The role of complexity for digital twins of cities.

We argue that theories and methods drawn from complexity science are urgently needed to guide the development and use of digital twins for cities. The theoretical framework from complexity science takes into account both the short-term and the long-term dynamics of cities and their interactions. This is the foundation for a new approach that treats cities not as large machines or logistic systems but as mutually interwoven self-organizing phenomena, which evolve, to an extent, like living systems.

Connectivity disruption sparks explosive epidemic spreading.

We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the susceptible-infected-susceptible model, typical of mathematical epidemiology, on a network. Infection spreads from infected to healthy nodes, with the addition that infected nodes can only recover when they remain connected to a predefined central node, through a path that contains only healthy nodes. In this system, clusters of infected nodes will absorb their noninfected interior because no path exists between the central node and encapsulated nodes. This gives rise to the simultaneous infection of multiple nodes. Interestingly, the system converges to only one of two stationary states: either the whole population is healthy or it becomes completely infected. This simultaneous cluster infection can give rise to discontinuous jumps of different sizes in the number of failed nodes. Larger jumps emerge at lower infection rates. The network topology has an important effect on the nature of the transition: we observed hysteresis for networks with dominating local interactions. Our model shows how local spread can abruptly turn uncontrollable when it disrupts connectivity at a larger spatial scale.

Disease-induced resource constraints can trigger explosive epidemics.

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into "explosive" spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.

From social data mining to forecasting socio-economic crises.

The purpose of this White Paper of the EU Support Action "Visioneer"(see www.visioneer.ethz.ch) is to address the following goals: Develop strategies to quickly increase the objective knowledge about social and economic systems.Describe requirements for efficient large-scale scientific data mining of anonymized social and economic data.Formulate strategies how to collect stylized facts extracted from large data set.Sketch ways how to successfully build up centers for computational social science.Propose plans how to create centers for risk analysis and crisis forecasting.Elaborate ethical standards regarding the storage, processing, evaluation, and publication of social and economic data.

Volatility clustering and scaling for financial time series due to attractor bubbling.

A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time heat bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit, the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering. For a proper choice of the model parameters, the probability distributions of returns exhibit power-law tails with scaling exponents close to the empirical ones.

Mexican waves in an excitable medium.

The Mexican wave, or La Ola, which rose to fame during the 1986 World Cup in Mexico, surges through the rows of spectators in a stadium as those in one section leap to their feet with their arms up, and then sit down again as the next section rises to repeat the motion. To interpret and quantify this collective human behaviour, we have used a variant of models that were originally developed to describe excitable media such as cardiac tissue. Modelling the reaction of the crowd to attempts to trigger the wave reveals how this phenomenon is stimulated, and may prove useful in controlling events that involve groups of excited people.

Congested traffic states in empirical observations and microscopic simulations

We present data from several German freeways showing different kinds of congested traffic forming near road inhomogeneities, specifically lane closings, intersections, or uphill gradients. The states are localized or extended, homogeneous or oscillating. Combined states are observed as well, like the coexistence of moving localized clusters and clusters pinned at road inhomogeneities, or regions of oscillating congested traffic upstream of nearly homogeneous congested traffic. The experimental findings are consistent with a recently proposed theoretical phase diagram for traffic near on-ramps [D. Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. 82, 4360 (1999)]. We simulate these situations with a continuous microscopic single-lane model, the "intelligent driver model," using empirical boundary conditions. All observations, including the coexistence of states, are qualitatively reproduced by describing inhomogeneities with local variations of one model parameter. We show that the results of the microscopic model can be understood by formulating the theoretical phase diagram for bottlenecks in a more general way. In particular, a local drop of the road capacity induced by parameter variations has essentially the same effect as an on-ramp.

Simulating dynamical features of escape panic.

