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.

MIRACLE Project Plan

Social scientists have used agent-based models (ABMs) to explore the interaction and feedbacks among social agents and their environments. The bottom-up structure of ABMs enables simulation and investigation of complex systems and their emergent behaviour with a high level of detail; however the stochastic nature and potential combinations of parameters of such models create large non-linear multidimensional “big data,” which are difficult to analyze using traditional statistical methods. Our proposed project seeks to address this challenge by developing algorithms and web-based analysis and visualization tools that provide automated means of discovering complex relationships among variables. The tools will enable modellers to easily manage, analyze, visualize, and compare their output data, and will provide stakeholders, policy makers and the general public with intuitive web interfaces to explore, interact with and provide feedback on otherwise difficult-to-understand models.

Multi-agent modelling for the simulation of a simple smart microgrid

The smart grid is a highly complex system that is being formed from the traditional power grid, adding new and sophisticated communication and control devices. This will enable integrating new elements for distributed power generation and also achieving an increasingly automated operation so for actions of the utilities as for customers. In order to model such systems a bottom-up method is followed, using only a few basic elements which are structured into two layers: a physical layer for the electrical power transmission, and one logical layer for element communication. A simple case study is presented to analyse the possibilities of simulation. It shows a microgrid model with dynamic load management and an integrated approach that can process both electrical and communication flows.

Emergent synchronisation properties of a refrigerator demand side management system

In order to analyse the possibilities of improving grid stability on island systems by local demand response mechanisms,a multi-agent simulation model is presented. To support the primary reserve, an under-frequency load shedding (UFLS)using refrigerator loads is modelled. The model represents the system at multiple scales, by recreating each refrigerator individually, and coupling the whole population of refrigerators to a model which simulates the frequency response of the energy system, allowing for cross-scale interactions. Using a simple UFLS strategy, emergent phenomena appear in the simulation. Synchronisation e ects among the individual loads were discovered, which can have strong, undesirable impacts on the system such as oscillations of loads and frequency. The phase transition from a stable to an oscillating system is discussed.

The Economics of Gasification: A Market-Based Approach

This paper deals with the economics of gasification facilities in general and IGCC power plants in particular. Regarding the prospects of these systems, passing the technological test is one thing, passing the economic test can be quite another. In this respect, traditional valuations assume constant input and/or output prices. Since this is hardly realistic, we allow for uncertainty in prices. We naturally look at the markets where many of the products involved are regularly traded. Futures markets on commodities are particularly useful for valuing uncertain future cash flows. Thus, revenues and variable costs can be assessed by means of sound financial concepts and actual market data. On the other hand, these complex systems provide a number of flexibility options (e.g., to choose among several inputs, outputs, modes of operation, etc.). Typically, flexibility contributes significantly to the overall value of real assets. Indeed, maximization of the asset value requires the optimal exercise of any flexibility option available. Yet the economic value of flexibility is elusive, the more so under (price) uncertainty. And the right choice of input fuels and/or output products is a main concern for the facility managers. As a particular application, we deal with the valuation of input flexibility. We follow the Real Options approach. In addition to economic variables, we also address technical and environmental issues such as energy efficiency, utility performance characteristics and emissions (note that carbon constraints are looming). Lastly, a brief introduction to some stochastic processes suitable for valuation purposes is provided.

Agent based modeling of energy networks

Attempts to model any present or future power grid face a huge challenge because a power grid is a complex system, with feedback and multi-agent behaviors, integrated by generation, distribution, storage and consumption systems, using various control and automation computing systems to manage electricity flows. Our approach to modeling is to build upon an established model of the low voltage electricity network which is tested and proven, by extending it to a generalized energy model. But, in order to address the crucial issues of energy efficiency, additional processes like energy conversion and storage, and further energy carriers, such as gas, heat, etc., besides the traditional electrical one, must be considered. Therefore a more powerful model, provided with enhanced nodes or conversion points, able to deal with multidimensional flows, is being required. This article addresses the issue of modeling a local multi-carrier energy network. This problem can be considered as an extension of modeling a low voltage distribution network located at some urban or rural geographic area. But instead of using an external power flow analysis package to do the power flow calculations, as used in electric networks, in this work we integrate a multiagent algorithm to perform the task, in a concurrent way to the other simulation tasks, and not only for the electric fluid but also for a number of additional energy carriers. As the model is mainly focused in system operation, generation and load models are not developed.

Quantum simulation of enzyme catalysis

Separating the dynamics of variables that evolve on different timescales is a common assumption in exploring complex systems, and a great deal of progress has been made in understanding chemical systems by treating independently the fast processes of an activated chemical species from the slower processes that proceed activation. Protein motion underlies all biocatalytic reactions, and understanding the nature of this motion is central to understanding how enzymes catalyze reactions with such specificity and such rate enhancement. This understanding is challenged by evidence of breakdowns in the separability of timescales of dynamics in the active site form motions of the solvating protein. Quantum simulation methods that bridge these timescales by simultaneously evolving quantum and classical degrees of freedom provide an important method on which to explore this breakdown. In the following dissertation, three problems of enzyme catalysis are explored through quantum simulation.

