Non-standard errors

In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence generating process (EGP). We claim that EGP variation across researchers adds uncertainty: Non-standard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for better reproducible or higher rated research. Adding peer-review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants

Neural Network-Based Narx Models in Non-Linear Adaptive Control

The applicability of approximate NARX models of non-linear dynamic systems is discussed. The models are obtained by a new version of Fourier analysis-based neural network also described in the paper. This constitutes a reformulation of a known method in a recursive manner, i.e. adapted to account for incoming data on-line. The method allows us to obtain an approximate model of the non-linear system. The estimation of the influence of the modelling error on the discrepancy between the model and real system outputs is given. Possible applications of this approach to the design of BIBO stable closed-loop control are proposed

Stability of a class of adaptive nonlinear systems

This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology

Negative feature selection algorithm for anomaly detection in real time

Anomaly detection methods are of common use in many fields, including databases and large computer systems. This article presents new algorithm based on negative feature selection, which can be used to find anomalies in real time. Proposed algorithm, called Negative Feature Selection algorithm (NegFS) can be also used as first step for preprocessing data analyzed by neural networks, rule-based systems or other anomaly detection tools, to speed up the process for large and very large datasets of different types

Probabilistic Sequence Mining : Evaluation and Extension of ProMFS Algorithm for Real-Time Problems

Sequential pattern mining is an extensively studied method for data mining. One of new and less documented approaches is estimation of statistical characteristics of sequence for creating model sequences, that can be used to speed up the process of sequence mining. This paper proposes extensive modifications to one of such algorithms, ProMFS (probabilistic algorithm for mining frequent sequences), which notably increases algorithm's processing speed by a significant reduction of its computational complexity. A new version of algorithm is evaluated for real-life and artificial data sets and proven to be useful in real-time applications and problems

Probabilistic Sequence Mining – Evaluation and Extension of ProMFS Algorithm for Real-Time Problems

Sequential pattern mining is an extensively studied method for data mining. One of new and less documented approaches is estimation of statistical characteristics of sequence for creating model sequences, that can be used to speed up the process of sequence mining. This paper proposes extensive modifications to one of such algorithms, ProMFS (probabilistic algorithm for mining frequent sequences), which notably increases algorithm's processing speed by a significant reduction of its computational complexity. A new version of algorithm is evaluated for real-life and artificial data sets and proven to be useful in real-time applications and problems

Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case

The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient ) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose

Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation

This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The paper also shows a simple numerical example of linear state estimation. Finally, as an example of nonlinear estimation, the paper discusses the possibility of using these algorithms for parameters and fractional order estimation for fractional order systems. Numerical examples of the use of these algorithms in a general nonlinear case are presented

Discrete Fractional Order Artificial Neural Network

In this paper the discrete time fractional order artificial neural network is presented. This structure is proposed for simulating the dynamics of non-linear fractional order systems. In the second part of this paper several numerical examples are shown. The final part of the paper presents the discussion on the use of fractional or integer discrete time neural network for modelling and simulating fractional order non-linear systems. The simulation results show the advantages of the proposed solution over the classical (integer) neural network approach to modelling of non-linear fractional order systems