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To scientifically evaluate the risk assessment level of lake reservoir type water source areas and take the Luokeng Reservoir water source area in Dianbai District, Maoming City as an example, based on the systematic literature review method, this paper constructs a risk assessment index system for lake reservoir type water source areas from three aspects: water element, management element, and socio-economic element, covering nine levels: water quality, water quantity, aquatic ecology, management and protection level, emergency level, agriculture, industry, economy, and life, with a total of 27 three-level indicators. And it analyzes and determines the risk threshold of the response index, uses fuzzy mathematics to calculate the fuzzy membership function value of the risk evaluation index, and uses the normalization formula of the mutation evaluation method to calculate the total membership function value of the first level evaluation index and the risk evaluation system step by step. The results indicate that the risk level of water sources is closely related to the investment in water source construction. Since the water source area of Luokeng Reservoir is designated as a drinking water source area in 2018, with the increase in investment in water source construction and the enhancement of protection efforts, the risk of water source areas has gradually decreased. From 2018 to 2022, the overall risk assessment level of the water source area of Luokeng Reservoir was ranked as higher risk, higher risk, medium risk, lower risk, and lower risk; The risk assessment levels of water elements are in order of high risk, low risk, low risk, low risk, and low risk. The level transformation of water elements is closely related to the improvement of the annual water supply guarantee rate, annual precipitation, and vegetation coverage rate of the third level indicators. The risk assessment levels of management elements are sequentially high risk, high risk, high risk, low risk, and medium risk. The risk assessment level transformation of management elements is synchronized with the construction investment of Luokeng Reservoir. The risk assessment levels of socio-economic factors are in order of lower risk, medium risk, medium risk, lower risk, and lower risk. The changes in risk levels of socio-economic factors are closely related to industrial wastewater discharge and economic growth rate. This result is consistent with the objective situation of Luokeng Reservoir and is highly reliable. Although the risk of Luokeng Reservoir is relatively low now, it still needs to increase investment in the future. The management department of the water source area of Luokeng Reservoir should actively cooperate with various relevant departments to accelerate the standardized construction of the protected area, increase the comprehensive renovation of the protected area, improve the monitoring level, management personnel level, and emergency level of the water source area, comprehensively ensure the safety of the water source area, and further reduce the risk level of the water source area. [ABSTRACT FROM AUTHOR]

Young's boundary wave theory provides an alternative view of diffraction being an interference of a geometric wave and a boundary wave. Here, we show theoretically and experimentally that the transverse structure of a plane wave diffracted through slits originates solely from the boundary waves. For polygonal slits, we demonstrate that the concept of the ordinary evolute is ill-defined, and we solve this problem by taking the limit of the evolute as the curvature goes to zero. We show that light focuses not on caustic as ordinarily described in catastrophe optics but on regions which we define as second order evolutes. Experimentally, we show that these second order evolutes still correspond to the brightest regions of the diffraction because of the boundary waves at the vertices of the polygon. This research is valuable in the study of diffraction of slits in general and in optical self-healing where the reconstruction of the transverse structure is investigated. [ABSTRACT FROM AUTHOR]

We consider a 2 m th-order nonlinear p -Laplacian difference equation containing both advance and retardation. Using the critical point theory, we establish some new and weaker criteria on the existence of homoclinic solutions with mixed nonlinearities. [ABSTRACT FROM AUTHOR]

The molecular mechanisms of three intramolecular rearrangements (I, the rearrangement of allyloxycycloheptatriene to yield tricyclic ketones; II, the cycloaddition of a nitrone-alkene to render two tricyclic isoxazolidines; and III, the decomposition of N-carbamoyl-L-proline in tetrahydro-1H-pyrrolo[1,2-c]imidazole-1,3(2H)-dione plus water, or tetrahydro-1H,3H-pyrrolo[1,2-c]oxazole-1,3-dione plus ammonia) have been studied by means of the bonding evolution theory (BET). The thermal rearrangement I is composed by a sigmatropic rearrangement coupled to an intramolecular Diels–Alder reaction. The sigmatropic reaction comprises four steps: (1) rupture of an O-C single chemical bond, (2) transformation of a C-O single to double bond, (3) creation of pseudo-radical centers on carbon atoms coupled with a double C-C bond evolving to single and the other C-C double bond migration, and (4) formation of the new C-C single bond. For the Diels–Alder reaction, the process can be described as an initial formation of up to four monosynaptic V(C) basins in two successive steps, coupled with the loss of the double bond character of the three initial double bonds, followed by the consecutive formation of two new C-C bonds, with the new double C-C bond formation sensed in between the formation of the first and the second C-C bonds. For reaction II, the bond forming process is described by the depopulation of N-C and C-C double bonds with the creation of a V(N) and two V(C) monosynaptic basins, followed by an O-C and C-C bond-forming processes via the creation of V(O,C) and V(C,C) disynaptic basins. Finally, for the thermal decomposition III, the reaction mechanism for the water elimination takes place in four events which can be summarized as follows: (1) the depopulation of V(N) with the formation of C-N, (2) the rupture of the C-O bond with transfer of its population to V(O), (3) the restoration of an N nitrogen lone pair via H-N bond cleavage, and (4) the formation of O-H illustrating the water molecule release. For the case of deamination, the events (1) and (2) correspond to the breaking and forming process of H-O and H-N bonds, respectively, while last events deal with the C-O bond formation and the elimination of the NH3 molecule. [ABSTRACT FROM AUTHOR]

Due to the rapid development of technology, process systems become dynamic, automated, and complex, resulting in the strong interdependence and interaction among components and ensuring system safety by conventional methods a challenge. Compared with traditional risk assessment methods, resilience assessment is a more appropriate method for ensuring the safety of process systems under uncertain disruptions. Resilience refers to absorbing and adapting to changing conditions and recovering from disruptions. This paper presents a comprehensive assessment model that combines the catastrophe theory (CT) with the dynamic Bayesian network (DBN) to measure dynamic resilience. Firstly, the CT is employed to quantify the intensity of disruptions. Subsequently, the performance response function (PRF) of the system is determined by DBN. A resilience metric is then introduced to measure system resilience under uncertain disruptions. The method is demonstrated through a release prevention barrier system. [ABSTRACT FROM AUTHOR]

