Query: cusp catastrophe

title: The Threshold Non linear Model for the Effects of Cumulative Stressors and Traumas: A Chained Cusp Catastrophe Analysis
abstract: Studying the macro dynamics of traumatization should significantly advance psychological science. The current article tested the validity of the non linear threshold model of the effects of cumulative stressors and traumas (CST) We used a combined data set of adults and adolescents from Egypt, Kuwait, and the UK (N 968) that measured CST, internalizing, externalizing and thought disorders. We used the cusp catastrophe analysis that can identify the non linear threshold dynamics. The non linear cusp (threshold) model accounted for a much higher variance than the linear model, indicating the presence of threshold effects of CST on internalizing, externalizing and thought disorders. Interventions should target the multiply traumatized who are at risk for the cusp effects and not only those who are victims of the cusp. The study provided evidence for the utility of a paradigm shift to study the macro dynamics of stressors and traumas, and not only their micro dynamics.

title: A method of railway system safety analysis based on cusp catastrophe model.
abstract: For rail transit systems, safety is one of the most important goals that need to be guaranteed. We build a method of railway system safety analysis based on the cusp catastrophe model. This method describes the continuous changing process of railway system safety and considers the emergent property of safety. This method solves the problem that the outputs of most static analysis methods of railway system safety do not have continuity and avoids the complex analysis process and heavy computation burden brought by using some dynamic models such as state transition models. The quantitative case study of the continuous changing process of system safety in the evolution process of the Yong Wen railway accident shows that the visualized outputs obtained by using this method are consistent with the actual situation. This method has the potential to be applied in the real time monitoring of railway system safety and the early warning of train accidents.

title: Risk state changes analysis of railway dangerous goods transportation system: Based on the cusp catastrophe model
abstract: In this paper, the cusp catastrophe model is applied to analyze the railway dangerous goods transportation system risk state changes. Firstly, a Risk Accident Catastrophe Tree is proposed to formulate the process that how the risk factors cause the accident. Secondly, the whole risk factors are classified into five categories including failure of human behavior, machine failure, transported materials, environment problems and management problems. Next, the cusp catastrophe model of railway dangerous goods transportation system is established, the Split Coefficient is defined to evaluate bifurcation set. The results of the case study show that the risk state changes of railway dangerous goods transportation system satisfy bimodality, inaccessibility, sudden transitions and divergence, but not satisfy hysteresis. The larger the Split Coefficient is, the easier the trajectory of system control point crosses with bifurcation sets. The reason of the system state changes from a safe state to a risk state is: as long as the trajectory of system control point crosses with bifurcation sets, there must be a cusp catastrophe in the system, and the system control point will cross the fold surface, which makes the risk energy increase sharply, the structure, information and energy of the system will also be destroyed.

title: Traffic Flow Catastrophe Border Identification for Urban High Density Area Based on Cusp Catastrophe Theory: A Case Study under Sudden Fire Disaster
abstract: For traffic management under sudden disasters in high density areas, the first and foremost step is to prevent traffic congestion in the disaster affected area by traffic flow management and control, so as to provide enough and flexible traffic capacity for emergency evacuation and emergency rescue. Catastrophe border identification is the foundation and the key to traffic congestion prediction under sudden disaster. This paper uses a mathematical model to study the regional traffic flow in the high density area under sudden fire disaster based on the Cusp Catastrophe Theory (CCT) The catastrophe border is identified by fitting the CCT based regional traffic flow model to explore the stable traffic flow changing to the instable state, as to provide a theoretical basis for traffic flow management and control in disaster affected areas, and to prevent the traffic flow being caught into disorder and congestion. Based on VISSIM simulator data by building simulation scenarios with and without sudden fire disaster in a Sudoku traffic network, the catastrophe border is identified as 439 pcu/lane/h, 529 pcu/lane/h, 377 pcu/lane/h at 5 s, 10 s, 15 s data collection interval in a Sudoku traffic network respectively. The corresponding relative precision, which compares to the method of Capacity Assessment Approach (CAA) is 89.1% 92.7% and 76.5% respectively. It means that 10 s data collection interval would be the suitable data collection interval in catastrophe border identification and regional traffic flow control in high density area under sudden fire disaster.

