## IIP Internships in Austria

**Complexity Science Hub Vienna**

**Location: **Vienna, Austria

**About:**The objective of the Complexity Science Hub Vienna is to host, educate, and inspire complex systems scientists who are dedicated to collect, handle, aggregate, and make sense of big data in ways that are directly valuable for science and society. Focus areas include smart cities, innovation dynamics, medical, social, ecological, and economic systems. CSH is a joint initiative of AIT, IIASA, Medical University of Vienna, TU Graz, TU Wien, and Vienna University of Economics and Business.

**Intern Responsibilities: **The IIP intern will contribute to the work of the Hub and may be able to conduct research for an independent project.

__Anticipating Collapses in Adaptive Networks__

Network dynamics in which the state of the nodes and the network topology co-evolve are called adaptive network models. They are frequently used to model ecological, epidemiological, socio-economic or political systems. We are interested in collapses of such systems. Depending on the context this could mean that the network disintegrates or that a particular state goes extinct. Before such an event the network is in a critical state. We would like to study these states with tools from statistical mechanics and bifurcation theory. More concretely we have shown that the extinction of a disease in an adaptive epidemic model [1] is preceded by maxima in several network quantities, such as the clustering coefficient or motif densities. There are two projects related to this phenomenon: 1) Using a mean field approach one can derive 3 ordinary differential equations that govern the dynamics of the node and link densities. The student should recover these equations, analyze which terms are crucial for the existence of the maximum and write down an abstract parameterized model that can reproduce this maximum. 2) Write an agent-based model where the agents can observe their neighborhood in the network and depending on that information change their contacts to shield themselves from the disease. The student should use the results obtained in [1] to make the agents successfully eradicate the disease. Both projects require programming. We encourage the use of C,C++, Matlab, R, python or Julia.

__Prerequisites:__

Basic course of calculus

Basic course of thermodynamics/statistical physics (optional)

Basic course of probability/statistics (optional)

__Calculation of Scaling Exponents for Systems with Structures and Emerging States__

The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states W(N) depends on the size N of the system. It has been recently shown [1], that all stochastic systems can be classified according to the so-called scaling expansion. The corresponding expansion coefficients (exponents) define the universality class the system belongs to. Systems within the same universality class share the same statistics and thermodynamics. For sub-exponentially growing systems such expansions have been shown to exist [2,3]. By using the scaling expansion this classification can be extended to all stochastic systems, including correlated, constraint and super-exponential systems. The extensive entropy of these systems can be easily expressed in terms of these scaling exponents. Systems with super-exponential phase space growth contain important systems, such as magnetic coins that combine combinatorial and structural statistics [4]. The main aim of the project is to calculate the scaling exponents for a some realistic models, where higher-order structures naturally arise. Examples of such systems are e.g., simplicial complexes representing multi-party interactions between the individuals [5], or molecule models. Calculation of exponents will allow us to study statistical properties of these systems and establish connections between different models with emergent structures.

__Prerequisites:__

Basic course of calculus

Basic course of thermodynamics/statistical physics (optional)

Basic course of probability/statistics (optional)

**Qualifications: **IIP candidates with interests in network science, big data and complexity science, understanding complex systems and computer science are encouraged to apply. Programming skills would be an asset.

TO APPLY, click here: Complexity Science Hub Vienna |