In covalent mechanochemistry, precise application of mechanical stress to molecules of interest ("mechanophores") is used to induce to promote desired reaction pathways. Computational prediction of such phenomena and rational mechanophore design involves the computationally costly task of finding relevant transition-state saddles on force-deformed molecular potential energy surfaces (PESs). Finding a transition state often requires an initial guess about the pathway by which the reaction will proceed. Unfortunately, chemical intuition often fails when predicting likely consequences of mechanical stress applied to molecular systems. Here, we describe a fully deterministic method for finding mechanochemically relevant transition states and reaction pathways. The method is based on the observation that application of a sufficiently high mechanical force will eventually destabilize any molecular structure. Mathematically, such destabilization proceeds via a "catastrophe" occurring at a critical force where the energy minimum corresponding to the stable molecular structure coalesces with a transition state. Catastrophe theory predicts the force-deformed PES to have universal behavior in the vicinity of the critical force, allowing us to deduce the molecular structure of the transition state just below the critical force analytically. We then use the previously developed method of tracking transition-state evolution with the force to map out the entire reaction path and to predict the complete force dependence of the reaction barrier. Beyond its applications in mechanochemistry, this approach may be useful as a general method of finding transition states using fictitious forces to target specific reaction mechanisms. [ABSTRACT FROM AUTHOR]

One of the biggest challenges the world face today is the mortality due to Cancer. One in four of all diagnosed cancers involve the lung cancer, where the mortality rate is high, even after so much of technical and medical advances. Most lung cancer cases are diagnosed either in the third or fourth stage, when the disease is not treatable. The main reason for the highest mortality, due to lung cancer is because of non availability of prescreening system which can analyze the cancer cells at early stages. So it is necessary to develop a prescreening system which helps doctors to find and detect lung cancer at early stages. Out of all various types of lung cancers, adenocarcinoma is increasing at an alarming rate. The reason is mainly attributed to the increased rate of smoking - both active and passive. In the present work, a system for the classification of lung glandular cells for early detection of Cancer using multiple color spaces is developed. For segmentation, various clustering techniques like K-Means clustering and Fuzzy C-Means clustering on various Color spaces such as HSV, CIELAB, CIEXYy and CIELUV are used. Features are Extracted and classified using Support Vector Machine (SVM). [ABSTRACT FROM AUTHOR]

The city of New Orleans has long narrated its own demise through reference to "the Big One," a singular hurricane that would destroy the city for good. The "catastrophe to come" is a more or less permanent spectral presence for many of its residents, evidence of which can be traced as far back as the city's founding in 1718. When it comes to memorialization of Katrina, the central question of this essay is: how does one analyze public memory of an event so thoroughly anticipated, indeed, whose historical anticipation is fundamental to the later memory of it? Rather than merely acting as the historical context within which public memory comes to be interpreted, this anticipation and the anxiety that marks its form figures directly into the reading of the later memory object itself. In this essay, I argue that the repeated narrativization of the Big One is an anxious rhetoric that prefigures post-Katrina memory objects through a process of melancholic rhetorical incorporation. I first engage the history of New Orleans and this anxiety, extrapolating my usage of anxiety and melancholy as rhetorical concepts along the way. Then, I tender a critical analysis that first reads two narratives of such destruction to describe memory's prefiguration and then turns symmetrically to two post-Katrina memory objects to demonstrate the work of incorporation in the production of memory objects. [ABSTRACT FROM AUTHOR]

In spite of the tangible advantages of cloud computing, it is still vulnerable to potential attacks and threats. In light of this, security has turned into one of the main concerns in the adoption of cloud computing. Therefore, an anomaly detection method plays an important role in providing a high protection level for network security. One of the challenges in anomaly detection, which has not been seriously considered in the literature, is applying the dynamic nature of cloud traffic in its prediction while maintaining an acceptable level of accuracy besides reducing the computational cost. On the other hand, to overcome the issue of additional training time, introducing a high-speed algorithm is essential. In this paper, a network traffic anomaly detection model grounded in Catastrophe Theory is proposed. This theory is effective in depicting sudden change processes of the network due to the dynamic nature of the cloud. Exponential Moving Average (EMA) is applied for the state variable in sliding window to better show the dynamicity of cloud network traffic. Entropy is used as one of the control variables in catastrophe theory to analyze the distribution of traffic features. Our work is compared with Wei Xiong et al.'s Catastrophe Theory and achieved a maximum improvement in the percentage of Detection Rate in week 4 Wednesday (7.83%) and a 0.31% reduction in False Positive Rate in week 5 Monday. Additional accuracy parameters are checked and the impact of sliding window size in sensitivity and specificity is considered. [ABSTRACT FROM AUTHOR]

The electronic structure of molecules is routinely assessed using a number of methodologies including Bader's Quantum Theory of Atoms in Molecules (QTAIM) and Weinhold's Natural Bond Orbital/Natural Resonance Theory (NBO/NRT). Previously these methods were applied to the study of isothiirane; however, the results obtained were incongruous with one another: the QTAIM analysis suggested an acyclic structure while NRT indicated a cyclic structure. The previous results assume the NRT description to be correct despite limitations in the analysis, while Foroutan‐Nejad et al. (Chem. Eur. J. 2014, 20, 10140) employed a multiple molecular graph analysis to resolve the QTAIM discrepancy. In this work, we re‐examine the electronic structure of isothiirane, employing a detailed NRT analysis and the catastrophe theory model originally described by Bader for the study of three‐membered ring systems; additional analysis is performed using NMR tensor calculations and studying substituent effects. A congruous description of the electronic structure of isothiirane and the substituted versions is achieved using all modes of analysis. These results highlight how the careful application of commonly used methodologies can achieve a unified description of electronic structure. © 2018 Wiley Periodicals, Inc. The electronic structure of isothiirane is studied using a combined QTAIM, NRT, 13C NMR tensor, and substituent effect analysis. The inner workings of the analysis tools used are critically evaluated. In opposition to previous analysis, which was in disagreement on the electronic structure, isothiirane is described as a hybrid of a carbene and zwitterion (1,3‐dipole). The given methodology can be used to determine any molecules electronic structure and isothiirane may be a new moiety for use in cycloaddition chemistry. [ABSTRACT FROM AUTHOR]

