Conference on Geometry and Mathematical Physics, Bulgaria, Zlatograd, 28.08-01.09.2005

List of Participants

Reading comprehension and mathematical concept acquisition through the use of math stories with bilingual children

Math storybooks are picture books in which the understanding of mathematical concepts is central to the comprehension of the story. Math stories have provided useful opportunities for children to expand their skills in the language arts area and to talk about mathematical factors that are related to their real lives. The purpose of this study was to examine bilingual children's reading and math comprehension of the math storybooks. ^ The participants were randomly selected from two Korean schools and two public elementary schools in Miami, Florida. The sample consisted of 63 Hispanic American and 43 Korean American children from ages five to seven. A 2 x 3 x (2) mixed-model design with two between- and one within-subjects variable was used to conduct this study. The two between-subjects variables were ethnicity and age, and the within-subjects variable was the subject area of comprehension. Subjects were read the three math stories individually, and then they were asked questions related to reading and math comprehension. ^ The overall ANOVA using multivariate tests was conducted to evaluate the factor of subject area for age and ethnicity. As follow-up tests for a significant main effect and a significant interaction effect, pairwise comparisons and simple main effect tests were conducted, respectively. ^ The results showed that there were significant ethnicity and age differences in total comprehension scores. There were also age differences in reading and math comprehension, but no significant differences were found in reading and math by ethnicity. Korean American children had higher scores in total comprehension than those of Hispanic American children, and they showed greater changes in their comprehension skills at the younger ages, from five to six, whereas Hispanic American children showed greater changes at the older ages, from six to seven. Children at ages five and six showed higher scores in reading than in math, but no significant differences between math and reading comprehension scores were found at age seven. ^ Through schooling with integrated instruction, young bilingual children can move into higher levels of abstraction and concepts. This study highlighted bilingual children's general nature of thinking and showed how they developed reading and mathematics comprehension in an integrated process. ^

An investigation into the tension arising between natural language and mathematical language experienced by mechanical engineering students

This investigation is grounded within the concept of embodied cognition where the mind is considered to be part of a biological system. A first year undergraduate Mechanical Engineering cohort of students was tasked with explaining the behaviour of three balls of different masses being rolled down a ramp. The explanations given by the students highlighted the cognitive conflict between the everyday interpretation of the word energy and its mathematical use. The results showed that even after many years of schooling, students found it challenging to interpret the mathematics they had learned and relied upon pseudo-scientific notions to account for the behaviour of the balls.

Monitoring Infection Risk for Air and Soil Borne Fungal Plant Pathogens using Antibody and DNA Techniques and Mathematical Models describing Environmental Parameters

Economic losses resulting from disease development can be reduced by accurate and early detection of plant pathogens. Early detection can provide the grower with useful information on optimal crop rotation patterns, varietal selections, appropriate control measures, harvest date and post harvest handling. Classical methods for the isolation of pathogens are commonly used only after disease symptoms. This frequently results in a delay in application of control measures at potentially important periods in crop production. This paper describes the application of both antibody and DNA based systems to monitor infection risk of air and soil borne fungal pathogens and the use of this information with mathematical models describing risk of disease associated with environmental parameters.

Fuzzy Logic Foundations and Industrial Applications (ed. D. Ruan), Springer US, 1996, ISBN: 978-0-7923-9774-8 [Book review]

Abstract not available

Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis

Gating of sensory information can be assessed using an auditory conditioning-test paradigm which measures the reduction in the auditory evoked response to a test stimulus following an initial conditioning stimulus. Recording brainwaves from specific areas of the brain using multiple electrodes is helpful in the study of the neurobiology of sensory gating. In this paper, we use such technology to investigate the role of cannabinoids in sensory gating in the CA3 region of the rat hippocampus. Our experimental results show that application of the exogenous cannabinoid agonist WIN55,212-2 can abolish sensory gating. We have developed a phenomenological model of cannabinoid dynamics incorporated within a spiking neural network model of CA3 with synaptically interacting pyramidal and basket cells. Direct numerical simulations of this model suggest that the basic mechanism for this effect can be traced to the suppression of inhibition of slow GABAB synapses. Furthermore, by working with a simpler mathematical firing rate model we are able to show the robustness of this mechanism for the abolition of sensory gating.

