On the sub-permutations of pattern avoiding permutations

There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and probabilistic properties of sub-permutations and to investigate the relationships between 'local' and 'global' features using the concept of pattern avoidance. First, given a pattern {\mu}, we study how the avoidance of {\mu} in a permutation {\pi} affects the presence of other patterns in the sub-permutations of {\pi}. More precisely, considering patterns of length 3, we solve instances of the following problem: given a class of permutations K and a pattern {\mu}, we ask for the number of permutations $\pi \in Av_n(\mu)$ whose sub-permutations in K satisfy certain additional constraints on their size. Second, we study the probability for a generic pattern to be contained in a random permutation {\pi} of size n without being present in the sub-permutations of {\pi} generated by the entry $1 \leq k \leq n$. These theoretical results can be useful to define efficient randomized pattern-search procedures based on classical algorithms of pattern-recognition, while the general problem of pattern-search is NP-complete

Yule-generated trees constrained by node imbalance

The Yule process generates a class of binary trees which is fundamental to population genetic models and other applications in evolutionary biology. In this paper, we introduce a family of sub-classes of ranked trees, called Omega-trees, which are characterized by imbalance of internal nodes. The degree of imbalance is defined by an integer 0 <= w. For caterpillars, the extreme case of unbalanced trees, w = 0. Under models of neutral evolution, for instance the Yule model, trees with small w are unlikely to occur by chance. Indeed, imbalance can be a signature of permanent selection pressure, such as observable in the genealogies of certain pathogens. From a mathematical point of view it is interesting to observe that the space of Omega-trees maintains several statistical invariants although it is drastically reduced in size compared to the space of unconstrained Yule trees. Using generating functions, we study here some basic combinatorial properties of Omega-trees. We focus on the distribution of the number of subtrees with two leaves. We show that expectation and variance of this distribution match those for unconstrained trees already for very small values of w

Play Your Fan : Exploring Hand Props and Gender on the Restoration Stage Through the Country Wife, the Man of Mode, the Rover, and the Way of the World

The full irony and wit of Restoration comedies relies not only on what characters communicate to each other, but also on what they communicate to the audience, both verbally and physically

Counting, grafting and evolving binary trees

Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by which trees are generated determines the probability distribution in tree space. Yule trees, for instance, are generated by a pure birth process. When considered as unordered, they have neither a closed-form enumeration nor a simple probability distribution. But their ordered siblings have both. They present the object of choice when studying tree structure in the framework of evolving genealogies

Processes determining genetic variability: mutations in sequence space and hitchhiking

Departing from the classical model of the so-called error threshold of mutating macro-molecules, I have reformulated the model in the context of diploid organisms evolving in sequence space and under conditions of a finite population size. I found - for instance - that dominance properties have a substantial impact on the details of the error threshold (Chpt. 1). I have then asked whether error thresholds can also be observed in more general fitness landscapes than the original single-peaked landscape. For smooth landscapes the answer is negative (Chpt. 2) Studying diploid organism, I also investigated the impact of recombination on the evolutionary dynamics and on the possibility for a population to reach a fitness maximum. I concluded that the recombination rate, i.e., the chromosomal distance between interacting genetic loci, has a much more important role in generating fitness-conferring allele combinations than manipulating the mutation rate (Chpt. 3). Finally, considering a two-locus model in which one locus experiences beneficial mutations and a second locus is selectively neutral, I investigated the much discussed model of genetic hitchhiking. Using diffusion theory, I predicted the impact on the level of neutral polymorphism imposed by a beneficial mutation on a neighbouring genetic locus (Chpt. 4) and compared the predictions to experimental data of observed genetic variability in the fruitfly Drosophila. This lead to an estimate on the rate and strength with which beneficial substitutions occur in natural populations (Chpt. 5).Ausgehend von dem klassischen Modell der sogenannten Fehlerschwelle mutierender Makromoleküle habe ich das Modell im Kontext von diploiden Organismen, die im Sequenzraum und unter den Bedingungen einer endlichen Populationsgröße evolvieren, neu formuliert. Ich fand zum Beispiel heraus, dass Dominanz-Eigenschaften einen wesentlichen Einfluss auf die Details der Fehlerschwelle haben (Kap. 1). Ich habe dann gefragt, ob sich Fehlerschwellen auch in allgemeineren Fitnesslandschaften, als der ursprünglichen Ein-Peak-Landschaft, zeigen. Für "weiche" Landschaften ist die Antwort negativ (Chpt. 2). An diploiden Organismen habe ich auch den Einfluss der Rekombination auf die evolutionäre Dynamik und auf die Möglichkeit einer Population, ein Fitnessmaximum zu erreichen, untersucht. Ich kam zu dem Schluss, dass die Rekombinationsrate, d.h. der chromosomale Abstand zwischen interagierenden genetischen Loci, eine viel wichtigere Rolle bei der Erzeugung von fitnessfördernden Allelkombinationen spielt, als die Manipulation der Mutationsrate (Kap. 3). Schließlich untersuchte ich in einem Zwei-Locus-Modell, in dem ein Locus vorteilhafte Mutationen erfährt und ein zweiter Locus selektiv neutral ist, das viel diskutierte Modell des "genetischen Hitchhiking". Mit Hilfe von Diffusionstheorie konnte ich die Auswirkung einer vorteilhaften Mutation auf das Niveau der neutralen Variabilität an einem benachbarten genetischen Locus vorhersagen (Kap. 4) und dann diese Ergebnisse mit experimentellen Daten beobachtbarer genetischer Variabilität bei der Fruchtfliege Drosophila vergleichen. Dies führte zu einer Abschätzung der Rate und Stärke, mit der vorteilhafte Substitutionen in natürlichen Populationen auftreten (Kap. 5)