Abstract We study invasion fronts and spreading speeds in two component reaction–diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both components invade at the same speed. Expansions of the wave speed as a function of the diffusion constant of one species are obtained. The bifurcation can be sub or super-critical depending on whether the locked fronts exist for parameter values above or below the bifurcation value. Interestingly, in the sub-critical case numerical simulations reveal that the spreading speed of the PDE system does not depend continuously on the coefficient of diffusion. [ABSTRACT FROM AUTHOR]

Abstract The pressure stability field of the Mg-perovskite phase was investigated by characterizing the evolution of the electron arrangement in the crystal. Ab initio calculations of the perovskite structures in the range 0–185 GPa were performed at the HF/DFT (Hartree-Fock/Density Functional Theory) exchange–correlation terms level. The electron densities, calculated throughout the ab-initio wave functions, were analysed by means of the Bader's theory, coupled with Thom's catastrophe theory. To the best of our knowledge the approach is used for the first time. The topological results show the occurrence of two topological anomalies at P~20 GPa and P~110 GPa which delineate the pressure range where Mg-perovskite is stable. The paper accomplishes the twofold objectives of providing a contribution in shading light into the behaviour of the dominant component of the Earth's lower mantle across the D" layer and of proposing a novel approach in predicting the stability of a compound at extreme conditions. [ABSTRACT FROM AUTHOR]

Highlights • Multicomponent solid solutions of semiconductors are unstable. • For stability analysis, computer simulations can be used. • The generalization of catastrophe theory is used to model stable phases. • Spaces of coexistence of phases of the order of two are found. Abstract Predicting of optimal properties of II–VI materials is an important task in solving the problems of micro- and nanoelectronics. Multicomponent solid solutions based on such semiconductors are promising for modern optoelectronics, for they allow creating devices that operate in a wide spectral range. However, under certain conditions multicomponent solid solutions lose their thermodynamic stability, and thus the properties of the devices based on such materials degrade. Modern methods of computer simulation are used to analyze processes of formation of self-organizing ordered structures. The authors use differential topological approach to obtaining multicomponent phase diagrams taking into account the possibility of existence of bifurcation spaces, critical spaces, and spaces of phase coexistence of different orders. [ABSTRACT FROM AUTHOR]

Abstract Transport planning is gradually shifting targets towards modifying the pedestrian streetscapes that favor walking and enhance urban sustainability. We cannot be optimistic about walkability on condition that walkable streets are not evenly distributed within urban settings. Auditing the street walkability and associated social inequalities in developing countries should provide critical implications for transport planning. This paper identifies the most common indicators in existing indicator classification frameworks based on word frequency; and then establishes an indicator classification system (connectivity, accessibility, suitability, serviceability, and perceptibility) through expert panel evaluation for auditing street walkability in China. Using a case of Hangzhou metropolitan area, a set of 13 indicators are first selected by referring to the established indicator classification system and then aggregated into an integrated walkability index (IWI) through the catastrophe theory (CT) model after appropriate data treatment (standardization, normalization and correlation calculation). Camera signaling data are employed to validate the developed IWI. Results show that IWI is efficient to audit street walkability. IWI presents great heterogeneity at segment level. In general, higher walkability is observed in streets across the central and western areas. Walkability profiles of the segments are further produced by the clustering approach and the categorized groups can inform more targeted planning options. Spatial regression is finally utilized to quantify the associations between community socio-demographics and neighborhood IWI at two levels. We discover that lower neighborhood walkability would be observed in socioeconomically disadvantaged communities. These results suggest that significant social inequalities in street walkability should exist across the communities within Hangzhou metropolitan area. The developed IWI not only brings a standardized measurement of street walkability in the field of transport planning, but also paves the way for addressing the social inequalities in street design across various jurisdictions. [ABSTRACT FROM AUTHOR]

The relationship among person factors, situational factors, and batting performance was examined during a collegiate softball tournament. Specifically, the purposes of the present study were to examine (a) cognitive and somatic anxiety and performance as related to athletes' trait anxiety and situation criticality, and (b) the catastrophe theory prediction that somatic anxiety would differentially relate to performance depending upon the level of cognitive anxiety. Standardized performance scores and intraindividual cognitive and somatic anxiety scores were computed for each athlete (N = 11). As hypothesized, high levels of situation criticality were associated with high levels of cognitive anxiety, but somatic anxiety did not differ in the two situations. Both person and situation factors were significant predictors of cognitive and somatic anxiety; however, the more salient factor was dependent upon the measurement of anxiety (raw scores vs. standardized score). Consistent with the catastrophe theory, somatic anxiety had a different relationship with performance in high criticality situations compared to low criticality situations. [ABSTRACT FROM AUTHOR]

Leading management scholars have called for the use of nonstandard research to help solve complex problems that are not tractable with standard approaches. This article demonstrates the use of multivariate catastrophe model estimation as a partial answer to that call. The approach makes catastrophe theory more useful for researching certain problematic phenomena. Furthermore, it prevents problems with the difference-regression technique used in the past. We use a small application taken from the organization theory literature to demonstrate how the method works and compare the results from this analysis to those from a LISREL analysis of the same data. [ABSTRACT FROM AUTHOR]