One of the most disastrous forms of collective human behaviour is the kind of crowd stampede induced by panic, often leading to fatalities as people are crushed or trampled. Sometimes this behaviour is triggered in life-threatening situations such as fires in crowded buildings; at other times, stampedes can arise during the rush for seats or seemingly without cause. Although engineers are finding ways to alleviate the scale of such disasters, their frequency seems to be increasing with the number and size of mass events. But systematic studies of panic behaviour and quantitative theories capable of predicting such crowd dynamics are rare. Here we use a model of pedestrian behaviour to investigate the mechanisms of (and preconditions for) panic and jamming by uncoordinated motion in crowds. Our simulations suggest practical ways to prevent dangerous crowd pressures. Moreover, we find an optimal strategy for escape from a smoke-filled room, involving a mixture of individualistic behaviour and collective 'herding' instinct.

Freezing by heating in a driven mesoscopic system

We investigate a simple model corresponding to particles driven in opposite directions and interacting via a repulsive potential. The particles move off-lattice on a periodic strip and are subject to random forces as well. We show that this model-which can be considered as a continuum version of some driven diffusive systems-exhibits a paradoxical, new kind of transition called here "freezing by heating." One interesting feature of this transition is that a crystallized state with a higher total energy is obtained from a fluid state by increasing the amount of fluctuations.

Macroscopic dynamics of multilane traffic.

We present a macroscopic model of mixed multilane freeway traffic that can be easily calibrated to empirical traffic data, as is shown for Dutch highway data. The model is derived from a gas-kinetic level of description, including effects of vehicular space requirements and velocity correlations between successive vehicles. We also give a derivation of the lane-changing rates. The resulting dynamic velocity equations contain nonlocal and anisotropic interaction terms which allow a robust and efficient numerical simulation of multilane traffic. As demonstrated by various examples, this facilitates the investigation of synchronization patterns among lanes and effects of on ramps, off ramps, lane closures, or accidents.

Modelling the evolution of human trail systems.

Many human social phenomena, such as cooperation, the growth of settlements, traffic dynamics and pedestrian movement, appear to be accessible to mathematical descriptions that invoke self-organization. Here we develop a model of pedestrian motion to explore the evolution of trails in urban green spaces such as parks. Our aim is to address such questions as what the topological structures of these trail systems are, and whether optimal path systems can be predicted for urban planning. We use an 'active walker' model that takes into account pedestrian motion and orientation and the concomitant feedbacks with the surrounding environment. Such models have previously been applied to the study of complex structure formation in physical, chemical and biological systems. We find that our model is able to reproduce many of the observed large-scale spatial features of trail systems.

Conformational states of pig brain myosin.

The conventional, longtailed myosins expressed in smooth muscle and nonmuscle tissue are generally thought to exist in two discrete monomeric configurations which in vitro can be interconverted by changes in the ionic strength of the buffer. For nonmuscle myosin, only two species had been investigated so far. Here, we show that dephosphorylated pig brain myosin, consisting of at least two electrophoretic variants, can also adopt an extended and a folded configuration as seen in rotary shadowed molecules. Monoclonal antibodies were employed to analyze the possible role of specific tail domains in these changes. One of these antibodies (a-PBM9) which binds to an epitope in the first third of the tail, was found to induce and stabilize the extended form, as seen in ELISA with soluble myosin and in rotary-shadowed immune complexes, while another antibody (a-PBM4), binding close to the carboxy terminus of the tail, showed no such effect. Our data support the model that all nonmuscle myosins can shuttle between an extended, assembly-competent and a folded or collapsed form, and that specific regions within the tail play a crucial role in this interconversion.

Enrichment of estradiol receptor from calf uterus.

A three-step procedure to enrich estradiol receptor protein from calf uterus nearly 30,000-fold has been described. Over-all yield is 12%. Control of the single steps has been performed by sodium dodecyl sulfate-electrophoresis, sucrose density gradient centrifugation, gel filtration and determination of receptor quantity. Immunological properties of the preparation obtained have not been controlled.

The upright position of brush border-type microvilli depends on myosin filaments.

