scholarly journals An Interval Temporal Logic for Time Series Specification and Data Integration

2021 ◽  
Vol 13 (12) ◽  
pp. 2236
Author(s):  
Piotr Kosiuczenko
Keyword(s):  
Time Series ◽  
Temporal Logic ◽  
Natural Extension ◽  
Complex Problem ◽  
Temporal Logics ◽  
Time Intervals ◽  
Duration Calculus ◽  
Temporal Series ◽  
Interval Temporal Logic ◽  
Multisensor Data

The analysis of temporal series—in particular, analysis of multisensor data—is a complex problem. It depends on the application domain, the way the data have to be used, and sensors available, among other factors. Various models, algorithms, and technologies have been designed for this goal. Temporal logics are used to describe temporal properties of systems. The properties may specify the occurrence and the order of events in time, recurring patterns, complex behaviors, and processes. In this paper, a new interval logic, called duration calculus for functions (DC4F), is proposed for the specification of temporal series corresponding to multisensor data. DC4F is a natural extension of the well-known duration calculus, an interval temporal logic for the specification of process duration. The adequacy of the proposed logic is analyzed in the case of multisensor data concerning volcanic eruption monitoring. It turns out that the relevant behavior concerns time intervals, not only accumulated history as it is described in other kinds of temporal logics. The examples analyzed demonstrate that a description language is required to specify time series of various kind relative to time intervals. The duration calculus cannot be successfully applied for this task. The proposed calculus allows one to specify temporal series and complex interval-dependent behaviors, and to evaluate the corresponding data within a unifying logical framework. It allows to formulate hypotheses concerning volcano eruption phenomena. However, the expressivity of DC4F comes at the cost of its decidability.

A complete robust control network based on skewed temporal logic

2021 ◽  
pp. 1-14
Author(s):  
Liuxing Li
Keyword(s):  
Time Series ◽  
Robust Control ◽  
Temporal Logic ◽  
Sufficient Conditions ◽  
Control Flow ◽  
Skewed Distribution ◽  
Linear Matrix ◽  
Distribution Data ◽  
Control Network ◽  
Depth Analysis

The robust control network for nonlinear large-scale systems with parametric uncertainties also considers the uncertain robust stabilization problem for controlled networks. In heterogeneous populations, hybrid regression models are the most important statistical analysis tools. To aim of the study is to conduct a more in-depth analysis of the existing completive robust control networks relying on biased temporal logic. Compared with the symmetric distribution, the skewed distribution can obtain accurate and effective information. Therefore, a time-series logic model under skewed distribution is proposed. The temporal logic under skew state is applied to describe the normative language of fuzzy systems. Firstly, the mixed nonlinear regression model under skewed distribution data is introduced to test whether the temporal logic formula can be realized under the skew state. Secondly, through the method of reduction, the control flow interval logic CFITL is studied, and the time series logic sequence is used to describe the measurement output loss. The sufficient conditions for the control network system to satisfy the exponential stability and H ∞ performance index are given. The linear matrix inequality obtains the completeness control network to be designed, and the effectiveness of the proposed method is verified by stochastic simulation experiments. Finally, the method is verified to be practical and feasible based on actual data. The maximum recognition rates of nearest neighbor classification, nearest subspace classification and biased distribution temporal logic classification reached 0.9019, 0.9622 and 0.9304, respectively.

scholarly journals Uncertainty quantification of the effects of biotic interactions on community dynamics from nonlinear time-series data

2018 ◽  
Vol 15 (147) ◽  
pp. 20180695 ◽  
Author(s):  
Simone Cenci ◽  
Serguei Saavedra
Keyword(s):  
Time Series ◽  
Community Dynamics ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Model Averaging ◽  
Biotic Interactions ◽  
Series Data ◽  
Time Intervals ◽  
Novel Approach ◽  
Data Generating Process

Biotic interactions are expected to play a major role in shaping the dynamics of ecological systems. Yet, quantifying the effects of biotic interactions has been challenging due to a lack of appropriate methods to extract accurate measurements of interaction parameters from experimental data. One of the main limitations of existing methods is that the parameters inferred from noisy, sparsely sampled, nonlinear data are seldom uniquely identifiable. That is, many different parameters can be compatible with the same dataset and can generalize to independent data equally well. Hence, it is difficult to justify conclusive assertions about the effect of biotic interactions without information about their associated uncertainty. Here, we develop an ensemble method based on model averaging to quantify the uncertainty associated with the effect of biotic interactions on community dynamics from non-equilibrium ecological time-series data. Our method is able to detect the most informative time intervals for each biotic interaction within a multivariate time series and can be easily adapted to different regression schemes. Overall, this novel approach can be used to associate a time-dependent uncertainty with the effect of biotic interactions. Moreover, because we quantify uncertainty with minimal assumptions about the data-generating process, our approach can be applied to any data for which interactions among variables strongly affect the overall dynamics of the system.

