A Multi-Step Richardson-Romberg Extrapolation Method For Stochastic Approximation

We obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in [Frikha2013]. This allows us to extend and develop the Richardson-Romberg extrapolation method for Monte Carlo linear estimator (introduced in [Talay & Tubaro 1990] and deeply studied in [Pag{\`e}s 2007]) to the framework of stochastic optimization by means of stochastic approximation algorithm. We notably apply the method to the estimation of the quantile of diffusion processes. Numerical results confirm the theoretical analysis and show a significant reduction in the initial computational cost.Comment: 31 pages, 1 figur

Between Two Worlds: Stories of the Second-Generation Black Caribbean Immigrant

People have an endless fascination with character information since it helps us to predict the behavior of those we interact with (King, Rumbaugh, and Savage-Rumbaugh 1999). Stories or narratives serve as an extension of this fascination. They help us make better decisions even without supplying immediate information. When we each talk about the past, our stories not only disclose currently relevant social particulars, but also provide tools for reasoning about action—our own and others’. In many instances, the stories we tell offer explanations of an outcome that resulted when we acted upon something—or serve as indirect memories of a place or a past event that guides our decisions today. Alternatively, the stories we tell can merely introduce us to a range of behaviors and experiences so that we have a richer context for understanding when we encounter something new. We tell stories because they appeal to our social intelligence. Storytelling arises out of our capacity to understand one another and direct others’ attention to real events. In the narrative process, the storyteller is a problem-solver, an individual with the capacity and preference to make strategic choices within particular situations, making different kinds of appeals to the cognitive preference and expectation of the listener. In doing so, the storyteller points to the challenges faced, choices made, and outcomes learned that could, ultimately, inspire the listener and move him or her toward some action. For those of us especially interested or engaged in community building, stories give expression to the histories and lives of people across our communities. Listening to and understanding these stories provide us the opportunity to explain why the people we listen to do what they do, and the impact their behaviors and experiences have in the overall vitality of our community. Put simply, to be an “understander” of the world is also to be an explainer of the world—and stories help us do this. So, why are stories of second-generation black Caribbean immigrants important? What do these stories tell us? Moreover, what do these stories mean to local racial-ethnic communities as a whole? The immigrant story is one that is deeply intertwined with our broader community story

EDS dirigées par des processus stables. Méthode paramétrix pour des estimées de densités et application aux algorithmes stochastiques.

First, we study a class of stochastic differential equations driven by a possibly tempered Lévy process, under mild conditions on the coefficients (Hölder continuity). We prove the well-posedness of the associated martingale problem as well as the existence of the density of the solution. Two sided heat kernel estimates are given as well. Our approach is based on the Parametrix series expansion.Then, we consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak Hörmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.Finally, we obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in [Fri13]. This allows us to extend and develop the Richardson-Romberg extrapolation method for Monte Carlo linear estimator (introduced in [TT90] and deeply studied in [Pag07]) to the framework of stochastic optimization by means of stochastic approximation algorithms. We notably apply the method to the estimation of the quantile of diffusion processes. Numerical results confirm the theoretical analysis and show a significant reduction in the initial computational cost.Dans un premier temps, nous étudions une classe d’équations différentielles stochastiques dirigées par des processus stables (possiblement tempérés), sous des hypothèses de régularité Hölder sur les coefficients. Nous prouvons que le problème de martingale associé est bien posé, établissant ainsi l’unicité faible pour l’EDS. Nous donnons aussi un encadrement de la densité de la solution par celle d’un processus stable (possiblement tempéré). Notre approche est basée sur la méthode parametrix.Dans un second temps, nous considérons une équation différentielle stochastique dégénérée dirigée par un processus stable dont les coefficients satisfont une sorte d’hypothèse de Hörmander faible. Sous de relativement faibles hypothèses de régularité et des restrictions dimensionnelles, nous prouvons que le problème de martingale est bien posé. Nous donnons également un majorant de la densité reflétant le caractère multi-échelle du processus sous-jacent dans le cas scalaire du stable tempéré.Enfin, nous obtenons un développement pour l’erreur de discrétisation de la cible d’un al- gorithme stochastique à la suite de [Fri13]. Ceci nous permet de mettre en place une extrapolation de Richardson-Romberg dans le cadre des algorithmes stochastiques, déjà obtenue pour les estimateurs de Monte Carlo linéaires (introduite par Talay et Tubaro [TT90] et pleinement étudiée dans Pagès [Pag07]). Nous appliquons nos résultats à l’estimation du quantile de la solution d’une EDS dirigée par un processus stable. Les résultats numériques produits à partir de notre méthode montrent uneréduction significative de la complexité