Clusters and shells based on icosahedral symmetry are characterised, constructed from component particles that retain memory of their neighbours in a specific reference structure. This memory provides the particles with ‘addressable’ characteristics, with a ground state corresponding to the structure where all the components are correctly addressed in terms of the local environment. The interparticle potentials have separate attractive and repulsive components, defined by the reference structure. For a single target structure, the relaxation efficiency is mostly determined by the variation of the attractive component for correctly and incorrectly addressed particles. The effects of varying the addressability can be visualised directly in terms of the underlying energy landscape, and follow quantitative predictions from catastrophe theory. A doubly-addressable landscape can be designed within the same framework. In well-defined regions of parameter space, the predicted global minima for aggregates of the target cluster (target monomer) form ‘superclusters’, which can be described in terms of multiple interacting copies of local minima for the monomer. The predicted lowest energy superclusters formed from aggregates of addressable icosahedral clusters and shells are themselves based on icosahedral packing. These hierarchical icosahedral structures could be realised experimentally if particles can be synthesised to match the interactions encoded in the addressable potentials. [ABSTRACT FROM AUTHOR]

Large amount of phthalate esters (PAEs) used as plasticizers in polyvinyl chloride (PVC) products has caused ubiquitous contamination to the environment and potential ecology security risk all around the world, especially in places plastic films were indispensably utilized due to the widely proposing of facility agriculture in China. A case of PAEs contamination in four suburb areas of Nanjing was analyzed and discussed in this study. A new frame work has been put forward based on multi-criteria evaluation model and mathematical method of catastrophe theory, using farming work, laboratory determination and relevant environmental standards to measure the ecology security risk of PAEs in study areas. The factors were selected based on the availability of the data and the local conditions. The assessment model involves the contamination status of PAEs in soil and vegetables, the contamination effects of PAEs to human and soil organisms and the contamination source of PAEs from plastic films and other products in the four study facility agriculture areas. An evaluation system of the model was composed of thirteen mesosphere indicators and twenty-five underlying indicators including total PAEs concentration in soils, single PAE concentration in soils, total PAEs concentrations in roots, leafy, solanaceous and stem vegetables, PAE human risks, soil microbial counts, microorganism diversity indices, atmospheric deposition of PAEs, whether sewage wastewater irrigation, planting mode of the facility agriculture areas and climate condition of study areas. The modified evaluation system was used in the assessment of ecology security of the same place based on the data of 2012, and the results suggested that the ecology security indicators were reliable and were agree well with the practical situation of the study areas. The results could provide guidance for the application of health risk assessment of soil environment for the strong objectivity of catastrophe theory compared with other evaluation methods. [ABSTRACT FROM AUTHOR]

Experimental investigation on deflection behaviour of fly ash cenosphere/epoxy syntactic foam at room temperature and under thermal environment (three different heating conditions) is investigated. Influence of fly ash cenosphere volume fraction and nature of temperature variation on deflection behaviour of syntactic foam beam is discussed elaborately. Results reveal that the syntactic foam beam experience snap-through buckling under thermal environment and is reflected by two bifurcation points in temperature-deflection plot. It is observed that the time duration for which the foam beam stays in the first buckled position increases with increase in cenosphere content. Thermal environment induces compressive stresses in the samples causing such snap-through buckling. However, such phenomenon is not observed when mechanical compressive loads are applied under room temperature conditions. Temperature variation across the beam strongly influences snap-through buckling in syntactic foams in addition to volume fraction of filler content. [ABSTRACT FROM AUTHOR]

Resilience thinking explores the sustainability discourse and transformation of urban complex systems. From the perspective of urban and human environment, this research simulated the resilience transformation of human-environment systems according to the modified catastrophe theory. The adaptive cycle model was performed an approach to interpret resilience transformations in the interactive human-environment systems. In this study, we quantified the resilience of human and environment sub-systems through four models of catastrophe theory (Fold, Cusp, Swallowtail and Butterfly model). The resilience transformation was addressed through the mechanism of adaptive cycle that contained four phases within four different time periods (exploitation- r : 2000–2002; release phase- Ω : 2002–2003; conservation- K : 2004–2008 and exploitation- r : 2008–2010). Ultimately, we explored the key drivers of the transformation in complex human-environmental systems, which included production, energy and pollution. Moreover, understanding the transformations in terms of the human and environmental components were indispensable in urban resilience management. [ABSTRACT FROM AUTHOR]

In this paper, the bifurcations of a discrete stage-structured population model with self-limitation between the two subgroups are investigated. We explore all possible codimension-one bifurcations associated with transcritical, flip (period doubling) and Neimark-Sacker bifurcations and discuss the stabilities of the fixed points in these non-hyperbolic cases. Meanwhile, we give the explicit approximate expression of the closed invariant curve which is caused by the Neimark-Sacker bifurcation. After that, through the theory of approximation by a flow, we explore the codimension two bifurcations associated with 1:3 strong resonance. We convert the nondegenerate condition of 1:3 resonance into a parametric polynomial, and determine its sign by the theory of complete discrimination system. We introduce new parameters and utilize some variable substitutions to obtain the bifurcation curves around 1:3 resonance, which are returned to the original variables and parameters to express for easy verification. By using a series of complicated approximate identity transformations and polar coordinate transformation, we explore 1:6 weak resonance. Moreover, we calculate the two boundaries of Arnold tongue which are caused by 1:6 weak resonance and defined as the resonance region. Numerical simulations and numerical bifurcation analyzes are made to demonstrate the effective of the theoretical analyzes and to present the relations between these bifurcations. Furthermore, our theoretical analyzes and numerical simulations are explained from the biological point of view. [ABSTRACT FROM AUTHOR]

Earthquake prediction has been a challenging research area, where a future occurrence of the devastating catastrophe is predicted. In this work, sixty seismic features are computed through employing seismological concepts, such as Gutenberg-Richter law, seismic rate changes, foreshock frequency, seismic energy release, total recurrence time. Further, Maximum Relevance and Minimum Redundancy (mRMR) criteria is applied to extract the relevant features. A Support Vector Regressor (SVR) and Hybrid Neural Network (HNN) based classification system is built to obtain the earthquake predictions. HNN is a step wise combination of three different Neural Networks, supported by Enhanced Particle Swarm Optimization (EPSO), to offer weight optimization at each layer. The newly computed seismic features in combination with SVR-HNN prediction system is applied on Hindukush, Chile and Southern California regions. The obtained numerical results show improved prediction performance for all the considered regions, compared to previous prediction studies. [ABSTRACT FROM AUTHOR]