Boron carbide reinforced aluminium matrix composite : physical, mechanical characterization and mathematical modelling

This paper investigates the manufacturing of aluminium-boron carbide composites using the stir casting method. Mechanical and physical properties tests to obtain hardness, ultimate tensile strength (UTS) and density are performed after solidification of specimens. The results show that hardness and tensile strength of aluminium based composite are higher than monolithic metal. Increasing the volume fraction of B4C, enhances the tensile strength and hardness of the composite; however over-loading of B4C caused particle agglomeration, rejection from molten metal and migration to slag. This phenomenon decreases the tensile strength and hardness of the aluminium based composite samples cast at 800 °C. For Al-15 vol% B4C samples, the ultimate tensile strength and Vickers hardness of the samples that were cast at 1000 °C, are the highest among all composites. To predict the mechanical properties of aluminium matrix composites, two key prediction modelling methods including Neural Network learned by Levenberg-Marquardt Algorithm (NN-LMA) and Thin Plate Spline (TPS) models are constructed based on experimental data. Although the results revealed that both mathematical models of mechanical properties of Al-B4C are reliable with a high level of accuracy, the TPS models predict the hardness and tensile strength values with less error compared to NN-LMA models.

Mathematical symbols and computing methods in high dimensional biomimetic informatics and their applications

High dimensional biomimetic informatics (HDBI) is a novel theory of informatics developed in recent years. Its primary object of research is points in high dimensional Euclidean space, and its exploratory and resolving procedures are based on simple geometric computations. However, the mathematical descriptions and computing of geometric objects are inconvenient because of the characters of geometry. With the increase of the dimension and the multiformity of geometric objects, these descriptions are more complicated and prolix especially in high dimensional space. In this paper, we give some definitions and mathematical symbols, and discuss some symbolic computing methods in high dimensional space systematically from the viewpoint of HDBI. With these methods, some multi-variables problems in high dimensional space can be solved easily. Three detailed algorithms are presented as examples to show the efficiency of our symbolic computing methods: the algorithm for judging the center of a circle given three points on this circle, the algorithm for judging whether two points are on the same side of a hyperplane, and the algorithm for judging whether a point is in a simplex constructed by points in high dimensional space. Two experiments in blurred image restoration and uneven lighting image correction are presented for all these algorithms to show their good behaviors.

Nietzsche's eternal recurrence of the same : the effect of logic abridgement, contradictions and inconsistencies

