A new algorithm to design minimal multi-functional observers for linear systems

Designing minimum possible order (minimal) observers for Multi-Input Multi-Output (MIMO) linear systems have always been an interesting subject. In this paper, a new methodology to design minimal multi-functional observers for Linear Time-Invariant (LTI) systems is proposed. The approach is applicable, and it also helps in regulating the convergence rate of the observed functions. It is assumed that the system is functional observable or functional detectable, which is less conservative than assuming the observability or detectability of the system. To satisfy the minimality of the observer, a recursive algorithm is provided that increases the order of the observer by appending the minimum required auxiliary functions to the desired functions that are going to be estimated. The algorithm increases the number of functions such that the necessary and sufficient conditions for the existence of a functional observer are satisfied. Moreover, a new methodology to solve the observer design interconnected equations is elaborated. Our new algorithm has advantages with regard to the other available methods in designing minimal order functional observers. Specifically, it is compared with the most common schemes, which are transformation based. Using numerical examples it is shown that under special circumstances, the conventional methods have some drawbacks. The problem partly lies in the lack of sufficient numerical degrees of freedom proposed by the conventional methods. It is shown that our proposed algorithm can resolve this issue. A recursive algorithm is also proposed to summarize the observer design procedure. Several numerical examples and simulation results illustrate the efficacy, superiority and different aspects of the theoretical findings.

Bioactive functions of milk proteins: a comparative genomics approach

The composition of milk includes factors required to provide appropriate nutrition for the growth of the neonate. However, it is now clear that milk has many functions and comprises bioactive molecules that play a central role in regulating developmental processes in the young while providing a protective function for both the suckled young and the mammary gland during the lactation cycle. Identifying these bioactives and their physiological function in eutherians can be difficult and requires extensive screening of milk components that may function to improve well-being and options for prevention and treatment of disease. New animal models with unique reproductive strategies are now becoming increasingly relevant to search for these factors.

On the weak monotonicity of Gini means and other mixture functions

Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation, and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise. We extended the study of weakly monotone averages by analyzing their ϕ-transforms, and we established weak monotonicity of several classes of averaging functions, in particular Gini means and mixture operators. Mixture operators with Gaussian weighting functions were shown to be weakly monotone for a broad range of their parameters. This study assists in identifying averaging functions suitable for data analysis and image processing tasks in the presence of outliers.

Introducing linear functions: an alternative statistical approach

The introduction of linear functions is the turning point where many students decide if mathematics is useful or not. This means the role of parameters and variables in linear functions could be considered to be ‘threshold concepts’. There is recognition that linear functions can be taught in context through the exploration of linear modelling examples, but this has its limitations. Currently, statistical data is easily attainable, and graphics or computer algebra system (CAS) calculators are common in many classrooms. The use of this technology provides ease of access to different representations of linear functions as well as the ability to fit a least-squares line for real-life data. This means these calculators could support a possible alternative approach to the introduction of linear functions. This study compares the results of an end-oftopic test for two classes of Australian middle secondary students at a regional school to determine if such an alternative approach is feasible. In this study, test questions were grouped by concept and subjected to concept by concept analysis of the means of test results of the two classes. This analysis revealed that the students following the alternative approach demonstrated greater competence with non-standard questions.

The effect of recursive detrending on panel unit root tests

This paper analyzes the properties of panel unit root tests based on recursively detrended data. The analysis is conducted while allowing for a (potentially) non-linear trend function, which represents a more general consideration than the current state of affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple. Indeed, the test statistic is not only asymptotically independent of the true trend polynomial, but also is in fact unique in that it is independent also of the degree of the fitted polynomial. However, this invariance property does not carry over to the local alternative, under which it is shown that local power is a decreasing function of the trend degree. But while power does decrease, the rate of shrinking of the local alternative is generally constant in the trend degree, which goes against the common belief that the rate of shrinking should be decreasing in the trend degree. The above results are based on simplifying assumptions. To compensate for this lack of generality, a second, robust, test statistic is proposed, whose validity does not require that the trend function is a polynomial or that the errors are iid.

Mentoring functions and turnover intention: the mediating role of perceived organizational support

Despite an increasing number of studies investigating the effects of mentoring on employee work outcomes, limited attention has been placed on the relationship between mentoring functions and turnover intentions. In this study, we examined the relationship between mentoring functions and turnover intentions, and the mediating role of perceived organizational support (POS) on this relationship. Using data collected from 176 employees in three Chinese banks, we found that POS partially mediated the relationship between mentoring functions and employees' turnover intentions.

Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems

Abstract
This paper presents new discrete inequalities for single summation and double summation. These inequalities are based on multiple auxiliary functions and include the Jensen discrete inequality and the discrete Wirtinger-based inequality as special cases. An application of these discrete inequalities to analyse stability of linear discrete systems with an interval time-varying delay is studied and a less conservative stability condition is obtained. Three numerical examples are given to show the effectiveness of the obtained stability condition.