Weighting social preferences in participatory multi-criteria evaluations: a case study on sustainable natural resource management

28 p.

Identifying social determinants of urban low carbon transitions: the case of energy transition in Bilbao, Basque Country

33 p.

Efficient methods for stochastic optimal control

The Hamilton Jacobi Bellman (HJB) equation is central to stochastic optimal control (SOC) theory, yielding the optimal solution to general problems specified by known dynamics and a specified cost functional. Given the assumption of quadratic cost on the control input, it is well known that the HJB reduces to a particular partial differential equation (PDE). While powerful, this reduction is not commonly used as the PDE is of second order, is nonlinear, and examples exist where the problem may not have a solution in a classical sense. Furthermore, each state of the system appears as another dimension of the PDE, giving rise to the curse of dimensionality. Since the number of degrees of freedom required to solve the optimal control problem grows exponentially with dimension, the problem becomes intractable for systems with all but modest dimension.

In the last decade researchers have found that under certain, fairly non-restrictive structural assumptions, the HJB may be transformed into a linear PDE, with an interesting analogue in the discretized domain of Markov Decision Processes (MDP). The work presented in this thesis uses the linearity of this particular form of the HJB PDE to push the computational boundaries of stochastic optimal control.

This is done by crafting together previously disjoint lines of research in computation. The first of these is the use of Sum of Squares (SOS) techniques for synthesis of control policies. A candidate polynomial with variable coefficients is proposed as the solution to the stochastic optimal control problem. An SOS relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function. It is shown that these results extend to arbitrary parabolic and elliptic PDEs, yielding a novel method for Uncertainty Quantification (UQ) of systems governed by partial differential constraints. Domain decomposition techniques are also made available, allowing for such problems to be solved via parallelization and low-order polynomials.

The optimization-based SOS technique is then contrasted with the Separated Representation (SR) approach from the applied mathematics community. The technique allows for systems of equations to be solved through a low-rank decomposition that results in algorithms that scale linearly with dimensionality. Its application in stochastic optimal control allows for previously uncomputable problems to be solved quickly, scaling to such complex systems as the Quadcopter and VTOL aircraft. This technique may be combined with the SOS approach, yielding not only a numerical technique, but also an analytical one that allows for entirely new classes of systems to be studied and for stability properties to be guaranteed.

The analysis of the linear HJB is completed by the study of its implications in application. It is shown that the HJB and a popular technique in robotics, the use of navigation functions, sit on opposite ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. Analytical solutions to the HJB in these settings are available in simplified domains, yielding guidance towards optimality for approximation schemes. Finally, the use of HJB equations in temporal multi-task planning problems is investigated. It is demonstrated that such problems are reducible to a sequence of SOC problems linked via boundary conditions. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification.

Applying systematic design: the flight refuelling probe project

This report is a product of close industry-academia collaboration between British Aerospace and the Cambridge Engineering Design Centre (EDC). British Aerospace designs and integrates some of the most complex systems in the world, and its expertise in this field has enabled the company to become the United Kingdom's largest exporter. However, to stay at the forefront of the highly competitive aerospace industry it is necessary to seek new ways to work more effectively and more efficiently. The Cambridge EDC has played a part in supporting these needs by providing access to the methods and tools that it has developed for improving the process of designing mechanical systems. The EDC has gained an international reputation for the quality of its work in this subject. Thus, the collaboration is between two organisations each of whom are leaders in their respective fields. The central aim of the project has been to demonstrate how a systematic design process can be applied to a real design task identified by industry. The task selected was the design of a flight refuelling probe which would enable a combat aircraft to refuel from a "flying tanker". However, the systematic approach, methods and tools described in this report are applicable to most engineering design tasks. The findings presented in this report provide a sound basis for comparing the recommended systematic design process with industrial practice. The results of this comparison would enable the company to define ways in which its existing design process can be improved. This research project has a high degree of industrial relevance. The value of the work may be judged in terms of the opportunities it opens up for positive changes to the company's engineering operations. Several members of the EDC have contributed to the project. These include Dr Lucienne Blessing, Dr Stuart Burgess, Dr Amaresh Chakrabarti, Major Mark Nowack, Aylmer Johnson and Dr Paul Weaver. At British Aerospace special thanks must go to Alan Dean and David Halliday for their interest and the support they have given. The project has been managed by Dr Nigel Upton of British Aerospace during a 3 year secondment to the EDC.