Expressing an observer in preferred coordinates by transforming an injective immersion into a surjective diffeomorphism

When designing observers for nonlinear systems, the dynamics of the given system and of the designed observer are usually not expressed in the same coordinates or even have states evolving in different spaces. In general, the function, denoted $\tau$ (or its inverse, denoted $\tau^*$) giving one state in terms of the other is not explicitly known and this creates implementation issues. We propose to round this problem by expressing the observer dynamics in the the same coordinates as the given system. But this may impose to add extra coordinates, problem that we call augmentation. This may also impose to modify the domain or the range of the augmented" $\tau$ or $\tau^*$, problem that we call extension. We show that the augmentation problem can be solved partly by a continuous completion of a free family of vectors and that the extension problem can be solved by a function extension making the image of the extended function the whole space. We also show how augmentation and extension can be done without modifying the observer dynamics and therefore with maintaining convergence.Several examples illustrate our results.Comment: Submitted for publication in SIAM Journal of Control and Optimizatio

The Paradox of Precaution

In the United States and most industrialized countries, regulatory policies and decision-making pertaining to food safety, occupational health and environmental protection are science-based. The actual pace and complexity of technological innovation, however, make it increasingly necessary to deal with situations where science cannot yet provide a definite picture. In this context, a now widely invoked rule, known as the 'Precautionary Principle', recommends to 'err on the side of preservation' until better scientific information becomes available. We draw a formal representation of this statement, and we show that it exhibits a logical contradiction. This negative result conveys a clarification of the type of actions science-based regulation should consider in the presence of scientific uncertainty. Aux États-Unis et dans la plupart des pays industrialisés, les règlements et politiques publics relatifs à la sécurité alimentaire, la santé au travail et la protection de l'environnement sont en principe basés sur l'information émanant des scientifiques. L'accélération et la complexité du progrès technologique rendent toutefois inévitable pour le régulateur de devoir prendre des décisions avant que la science puisse fournir une représentation claire du risque. Dans ce contexte, l'approche dite du «Principe de précaution» recommande d'«errer du côté de la prévention» jusqu'à ce que les scientifiques puissent donner le ton juste. Nous produisons une représentation formelle de ce principe, et nous montrons qu'il contient une incohérence logique. Ce résultat négatif permet néanmoins de préciser le type d'actions que la réglementation des risques basée sur la science devrait promouvoir en présence d'incertitude scientifique.Environmental and health risks; science-based regulation; scientific uncertainty; Precautionary Principle, Risques à la santé humaine et à l'environnement, réglementation basée sur la science, incertitude scientifique, principe de précaution

Robust Observer Design for Hybrid Dynamical Systems with Linear Maps and Approximately Known Jump Times

This paper proposes a general framework for the state estimation of plants given by hybrid systems with linear flow and jump maps, in the favorable case where their jump events can be detected (almost) instantaneously. A candidate observer consists of a copy of the plant's hybrid dynamics with continuous-time and/or discrete-time correction terms multiplied by two constant gains, and with jumps triggered by those of the plant. Assuming that the time between successive jumps is known to belong to a given closed set allows us to formulate an augmented system with a timer which keeps track of the time elapsed between successive jumps and facilitates the analysis. Then, since the jumps of the plant and of the observer are synchronized, the error system has time-invariant linear flow and jump maps, and a Lyapunov analysis leads to sufficient conditions for the design of the observer gains for uniform asymptotic stability in three different settings: continuous and discrete updates, only discrete updates, and only continuous updates. These conditions take the form of matrix inequalities, which we solve in examples including cases where the time between successive jumps is unbounded or tends to zero (Zeno behavior), and cases where either both the continuous and discrete dynamics, only one of them, or neither of them are detectable. Finally, we study the robustness of this approach when the jumps of the observer are delayed with respect to those of the plant. We show that if the plant's trajectories are bounded and the time between successive jumps is lower-bounded away from zero, the estimation error is bounded, and arbitrarily small outside the delay intervals between the plant's and the observer's jumps

HEALTH INFORMATION PROVISION AND UTILIZATION AS PREDICTORS OF SAFE HEALTH PRACTICES OF NURSING MOTHERS IN IMO STATE, NIGERIA

Abstract The study investigated health information provision and utilization as predictors of safe health practices of nursing mothers in Imo State. Four research purposes and four research questions guided the study. The researcher adopted descriptive design. The population of the study is 9735 nursing mothers in Okigwe Senatorial Zone, Imo State. Using proportionate sampling, 94 nursing mothers were selected from each of the six local government areas in Okigwe Zone, totaling 564. A researcher-made questionnaire “Information Provision and Utilization on Safe Health Practices of Nursing Mothers in Imo State Questionnaire” (IPAUOSHPONIMQ) was used as instrument for data collection. The reliability of the study was tested using Cronbach Alpha with 0.92 reliability coefficient. Descriptive statistics of mean with a criterion mean of 2.5was used to analyze data. Results showed that Types of health information provided for nursing mother include environmental cleanliness, body cleanliness practices, general baby care, maternal nutrition and breastfeeding. Sources of health information include social media, TV, family members, radio and postnatal clinics. Health journals and health workers are not accepted as nursing mothers’ sources of health information in Imo State. Child care, breastfeeding, hygiene practices, regular postnatal clinic and environmental cleanliness are the health needs for which nursing mothers seek health information. Adequate sleep/rest, avoidance of drug abuse, drinking enough water, good eating habit, avoidance of smoking/alcohol, maintenance of hygiene in the environment, regular visits for medical checkups and washing of breast/body before breastfeeding are the impacts of utilization of health information among nursing mothers in Imo State. it was recommended among others that Government should make health information available for nursing mothers in Imo State for their safe health practices through subsidized medicare, radio and TV jingles. Nursing mothers should consult professional health personnel for their health information through postnatal clinic

