System design of stochastic models using robustness of temporal properties

Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling is the model checking problem, i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process. However, one may not only be interested in the notion of satisfiability, but also in the capacity of a system to maintain a particular emergent behaviour unaffected by the perturbations, caused e.g. from extrinsic noise, or by possible small changes in the model parameters. To address this issue, researchers from the verification community have recently proposed several notions of robustness for temporal logic providing suitable definitions of distance between a trajectory of a (deterministic) dynamical system and the boundaries of the set of trajectories satisfying the property of interest. The contributions of this paper are twofold. First, we extend the notion of robustness to stochastic systems, showing that this naturally leads to a distribution of robustness degrees. By discussing three examples, we show how to approximate the distribution of the robustness degree and the average robustness. Secondly, we show how to exploit this notion to address the system design problem, where the goal is to optimise some control parameters of a stochastic model in order to maximise robustness of the desired specifications

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

Neural-Kalman Schemes for Non-Stationary Channel Tracking and Learning

This Thesis focuses on channel tracking in Orthogonal Frequency-Division Multiplexing (OFDM), a widely-used method of data transmission in wireless communications, when abrupt changes occur in the channel. In highly mobile applications, new dynamics appear that might make channel tracking non-stationary, e.g. channels might vary with location, and location rapidly varies with time. Simple examples might be the di erent channel dynamics a train receiver faces when it is close to a station vs. crossing a bridge vs. entering a tunnel, or a car receiver in a route that grows more tra c-dense. Some of these dynamics can be modelled as channel taps dying or being reborn, and so tap birth-death detection is of the essence. In order to improve the quality of communications, we delved into mathematical methods to detect such abrupt changes in the channel, such as the mathematical areas of Sequential Analysis/ Abrupt Change Detection and Random Set Theory (RST), as well as the engineering advances in Neural Network schemes. This knowledge helped us nd a solution to the problem of abrupt change detection by informing and inspiring the creation of low-complexity implementations for real-world channel tracking. In particular, two such novel trackers were created: the Simpli- ed Maximum A Posteriori (SMAP) and the Neural-Network-switched Kalman Filtering (NNKF) schemes. The SMAP is a computationally inexpensive, threshold-based abrupt-change detector. It applies the three following heuristics for tap birth-death detection: a) detect death if the tap gain jumps into approximately zero (memoryless detection); b) detect death if the tap gain has slowly converged into approximately zero (memory detection); c) detect birth if the tap gain is far from zero. The precise parameters for these three simple rules can be approximated with simple theoretical derivations and then ne-tuned through extensive simulations. The status detector for each tap using only these three computationally inexpensive threshold comparisons achieves an error reduction matching that of a close-to-perfect path death/birth detection, as shown in simulations. This estimator was shown to greatly reduce channel tracking error in the target Signal-to-Noise Ratio (SNR) range at a very small computational cost, thus outperforming previously known systems. The underlying RST framework for the SMAP was then extended to combined death/birth and SNR detection when SNR is dynamical and may drift. We analyzed how di erent quasi-ideal SNR detectors a ect the SMAP-enhanced Kalman tracker's performance. Simulations showed SMAP is robust to SNR drift in simulations, although it was also shown to bene t from an accurate SNR detection. The core idea behind the second novel tracker, NNKFs, is similar to the SMAP, but now the tap birth/death detection will be performed via an arti cial neuronal network (NN). Simulations show that the proposed NNKF estimator provides extremely good performance, practically identical to a detector with 100% accuracy. These proposed Neural-Kalman schemes can work as novel trackers for multipath channels, since they are robust to wide variations in the probabilities of tap birth and death. Such robustness suggests a single, low-complexity NNKF could be reusable over di erent tap indices and communication environments. Furthermore, a di erent kind of abrupt change was proposed and analyzed: energy shifts from one channel tap to adjacent taps (partial tap lateral hops). This Thesis also discusses how to model, detect and track such changes, providing a geometric justi cation for this and additional non-stationary dynamics in vehicular situations, such as road scenarios where re ections on trucks and vans are involved, or the visual appearance/disappearance of drone swarms. An extensive literature review of empirically-backed abrupt-change dynamics in channel modelling/measuring campaigns is included. For this generalized framework of abrupt channel changes that includes partial tap lateral hopping, a neural detector for lateral hops with large energy transfers is introduced. Simulation results suggest the proposed NN architecture might be a feasible lateral hop detector, suitable for integration in NNKF schemes. Finally, the newly found understanding of abrupt changes and the interactions between Kalman lters and neural networks is leveraged to analyze the neural consequences of abrupt changes and brie y sketch a novel, abrupt-change-derived stochastic model for neural intelligence, extract some neuro nancial consequences of unstereotyped abrupt dynamics, and propose a new portfolio-building mechanism in nance: Highly Leveraged Abrupt Bets Against Failing Experts (HLABAFEOs). Some communication-engineering-relevant topics, such as a Bayesian stochastic stereotyper for hopping Linear Gauss-Markov (LGM) models, are discussed in the process. The forecasting problem in the presence of expert disagreements is illustrated with a hopping LGM model and a novel structure for a Bayesian stereotyper is introduced that might eventually solve such problems through bio-inspired, neuroscienti cally-backed mechanisms, like dreaming and surprise (biological Neural-Kalman). A generalized framework for abrupt changes and expert disagreements was introduced with the novel concept of Neural-Kalman Phenomena. This Thesis suggests mathematical (Neural-Kalman Problem Category Conjecture), neuro-evolutionary and social reasons why Neural-Kalman Phenomena might exist and found signi cant evidence for their existence in the areas of neuroscience and nance. Apart from providing speci c examples, practical guidelines and historical (out)performance for some HLABAFEO investing portfolios, this multidisciplinary research suggests that a Neural- Kalman architecture for ever granular stereotyping providing a practical solution for continual learning in the presence of unstereotyped abrupt dynamics would be extremely useful in communications and other continual learning tasks.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Luis Castedo Ribas.- Secretaria: Ana García Armada.- Vocal: José Antonio Portilla Figuera

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book