We develop novel mathematical techniques to study spot patterns in reaction-diffusion systems with space-dependent feed rate. The techniques are illustrated on the Schnakenberg model, which is a prototypical model of spot formation. Previous works have mostly addressed spot formation assuming the feed rate A is a constant, in which case the spots are uniformly distributed throughout the domain. By contrast, the spatially dependent feed rate A(x) occurs naturally in applications, and very few studies exist in this case. In this work we determine analytically how this inhomogeneity affects spot creation, spot density, and spot death. We characterize the asymptotic density of spots and their heights for any spatially dependent feed rate A(x). We also demonstrate a novel phenomenon which only happens when the feed rate is sufficiently inhomogeneous in space. Namely, new spots are continuously created in regions of high feed rate, travel toward regions of lower feed rate, and are destroyed there. This \creation-destruction loop" is only possible in the presence of heterogeneity. A key new technique is the use of the Euler{Maclaurin formula to estimate the effective spike density. For a sufficiently large feed rate, we find that the effective spot density scales like A2/3(x), whereas the spot mass scales like A1/3(x). We derive asymptotic bounds for the existence of N spots. As the feed rate is increased, new spots are created through self-replication, whereas the spots are destroyed as the feed rate is decreased. The thresholds for both spike creation and spike death are computed asymptotically. [ABSTRACT FROM AUTHOR]

The aim of this article is the identification of the occurrence mechanism of sudden quantitative changes in real-estate market prices, which were observed during the global financial crisis. Since such phenomena did not occur to such an intensity during previous crises, it can be assumed that a new economic dynamic type has emerged in real-estate markets. The most promising of the methods of studying such phenomena seems to be the bifurcation method and particularly the catastrophe theory. This study analyzes changes in the prices of residential property based on cusp catastrophes. Empirical data were fit to a stochastic cusp model to visualize the evolutionary path of real estate market. Two other popular models (linear and logistic) were also estimated to compare results. A comparative analysis proved that the cusp model can best explain structural price instabilities in real-estate markets. The results confirmed that the evolution of the real estate market combines two processes: long-term evolution in the area of non-degenerate stability and discontinuous changes in the area of degenerate stability. Structural changes take place in the system only in the area of degenerate stability. The theoretical and practical results show that the catastrophe theory may have predictive potential, which could support traditional methods of predicting changes on real estate markets. [ABSTRACT FROM AUTHOR]

In the note a comprehensive and optimal passive-active mode for describing tire limit failure of circular shallow tunnel with settlement is put forward to predict the catastrophic stability during the geotechnical construction. Since the surrounding soil mass around tunnel roof is not homogeneous, with tools of variation calculus, several different curve functions which depict several failure shapes in different soil layers are obtained using virtual work formulae. By making reference to the simple-fonn of Power-law failure criteria based on numerous experiments, a numerical procedure with consideration of combination of upper bound theorem and stochastic medium theory is applied to the optimal analysis of shallow-buried tunnel failure. With help of functional catastrophe theory, this work presented a more accurate and optimal failure profile compared with previous work. Lastly the note discusses different effects of parameters in new yield rule and soil mechanical coefficients on failure mechanisms. The scope of failure block becomes smaller with increase of the parameter A and the range of failure soil mass tends to decrease with decrease of unit weight of the soil and tunnel radius, which verifies the geomechanics and practical case in engineering. [ABSTRACT FROM AUTHOR]

Highlights • Expression level homeostasis is a biological property that is linked to feed-forward loop GRN motif topology. • The analysis of homeostasis uses the new concepts of infinitesimal homeostasis (points where the input-output map has a critical point) and infinitesimal chair points (vanishing second derivatives). • Infinitesimal homeostasis can be located analytically by using implicit differentiation in model equations. • The analytic techniques are based on singularity theory, specifically elementary catastrophe theory, and, as such, can be applied to many models and many network motifs. Moreover, singularity theory universal unfoldings provide a type of structural stability for chair points. • The techniques lead naturally to a method for numerical exploration that can be used on more complicated model equations or network topologies. Abstract The internal state of a cell is affected by inputs from the extra-cellular environment such as external temperature. If some output, such as the concentration of a target protein, remains approximately constant as inputs vary, the system exhibits homeostasis. Special sub-networks called motifs are unusually common in gene regulatory networks (GRNs), suggesting that they may have a significant biological function. Potentially, one such function is homeostasis. In support of this hypothesis, we show that the feed-forward loop GRN produces homeostasis. Here the inputs are subsumed into a single parameter that affects only the first node in the motif, and the output is the concentration of a target protein. The analysis uses the notion of infinitesimal homeostasis, which occurs when the input-output map has a critical point (zero derivative). In model equations such points can be located using implicit differentiation. If the second derivative of the input-output map also vanishes, the critical point is a chair : the output rises roughly linearly, then flattens out (the homeostasis region or plateau ), and then starts to rise again. Chair points are a common cause of homeostasis. In more complicated equations or networks, numerical exploration would have to augment analysis. Thus, in terms of finding chairs, this paper presents a proof of concept. We apply this method to a standard family of differential equations modeling the feed-forward loop GRN, and deduce that chair points occur. This function determines the production of a particular mRNA and the resulting chair points are found analytically. The same method can potentially be used to find homeostasis regions in other GRNs. In the discussion and conclusion section, we also discuss why homeostasis in the motif may persist even when the rest of the network is taken into account. [ABSTRACT FROM AUTHOR]

