The STADYCS consortium conducts an interdisciplinary study into the stochastic adaptive dynamics of complex systems, and their modeling applications in physics, biology, and economics. We build on our earlier work in the area of complex systems modeling, with an increased emphasis on the effects of stochasticity in such systems, and the interaction of processes evolving at different time scales in their dynamics.
The consortium has had mainly an enabling role, by bringing together people from different specialties and arranging multidisciplinary workshops on topics of common interest (more information). As a result of this coordinating activity, some collaborative research between the participating groups has emerged, most notably between the Physics and Ecology subprojects. Another area of natural collaborative arrangements is between the Ecology and Biomathematics groups. There are also many other contact points in the research work performed by the different groups (as listed below), but collaboration leading to actual joint publications has been limited, mainly due to geographical and disciplinary factors.
Group leader: Pekka Orponen.
2002-03: Computational Complexity and Combinatorics Group, Helsinki University of Technology, Laboratory for Theoretical Computer Science.
The project commenced at a time when the group leader was moving from the University of Jyväskylä to the Helsinki University of Technology, and thus project activity was limited in 2000-01.
| Position | Number of researchers at most | Total number of months in 3 years |
|---|---|---|
| Professors | 1 (10 %, other funding) | 4 (other funding) |
| Senior researchers | N/A | N/A |
| Young researchers | 1 (other funding) | 8 (other funding) |
| Post-graduate students | 2 (100% + 10%) | 19 (12 MaDaMe, 7 other funds) |
| Under-graduate students | 1 (50%) | 3 |
Research has focused on three areas in the computational theory and applications of complex system models. First, in the area of recurrent neural networks it was established in [1.1] that so called continuous-time Hopfield networks have universal computational power, despite the fact that their dynamics are controlled by Liapunov functions. It follows as a corollary [1.3] that Liapunov-type dynamical systems can have transients that are exponentially long w.r.t. the system dimension. Similar results had been obtained earlier for discrete-time versions of this model (which correspond to zero-temperature versions of Sherrington-Kirkpatrick spin glasses with Glauber dynamics); the results on the continuous-time version now more or less complete the work in this area, summarised in the survey paper [1.2]. A second direction of work has been the development of efficient stochastic solution methods for the NP-complete Satisfiability problem. In [1.4] a little-known focused random walk -based technique was tested on problem instances of up to 106 variables, quite close to the conjectured unsatisfiability threshold of alpha = 4.26 clauses per variable. It was observed that the method apparently can be adjusted to work in linear time w.r.t. the number of variables right up to the threshold, despite an earlier conjecture that all random-walk based solution techniques would become nonlinear already at clauses-to-variables ratios in the range of alpha = 2,7 ... 2,8. (However the coefficient of linearity necessarily grows arbitrarily large as the method is pushed closer to alpha.) Analytical explanations of this discrepancy are under investigation. In a third direction, so called small-world network models have been investigated [1.9]. In particular, a novel clustering method has been developed [1.7, 1.8] that is capable of detecting clusters of nodes with locally high interconnection density, without information on the global structure of the network.
It may also be worth mentioning that based on the experiences with the project, a new graduate-level computer science course on "Combinatorial Models and Stochastic Algorithms" was developed and given for the first time in Spring 2003 at the Helsinki University of Technology. Also several seminars have been arranged on topics related to the project, e.g. one on "Fitness Landscapes" in Spring 2002.
Statistical Physics and Complex Materials Group, Helsinki University of Technology, Laboratory of Physics.
Group leader: Tapio Ala-Nissilä.
| Position | Number of researchers at most | Total number of months in 3 years |
|---|---|---|
| Professors | N/A | 36 |
| Senior researchers | N/A | 72 |
| Young researchers | N/A | 108 |
| Post-graduate students | N/A | 144 |
| Under-graduate students | N/A | 108 |
The main objectives of the physics project on Stochastic Dynamics of Nonequilibrium Systems were
Research within the Stochastic Dynamics of Nonequilibrium Systems project has focused on the theoretical aspects of nonequilibrium interfaces (NEI's) in lattice and continuum models. We have successfully modelled and measured various kinetic fronts such as slow combustion [2.2, 2.8] and wetting [2.3, 2.7, 2.9, 2.16] using the so-called phase field approach. Systematic formalism has been developed to derive phase-field type of models from underlying microscopic dynamics. We have also studied lattice models where NEI's emerge from cellular automaton type of rules [2.11, 2.12]. In conjunction with working with different modelling approaches, we have developed methodology for more efficient numerical solution of random interface problems [2.13]. We have also developed methodology to find ground states for complicated many-particle systems [2.10].