DYNAMICAL RECURRENT NEURAL NETWORKS — TOWARDS ENVIRONMENTAL TIME SERIES PREDICTION

1995 ◽  
Vol 06 (02) ◽  
pp. 145-170 ◽  
Author(s):  
ALEX AUSSEM ◽  
FIONN MURTAGH ◽  
MARC SARAZIN
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Recurrent Neural Networks ◽  
Time Series Prediction ◽  
Predictive Ability ◽  
Complex Problem ◽  
Internal Variables ◽  
Internal Dynamic ◽  
K Nearest Neighbors ◽  
Fuzzy Coding

Dynamical Recurrent Neural Networks (DRNN) (Aussem 1995a) are a class of fully recurrent networks obtained by modeling synapses as autoregressive filters. By virtue of their internal dynamic, these networks approximate the underlying law governing the time series by a system of nonlinear difference equations of internal variables. They therefore provide history-sensitive forecasts without having to be explicitly fed with external memory. The model is trained by a local and recursive error propagation algorithm called temporal-recurrent-backpropagation. The efficiency of the procedure benefits from the exponential decay of the gradient terms backpropagated through the adjoint network. We assess the predictive ability of the DRNN model with meteorological and astronomical time series recorded around the candidate observation sites for the future VLT telescope. The hope is that reliable environmental forecasts provided with the model will allow the modern telescopes to be preset, a few hours in advance, in the most suited instrumental mode. In this perspective, the model is first appraised on precipitation measurements with traditional nonlinear AR and ARMA techniques using feedforward networks. Then we tackle a complex problem, namely the prediction of astronomical seeing, known to be a very erratic time series. A fuzzy coding approach is used to reduce the complexity of the underlying laws governing the seeing. Then, a fuzzy correspondence analysis is carried out to explore the internal relationships in the data. Based on a carefully selected set of meteorological variables at the same time-point, a nonlinear multiple regression, termed nowcasting (Murtagh et al. 1993, 1995), is carried out on the fuzzily coded seeing records. The DRNN is shown to outperform the fuzzy k-nearest neighbors method.

scholarly journals The temporal logic of coalgebras via Galois algebras

2002 ◽  
Vol 12 (6) ◽  
pp. 875-903 ◽  
Author(s):  
BART JACOBS
Keyword(s):  
State Space ◽  
Temporal Logic ◽  
Metric Spaces ◽  
Linear Temporal Logic ◽  
The State ◽  
Temporal Logics ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Polynomial Functors

This paper introduces a temporal logic for coalgebras. Nexttime and lasttime operators are defined for a coalgebra, acting on predicates on the state space. They give rise to what is called a Galois algebra. Galois algebras form models of temporal logics like Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). The mapping from coalgebras to Galois algebras turns out to be functorial, yielding indexed categorical structures. This construction gives many examples, for coalgebras of polynomial functors on sets. More generally, it will be shown how ‘fuzzy’ predicates on metric spaces, and predicates on presheaves, yield indexed Galois algebras, in basically the same coalgebraic manner.

scholarly journals Extracting Features from Time Series

2018 ◽  
pp. 85-100 ◽  
Author(s):  
Christian Herff ◽  
Dean J. Krusienski
Keyword(s):  
Time Series ◽  
Feature Extraction ◽  
Clinical Data ◽  
Noise Filtering ◽  
Time Intervals ◽  
Time Points ◽  
Biomedical Systems ◽  
Patient Weight ◽  
Short Time

AbstractClinical data is often collected and processed as time series: a sequence of data indexed by successive time points. Such time series can be from sources that are sampled over short time intervals to represent continuous biophysical wave-(one word waveforms) forms such as the voltage measurements representing the electrocardiogram, to measurements that are sampled daily, weekly, yearly, etc. such as patient weight, blood triglyceride levels, etc. When analyzing clinical data or designing biomedical systems for measurements, interventions, or diagnostic aids, it is important to represent the information contained within such time series in a more compact or meaningful form (e.g., noise filtering), amenable to interpretation by a human or computer. This process is known as feature extraction. This chapter will discuss some fundamental techniques for extracting features from time series representing general forms of clinical data.

scholarly journals Temporal Logics Over Finite Traces with Uncertainty

2020 ◽  
Vol 34 (06) ◽  
pp. 10218-10225 ◽  
Author(s):  
Fabrizio M Maggi ◽  
Marco Montali ◽  
Rafael Peñaloza
Keyword(s):  
Decision Making ◽  
Temporal Logic ◽  
Business Process ◽  
Dynamic Systems ◽  
Real Life ◽  
Temporal Logics ◽  
Business Process Modelling ◽  
Process Discovery ◽  
Event Log ◽  
Computational Properties

Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of uncertainty which cannot be handled with classical logics. We thus propose a new probabilistic temporal logic over finite traces using superposition semantics, where all possible evolutions are possible, until observed. We study the properties of the logic and provide automata-based mechanisms for deriving probabilistic inferences from its formulas. We then study a fragment of the logic with better computational properties. Notably, formulas in this fragment can be discovered from event log data using off-the-shelf existing declarative process discovery techniques.

Sign in / Sign up

Export Citation Format

Share Document