I will argue that the doctrine of eternal recurrence of the same no better interprets cosmology than pink elephants interpret zoology. I will also argue that the eternal-reiurn-of-the-same doctrine as what Magnus calls "existential imperative" is without possibility of application and thus futile. To facilitate those arguments, the validity of the doctrine of the eternal recurrence of the same will be tested under distinct rubrics. Although each rubric will stand alone, one per chapter, as an evaluation of some specific aspect of eternal recurrence, the rubric sequence has been selected to accommodate the identification of what I shall be calling logic abridgments. The conclusions to be extracted from each rubric are grouped under the heading CONCLUSION and appear immediately following rubric ten. Then, or if, at the end of a rubric a reader is inclined to wonder which rubric or topic is next, and why, the answer can be found at the top of the following page. The question is usually answered in the very first sentence, but always answered in the first paragraph. The first rubric has been placed in order by chronological entitlement in that it deals with the evolution of the idea of eternal recurrence from the time of the ancient Greeks to Nietzsche's August, 1881 inspiration. This much-recommended technique is also known as starting at the beginning. Rubric 1 also deals with 20th. Century philosophers' assessments of the relationship between Nietzsche and ancient Greek thought. The only experience of E-R, Zarathustra's mountain vision, is second only because it sets the scene alluded to in following rubrics. The third rubric explores .ii?.ih T jc,i -I'w Nietzsche's evaluation of rationality so that his thought processes will be understood appropriately. The actual mechanism of E-R is tested in rubric four...The scientific proof Nietzsche assembled in support of E-R is assessed by contemporary philosophers in rubric five. E-R's function as an ethical imperative is debated in rubrics six and seven.. .The extent to which E-R fulfills its purpose in overcoming nihilism is measured against the comfort assured by major world religions in rubric eight. Whether E-R also serves as a redemption for revenge is questioned in rubric nine. Rubric ten assures that E-R refers to return of the identically same and not merely the similar. In addition to assemblage and evaluation of all ten rubrics, at the end of each rubric a brief recapitulation of its principal points concludes the chapter. In this essay I will assess the theoretical conditions under which the doctrine cannot be applicable and will show what contradictions and inconsistencies follow if the doctrine is taken to be operable. Harold Alderman in his book Nietzsche's Gift wrote, the "doctrine of eternal recurrence gives us a problem not in Platonic cosmology, but in Socratic selfreflection." ^ I will illustrate that the recurrence doctrine's cosmogony is unworkable and that if it were workable, it would negate self-reflection on the grounds that selfreflection cannot find its cause in eternal recurrence of the same. Thus, when the cosmology is shown to be impossible, any expected ensuing results or benefits will be rendered also impossible. The so-called "heaviest burden" will be exposed as complex, engrossing "what if speculations deserving no linkings to reality. To identify ^Alderman p. 84 abridgments of logic, contradictions and inconsistencies in Nietzsche's doctrine of eternal recurrence of the same, I. will examine the subject under the following schedule. In Chapter 1 the ancient origins of recurrence theories will be introduced. ..This chapter is intended to establish the boundaries within which the subsequent chapters, except Chapter 10, will be confined. Chapter 2, Zarathustra's vision of E-R, assesses the sections of Thus Spoke Zarathustra in which the phenomenon of recurrence of the same is reported. ..Nihilism as a psychological difficulty is introduced in this rubric, but that subject will be studied in detail in Chapter 8. In Chapter 2 the symbols of eternal recurrence of the same will be considered. Whether the recurrence image should be of a closed ring or as a coil will be of significance in many sections of my essay. I will argue that neither symbolic configuration can accommodate Nietzsche's supposed intention. Chapter 3 defends the description of E-R given by Zarathustra. Chapter 4, the cosmological mechanics of E-R, speculates on the seriousness with which Nietzsche might have intended the doctrine of eternal recurrence to be taken. My essay reports, and then assesses, the argument of those who suppose the doctrine to have been merely exploratory musings by Nietzsche on cosmological hypotheses...The cosmogony of E-R is examined. In Chapter 5, cosmological proofs tested, the proofs for Nietzsche's doctrine of return of the same are evaluated. This chapter features the position taken by Martin ' Heidegger. My essay suggests that while Heidegger's argument that recurrence of the same is a genuine cosmic agenda is admirable, it is not at all persuasive. Chapter 6, E-R is an ethical imperative, is in essence the reporting of a debate between two scholars regarding the possibility of an imperative in the doctrine of recurrence. Their debate polarizes the arguments I intend to develop. Chapter 7, does E-R of the same preclude alteration of attitudes, is a continuation of the debate presented in Chapter 6 with the focus shifted to the psychological from the cosmological aspects of eternal recurrence of the same. Chapter 8, Can E-R Overcome Nihilism?, is divided into two parts. In the first, nihilism as it applies to Nietzsche's theory is discussed. ..In part 2, the broader consequences, sources and definitions of nihilism are outlined. My essay argues that Nietzsche's doctrine is more nihilistic than are the world's major religions. Chapter 9, Is E-R a redemption for revenge?, examines the suggestion extracted from Thus Spoke Zarathustra that the doctrine of eternal recurrence is intended, among other purposes, as a redemption for mankind from the destructiveness of revenge. Chapter 10, E-R of the similar refuted, analyses a position that an element of chance can influence the doctrine of recurrence. This view appears to allow, not for recurrence of the same, but recurrence of the similar. A summary will recount briefly the various significant logic abridgments, contradictions, and inconsistencies associated with Nietzsche's doctrine of eternal recurrence of the same. In the 'conclusion' section of my essay my own opinions and observations will be assembled from the body of the essay.

Mathematics as a second language : looking for a bridge between mathematical language and the language of thought

Our thoughts are in one language, and mathematical results are expressed in a language foreign to the way we think. Mathematics is a unique foreign language with all the components of a language; it has its own grammar, vocabulary, conventions, synonyms, sentence structure, and paragraph structure. Students need to learn these components to partake in a thorough discussion of how to read, write, speak and think mathematics. Beginning with the students natural language and expanding that language to include symbolism and logic is the key. Providing lessons in concrete, pictorial, written and verbal terms allows the instructor to create a translation bridge between the grammar of the mother language and the grammar of mathematics. This papers presents methods to create the translation bridge for students so that they become articulate members of the mathematics community. The students "mother" language, expanded to include the symbols of mathematics and logic, is the the key to both the learning of mathematics and its effective application to problem situations. The use of appropriate language is the key to making mathematics understandable.

