Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

Smooth Path Planning for Passages with Heading and Curvature Discontinuities

The problem of continuous curvature path planning for passages is considered. This problem arises when an autonomous vehicle traverses between prescribed boundaries such as corridors, tunnels, channels, etc. Passage boundaries with curvature and heading discontinuities pose challenges for generating smooth paths passing through them. Continuous curvature half-S shaped paths derived from the Four Parameter Logistic Curve family are proposed as a prospective path planning solution. Analytic conditions are derived for generating continuous curvature paths confined within the passage boundaries. Zero end curvature highlights the scalability of the proposed solution and its compatibility with other path planners in terms of larger path planning domains. Various scenarios with curvature and heading discontinuities are considered presenting viability of the proposed solution.

Multi-scale vulnerability assessment for adaptation planning

Vulnerability of communities and natural ecosystems, to potential impacts of climate change in developing countries like India, and the need for adaptation are rapidly emerging as central issues in the debate around policy responses to climate change. The present study presents an approach to identify and prioritize the most vulnerable districts, villages and households in Karnataka State, through a multi-scale assessment of inherent vulnerability to current climate variability. It also identifies the drivers of inherent vulnerability, thereby providing a tool for developing and mainstreaming adaptation strategies, in ongoing developmental or dedicated adaptation programmes. The multi-scale assessment was made for all 30 districts at the state level in Karnataka, about 1220 villages in Chikballapur district, and at the household level for two villages - Gundlapalli and Saddapalli - in Bagepalli taluk of Chikballapur district. At the district, village and household levels, low levels of education and skills are the dominant factors contributing to vulnerability. At the village and household level, the lack of income diversification and livelihood support institutions are key drivers of vulnerability. The approach of multi-scale vulnerability assessment facilitates identification and prioritization of the drivers of vulnerability at different scales, to focus adaptation interventions to address these drivers.