This main research project in direct collaboration with other Consortium members has been based on collaboration between the Metapopulation Research Group in the Department of Ecology and Systematics at the University of Helsinki and the Physics Group of Tapio Ala-Nissilä. The project has dealt with the population dynamics of boreal moths (genus Xestia) and their parasitoid wasps (Phion luteus). A long time-series of light trap data from the station in Värriö, Finland, showed biennial abundancy oscillations in both. Parasitic interaction between both was shown to be the cause, by indirect means of (i) establishing a model of population dynamics including the temporal aspect of exposure to parasitism and (ii) excluding other causes [2.14]. An extension of the model to a coupled map lattice helped to interpret the apparent geographical pattern of oscillation phases (high abundance in odd years vs. even years) and the role of areas with less forest (such as swamps and lakes) to stabilise the boundary zone between the regions of opposite oscillation phase [2.6]. Currently long time observations of the dynamics of the butterfly Melitaea cinxia and its parasitoid Cotesia melitaearum on Åland are used to establish the importance of irregularity in the underlying habitat landscape as compared to dynamical randomness.
Metapopulation Research Group, University of Helsinki, Department of Ecology and Systematics.
Group leader: Ilkka Hanski.
| Position | Number of researchers at most | Total number of months in 3 years |
|---|---|---|
| Professors | 1 | 1 |
| Senior researchers | N/A | N/A |
| Young researchers | 1 | 1 |
| Post-graduate students | N/A | N/A |
| Under-graduate students | N/A | N/A |
Populations living in discrete fragments of habitat are called metapopulations. Over the past 10 years, the Metapopulation Research Group (MRG) at the University of Helsinki has established a leading position internationally in the field of metapopulation biology. A speciality of the MRG has been the close integration of theoretical and empirical research. The MRG has been especially strong in developing spatially realistic metapopulation models and methods for parameterising them (see e.g. [3.19]).
The main objective of the MaDaMe project was to contribute to the ongoing development of general theory of ecological metapopulation dynamics. Our first aim was to enhance the qualitative understanding of how regional scale spatio-temporal patterns depend on smaller scale processes, ultimately on individual behaviour and its interplay with spatially and temporally varying environmental conditions. Our second aim was to develop general and unified theory that would provide a robust backbone for developing detailed models of more quantitative nature.
During the MaDaMe-project, the goal described above was supplemented with another theme, which is to develop both theoretical and practical models for understanding better how individuals disperse in heterogeneous landscapes. This subproject was started to provide building blocks for metapopulation models, but it has turned out to have lot of scientific interest also outside metapopulation theory. Recently, we have been integrating these two themes together.
In the metapopulation research group the MaDaMe project has been carried out by prof. Ilkka Hanski (project leader) and by Dr. Otso Ovaskainen (post doc 2000-2002, senior researcher 2003 onwards).
The research conducted by the Metapopulation research may be put under two categories: metapopulation theory and dispersal theory.
The main emphasis in the development of metapopulation theory has been on stochastic patch occupancy models (SPOMs), which are based on describing the landscape as a network of n habitat patches, each of which is scored either as occupied or empty. The increasing number of practical applications has shown that SPOMs provide a structurally flexible family of models that may be applied to real heterogeneous landscapes [3.19].
Many of our analyses have dealt with deterministic mean-field approximations, where the term "mean-field" refers to averaging over time, but retaining the setting of n habitat patches with given areas and spatial locations. One of the main concepts stemming from the deterministic theory is the metapopulation capacity [3.1], which is a landscape index characterising the ability of a landscape to support a viable metapopulation. The metapopulation capacity may be readily calculated for real landscapes and it may be used e.g. to compare the consequences of different scenarios of habitat loss and fragmentation. The deterministic theory was generalised and developed further in [3.3, 3.4, 3.5, 3.6, 3.8, 3.9, 3.13], in which we have considered non-linearities arising from interactions between individuals, transient behaviour, and other elaborations motivated by biological questions. We have utilised the diffusion approximation and some other mathematical techniques to analyse also stochastic metapopulation theory [3.2, 3.7,3.11], which is still a topic of active research in the MRG.
The dispersal project aims at analysing the movement behaviour of individuals in heterogeneous landscapes. We have examined the mathematical links between mechanistic random walk models and their diffusion approximations [3.15], and used the theoretical results to analyse spatial mark-recapture data collected for the heath fritillary butterfly [3.14]. Recently we have been working with models that aim at connecting metapopulation dynamics to the movement behaviour of individuals [3.18].
Research Unit on Economic Structures and Growth, University of Helsinki, Department of Economics.
