Poisson-Nijenhuis structures on quiver path algebras

We introduce a notion of noncommutative Poisson-Nijenhuis structure on the path algebra of a quiver. In particular, we focus on the case when the Poisson bracket arises from a noncommutative symplectic form. The formalism is then applied to the study of the Calogero-Moser and Gibbons-Hermsen integrable systems. In the former case, we give a new interpretation of the bihamiltonian reduction performed in [3].Comment: 23 page

Monitoring with uncertainty

We discuss the problem of runtime verification of an instrumented program that misses to emit and to monitor some events. These gaps can occur when a monitoring overhead control mechanism is introduced to disable the monitor of an application with real-time constraints. We show how to use statistical models to learn the application behavior and to "fill in" the introduced gaps. Finally, we present and discuss some techniques developed in the last three years to estimate the probability that a property of interest is violated in the presence of an incomplete trace.Comment: In Proceedings HAS 2013, arXiv:1308.490

SEA-PARAM: Exploring Schedulers in Parametric MDPs

We study parametric Markov decision processes (PMDPs) and their reachability probabilities "independent" of the parameters. Different to existing work on parameter synthesis (implemented in the tools PARAM and PRISM), our main focus is on describing different types of optimal deterministic memoryless schedulers for the whole parameter range. We implement a simple prototype tool SEA-PARAM that computes these optimal schedulers and show experimental results.Comment: In Proceedings QAPL 2017, arXiv:1707.0366

A temporal logic approach to modular design of synthetic biological circuits

We present a new approach for the design of a synthetic biological circuit whose behaviour is specified in terms of signal temporal logic (STL) formulae. We first show how to characterise with STL formulae the input/output behaviour of biological modules miming the classical logical gates (AND, NOT, OR). Hence, we provide the regions of the parameter space for which these specifications are satisfied. Given a STL specification of the target circuit to be designed and the networks of its constituent components, we propose a methodology to constrain the behaviour of each module, then identifying the subset of the parameter space in which those constraints are satisfied, providing also a measure of the robustness for the target circuit design. This approach, which leverages recent results on the quantitative semantics of Signal Temporal Logic, is illustrated by synthesising a biological implementation of an half-adder

A Fourier-Mukai Transform for Stable Bundles on K3 Surfaces

We define a Fourier-Mukai transform for sheaves on K3 surfaces over \C, and show that it maps polystable bundles to polystable ones. The role of ``dual'' variety to the given K3 surface $X$ is here played by a suitable component $\hat X$ of the moduli space of stable sheaves on $X$. For a wide class of K3 surfaces $\hat X$ can be chosen to be isomorphic to $X$; then the Fourier-Mukai transform is invertible, and the image of a zero-degree stable bundle $F$ is stable and has the same Euler characteristic as $F$.Comment: Revised version, 15 pages AMSTeX with AMSppt.sty v. 2.1

A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned image. We show that formulas in this logic can be efficiently learned from positive and negative examples of several types of patterns. We also demonstrate that pattern detection, which is implemented as a model checking algorithm, performs very well for test data sets different from the learning sets. We define a quantitative semantics for the logic and integrate the model checking algorithm with particle swarm optimization in a computational framework for synthesis of parameters leading to desired patterns in reaction-diffusion systems