title: A Cusp Catastrophe Model for Alluvial Channel Pattern and Stability
abstract: The self adjustment of an alluvial channel is a complicated process with various factors influencing the stability and transformation of channel patterns. A cusp catastrophe model for the alluvial channel regime is established by selecting suitable parameters to quantify the channel pattern and stability. The channel patterns can be identified by such a model in a direct way with a quantified index, which is a 2D projection of the cusp catastrophe surface, and the discriminant function is obtained from the model to distinguish the river state. Predictions based on this model are consistent with the field observations involving about 150 natural rivers of small or medium sizes. This new approach enables us to classify the channel pattern and determine a river stability state, and it paves the way toward a better understanding of the regime of natural rivers to assist decision making in river management.

title: Cusp Catastrophe Regression Analysis of Testosterone in Bifurcating the Age Related Changes in PSA, a Biomarker for Prostate Cancer
abstract: Advancing cancer research needs to adapt nonlinear dynamic systems (NDS) approach in addition to the linear dynamic systems (LDS) Dynamic changes in prostate specific antigen (PSA) a biomarker of prostate cancer showed NDS character but this character has not been examined in literature. In this study, we examine PSA guided by a NDS paradigm. Participants were urology patients diagnosed with either prostate cancer (n 27) or benign prostate disorder (n 352) from a tertiary hospital in northcentral Florida. Data were derived from the 2001 to 2015 electronic medical records (EMR) PSA levels (ng/mL) were analyzed with cusp catastrophe mode in which participants' age at the PSA level was used as the asymmetry variable, and testosterone levels (ng/dL) as the bifurcation variable. Modeling analyses were executed in the open source R software. LDS based linear correlation and regression analyses were also conducted as a comparison purpose. The mean age of the participants was 66.1 (SD 9.8) years old; the PSA range was 0.05 13.8 with mean 1.7 (SD 1.2) ng/mL; and the total testosterone range was 27.00 1297.00 with mean 318.0(SD 191.6) ng/dL. Results from Chen Chen cusp regression indicate better data model fit for cusp (R2 0.47) than for linear regression (R2 0.027) Serum PSA was significantly associated with age (a1 0.2691, p .001) and bifurcated by blood testosterone (b1 1.0265, p .00) with the estimated cusp point (age 63, testosterone 630 ng/mL) The estimated cusp point was close to the epidemiology data that the risk of prostate cancer started to accelerate at about ages 60 65 years; and testosterone level of 630 ng/mL, closer to the up limit 800 ng/dL of normal range (280 800) by the American Association of Clinical Endocrinologists (AACE) In conclusion, this is the first study that examined the dynamics of PSA in men and demonstrated that serum PSA level follow the NDS. In addition to confirming the relationship between age, testosterone and PSA, findings of this analysis provide a reasonable explanation of the large PSA range in healthy men and the small difference in mean PSA between healthy men and men with prostate cancer (1.2 vs. 2.6) There is a need to re evaluate the role of PSA for prostate cancer screening guided by NDS paradigm.

title: Traffic Flow Catastrophe Border Identification for Urban High density Area Based on Cusp Catastrophe Theory: A Case Study under Sudden Fire Disaster
abstract: For traffic management under sudden disasters in high density areas, the first and foremost step is to prevent traffic congestion in the disaster affected area by traffic flow management and control, so as to provide enough and flexible traffic capacity for emergency evacuation and emergency rescue. Catastrophe border identification is the foundation and the key to traffic congestion prediction under sudden disaster. This paper uses a mathematical model to study the regional traffic flow in the high density area under sudden fire disaster based on the Cusp Catastrophe Theory (CCT) The catastrophe border is identified by fitting the CCT based regional traffic flow model to explore the stable traffic flow changing to the instable state, as to provide a theoretical basis for traffic flow management and control in disaster affected areas, and to prevent the traffic flow being caught into disorder and congestion. Based on VISSIM simulator data by building simulation scenarios with and without sudden fire disaster in a Sudoku traffic network, the catastrophe border is identified as 439 pcu/lane/h, 529 pcu/lane/h, 377 pcu/lane/h at 5 s, 10 s, 15 s data collection interval in a Sudoku traffic network respectively. The corresponding relative precision, which compares to the method of Capacity Assessment Approach (CAA) is 89.1% 92.7% and 76.5% respectively. It means that 10 s data collection interval would be the suitable data collection interval in catastrophe border identification and regional traffic flow control in high density area under sudden fire disaster.