Envisioning and Implementing a Servant/Event Evangelism Strategy in the Local Church

In examining the most effective evangelism models used by churches today, churches have a unique opportunity to reach a large number of people while utilizing gifts of service. This Thesis examines the current status of evangelism in churches and gives churches an opportunity to envision and develop a strategy that is two fold. This project will help church\u27s to serve like Jesus, while at the same time share the gospel. This Thesis will do this by examining the need for a servant/event strategy while giving practical examples of how to implement such a strategy in their local context

Effectiveness of struvite precipitation and ammonia stripping for recovery of phosphorus and nitrogen from anaerobic digestate: a systematic review

Background: A regular supply of nutrients such as nitrogen and phosphorus to agriculture is needed for global food security, and increased recycling of nutrients back to agriculture from organic waste streams is necessary for increased rural-urban sustainability. Anaerobic digestion of sewage sludge and agricultural wastes is widely applied to stabilize the substrate and capture some of its energetic value via biogas production. Anaerobic digestate is a concentrated source of nutrients to which nutrient recovery technologies can be applied. By combining anaerobic digestion and nutrient recovery technologies on the digestate, both energy and nutrient recovery can be achieved. Two promising technologies that could increase nutrient recycling from different types of wastewater are struvite precipitation and ammonia stripping. This review examined the effectiveness of these ecotechnologies for the recovery of nitrogen and phosphorus from anaerobic digestate with the aim of reducing the impact of waste on the environment.Methods: We searched for academic and grey literature published after 2013. Searches were performed in 5 bibliographic databases in English, in the search engine Google Scholar in English, Swedish, Finnish and Polish, and across a range of organisational websites in English, Swedish, Finnish and Polish. Eligibility screening was conducted at two levels: 'title and abstract' and 'full text'. Included eligible studies were subject to a critical appraisal that assessed external and internal study validity. We extracted information on study characteristics, intervention, comparators, effect modifiers, and measured outcomes. Data synthesis included narrative synthesis of each study of sufficient validity. We performed quantitative synthesis on a subset of studies.Review findings: The review included 30 studies on struvite precipitation and 8 studies on ammonia stripping. Both pH and Mg:PO4 ratio were found to have a clear influence on the effectiveness of struvite precipitation process (and thus nutrient removal rates). The response to pH was found to be non-linear, resembling a bell curve with a maximum around pH 9.5. Mg:PO4 ratio was found to have a positive effect on removal up to a ratio as high as 4:1. However, it should be noted that high removal efficiencies were sometimes achieved at a ratio as low as 1:1 as well. Although the effects of pH and Mg:PO4 ratio were clear, the model developed could not accurately predict removal based on these two parameters alone. Studies on ammonia stripping were relatively heterogeneous. Due to the small size of the evidence base, and the heterogeneity between studies, no conclusions are presented regarding the influence of different process parameters on the outcome of ammonia stripping.Conclusions: In conclusion, when performed under the right conditions (i.e. pH around 9.5 and Mg:PO4 ratio of at least 1:1), available evidence suggests that struvite precipitation is an effective technology for the recovery of nutrients from the liquid phase of anaerobic digestate. The evidence base is limited for ammonia stripping. We provided suggestions of which data to report in future studies

Evaluative Feedback: How K-12 Teachers Respond

This sequential mixed methods study addressed the need for research that both described and explained how teachers of varying experience respond to administrative evaluative feedback. Formative evaluation theory of Scriven and professional growth models of Steffy and Fessler served as theoretical models for data analysis. An online survey asking teachers how they changed their practices and what accounted for their response was received from 270 teachers in 1 Midwestern state. Of these, 9 teachers of varying experience were interviewed. The quantitative data showed that most teachers do not change practices on the 8 state teaching standards in response to feedback. An independent sample t test revealed statistically significant differences between teachers of varying experience in 3 standards: support of district goals, classroom management, and instruction. . An ANOVA found no significant effect between teaching experience and the length of time since the feedback was provided to the teacher. Qualitative data found a variety of social, personal, organizational, and student-based needs that accounted for teachers\u27 response to feedback. In teachers that made changes to practices, administrator suggestion was the most important factor, but conversations with colleagues were also important. However, most teachers did not receive formative feedback. Organizational factors such as state initiatives to change instruction influenced teachers of more experience than novice teachers. These findings can help administrators improve the formative effect of their feedback. Understanding how evaluative feedback leads to changes in teaching practices should improve feedback systems in schools across the nation which subsequently should lead to in more effective teaching practices