Autobiographical memory and depression: identity-continuity and problem-solving functions indirectly predict symptoms over time through psychological well-being

The aim of this study was to assess the longitudinal associations between adaptive autobiographical memory functions and depressive symptoms. Consistent with the proposed mechanisms of change underpinning cognitive-reminiscence therapy (CRT), it was hypothesised that more frequent adaptive reminiscence would lead to increases in psychological resources over time and indirectly affect depressive symptoms through this pathway. A sample of 171 young adults (mean age=25.9years, SD=3.5) completed measures of how frequently they utilised autobiographical memory for identity-continuity and problem-solving purposes, depressive symptoms and personal resources (self-esteem, self-efficacy, meaning in life and optimism) at two time-points. The results of structural equation modelling supported the model of indirect influence between reminiscence functions and depression through these psychological resources. These findings clarify the effects of adaptive autobiographical memory on depressive symptoms in young adults and indicate potential benefits of interventions such as CRT.

On unknown-input functional observability of linear systems

Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability is introduced,and it is used as a certificate of the convergence of our algorithm. The proposed procedure looks for a number of additional auxiliary functions to be augmented to the original functions desired for reconstruction. The resulting UIFO is proper, and minimal (of minimum possible order). Moreover, the algorithm does not need the system to be unknown-input observable. A numerical example shows the procedure as well as the effectiveness of the proposed algorithm.

Testing production functions used in empirical growth studies

We estimate and test two alternative functional forms, which have been used in the growth literature, representing the aggregate production function for a panel of countries: the model of Mankiw, Romer and Weil (Quarterly Journal of Economics, 1992), and a mincerian formulation of schooling-returns to skills. Estimation is performed using instrumental-variable techniques, and both functional forms are confronted using a Box-Cox test, since human capital inputs enter in levels in the mincerian specification and in logs in the extended neoclassical growth model.

On the consistency of arbitrary money-demand functions with the Sidrauski and the shopping-time models

This paper investigates which properties money-demand functions have to satisfy to be consistent with multidimensional extensions of Lucasí(2000) versions of the Sidrauski (1967) and the shopping-time models. We also investigate how such classes of models relate to each other regarding the rationalization of money demands. We conclude that money demand functions rationalizable by the shoppingtime model are always rationalizable by the Sidrauski model, but that the converse is not true. The log-log money demand with an interest-rate elasticity greater than or equal to one and the semi-log money demand are counterexamples.

Testing production functions used in empirical growth studies

We estimate and test two alternative functional forms representing the aggregate production function for a panel of countries: the extended neoclassical growth model, and a mincerian formulation of schooling-returns to skills. Estimation is performed using instrumentalvariable techniques, and both functional forms are confronted using a Box-Cox test, since human capital inputs enter in levels in the mincerian specification and in logs in the extended neoclassical growth model. Our evidence rejects the extended neoclassical growth model in favor of the mincerian specification, with an estimated capital share of about 42%, a marginal return to education of about 7.5% per year, and an estimated productivity growth of about 1.4% per year. Differences in productivity cannot be disregarded as an explanation of why output per worker varies so much across countries: a variance decomposition exercise shows that productivity alone explains 54% of the variation in output per worker across countries.

Exogenous expectations on endogenous uncertainty: recursive equilibrium and survival

This paper analyses general equilibrium models with finite heterogeneous agents having exogenous expectations on endogenous uncertainty. It is shown that there exists a recursive equilibrium with the state space consisting of the past aggregate portfolio distribution and the current state of the nature and that it implements the sequential equilibrium. We establish conditions under which the recursive equilibrium is continuous. Moreover, we use the continuous recursive relation of the aggregate variables to prove that if the economy has two types of agents, the one who commits persistent mistakes on the expectation rules of the future endogenous variables is driven out of the market by the others with correct anticipations of the variables, that is, the rational expectations agents.

Essays in recursive equilibrium and market selection hypothesis

Este trabalho consiste em estudar modelos incluindo agentes com informação completa e incompleta sobre o ambiente econômico. Prova-se a existência de equilíbrio em que esses dois agentes coexistem e sob, algumas condições, obtêm-se que esse equilíbrio é recursivo e contínuo, ou seja, pode ser implementado por uma função contínua de transição que relaciona as variáveis de equilíbrio entre dois períodos consecutivos. Mostra-se, sob algumas hipóteses, que em equilíbrios recursivos contínuos, os agentes que cometem erros persistentes nas antecipações dos preços de equilíbrio são eliminados do mercado. Finalmente, exibimos diversos exemplos numéricos, no caso de mercados incompletos e informação completa, em que os agentes com expectativas racionais são eliminados do mercado. Usam-se métodos numéricos alternativos que possibilitam computar um equilíbrio em modelos com agentes heterogêneos.