Mixed mock modular forms are functions which lie in the tensor space of mock modular forms and modular forms. As q-hypergeometric series, mixed mock modular forms appear to be much more common than mock theta functions. In this survey, we discuss some of the ways such series arise.

This paper presents a stochastic modelling framework for complex biochemical reaction networks from a component-based perspective. Our approach takes into account the discrete character of quantities of participating entities (i.e. the individual populations of the involved chemical species) and the inherent probabilistic nature of microscopic molecular collisions. We collect all instances of o...

We describe the main features of SmArT, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. SmArT can combine different formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic state-space generation techniques, as well as symbolic CTL model-checking algorithms, are available. For the stu...

We investigate a class of distributionally robust optimization problems that have direct applications in finance. They are semi-infinite programming problems with ambiguous expectation constraints in which fractional functions represent reward-risk ratios. We develop a reformulation and algorithmic data-driven framework based on the Wasserstein metric to model ambiguity and to derive probabilis...

In the context of probabilistic automata, time efficient algorithms for probabilistic simulations have been proposed lately. The space complexity thereof is quadratic in the size of the transition relation, thus space requirements often become the practical bottleneck. In this paper, we exploit ideas from [6] to arrive at a space-efficient algorithm for computing probabilistic simulations based...

Mathematical approaches are reviewed to interpret intermittent singular space-time dynamics observed in brain imaging experiments. The following aspects of brain dynamics are considered: nonlinear dynamics (chaos), phase transitions, and criticality. Probabilistic cellular automata and random graph models are described, which develop equations for the probability distributions of macroscopic st...

This paper presents an XML-based flexible and modular architecture for the modelling and the run-time support of web-based Adaptive Hypermedia Systems supporting multi-channel access. The proposed XML Adaptive Hypermedia Model (XAHM) and the supporting architecture allow the hypermedia adaptation along three different "adaptivity dimensions": user`s behaviour; technology, external environment. ...

We describe the main features of SmArT, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. SmArT can combine different formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic state-space generation techniques, as well as symbolic CTL model-checking algorithms, are available. For the stu...

The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the A∞ cyclic operad. This gives a new proof of the result of Harer-Mumford-Thurston-Penner-Kontsevich that a cell complex built from ribbon graphs is homotopy equiva...

We present thread-modular model checking, a novel technique for verifying correctness properties of loosely-coupled multithreaded software systems. Thread-modular model checking verifies each thread separately using an automatically inferred environment assumption that abstracts the possible steps of other threads. Separate verification of each thread yields significant space and time savings. ...