title: Investigation of cusp catastrophe model of rock slope instability with general constitutive equations
abstract: The unsteadiness of rock slopes is often triggered by water softening. Based on catastrophe theory and the general constitutive equations of the strain softening section in the weak interlayer, the present study investigated the catastrophic failure mechanism of rock slopes. Using theoretical analysis, the cusp catastrophe model for the failure of a rock slope with a strain softening section in the soft rock strata was established, and the balance equation, bifurcation set, and formulas of displacement jumping and energy jumping were deduced. The changes of displacement jumping and energy jumping following the variation of the systematic rigidity ratio are discussed with regard to the occurrence of water softening. Regardless of which type of constitutive equation is adopted, the control variables and sudden jump values of the rock slope's displacement and energy can be determined by the systematic rigidity ratio when the systematic rigidity ratio is constant. Whether a rock slope is stable or not depends only on the mechanical and geometrical parameters of the system itself, and is unrelated to the constitutive equation of the strain softening section. The sudden jump values of the displacement and energy are both inversely proportional to the systematic rigidity ratio. By comparing the formula of the systematic rigidity ratio deduced under different constitutive equations with the results obtained by other studies, the results of the present study were verified through the consideration of actual engineering projects. Based on catastrophe theory, the present paper discusses the principle of correctly selecting a constitutive equation to assess the rock slope stability in practical engineering.

title: Logistic Cusp Catastrophe Regression for Binary Outcome: Method Development and Empirical Testing
abstract: Cusp catastrophe models are unique to advance life sciences, psychology and behavioral studies. Extensive progresses have been made to utilize this modeling technique for continuous outcome and there is no development for binary data. To fill this gap, this chapter is then aimed to develop a cusp catastrophe modelling method for binary outcome. Building upon our previous research on the nonlinear regression cusp (RegCusp) catastrophe model for continuous outcome, we propose a logistic cusp catastrophe regression (LogisticCusp) LogisticCusp is based on the principles of logistic regression for binary outcome variable y (yes/no) being expressed as a latent binary variable Y through a logit link. This latent regression provides a mathematical connection between an observed outcome variable as a binomially distributed random variable and the deterministic cusp catastrophe at its equilibrium. By connecting the two, Y in the LogisticCusp is considered as one of the true roots of the deterministic cusp catastrophe model determined using the Maxwell or Delay conventions. We validate the method using a 5 step Monte Carlo simulation with two predictors and three parameters for both bifurcation and asymmetry control variables. We further tested the method with binge drinking behavior in youth with data from the Monitoring the Future Study. Results from 5000 Monte Carlo simulations indicate that the parameter estimates obtained through LogisticCusp are unbiased and efficient using maximum likelihood estimation with quasi Newton numerical search algorithm. Results from empirical testing with real data are consistent with those estimated using other methods. LogisticCusp adds a new tool for researchers to examine many issues in psychology, life sciences, and behavioral studies, particularly, issues in medicine and public health with the powerful cusp catastrophe modeling for binary outcome.

title: Deep Neural Network in Cusp Catastrophe Model
abstract: Catastrophe theory was originally proposed to study dynamical systems that exhibit sudden shifts in behavior arising from small changes in input. These models can generate reasonable explanation behind abrupt jumps in nonlinear dynamic models. Among the different catastrophe models, the Cusp Catastrophe model attracted the most attention due to it's relatively simpler dynamics and rich domain of application. Due to the complex behavior of the response, the parameter space becomes highly non convex and hence it becomes very hard to optimize to figure out the generating parameters. Instead of solving for these generating parameters, we demonstrated how a Machine learning model can be trained to learn the dynamics of the Cusp catastrophe models, without ever really solving for the generating model parameters. Simulation studies and application on a few famous datasets are used to validate our approach. To our knowledge, this is the first paper of such kind where a neural network based approach has been applied in Cusp Catastrophe model.