Parallelizing irregular and pointer-based computations automatically: perspectives from logic and constraint programming

Irregular computations pose sorne of the most interesting and challenging problems in automatic parallelization. Irregularity appears in certain kinds of numerical problems and is pervasive in symbolic applications. Such computations often use dynamic data structures, which make heavy use of pointers. This complicates all the steps of a parallelizing compiler, from independence detection to task partitioning and placement. Starting in the mid 80s there has been significant progress in the development of parallelizing compilers for logic pro­gramming (and more recently, constraint programming) resulting in quite capable paralle­lizers. The typical applications of these paradigms frequently involve irregular computations, and make heavy use of dynamic data structures with pointers, since logical variables represent in practice a well-behaved form of pointers. This arguably makes the techniques used in these compilers potentially interesting. In this paper, we introduce in a tutoríal way, sorne of the problems faced by parallelizing compilers for logic and constraint programs and provide pointers to sorne of the significant progress made in the area. In particular, this work has resulted in a series of achievements in the areas of inter-procedural pointer aliasing analysis for independence detection, cost models and cost analysis, cactus-stack memory management, techniques for managing speculative and irregular computations through task granularity control and dynamic task allocation such as work-stealing schedulers), etc.

Automatic parallelization of irregular and pointer-based computations: perspectives from logic and constraint programming

Irregular computations pose some of the most interesting and challenging problems in automatic parallelization. Irregularity appears in certain kinds of numerical problems and is pervasive in symbolic applications. Such computations often use dynamic data structures which make heavy use of pointers. This complicates all the steps of a parallelizing compiler, from independence detection to task partitioning and placement. In the past decade there has been significant progress in the development of parallelizing compilers for logic programming and, more recently, constraint programming. The typical applications of these paradigms frequently involve irregular computations, which arguably makes the techniques used in these compilers potentially interesting. In this paper we introduce in a tutorial way some of the problems faced by parallelizing compilers for logic and constraint programs. These include the need for inter-procedural pointer aliasing analysis for independence detection and having to manage speculative and irregular computations through task granularity control and dynamic task allocation. We also provide pointers to some of the progress made in these áreas. In the associated talk we demónstrate representatives of several generations of these parallelizing compilers.

Crisis communication under transformative change : the emergent context and roles of primary and secondary organisations

