Simulation and Analysis of Animal Movement Paths using Numerus Model Builder

ABSTRACT Animal movement paths are represented by point-location time series called relocation data. How well such paths can be simulated, when the rules governing movement depend on the internal state of individuals and environmental factors (both local and, when memory is involved, global) remains an open question. To answer this, we formulate and test models able to capture the essential statistics of multiphase versions of such paths (viz., movement-phase-specific step-length and turning-angle means, variances, auto-correlation, and cross correlation values), as well as broad scale movement patterns. The latter may include patchy coverage of the landscape, as well as the existence of home-range boundaries and gravitational centers-of-movement (e.g., centered around nests). Here we present a Numerus Model Builder implementation of two kinds of models: a high-frequency, multi-mode, biased, correlated random walk designed to simulate real movement data at a scale that permits simulation and identification of path segments that range from minutes to days; and a model that uses statistics extracted from relocation data—either empirical or simulated—to construct movement modes and phases at subhourly to daily scales. We evaluate how well our derived statistical movement model captures patterns produced by our more detailed simulation model as a way to evaluate how well derived statistical movement models may capture patterns occurring in empirical data

Automatic verification of reliability requirements of spatio-temporal analysis using Three-Valued Spatio-Temporal Logic

In this paper we present the recently introduced Three-Valued Spatio-Temporal Logic (TSTL), which extends the available spatio-temporal analysis of stochastic systems, and an automatic procedure to verify whether this analysis satisfies given reliability requirements. The novel spatio-temporal logic TSTL enriches the analysis of properties expressed in Signal Spatio-Temporal Logic (SSTL), providing further insight into the dynamic behaviour of systems. Starting from the estimated satisfaction probabilities of given SSTL properties, it enables the analysis of their temporal and spatial evolution. We use a three-valued approach in our verification procedure to include the uncertainty associated with the simulation-based statistical method used to estimate the satisfaction probabilities. In relation to this aspect, we introduce a reliability specification for the TSTL analysis and we present a specific algorithm to automatically assess whether it is satisfied by the evaluation of TSTL formulas. \ua9 2017 ACM

Analysis of spatio-temporal properties of stochastic systems using TSTL

In this article, we present Three-Valued spatio-temporal Logic (TSTL), which enriches the available spatiotemporal analysis of properties expressed in Signal spatio-temporal Logic (SSTL), to give further insight into the dynamic behavior of systems. Our novel analysis starts from the estimation of satisfaction probabilities of given SSTL properties and allows the analysis of their temporal and spatial evolution. Moreover, in our verification procedure, we use a three-valued approach to include the intrinsic and unavoidable uncertainty related to the simulation-based statistical evaluation of the estimates; this can be also used to assess the appropriate number of simulations to use depending on the analysis needs. We present the syntax and three-valued semantics of TSTL and specific extended monitoring algorithms to check the validity of TSTL formulas. We introduce a reliability requirement for TSTL monitoring and an automatic procedure to verify it. Two case studies demonstrate how TSTL broadens the application of spatio-temporal logics in realistic scenarios, enabling analysis of threat monitoring and privacy preservation based on spatial stochastic population models

Three-Valued Spatio-Temporal Logic: a further analysis on spatio-temporal properties of stochastic systems

In this paper we present Three-Valued Spatio-Temporal Logic (TSTL), which enriches the available spatio-temporal analysis of properties expressed in Signal Spatio-Temporal Logic (SSTL), to give further insight into the dynamic behaviour of systems. Our novel analysis starts from the estimation of satisfaction probabilities of given SSTL properties and allows the analysis of their temporal and spatial evolution. Moreover, in our verification procedure, we use a three-valued approach to include the intrinsic and unavoidable uncertainty related to the simulation-based statistical evaluation of the estimates; this can be also used to assess the appropriate number of simulations to use depending on the analysis needs. We present the syntax and three-valued semantics of TSTL and a specific extended monitoring algorithm to check the validity of TSTL formulas. We conclude with two case studies that demonstrate how TSTL broadens the application of spatio-temporal logics in realistic scenarios, enabling analysis of threat monitoring and control programmes based on spatial stochastic population models

MELA: Modelling in Ecology with Location Attributes

Ecology studies the interactions between individuals, species and the environment. The ability to predict the dynamics of ecological systems would support the design and monitoring of control strategies and would help to address pressing global environmental issues. It is also important to plan for efficient use of natural resources and maintenance of critical ecosystem services. The mathematical modelling of ecological systems often includes nontrivial specifications of processes that influence the birth, death, development and movement of individuals in the environment, that take into account both biotic and abiotic interactions. To assist in the specification of such models, we introduce MELA, a process algebra for Modelling in Ecology with Location Attributes. Process algebras allow the modeller to describe concurrent systems in a high-level language. A key feature of concurrent systems is that they are composed of agents that can progress simultaneously but also interact - a good match to ecological systems. MELA aims to provide ecologists with a straightforward yet flexible tool for modelling ecological systems, with particular emphasis on the description of space and the environment. Here we present four example MELA models, illustrating the different spatial arrangements which can be accommodated and demonstrating the use of MELA in epidemiological and predator-prey scenarios.Comment: In Proceedings QAPL'16, arXiv:1610.0769

Finding Optimal Timetables for Edinburgh Bus Routes

AbstractWe present a novel application of stochastic simulation and model-checking methods to determining whether bus services are fulfilling their service-level agreement to provide on-time departures of buses from stops sufficiently often. We use open data on predicted bus arrival times to parameterise a stochastic model of a particular bus route from Edinburgh city centre out to suburban and rural areas to the south of the city. We validate and then analyse our stochastic model using both simulation and model-checking methods. Finally, we complete an optimisation study on the model and discover a better timetable for the service which would expose the bus service operator to less financial risk of penalties being applied by the regulatory authorities which define standards for bus service, punctuality and reliability

Modelling and spatio-temporal analysis of spatial stochastic systems

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Simulation and Analysis of Animal Movement Paths using Numerus Model Builder

ABSTRACT Animal movement paths are represented by point-location time series called relocation data. How well such paths can be simulated, when the rules governing movement depend on the internal state of individuals and environmental factors (both local and, when memory is involved, global) remains an open question. To answer this, we formulate and test models able to capture the essential statistics of multiphase versions of such paths (viz., movement-phase-specific step-length and turning-angle means, variances, auto-correlation, and cross correlation values), as well as broad scale movement patterns. The latter may include patchy coverage of the landscape, as well as the existence of home-range boundaries and gravitational centers-of-movement (e.g., centered around nests). Here we present a Numerus Model Builder implementation of two kinds of models: a high-frequency, multi-mode, biased, correlated random walk designed to simulate real movement data at a scale that permits simulation and identification of path segments that range from minutes to days; and a model that uses statistics extracted from relocation data—either empirical or simulated—to construct movement modes and phases at subhourly to daily scales. We evaluate how well our derived statistical movement model captures patterns produced by our more detailed simulation model as a way to evaluate how well derived statistical movement models may capture patterns occurring in empirical data