The stress path characteristics of surrounding rock in the formation of gob were analysed and the unloading was solved. Taking Chengchao Iron Mine as the engineering background, the model for analysing the instability of deep gob was established based on the mechanism of stress relief in deep mining. The energy evolution law was investigated by introducing the local energy release rate index (LERR), and the energy criterion of instability of surrounding rock was established based on the cusp catastrophe theory. The results showed that the evolution equation of the local energy release energy of the surrounding rock was quartic function with one unknown and the release rate increased gradually during the mining. The calculation results showed that the gob was stable. The LERR per unit volume of the bottom structure was relatively smaller, which mean the stability was better. The LERR distribution showed that there was main energy release in the horizontal direction and energy concentration in the vertical direction which meet the characteristics of deep mining. In summary, this model could effectively calculate the stability of surrounding rock in the formation of gob. The LERR could reflect the dynamic process of energy release, transfer and dissipation which provided an important reference for the study of the stability of deep mined out area. [ABSTRACT FROM AUTHOR]

Using catastrophe theory and the concept of a mutation path, an algorithm is developed that leads to the direct correlation of the normal vibrational modes of two structurally related molecules. The mutation path is defined by weighted incremental changes in mass and geometry of the molecules in question, which are successively applied to mutate a molecule into a structurally related molecule and thus continuously converting their normal vibrational spectra from one into the other. Correlation diagrams are generated that accurately relate the normal vibrational modes to each other by utilizing mode-mode overlap criteria and resolving allowed and avoided crossings of vibrational eigenstates. The limitations of normal mode correlation, however, foster the correlation of local vibrational modes, which offer a novel vibrational measure of similarity. It will be shown how this will open new avenues for chemical studies. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The critical points analysis of electron density, i.e. ρ(x), from ab initio calculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/ temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points, i.e. such that ▿(xc) = 0 and λ1 , λ2, λ3 6≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) at xc], towards degenerate critical points, i.e. ▿(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood of xc and allows one to rationalize the occurrence of instability in terms of electrondensity topology and Gibbs energy. The phase/state transitions that TiO2 (rutile structure), MgO (periclase structure) and Al2O3 (corundum structure) undergo because of pressure and/or temperature are here discussed. An agreement of 3- 5% is observed between the theoretical model and experimental pressure/ temperature of transformation. [ABSTRACT FROM AUTHOR]

The possibilities of the Catastrophe Theory for predicting the dynamics of forest ecosystems and developing scenarios for sustainable forest management are discussed. The main features of the approach are described. The achievements and difficulties of application for the Catastrophe Theory in scientific research have been discussed. Examples are given of the application for the study of ecotones (steppe - forest), succession modeling, forest restoration prediction and forest description as a multilayer system. Particular attention is paid to the problem of reforestation. The Catastrophe Theory can provide an explanation for the appearance of abrupt changes in reforestation as a result of minor changes in controlling factors and why such changes occur in different configurations of control factors. Methods of Catastrophe Theory allow, identifying and predicting crises in the forest development, which is very important for the management of bioresources. A great achievement of modern Catastrophe Theory is the transition from qualitative forecasting of generalized situations to quantitative prediction of real situations. Modern models, built on its basis and parameterized using field observations, describe real situations quantitatively. These models can be used to assess whether the trajectory is following the desired path and to estimate recovery rate or to forecasting possible scenarios. The methods of Catastrophe Theory are universal and can be used for all forests of the world and other ecosystems. [ABSTRACT FROM AUTHOR]

Discontinuities as a crucial aspect of economic systems have been discussed both verbally—particularly in institutionality theory—and formally, chiefly using catastrophe theory. Catastrophe theory has, however, been criticized heavily for lacking micro-foundations and has mainly fallen out of use in economics and social sciences. The present paper proposes a simple catastrophe theory model of technological change with network externalities and reevaluates the value of such a model by adding an agent-based micro layer. To this end an agent-based variant of the model is proposed and investigated specifically with regard to the network structure among the agents. While the macro level of the model produces a classical cusp catastrophe—a result that is preserved in the agent-based form—it is found that the behavior of the model changes locally depending on the network structure, especially if networks with features that resemble social networks (low diameter, high clustering, power law distributed node degree) are considered. While the present work investigates merely an aspect out of a large possibility space, it encourages further research using agent-based catastrophe theory models especially of economic aspects to which catastrophe theory has previously successfully been applied; aspects such as technological and institutional change, economic crises, or industry structure. [ABSTRACT FROM AUTHOR]

Bursting discharge is a ubiquitous behavior in neurons, and abundant bursting patterns imply many physiological information. There exists a closely potential link between bifurcation phenomenon and the number of spikes per burst as well as mixed-mode oscillations (MMOs). In this paper, we have mainly explored the dynamical behavior of the reduced Purkinje cell and the existence of MMOs. First, we adopted the codimension-one bifurcation to illustrate the generation mechanism of bursting in the reduced Purkinje cell model via slow-fast dynamics analysis and demonstrate the process of spike-adding. Furthermore, we have computed the first Lyapunov coefficient of Hopf bifurcation to determine whether it is subcritical or supercritical and depicted the diagrams of inter-spike intervals (ISIs) to examine the chaos. Moreover, the bifurcation diagram near the cusp point is obtained by making the codimension-two bifurcation analysis for the fast subsystem. Finally, we have a discussion on mixed-mode oscillations and it is further investigated using the characteristic index that is Devil's staircase. [ABSTRACT FROM AUTHOR]

Considering the change of the parameter related to the natural enemy population and the impact on the aphid populations in the fold catastrophe manifold, the singular system model of aphid ecosystems is proposed. Combining singular system theory with catastrophe theory, the corresponding dynamics behaviors and the existence conditions of the impasse points are given by using the qualitative analysis. The biological significance of the analytical results is also discussed. The controllers are designed to make the aphid populations stabilize the refuge level by releasing natural enemy. Some numerical simulations are carried out to prove the results. [ABSTRACT FROM AUTHOR]