Group leader: Seppo Honkapohja.
| Position | Number of researchers at most | Total number of months in 3 years |
|---|---|---|
| Professors | 1 (10 %) | 4 (other funding) |
| Senior researchers | N/A | N/A |
| Young researchers | 1 (100 %) | 36 |
| Post-graduate students | 1 (20 %) | 7 (other funding) |
| Under-graduate students | N/A | N/A |
The goal was to study selected topics in dynamic economic modelling, including
(Markus Haavio and Heikki Kauppi)
Recent empirical studies have indicated that owner-occupation may be inferior to private rental housing in enhancing efficient spatial matching of labour and jobs. Since existing economic theory does not provide satisfactory explanations for this finding, the aim of this research project has been to fill a part of this gap. To do so we have developed a sequence of dynamic multi-region models with stochastic regional business cycles and idiosyncratic shocks changing individual agents' match with the current job or technology. Regional business cycles play a dual role in the argument: On the one hand they create a need for labour mobility. On the other hand they are a crucial element in the mechanism preventing mobility as changes in regional fortunes give rise to changes in regional housing prices, and capital losses (and gains). The potential inefficiency in the models then derives from incomplete markets: consistent with empirical evidence, we assume that there are no insurance markets against capital losses made in the housing sector. However, as it is likely to be the case in reality, the agents can engage in precautionary saving and borrow up to a certain limit.
Our main findings are the following. First we propose that the asset nature of owner-occupied housing, combined with incomplete insurance markets, may hamper efficient labour mobility. Second, owner-occupation should however perform poorly compared to rental markets only under certain circumstances. To be more specific, our models imply that owner-occupation is likely to inefficient (efficient) when (i) regional shocks are large and persistent (small and transitory), (ii) idiosyncratic shocks are frequent (rare) and (iii) at least some low income agents should optimally live in booming regions, where housing prices are high. These predictions may provide testable hypotheses for future empirical research.
(Markus Haavio)
Recent literature has shown that perfect household mobility may induce individual jurisdictions to internalise interregional externalities caused by e.g. transboundary pollution. The gist of this result lies in the observation that perfect household mobility immediately levels down regional welfare differences: in equilibrium no jurisdiction can be better off than any other jurisdiction, and thus socially harmful policies cannot be individually rational. In practical terms, the result suggests that in a world with a mobile population international co-operation may not be necessary in settling problems like acid rain or the green house effect.
The efficiency result has been established in static models with costless migration. I my research project I adopt the basic framework from the literature, but add migration costs and real time dynamics. Compared to the static settings, the dynamic framework allows me to address some new issues, which I think are relevant. First, many environmental problems, ranging from acid rain and toxic waste to the use of natural resources, are essentially intertemporal, and involve stocks rather than flows. Second, migration is a costly and gradual process: changes in regional demographics do not occur instantaneously. Finally, public policies are typically not set once and for all. If given a chance, rational governments reoptimise.
My main findings are as follows: I show that the combination of stock pollution, costly migration and time consistent environmental policies implies a major departure from the efficiency result established in the literature. Rather than neutralising distortions from transboundary pollution, household mobility reinforces the incentives to overemit. Environmental damages are excessive even when pollution is local. Moreover these intertemporal externalities get worse as the degree of household mobility increases. As migration costs approach zero (but do not reach it), the economy becomes as distorted as under global pollution. These findings suggest that household mobility may not be a substitute for explicit international cooperation, but that it may quite the contrary reinforce the need for policy coordination.
Laboratory of Computational Engineering, Helsinki University of Technology.
Group leader: Kimmo Kaski.
| Position | Number of researchers at most | Total number of months in 3 years |
|---|---|---|
| Professors | TODO | TODO |
| Senior researchers | TODO | TODO |
| Young researchers | TODO | TODO |
| Post-graduate students | TODO | TODO |
| Under-graduate students | TODO | TODO |
TODO: description missing from the document at the moment
Biomathematics Research Group, University of Turku, Department of Mathematics.
Group leader: Mats Gyllenberg.
| Position | Number of researchers at most | Total number of months in 3 years |
|---|---|---|
| Professors | 1 | 36 |
| Senior researchers | 2 | 72 |
| Young researchers | 3 | 19 |
| Post-graduate students | 2 | 23 |
| Under-graduate students | N/A | N/A |
Adaptive dynamics is a mathematical framework to model evolution by natural selection in complex ecological systems, where the fitness of a strategy depends (usually in a nonlinear way) on the frequencies of all other strategies present in the population (Metz et al. 1992; Dieckmann and Law 1996; Abrams 2001) and where biodiversity may increase by strategies gradually splitting into two diverging lineages (evolutionary branching, Geritz et al. 1998). The aim of this research project was to establish the adaptive dynamics theory of metapopulations (systems of local populations connected by dispersal; Hanski and Gilpin 1997), to further develop the general theory of adaptive dynamics in directions relevant for metapopulation applications, and to study particular problems of metapopulation evolution.