We have studied the correlation between the actomyosin organization and microvillar position in an epithelial cell line derived from the proximal pig kidney tubule (LLC-PK1). When grown on glass, these cells are approximately 5-6 microns in height and develop numerous microvilli that project from the dorsal membrane. A fairly homogeneous distribution of microvilli was achieved by synchronization of the cell cycle. These microvilli are of the brush border type, as defined by their content of villin and their anchorage in a myosin-rich terminal web-like structure. When LLC-PK1 cells were injected with two monoclonal antibodies against pig brain nonmuscle myosin, in concentrations yielding a 1:1 ratio of antibody to myosin, neither microvillar number nor length was affected. However, when we examined the cells by scanning electron microscopy 1-3 h after microinjection, we found that one of the antibodies (a-PBM 4) had a profound effect on microvillar position: more than 50% were seen tilted or lying prone on the plasma membrane. The microvilli of cells injected with the other antibody (a-PBM 9) were not significantly different from those of cells injected with control antibodies. This difference correlates with in vitro properties of the antibodies: a-PBM 4 decreases the actin-activated Mg(2+)-ATPase of pig brain nonmuscle myosin quite substantially, while a-PBM 9 affects it only moderately. These differential effects are probably a consequence of the different epitope location as determined for both antibodies, not of differences in antibody affinity. Our data are compatible with the hypothesis that a-PBM 4 also interferes with the actomyosin interaction in situ, thus decreasing the effective cross-linking of microvillar rootlets by myosin filaments in the terminal web. On the basis of this model, we suggest that myosin filaments are essential for the upright position of brush-border type microvilli.

Activation of the estrogen receptor from N-nitrosomethylurea-induced rat mammary tumors.

The activation of the estrogen receptor (ER) from N-nitrosomethylurea (NMU)-induced rat mammary tumors was studied in vitro. The activation of the receptor induced by heating of the cytosol containing occupied ER was measured by a 3-4-fold increase of receptor binding to nuclei in comparison with the nuclear binding of the nonactivated ER. The activation of the ER was further shown by alteration of the elution profile from DEAE-cellulose. A shift of the receptor peak from 234 mM (Peak II, nonactivated ER) to 70 mM (Peak I, activated ER) phosphate buffer could be obtained. The overall recoveries of activated ER following chromatography on DEAE-cellulose were significantly lower than the recoveries of the nonactivated ER, 71 and 85%, respectively. Binding of the activated ER to nuclei and chromatography of the supernatant which is not able to bind to nuclei on DEAE-cellulose resulted in a decrease of Peak I and in an increase of the overall recovery. These findings suggest that the nuclear bound ER consists of two parts. One is represented partially by Peak I of the elution profile and the other one by that part of the receptor which can not be eluted from the column under the conditions used. Furthermore, the dissociation of tritiated estradiol (E3H) from the nonactivated ER followed a two component exponential function whereas after activation a monophasic dissociation curve could be observed. The mean half times for the dissociation of E3H from the activated and nonactivated ER were 101 and 7.2 min, respectively. Finally, the nonactivated molybdate stabilized ER sedimented in 5-20% sucrose density gradients as two peaks, one at 9.5 S and the other at 4 S. After activation of the ER only the smaller 4 S peak was evident. Molybdate inhibited the activation of the ER measured by nuclear binding assays, sucrose density gradient analysis, dissociation kinetics or ion exchange chromatography but not completely in every case.

Immunochemical differentiation of glucose phosphate isomerase (GPI) allozymes of the mouse.

Polyclonal xenoantisera against mouse GPI-1B and GPI-1C were produced in rabbits and analyzed for their ability to recognize allozyme-specific determinants. These studies showed a high degree of serological similarity among the three allozymes of mouse glucose phosphate isomerase (GPI). However, GPI-1B and GPI-1C could be differentiated from GPI-1A as well as GPI-1A and GPI-1B from GPI-1C using quantitative solid-phase immunobinding assays. In addition, polyclonal and monoclonal alloantibodies specific for GPI-1C were produced in BALB/c (Gpi-1a/Gpi-1a) mice. As indicated by immunoblotting data, the allozyme specificity of rabbit antisera and monoclonal alloantibodies against GPI-1C is dependent on the native structure of that allozyme.