Reducing the fuel load in fire-prone landscapes is aimed at mitigating the risk of catastrophic wildfires but there are ecological consequences. Maintaining habitat for fauna of both sufficient extent and connectivity while fragmenting areas of high fuel loads presents land managers with seemingly contrasting objectives. Faced with this dichotomy, we propose a Mixed Integer Programming (MIP) model that can optimally schedule fuel treatments to reduce fuel hazards by fragmenting high fuel load regions while considering critical ecological requirements over time and space. The model takes into account both the frequency of fire that vegetation can tolerate and the frequency of fire necessary for fire-dependent species. Our approach also ensures that suitable alternate habitat is available and accessible to fauna affected by a treated area. More importantly, to conserve fauna the model sets a minimum acceptable target for the connectivity of habitat at any time. These factors are all included in the formulation of a model that yields a multi-period spatially-explicit schedule for treatment planning. Our approach is then demonstrated in a series of computational experiments with hypothetical landscapes, a single vegetation type and a group of faunal species with the same habitat requirements. Our experiments show that it is possible to fragment areas of high fuel loads while ensuring sufficient connectivity of habitat over both space and time. Furthermore, it is demonstrated that the habitat connectivity constraint is more effective than neighbourhood habitat constraints. This is critical for the conservation of fauna and of special concern for vulnerable or endangered species. [ABSTRACT FROM AUTHOR]

Cooperative control consensus is one of the most actively studied topics within the realm of multi-agent systems. It generally aims to drive multi-agent systems to achieve a common group objective. The core aim of this paper is to promote research in cooperative control community by presenting the latest trends in this field. A summary of theoretical results regarding consensus for agreement analysis for complex dynamic systems and time-invariant information exchange topologies is briefly described in a unified way. The application under both non-formation and formation cooperative control consensus for multi-agent system also investigated. In addition, future recommendations and some open problems are also proposed. [ABSTRACT FROM AUTHOR]

An abrupt increase in urban road traffic flow caused by incidental congestion is considered. The residual traffic capacity varies in different lanes after an accident, and the influence of accident duration on traffic flow is taken into account. The swallowtail catastrophe model was built based on catastrophe theory. The critical state of traffic congestion under incidental congestion was analyzed using this model, and a traffic flow control scheme is proposed with the goal of maximizing the traffic capacity. Finally, the operational state of traffic flow under different scenarios is analyzed through case study and the feasibility of the model is validated. [ABSTRACT FROM AUTHOR]

The improved catastrophe theory is introduced into the study of water environment carrying capacity. With coupling of 4 subsystems which are, water resource factors, ecological environment factors, social resources allocation capacity factors, social and economic factors as the basic framework, 12 indexes were selected to construct the model of water environment carrying capacity. Based on the characteristics of normalization formula of aggregation, the rating scale refinement method was used to improve conventional catastrophe theory and to obtain the adjusted comprehensive value. Then according to the evaluation habits, fuzzy judgment was selected to determine the evaluation threshold, five grade evaluation was used to evaluate water environment carrying capacity. At the last, the water environment carrying capacity in Yichang city was evaluated, the results show that: during 2010-2015, water environmental carrying capacity in Yichang city was on the rise, but in 2020 the Yichang city water environmental carrying capacity will decrease sharply. We need to strengthen environmental protection and governance level. [ABSTRACT FROM AUTHOR]

This article deals with the problem of probabilistic prediction of the time distance to default for a firm. To model the credit risk, the dynamics of an asset is described as a function of a homogeneous discrete time Markov chain subject to a catastrophe, the default. The behaviour of the Markov chain is investigated and the mean time to the default is expressed in a closed form. The methodology to estimate the parameters is given. Numerical results are provided to illustrate the applicability of the proposed model on real data and their analysis is discussed. [ABSTRACT FROM AUTHOR]

In a 1350-W Hall-effect thruster, in which a technique for pushing down the magnetic field is implemented, a catastrophic discharge phenomenon is identified by varying the magnetic field strength while keeping all other operating parameters constant. According to experiments, before and after the discharge catastrophe, the plume changes from focusing state to a divergent state, and discharge parameters such as discharge current and thrust exhibit noticeable changes. The divergence half-angle of the plume increases from 22° to 46°. The oscillation amplitude and mean values of the discharge current significantly increase from 0.8 A to 4 A and from 4.6 A to 6.3 A, respectively, while the thrust increases from 89.3 mN to 91 mN. Analysis of the experimental results shows that as the maximum magnetic field of the thruster we developed is in the plume region, the acceleration occurs in the plume region and a large number of Xe 2+ ions appear in the plume area, the catastrophic discharge phenomenon observed. [ABSTRACT FROM AUTHOR]

The routinely made assumptions for simulating solid materials are briefly summarized, since they need to be critically assessed when new aspects become important, such as excited states, finite temperature, time-dependence, etc. The significantly higher computer power combined with improved experimental data open new areas for interdisciplinary research, for which new ideas and concepts are needed. [ABSTRACT FROM AUTHOR]

To overcome the inherent shortcomings of the human development index (HDI) and to improve the comparability of evaluation results, in this study, an evaluation indicator system of regional sustainable development pressures was constructed based on catastrophe theory. An improved catastrophe model was used to calculate the sustainable development pressure index (SPI), which was combined with the human development index (HDI) proposed by the United Nations Development Program (UNDP) to explore the human welfare and sustainable development pressures in 9 countries bordering the South China Sea in the period 2003–2015 based on statistical data provided by the World Bank. It was found that during the period of investigation, the level of human welfare in the region gradually increased and the HDI steadily rose, with an average annual growth rate between 0.29% and 2.50%. The sustainable development pressures in the South China Sea neighboring region were very high, and the development models in this region can be divided into 4 types: very high level human welfare with very high sustainable development pressures; high level human welfare with very high sustainable development pressures; medium level human welfare with very high sustainable development pressures; and low level human welfare with very high sustainable development pressures. It is recommended that a country should explore its own development path based on the actual situation in the country to reduce sustainable development obstacles. Moreover, bilateral or multilateral cooperation should be actively pursued to solve the bottleneck problems that restrict regional sustainable development. [ABSTRACT FROM AUTHOR]

