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The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge…

Markov chains are an important tool for modelling and evaluating systems in computer science, economics, biology and numerous other fields. Thus, approximating Markov chains is a useful tool for decreasing the computational effort needed…

This paper gives new, efficient algorithms for approximate uniform sampling of contingency tables and integer partitions. The algorithms use the Burnside process, a general algorithm for sampling a uniform orbit of a finite group acting on…

In the absence of impurities and boundary effects, first order phase transitions are initiated by the nucleation of critical bubbles. In thermally driven transitions many systems can remain metastable for an extended time, possibly tens of…

Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…

Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found…

Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in…

We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the `high acceptance regime'. The approach uses a localization argument to boost local mixing of…

Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling…

Many real-world systems, from social networks to protein-protein interactions and species distributions, exhibit overlapping flow-based communities that reflect their functional organisation. However, reliably identifying such overlapping…

Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…

We introduce an aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state…

We devise an abstract, modular scheme to prove continuity of the Lyapunov exponents for a general class of linear cocycles. The main assumption is the availability of appropriate large deviation type (LDT) estimates which are uniform in the…

We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how the subgroup chains of finite permutation groups yield…

For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic…

To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating…

Understanding how structured sequence information can be represented and generalized in neural systems is key to modeling the transition from acoustic input to emergent structure. In this study, we propose a rank-order based neural network…

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

Time-resolved X-ray absorption can reveal the dynamical screening of the local Coulomb interaction in strongly correlated photo-excited materials. Here, we focus on the theoretical prediction of X-ray absorption in the presence of dynamical…

Functions of chemical composition are complex and discrete in nature making it impossible to optimize them with gradient methods. Genetic algorithms, which do not use derivative information, are used to maximize the thermal conductivity of…