Correlations, risk and crisis: From physiology to finance

Abstract

a b s t r a c tWe study the dynamics of correlation and variance in systems under the load of environmental factors. A universal effect in ensembles of similar systems under the load of similar factors is described: in crisis, typically, even before obvious symptoms of crisis appear, correlation increases, and, at the same time, variance (and volatility) increases too. This effect is supported by many experiments and observations of groups of humans, mice, trees, grassy plants, and on financial time series.A general approach to the explanation of the effect through dynamics of individual adaptation of similar non-interactive individuals to a similar system of external factors is developed. Qualitatively, this approach follows Selye's idea about adaptation energy.In many areas of practice, from physiology to economics, psychology, and engineering we have to analyze the behavior of groups of many similar systems, which are adapting to the same or similar environment. Groups of humans in hard living conditions (Far North city, polar expedition, or a hospital, for example), trees under the influence of anthropogenic air pollution, rats under poisoning, banks in financial crisis, enterprises in recession, and many other situations of that type provide us with plenty of important problems, problems of diagnostics and prediction.For many such situations, it was found that the correlations between individual systems are better indicators than the value of attributes. More specifically, in thousands of experiments it was shown that in crisis, typically, even before obvious symptoms of crisis appear, the correlations increase, and, at the same time, the variance (volatility) increases too (Fig. 1).On the other hand, situations with inverse behavior were predicted theoretically and found experimentally [1]. For some systems, it was demonstrated that after the crisis achieves its bottom, it can develop into two directions: recovering (both the correlations and the variance decrease) or fatal catastrophe (the correlations decrease, but the variance continues to increase) (Fig. 1). This makes the problem more intriguing.If we look only on the state but not on the history then the only difference between comfort and disadaptation in this scheme is the value of variance: in the disadaptation state the variance is larger and the correlations in both cases are low. Qualitatively, the typical behavior of an ensemble of similar systems, which are adapting to the same or similar environment looks as follows:• In a well-adapted state, the deviations of the systems' state from the average value have relatively low correlations; • Under increasing of the load of environmental factors some of the systems leave the low correlated comfort cloud and form a low-dimensional highly correlated group (an order parameter appears). With further increasing of the load more * Corresponding address: Centre for Mathematical Modelling,

Transcriptional Network Architecture of Breast Cancer Molecular Subtypes

“…These differences in structure can be thought of as a representation of potential differences in the transcriptional regulatory program. As it has been discussed previously (Censi et al, 2011), in systems under stress (high correlation, and high variance) (Gorban et al, 2010) changes in the general correlation structure become visible as changes in the associated networks. The most evident differences in network structure are seen between the tumor and the non-tumor networks: the non-tumor network is dominated by a giant component; meanwhile, the subtype networks are formed by several coexisting components of different sizes.…”

“…It is important to notice that the disruption of connected components in the cancer networks is a phenomenon that it is very likely intertwined with the presence of stress induced correlations (Gorban et al, 2010), as such one need to be cautious as to assign a degree of importance to each of these two features on the issue of phenotypic differences on subtype-associated networks.…”

Human Perception of Visual Realism for Photo and Computer-Generated Face Images

“…We also found the realism ratings of upright-unrealistic images were not affected by inversion (see Figure 5). Based on the Anna Karenina principle [Gorban et al 2010], people might judge using a strategy of "it is CG if it has something weird and photo if not." Inverting realistic images might make image parts look weird (e.g., inverted eyes), but inverting weird (CG) images may make the weirdness less apparent, yet still identifiable.…”

RQA correlations on real business cycles time series

“…The ability of RQA to predict catastrophic changes is in line with the fact that RQA is based upon the change in correlation structure of the observed phenomenon known to precede the actual event in many different systems ranging from physiology [2] and geophysics [3] to economy [4]. Gorban et al [5] found that even before crisis, correlation increases as does variance (and volatility). In particular their dataset, composed of the thirty largest companies from the UK stock market in the period 2006-2008, supports the hypothesis of increasing correlations during a crisis and, therefore, that correlation (or equivalently determinism) increases when the market goes down (respectively decreases when it recovers).…”