeneity enhances CA performance in approximately 90% of regions. Introducing spatially heterogenous spontaneous or self-organized urban growth rules alone can improve the simulation performance of CA. Furthermore, their integration leverages the strengths of both rules and makes SHSS-CA the optimal choice, resulting in a notable improvement in the figure of merit (FoM)—approximately 9% during calibration and around 5% during validation—when compared with ANN-CA. This study contributes new methodologies for developing urban growth simulation rules and has the capacity to effectively help urban planners understand and analyze the complicated urban growth processes.

Choosing the European fiscal rule

ABSTRACT In order to quantitatively assess the potential effects from the ongoing transformation of the fiscal framework of the European Union, we evaluate the economic and public finance stabilization properties of two benchmark fiscal rules using a New Keynesian small open economy model. If these fiscal rules are implemented one at a time, having just an expenditure growth rule tends to yield more stable macroeconomic outcomes but more volatile public finances, as compared to having only a structural balance rule. Much of the quantitative differences in relative volatilities can be accounted for by using a modified public expenditure definition in the expenditure growth rule, in particular the removal of debt service payments. The expenditure growth rule with a strong-enough debt anchor strikes the balance between the short-term macroeconomic stability and the medium-term public debt convergence. There is a welfare gain for households from having only an expenditure growth rule.

Bio-inspired Generative Design for Contact Interfaces

Synovial joints are known by their resistance to wear as they can withstand millions of load cycles. Such performance is attributed to the development process where joints are adapted to the loading environment. In engineering applications, wear is frequently a cause of failure. Classical joint design usually leads to uneven pressure distribution, accelerating wear in concentrated regions. In this work, we use a bio-inspired design methodology to generate contact interfaces. The key point of this methodology is the use of the growth rules of synovial joint during development. Specifically, hydrostatic stress promotes growth and high shear stress inhibits it. We apply these rules in an iterative algorithm to generate contact interfaces adapted to the loading environment. We present a case study to generate the shape of body in frictionless contact with an elastic half space using the bio-inspired approach. We compare the pressure and wear distribution between the bio-inspired and classical designs. The results highlight that the bio-inspired methodology produces almost uniform contact pressure and wear distribution, in contrast to the concentration inherent in classical designs. Thus, this study accentuates the potential advantages of this bio-inspired methodology, offering a compelling avenue for achieving high-performance contact interfaces.

Achieving Superior Corrosion Resistance of TiB2 Reinforced Al-Zn-Mg-Cu Composites via Optimizing Particle Distribution and Anodic Oxidation Time

In this study, the effects of particle distribution and anodizing time on the microstructure and corrosion resistance of the TiB2 particle-reinforced Al-Zn-Mg-Cu composite were investigated. Relationships between TiB2 particle distribution, anodizing time, coating growth rule, and corrosion resistance were characterized and discussed using an optical microscope, a scanning electron microscope, an electrochemical test, and a salt spray test. Dispersion of TiB2 particles by powder metallurgy improved the corrosion resistance of the anodized coating on composites. Compared with the matrix, the corrosion potential (Ecorr) of the anodized coating shifted to the positive direction, and the corrosion current density (icorr) decreased. Meanwhile, the icorr of the coating decreased initially and then increased with the extension of the anodization time. The corrosion resistance of the coating was optimal at an anodization time of 20 min. The corrosion resistance of the composite was determined by both the porosity and thickness of the coating. Additionally, all samples treated by potassium dichromate sealing had no corrosion points after a 336-h salt spray test, demonstrating an excellent corrosion resistance suitable for harsh environmental applications in industry.