3,531 research outputs found
On Expressing and Monitoring Oscillatory Dynamics
To express temporal properties of dense-time real-valued signals, the Signal
Temporal Logic (STL) has been defined by Maler et al. The work presented a
monitoring algorithm deciding the satisfiability of STL formulae on finite
discrete samples of continuous signals. The logic has been used to express and
analyse biological systems, but it is not expressive enough to sufficiently
distinguish oscillatory properties important in biology. In this paper we
define the extended logic STL* in which STL is augmented with a signal-value
freezing operator allowing us to express (and distinguish) detailed properties
of biological oscillations. The logic is supported by a monitoring algorithm
prototyped in Matlab. The monitoring procedure of STL* is evaluated on a
biologically-relevant case study.Comment: In Proceedings HSB 2012, arXiv:1208.315
Learning and Designing Stochastic Processes from Logical Constraints
Stochastic processes offer a flexible mathematical formalism to model and
reason about systems. Most analysis tools, however, start from the premises
that models are fully specified, so that any parameters controlling the
system's dynamics must be known exactly. As this is seldom the case, many
methods have been devised over the last decade to infer (learn) such parameters
from observations of the state of the system. In this paper, we depart from
this approach by assuming that our observations are {\it qualitative}
properties encoded as satisfaction of linear temporal logic formulae, as
opposed to quantitative observations of the state of the system. An important
feature of this approach is that it unifies naturally the system identification
and the system design problems, where the properties, instead of observations,
represent requirements to be satisfied. We develop a principled statistical
estimation procedure based on maximising the likelihood of the system's
parameters, using recent ideas from statistical machine learning. We
demonstrate the efficacy and broad applicability of our method on a range of
simple but non-trivial examples, including rumour spreading in social networks
and hybrid models of gene regulation
Trend-based analysis of a population model of the AKAP scaffold protein
We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system
A general computational method for robustness analysis with applications to synthetic gene networks
Motivation: Robustness is the capacity of a system to maintain a function in the face of perturbations. It is essential for the correct functioning of natural and engineered biological systems. Robustness is generally defined in an ad hoc, problem-dependent manner, thus hampering the fruitful development of a theory of biological robustness, recently advocated by Kitano
On the robustness of temporal properties for stochastic models
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 mantain 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 scores. By discussing two examples, we show how to approximate the distribution of the robustness score and its key indicators: the average robustness and the conditional average robustness. Secondly, we show how to combine these indicators with the satisfaction probability to address the system design problem, where the goal is to optimize some control parameters of a stochastic model in order to best maximize robustness of the desired specifications
Traffic Network Control from Temporal Logic Specifications
We propose a framework for generating a signal control policy for a traffic
network of signalized intersections to accomplish control objectives
expressible using linear temporal logic. By applying techniques from model
checking and formal methods, we obtain a correct-by-construction controller
that is guaranteed to satisfy complex specifications. To apply these tools, we
identify and exploit structural properties particular to traffic networks that
allow for efficient computation of a finite state abstraction. In particular,
traffic networks exhibit a componentwise monotonicity property which allows
reach set computations that scale linearly with the dimension of the continuous
state space
Metrics for Signal Temporal Logic Formulae
Signal Temporal Logic (STL) is a formal language for describing a broad range
of real-valued, temporal properties in cyber-physical systems. While there has
been extensive research on verification and control synthesis from STL
requirements, there is no formal framework for comparing two STL formulae. In
this paper, we show that under mild assumptions, STL formulae admit a metric
space. We propose two metrics over this space based on i) the Pompeiu-Hausdorff
distance and ii) the symmetric difference measure, and present algorithms to
compute them. Alongside illustrative examples, we present applications of these
metrics for two fundamental problems: a) design quality measures: to compare
all the temporal behaviors of a designed system, such as a synthetic genetic
circuit, with the "desired" specification, and b) loss functions: to quantify
errors in Temporal Logic Inference (TLI) as a first step to establish formal
performance guarantees of TLI algorithms.Comment: This paper has been accepted for presentation at, and publication in
the proceedings of, the 2018 IEEE Conference on Decision and Control (CDC),
to be held in Fontainebleau, Miami Beach, FL, USA on Dec. 17-19, 201
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