This study developed a new paradigm for groundwater vulnerability assessment by modifying the standard DRASTIC index (DI) model based on catastrophe theory. The developed paradigm was called the catastrophe theory-based DI (CDI) model. The proposed model was applied to assess groundwater vulnerability to pollution index (GVPI) in Perak Province, Malaysia. The area vulnerability index was modeled by considering the DRASTIC multiple vulnerability causative factors (VCFs) obtained from different data sources. The weights and ranking of the VCFs were computed by using the inner fuzzy membership mechanism of the CDI model. The estimated vulnerability index values of the CDI model were processed in a geographic information system (GIS) environment to produce a catastrophe theory-DRASTIC groundwater vulnerability to pollution index (CDGVPI) map, which demarcated the area into five vulnerability zones. The produced CDGVPI map was validated by applying the water quality status-vulnerability zone relationship (WVR) approach and the relative operating characteristic (ROC) curve method. The performance of the developed CDI model was compared with that of the standard DI model. The validation results of the WVR approach exhibits 89.29% prediction accuracy for the CDI model compared with 75% for the DI model. Meanwhile, the ROC validation results for the CDI and DI models are 88.8% and 78%, respectively. The GIS-based CDI model demonstrated better performance than the DI model. The GVPI maps produced in this study can be used for precise decision making process in environmental planning and groundwater management. [ABSTRACT FROM AUTHOR]

This paper develops and estimates catastrophe-augmented models of the financial crisis. We employ catastrophe theory to explain discontinuous jumps in state variables of dynamic systems. We estimate an augmented bank failure model showing that the buildup of risk and an increase in the Federal Funds rate combined with low reserves (negative insurance effect) have been the main drivers of the financial crisis. Therefore, macroprudential policy and rating agencies play a key role in preventing the buildup of (systemic) risk and preventing the economy from entering a bifurcation area. [ABSTRACT FROM AUTHOR]

The critical behavior of 100–106 Ru isotopes is investigated in the U ( 5 ) ↔ SO ( 9 ) transitional region of the spd-interacting boson model. We have developed a solvable extended transitional Hamiltonian based on affine SU ( 1 , 1 ) Lie algebra within the framework of the spd-interacting boson model. Also, we have used the catastrophe theory in combination with coherent state formalism to generate the energy surfaces of considered isotopes. The parameters of the transitional Hamiltonian are determined via Least-Square Fitting (LSF) to the experimental data of Ru isotopes to describe both positive and negative parity states and also E ( 1 ) and E ( 2 ) transition probabilities. Results describe experimental counterparts with satisfactory degrees of agreement and also suggest 100 Ru as the best candidate for the critical point of this transitional region. [ABSTRACT FROM AUTHOR]

Exploring the intersection of new ideas of ecological complexity with insights from traditional agricultural systems is the fundamental subject of this article, with an emphasis on seven themes of ecological complexity, as reflecting contemporary themes in ecology. The seven themes are as follows: 1) turing processes and spatial structure, 2) chaotic dynamics, 3) stochastic processes, 4) coupled oscillators, 5) multidimensionality, 6) trait-mediated indirect interactions, and 7) critical transitions (catastrophe theory). We suggest that these themes of complexity naturally integrate to form one qualitative whole that could be considered a single subject—ecological complexity. [ABSTRACT FROM AUTHOR]

Catastrophe theory is a highly generalized mathematical theory that summarizes the rules of nonequilibrium phase transition by several catastrophe models. This paper investigates the general nonequilibrium phase transition process quantitatively using catastrophe theory for the first time, to our knowledge. First, a newapproach is proposed by combining the catastrophe theory with dimensionless analysis. Second, the new approach is applied to two classic examples: one is the turbulent phase transition and the other is the bottleneck effect of particle flow. For the turbulence phase transition process, the quantitative relationships are obtained. Comparing with Kolmogorov's turbulent theory, the new method proposed in this paper is able to evaluate not only the complete turbulence condition but also the development of turbulence, and Kolmogorov's turbulent theory is only a special case of our results by this new approach. For the particle flow bottleneck effect, the results obtained by this new method correspond with the empirical formulated results. Therefore, the proposed method can solve non-equilibrium phase transition process problems and has the potential to extend to fluid, aerodynamics, and so forth. [ABSTRACT FROM AUTHOR]

Electric vehicles have undergone a recent faddy trend in the United States and Europe, and several recent publications trumpet the continued rise of electric vehicles citing steadily-climbing monthly vehicle sales. The broad purpose of this study is to examine this optimism with some degree of mathematical rigor. Specifically, the methodology will use catastrophe theory to explore the possibility of a sudden, seemingly-unexplainable crash in vehicle sales. The study begins by defining optimal system equations that well-model the available sales data. Next, these optimal models are used to investigate the potential response to a slow dynamic acting on the relatively faster dynamic of the optimal system equations. Catastrophe theory indicates a potential sudden crash in sales when a slow dynamic is at-work. It is noteworthy that the prediction can be made even while sales are increasing. [ABSTRACT FROM AUTHOR]

When a group of identical products is operating in field, the aggregation of failures is a catastrophe to engineers and customers who strive to develop reliable and safe products. In order to avoid a swarm of failures in a short time, it is essential to measure the degree of dispersion from different failure times in a group of products to the first failure time. This phenomenon is relevant to the crowding of system conditions near the worst one among a group of products. The group size in this paper represents a finite number of products, instead of infinite number or a single product. We evaluate the reliability of the product fleet from two aspects. First, we define near-extreme system condition and near-extreme failure time for offline solutions, which means no online observations. Second, we apply them to a continuous degradation system that breaks down when it reaches a soft failure threshold. By using particle filtering in the framework of prognostics and health management for a group of products, we aim to estimate near-extreme system condition and further predict the remaining useful life (RUL) using online solutions. Numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]