Let\u27s Play A Story: Early Educators\u27 Experience Implementing Story Drama with Support from Coaching

While imaginative play, music, movement, and the visual arts are established components of the curriculum in early childhood education (ECE), teacher-guided story drama, or “improvised role play stimulated by a story” (Booth, 2005, p. 8), is an underutilized arts-based practice that supports children’s early literacy skills, creativity, and enjoyment of learning. There are numerous practitioner books and resources about the benefits of and strategies for how to incorporate storytelling, dramatic play, theater, and creative dramatics into the early learning environment (Bolton & Heathcote, 1999; Booth, 2005; V. Brown & Pleydell, 1999; Carleton, 2012), however, there is little research examining the process early educators undergo when they attempt to integrate process-based dramatic pedagogies into their practice. This phenomenological case study examined four preschool teachers’ experience adopting story drama as an instructional practice with support from coaching. It explored the ways coaching supported preschool teachers’ adoption of story drama in their literacy curriculum; teachers’ experience engaging in story drama, a creative play-based pedagogy; and what teachers valued about integrating story drama into their pedagogical repertoire. Teachers participated in six weeks of coaching in story drama lesson planning, creative dramatics and storytelling techniques, coupled with observations of them implementing story drama lessons. Data were gathered from class observations and reflective dialogic interviews with participants before, during, and after the coaching intervention. The results reveal that teachers had a positive experience adopting story drama into their pedagogical repertoire. They felt that coaching introduced them to new techniques, resources, and perspectives while supporting their confidence with implementing story drama independently. Teachers felt that story drama was a meaningful practice in their curriculum with benefits to children’s social emotional and literacy skills. Engaging in story drama impacted teachers’ relationships with children and colleagues positively. Finally, teachers reported experiencing fun and joy in their workday as a result of playing with children during story drama lessons. While decades of research have focused on children’s play as a vehicle for authentic learning, few studies have examined the role of play in teachers’ practice. This study offers a unique view into the experience of early educators’ perceptions, in their own words, of adopting a playful process-centered theater-inspired pedagogy and the function of coaching to support their own creative self-efficacy. Findings of this study will allow relevant stakeholders to design professional development opportunities informed by early educators’ perspectives on their experience with coaching, play, and story drama

Social Casework Principles of Value to a Pastor in Counseling

There has been much discussion in the past years concerning the work of the pastor as a counselor. Many books have been written and many lectures have been delivered on the subject. Various approaches and techniques are advocated by those dealing with the subject. This thesis shall attempt to prove that the principles of social casework can be applied by the pastor as a counselor. Seven casework principles will be discussed, first as they relate to the social casework process, and then as they can be of value to the pastor in counseling

The Role of the Clergyman in the Grief Process

The author presents a psychological and physiological discussion of the reactions of the bereaved to the loss experienced in death and offers some guidelines to clergymen for counseling and preaching in grief situations

Crisis and the Clergyman

As a minister views his pastoral role, he realizes he is on the front line when problem situations arise in the lives of his parishioners. There are frequent telephone calls in which people request counseling in the privacy of his study for a variety of problem situations. Often a casual contact with a parishioner results in a conversation that reveals deeply troubled feelings. These are a few of the indicators to any pastor that he is a significant person in the life of his parishioners, particularly at a time of crisis. Clergymen are also regarded on the front line in problem-solving from the perspective of social agencies, hospitals, and mental health clinics