On diffeomorphism extension

We state and prove a result concerning the fact that a diffeomorphism can be " extended " in such a way that its image is R^

Assessing contaminated land cleanup costs and strategies

The remediation of contaminated sites is often subject to substantial cost overruns. This persistent discrepancy between estimated and realized costs is chiefly responsible for misguided land use and wasteful delays in the reconversion of former industrial sites. In order to deal with incomplete information and uncertainty in this context, this paper draws on stochastic modeling and mathematical finance methods. We show that relatively simple and usable formulas can then be derived for better assessing cleanup strategies. These formulas apply to generic remediation technologies and scenarios. They are robust to misspecification of key parameters (like the effectiveness of a prescribed treatment). They also yield practical rules for decision making and budget provisioning

SOCIO-CULTURAL CONTEXT OF DEVELOPMENTAL MILESTONES IN INFANCY IN SOUTH WEST NIGERIA: A QUALITATIVE STUDY

Developmental milestones are generally understood to be milestones of neurological development such as neck control, sitting without support, crawling and standing. Child health care providers routinely use normative data on such milestones to evaluate child development. However, there is often a cultural context to expectations of developmental milestones. The goal of this research is to explore the socio-cultural context of developmental milestones in infancy in a Nigerian community. In-depth interview was conducted with 30 mothers enrolled from an infant welfare clinic, southwest, Nigeria The transcripts were coded and analyzed using the Atlas ti 7.0 software package in a combination of thematic and narrative approaches. Mean age of participants was 33.3 (SD 5.1) years, 73% were married, 80% had two or more older children. Mothers expect that a child will be able to sit unaided, crawl and be able to stand by the age of one year. Opinion was divided about if it was possible to predict the age a child will attain a specific milestone. Most mothers reported that the age at which babies attain developmental milestones depends on childrearing practices utilized by the mother. Other factors they perceive as influencing developmental milestones include: having siblings, the age at which siblings and/or parents achieve similar milestones and the environment the child is reared in. Teething was considered an important milestone which has specific culture-bound connotations. Walking was considered one of the most significant milestones, not only indicating normal development but also signifying some independence for both mother and child. In this study of Nigerian mothers, developmental milestones in the first year of life have recognized influencing factors and a number of specific culturebound associated beliefs. This exploratory study provides insights into intersections between biomedical and cultural concepts of childhood development

SOCIO-CULTURAL CONTEXT OF DEVELOPMENTAL MILESTONES IN INFANCY IN SOUTH WEST NIGERIA: A QUALITATIVE STUDY

Developmental milestones are generally understood to be milestones of neurological development such as neck control, sitting without support, crawling and standing. Child health care providers routinely use normative data on such milestones to evaluate child development. However, there is often a cultural context to expectations of developmental milestones. The goal of this research is to explore the socio-cultural context of developmental milestones in infancy in a Nigerian community. In-depth interview was conducted with 30 mothers enrolled from an infant welfare clinic, southwest, Nigeria The transcripts were coded and analyzed using the Atlas ti 7.0 software package in a combination of thematic and narrative approaches. Mean age of participants was 33.3 (SD 5.1) years, 73% were married, 80% had two or more older children. Mothers expect that a child will be able to sit unaided, crawl and be able to stand by the age of one year. Opinion was divided about if it was possible to predict the age a child will attain a specific milestone. Most mothers reported that the age at which babies attain developmental milestones depends on childrearing practices utilized by the mother. Other factors they perceive as influencing developmental milestones include: having siblings, the age at which siblings and/or parents achieve similar milestones and the environment the child is reared in. Teething was considered an important milestone which has specific culture-bound connotations. Walking was considered one of the most significant milestones, not only indicating normal development but also signifying some independence for both mother and child. In this study of Nigerian mothers, developmental milestones in the first year of life have recognized influencing factors and a number of specific culturebound associated beliefs. This exploratory study provides insights into intersections between biomedical and cultural concepts of childhood development

What Skills do Somali Refugees Bring With Them?

To get a better idea of why refugees have difficulties getting employment, we interviewed 90 Somali (35 men, 55 women) about their employment histories prior to resettlement in New Zealand and their experiences of employment in New Zealand. Close investigation of employment histories showed that most had numerous skills and that a large number had previously run their own businesses (mostly import/export). However, we that found several properties of their prior skills did not transfer well to their current setting due to language, cultural, and environmental issues. In particular, previous business owners relied heavily on informal language use to influence customers and sellers; many relied on informal social networking over different countries; many depended heavily on informal negotiation; they had trade routes over land rather than sea; they traded goods specific to the region; they ran informal economies on the side; and businesses had few government rules and legal requirements to meet. We make some new suggestions that might help overcome these more subtle difficulties and form the basis for future research interventions