We have derived the necessary fitness measures in structured metapopulation models for both infinite and finite local populations and for monomorphic and polymorphic clonal or sexual resident populations [6.2, 6.7, 6.15, 6.37], such that the general methods of adaptive dynamics, which assume that fitness is known, are now applicable to metapopulations. Next, we have extended adaptive dynamics to the case of multiple demographic attractors [6.8] which readily occur in metapopulation models, and showed that invasion of a new strategy generically implies substitution rather than coexistence. Coexistence of infinitely many strategies is degenerate even in an infinite world [6.39]. We studied evolutionary branching of multi-dimensional strategies, focusing on what determines the number of branches, the directions of the individual branches and the rate of divergence of the branches.
The most important applications are (i) the evolution of dispersal in structured metapopulations, which we modelled extensively both in homogeneous [6.2, 6.7, 6.11, 6.21] and heterogeneous metapopulations [6.12, 6.15], and (ii) local adaptation in heterogeneous metapopulations [6.4, 6.12]. Other applications of adaptive dynamics included cycles of evolutionary branching and extinction [6.6], the reversal of evolutionary arms races [6.5], evolutionary suicide [6.3, 6.11, 6.28], evolution in predator-prey systems [6.22], and the evolution of dioecy in plants [6.1]. We also advanced the theory of structured populations in general [6.10, 6.17, 6.26, 6.30], modelled the dynamics of symbionts in metapopulations [6.9, 6.16] and the coexistence of species by the competition-colonisation trade-off [6.19, 6.20]. In population dynamics, we studied competitive-cooperative systems [6.23, 6.36, 6.41, 6.43], and gave a new ecological underpinning for discrete-time population models with chaos [6.38]; one postdoc continued previous research on applied microbial dynamics.
Mathematical Physics Group, University of Helsinki, Department of Mathematics.
Group leader: Antti Kupiainen.
| Position | Number of researchers at most | Total number of months in 3 years |
|---|---|---|
| Professors | 1 | 36 |
| Senior researchers | 1 | 36 |
| Young researchers | 5 | 80 |
| Post-graduate students | 7 | 180 |
| Under-graduate students | 3 | 60 |
The main objectives in the mathematics group were to study various aspects of extended dynamical systems, in particular pattern formation in partial differential equations, coupled map lattices and turbulence. All these aspects have been studied and main progress consists of the following:
Together with J. Taskinen and T. Korvola we have been studying the stability of front solutions in the Cahn-Hilliard equation. This is a parabolic equation of fourth order in spatial derivatives and has plenty of applications in various applied fields. It is also an important testing ground for mathematical techniques and has successfully resisted rigorous analysis since standard techniques such as the maximum principle are not applicable. We showed that the solutions exhibit peculiar scaling properties for large times. In particular we proved that instead of the standard diffusive decay inversely proportional to the square root of time the solutions show an anomalous decay where cube root occurs.
Coupled Map Lattices can be thought of as space time discretisations of PDE's: one envisions a coarse graining procedure in spatial variables so that the resulting variables are defined on a spatial lattice and then one discretises time e.g. by considering the time one map.
In earlier work we have constructed Sinai-Ruelle-Bowen measures that describe the statistical properties of these chaotic systems in a uniformly hyperbolic situation of weakly coupled expansive circle maps. Recently together with F. Bonetto and J. Lebowitz we have been studying the properties of the SRB measures for coupled map lattices where infinitely many hyperbolic torus automorphisms, indexed by a d-dimensional lattice, are coupled together with analytic perturbation. We show that the projection of the SRB measure on a finite number of tori is absolutely continuous with respect to the Lebesgue measure unless the perturbation has a non-generic form. Thus the fractal nature of the SRB measure is not "physically relevant".In the field of turbulence we have studied dispersion of tracers (like impurities) in model ensembles of turbulent velocities. We have considered Gaussian scale invariant velocity ensembles where the velocity of the fluid is spatially rough and exhibits temporal correlation. We have given arguments that the Lagrangian dispersion in those models is determined by the scale dependence of the ratio between the correlation time of velocity differences and the so-called eddy turnover time. This has led to the prediction of the existence of different phases with deterministic, stochastic and collapsing Lagrangian trajectories and to conjecture the location of the phase transition as a function of the scale dependence of the velocity.
Another direction in turbulence has been the study of two-dimensional statistical hydrodynamics. We have proven exponential mixing for this system in the turbulent regime.
The overarching idea here is to find unifying concepts and results for higher dimensional symbolic dynamics. Specific models under study have been cellular automata - both deterministic and stochastic, dimer and vertex models as well as more complex polyominoes and related lattice-packing models. Results include efficient and novel algorithms for relaxation in the models above, Arctic Circle -type results have been established outside the dimer context and a clear chacterisation of its breakdown in the context of Archimedean lattices has been given. Moreover a new research direction has been found that has already yielded insight and results on the nature of densest lattice packings.
Last update July 11th, 2003.
URL: http://www.tcs.hut.fi/Research/CCC/Projects/STADYCS/partners.html