In an era of complex challenges that draw sustained media attention and entangle multiple organisational actors, this thesis addresses the gap between current trends in society and business, and existing scholarship in public relations and crisis communication. By responding to calls from crisis communication researchers to develop theory (Coombs, 2006a), to examine the interdependencies of crises (Seeger, Sellnow, & Ulmer, 1998), and to consider variation in crisis response (Seeger, 2002), this thesis contributes to theory development in crisis communication and public relations. Through transformative change, this thesis extends existing scholarship built on a preservation or conservation logic where public relations is used to maintain stability by incrementally responding to changes in an organisation‘s environment (Cutlip, Center, & Broom, 2006; Everett, 2001; Grunig, 2000; Spicer, 1997). Based on the opportunity to contribute to ongoing theoretical development in the literature, the overall research problem guiding this thesis asks: How does transformative change during crisis influence corporate actors’ communication? This thesis adopts punctuated equilibrium theory, which describes change as alternating between long periods of stability and short periods of revolutionary or transformative change (Gersick, 1991; Romanelli & Tushman, 1994; Siggelkow, 2002; Tushman, Newman, & Romanelli, 1986; Tushman & Romanelli, 1985). As a theory for change, punctuated equilibrium provides an opportunity to examine public relations and transformative change, building on scholarship that is based primarily on incremental change. Further, existing scholarship in public relations and crisis communication focuses on the actions of single organisations in situational or short-term crisis events. Punctuated equilibrium theory enables the study of multiple crises and multiple organisational responses during transformative change. In doing so, punctuated equilibrium theory provides a framework to explain both the context for transformative change and actions or strategies enacted by organisations during transformative change (Tushman, Newman, & Romanelli, 1986; Tushman & Romanelli, 1985; Tushman, Virany, & Romanelli, 1986). The connections between context and action inform the research questions that guide this thesis: RQ1: What symbolic and substantive strategies persist and change as crises develop from situational events to transformative and multiple linked events? RQ2: What features of the crisis context influence changes in symbolic and substantive strategies? To shed light on these research questions, the thesis adopts a qualitative approach guided by process theory and methods to explicate the events, sequences and activities that were essential to change (Pettigrew, 1992; Van de Ven, 1992). Specifically, the thesis draws on an alternative template strategy (Langley, 1999) that provides several alternative interpretations of the same events (Allison, 1971; Allison & Zelikow, 1999). Following Allison (1971) and Allison and Zelikow (1999), this thesis uses three alternative templates of crisis or strategic response typologies to construct three narratives using media articles and organisational documents. The narratives are compared to identify and draw out different patterns of crisis communication strategies that operate within different crisis contexts. The thesis is based on the crisis events that affected three organisations within the pharmaceutical industry for four years. The primary organisation is Merck, as its product recall crisis triggered transformative change affecting, in different ways, the secondary organisations of Pfizer and Novartis. Three narratives are presented based on the crisis or strategic response typologies of Coombs (2006b), Allen and Caillouet (1994), and Oliver (1991). The findings of this thesis reveal different stories about crisis communication under transformative change. By zooming in to a micro perspective (Nicolini, 2009) to focus on the crisis communication and actions of a single organisation and zooming out to a macro perspective (Nicolini, 2009) to consider multiple organisations, new insights about crisis communication, change and the relationships among multiple organisations are revealed at context and action levels. At the context level, each subsequent narrative demonstrates greater connections among multiple corporate actors. By zooming out from Coombs‘ (2006b) focus on single organisations to consider Allen and Caillouet‘s (1994) integration of the web of corporate actors, the thesis demonstrates how corporate actors add accountability pressures to the primary organisation. Next, by zooming further out to the macro perspective by considering Oliver‘s (1991) strategic responses to institutional processes, the thesis reveals a greater range of corporate actors that are caught up in the process of transformative change and accounts for their varying levels of agency over their environment. By zooming in to a micro perspective and out to a macro perspective (Nicolini, 2009) across alternative templates, the thesis sheds light on sequences, events, and actions of primary and secondary organisations. Although the primary organisation remains the focus of sustained media attention across the four-year time frame, the secondary organisations, even when one faced a similar starting situation to the primary organisation, were buffered by the process of transformative change. This understanding of crisis contexts in transforming environments builds on existing knowledge in crisis communication. At the action level, the thesis also reveals different interpretations from each alternative template. Coombs‘ (2006b) narrative shows persistence in the primary organisation‘s crisis or strategic responses over the four-year time frame of the thesis. That is, the primary organisation consistently applies a diminish crisis response. At times, the primary organisation drew on denial responses when corporate actors questioned its legitimacy or actions. To close the crisis, the primary organisation uses a rebuild crisis posture (Coombs, 2006). These finding are replicated in Allen and Caillouet‘s (1994) narrative, noting this template‘s limitation to communication messages only. Oliver‘s (1991) narrative is consistent with Coombs‘ (2006b) but also demonstrated a shift from a strategic response that signals conformity to the environment to one that signals more active resistance to the environment over time. Specifically, the primary organisation‘s initial response demonstrates conformity but these same messages were used some three years later to set new expectations in the environment in order to shape criteria and build acceptance for future organisational decisions. In summary, the findings demonstrate the power of crisis or strategic responses when considered over time and in the context of transformative change. The conclusions of this research contribute to scholarship in the public relations and management literatures. Based on the significance of organisational theory, the primary contribution of the theory relates to the role of interorganisational linkages or legitimacy buffers that form during the punctuation of equilibrium. The network of linkages among the corporate actors are significant also to the crisis communication literature as they form part of the process model of crisis communication under punctuated equilibrium. This model extends existing research that focuses on crisis communication of single organisations to consider the emergent context that incorporates secondary organisations as well as the localised contests of legitimacy and buffers from regulatory authorities. The thesis also provides an empirical base for punctuated equilibrium in public relations and crisis communication, extending Murphy‘s (2000) introduction of the theory to the public relations literature. In doing this, punctuated equilibrium theory reinvigorates theoretical development in crisis communication by extending existing scholarship around incrementalist approaches and demonstrating how public relations works in the context of transformative change. Further research in this area could consider using alternative templates to study transformative change caused by a range of crisis types from natural disasters to product tampering, and to add further insight into the dynamics between primary and secondary organisations. This thesis contributes to practice by providing guidelines for crisis response strategy selection and indicators related to the emergent context for crises under transformative change that will help primary and secondary organisations‘ responses to crises.

Purposeful program theory: Effective use of theories of change and logic models [Book Review]

The purpose of this book by two Australian authors is to: introduce the audience to the full complement of contextual elements found within program theory; offer practical suggestions to engage with theories of change, theories of action and logic models; and provide substantial evidence for this approach through scholarly literature, practice case studies together with the authors' combined experience of 60 years.