Sebastian M. Krause

Econophysics of adaptive power markets: When a market does not dampen fluctuations but amplifies them.

The average economic agent is often used to model the dynamics of simple markets, based on the assumption that the dynamics of a system of many agents can be averaged over in time and space. A popular idea that is based on this seemingly intuitive notion is to dampen electric power fluctuations from fluctuating sources (as, e.g., wind or solar) via a market mechanism, namely by variable power prices that adapt demand to supply. The standard model of an average economic agent predicts that fluctuations are reduced by such an adaptive pricing mechanism. However, the underlying assumption that the actions of all agents average out on the time axis is not always true in a market of many agents. We numerically study an econophysics agent model of an adaptive power market that does not assume averaging a priori. We find that when agents are exposed to source noise via correlated price fluctuations (as adaptive pricing schemes suggest), the market may amplify those fluctuations. In particular, small price changes may translate to large load fluctuations through catastrophic consumer synchronization. As a result, an adaptive power market may cause the opposite effect than intended: Power demand fluctuations are not dampened but amplified instead.

Mean-field-like behavior of the generalized voter-model-class kinetic Ising model.

We analyze a kinetic Ising model with suppressed bulk noise, which is a prominent representative of the generalized voter model phase transition. On the one hand, we discuss the model in the context of social systems and opinion formation in the presence of a tunable social temperature. On the other hand, we characterize the abrupt phase transition. The system shows nonequilibrium dynamics in the presence of absorbing states. We slightly change the system to get a stationary-state model variant exhibiting the same kind of phase transition. Using a Fokker-Planck description and comparing to mean-field calculations, we investigate the phase transition, finite-size effects, and the effect of the absorbing states resulting in a dynamic slowing down.

Opinion formation model for markets with a social temperature and fear.

In the spirit of behavioral finance, we study the process of opinion formation among investors using a variant of the two-dimensional voter model with a tunable social temperature. Further, a feedback acting on the temperature is introduced, such that social temperature reacts to market imbalances and thus becomes time dependent. In this toy market model, social temperature represents nervousness of agents toward market imbalances representing speculative risk. We use the knowledge about the discontinuous generalized voter model phase transition to determine critical fixed points. The system exhibits metastable phases around these fixed points characterized by structured lattice states, with intermittent excursions away from the fixed points. The statistical mechanics of the model is characterized, and its relation to dynamics of opinion formation among investors in real markets is discussed.

Mixed quantum-classical approach to multiphoton dissociation of the hydrogen molecular ion

We present a mixed quantum-classical propagation method for the time-dependent dynamics of nuclear as well as electronic degrees of freedom for para-H2+ exposed to short intense laser pulses of 800 nm wavelength. Depending on the initial vibrational state, the angular distributions of photofragments show characteristic shapes in very good agreement with our full-dimensional nuclear dynamics quantum calculations. The results can be understood in terms of two-dimensional adiabatic Floquet surfaces, which depend on the internuclear separation and rotation angle, demonstrating that adiabatic light-dressed surfaces are also a useful concept for full-dimensional nuclear dynamics. Using kinetic energy release spectra, we are also able to extract the contributions of different photon channels in the quantum-classical case.

Steering a molecule into dissociation via vibrational excitation

For a laser driven molecule, we show that the ionization and the dissociation channels can be separated by preparing the molecule in a specific vibrational state. Specifically, we investigate the dynamics of the hydrogen molecular ion under a femtosecond infrared laser field aligned with the molecular axis. We find dissociation probabilities of more than 60%, considerably higher than reported so far. We demonstrate that a full dimensional description of the electron dynamics is necessary to obtain accurate results for the combined ionization/dissociation dynamics.

Spontaneous centralization of control in a network of company ownerships

We introduce a model for the adaptive evolution of a network of company ownerships. In a recent work it has been shown that the empirical global network of corporate control is marked by a central, tightly connected “core” made of a small number of large companies which control a significant part of the global economy. Here we show how a simple, adaptive “rich get richer” dynamics can account for this characteristic, which incorporates the increased buying power of more influential companies, and in turn results in even higher control. We conclude that this kind of centralized structure can emerge without it being an explicit goal of these companies, or as a result of a well-organized strategy.

Hidden Connectivity in Networks with Vulnerable Classes of Nodes

Redundancy is commonly used to guarantee continued functionality in networked systems. However, often many nodes are vulnerable to the same failure or adversary. A “backup” path is not sufficient if both paths depend on nodes which share a vulnerability. For example, if two nodes of the Internet cannot be connected without using routers belonging to a given untrusted entity, then all of their communication–regardless of the specific paths utilized–will be intercepted by the controlling entity. In this and many other cases, the vulnerabilities affecting the network are disjoint: each node has exactly one vulnerability but the same vulnerability can affect many nodes. To discover optimal redundancy in this scenario, we describe each vulnerability as a color and develop a “color-avoiding percolation” which uncovers a hidden color-avoiding connectivity. We present algorithms for coloravoiding percolation of general networks and an analytic theory for random graphs with uniformly distributed colors including critical phenomena. We demonstrate our theory by uncovering the hidden color-avoiding connectivity of the Internet. We find that less well-connected countries are more likely able to communicate securely through optimally redundant paths than highly connected countries like the US. Our results reveal a new layer of hidden structure in complex systems and can enhance security and robustness through optimal redundancy in a wide range of systems including biological, economic and communications networks.

Impact and Recovery Process of Mini Flash Crashes: An Empirical Study

In an Ultrafast Extreme Event (or Mini Flash Crash), the price of a traded stock increases or decreases strongly within milliseconds. We present a detailed study of Ultrafast Extreme Events in stock market data. In contrast to popular belief, our analysis suggests that most of the Ultrafast Extreme Events are not necessarily due to feedbacks in High Frequency Trading: In at least 60 percent of the observed Ultrafast Extreme Events, the largest fraction of the price change is due to a single market order. In times of financial crisis, large market orders are more likely which leads to a significant increase of Ultrafast Extreme Events occurrences. Furthermore, we analyze the 100 trades following each Ultrafast Extreme Events. While we observe a tendency of the prices to partially recover, less than 40 percent recover completely. On the other hand we find 25 percent of the Ultrafast Extreme Events to be almost recovered after only one trade which differs from the usually found price impact of market orders.

Regularities and irregularities in order flow data

Abstract We identify and analyze statistical regularities and irregularities in the recent order flow of different NASDAQ stocks, focusing on the positions where orders are placed in the order book. This includes limit orders being placed outside of the spread, inside the spread and (effective) market orders. Based on the pairwise comparison of the order flow of different stocks, we perform a clustering of stocks into groups with similar behavior. This is useful to assess systemic aspects of stock price dynamics. We find that limit order placement inside the spread is strongly determined by the dynamics of the spread size. Most orders, however, arrive outside of the spread. While for some stocks order placement on or next to the quotes is dominating, deeper price levels are more important for other stocks. As market orders are usually adjusted to the quote volume, the impact of market orders depends on the order book structure, which we find to be quite diverse among the analyzed stocks as a result of the way limit order placement takes place.

The importance of antipersistence for traffic jams

Universal characteristics of road networks and traffic patterns can help to forecast and control traffic congestion. The antipersistence of traffic flow time series has been found for many data sets, but its relevance for congestion has been overseen. Based on empirical data from motorways in Germany, we study how antipersistence of traffic flow time-series impacts the duration of traffic congestion on a wide range of time scales. We find a large number of short-lasting traffic jams, which implies a large risk for rear-end collisions.