Browsing by Author "Awichi Richard"

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DG 6
(2015) Awichi Richard; Castela Corine; Valero Paola; Lott Johnny W
The aim of the DG was to engage participants in fruitful dialogue about the nature and roles of international co-operation in mathematics education. Mathematics education, both research and practice, is international. This means that it is carried out in most places in the world and that, despite particular national or local characteristics, practitioners experience similar predicaments and share similar bodies of knowledge not only about mathematics but also about teaching and learning phenomena related to mathematics. Being international, relations among people in different national contexts have always been at the basis for the development of new trends in the field. The history of ICMI as an international organisation promoting coordinated effort towards the betterment of mathematical instruction is a clear example of how the development of the field is international from its outset (Menghini, Furinghetti, Giacardi, & Arzarello, 2008). The nature and role of internationalisation in relation to the advancement of mathematics education has changed with time. From being an exchange between mainly European and North American mathematicians interested in exploring ideas for instruction at the beginning of the 20th century, in the last decade we have an extensive network of mathematicians and mathematics educators placed in a variety of research and teaching institutions, all around the world. In ICME-10, DG 5 had already taken up this issue under the heading “International cooperation in mathematics education”. The group concluded the following important points (Atweh & Boero, 2008).  In a globalised world with increasing inequality, international cooperation can be strategic to get access to scarce resources. However, the difference in resources in a partnership can lead to a dominant role of those who have access to the resources and thereby creating an unequal partnership.  There are clear barriers to cooperation, namely financial resources, language barriers, cultural norms, conflicting agendas and issues of voicing the results of cooperation.  The search for a genuine, mutually beneficial, equitable cooperation could diminish the impact of the barriers.  Whether internationalisation leads to homogenisation depends on whether cooperative participants succeed in building strong links “from the bottom” so that diversification of perspectives and forms of contribution in cooperation can emerge. DG 6 ICME-11 built on the discussions and lessons from the previous group. The following questions guided our discussions.  What are the goals of international co-operation?  Cooperation can take many forms, be organised in many ways, and be implemented accordingly. What are the advantages and disadvantages of different forms, organisations, and implementations? What topics best fit into which version of cooperation?  What are the advantages and disadvantages of using regional versus global cooperation?  What are concrete examples of international co-operation and what has been learned that can be disseminated to all?  What are the barriers to international cooperation and how they can be dealt with?  Would international cooperation lead to homogenisation? Would that be to the detriment of mathematics education or in its favour for acceptance of the discipline at large? As a response for a broad paper call, we received nine written contributions, which were made available prior to the conference. The sessions during the conference were organised to build on the written contributions but also to integrate the experience of the twenty participants, from countries such as Australia, Colombia, Denmark, Finland, France, Germany, Japan, Mexico, Peru, Thailand, United Kingdom, Unites States of America and Vietnam. In what follows, a thematic discussion of the main issues that emerged during the sessions as a response to the motivating questions is presented. We will support the points raised using the written contributions submitted to the group.
In-Sample Spatio-temporal Predictions by Multivariate Singular Spectrum Analysis
(Elsevier, 2015) Awichi Richard
In this paper, we present a method of utilizing spatial information, usually intrinsic in spatial data sets, to improve the quality of temporal predictions within the framework of singular spectrum analysis (SSA) techniques. Those constitute a model free approach to time series analysis and SSA can be applied to any time series with a notable structure. Indeed it has a wide area of application including social sciences, medical sciences, finance, environmental sciences, mathematics, dynamical systems and economics. The aim of SSA is twofold: i) to make a decomposition of the original series into a sum of a small number of independent and interpretable components such as a slowly varying trend, oscillatory components and a structureless noise; ii) to reconstruct the decomposed series to make a forecast in the absence of the noise component. It has two stages each with two steps. The first stage is the Decomposition Stage with steps comprising: (i) embedding–a usual procedure in time series analysis; the result of which is a called a trajectory matrix in SSA literature; (ii) singular value decomposition step that computes and arranges eigenvalues of this matrix for further analysis. The second stage is the Reconstruction Stage: it comprises two steps of (i) grouping the eigenvalues of the SVD step and (ii) diagonal averaging that works on the grouped matrices to realize a series close to the original series and this series is then used for further analysis. Multivariate Singular Spectrum Analysis (MSSA) is an extension of SSA to multivariate statistics and takes advantage of the delay procedure to obtain a similar formulation as SSA though with larger matrices for multivariate data. In environmental sciences and other areas where spatial data is an important focus of investigation, it is not uncommon to have attributes whose values change with space and time and an accurate prediction is thus important. Spatial dependence subsequently influences data analysis. The usual question asked is whether the location parameters can be of use in the analysis of such data sets. We present a method that can be used to harness the location attributes to enhance prediction of spatial data sets using an MSSA approach. This technique is applied to climate data recordings (particularly rainfall data) from Upper Austria.
A Mathematical Model Approach for Prevention and Intervention Measures of the COVID–19 Pandemic in Uganda
(Cold Spring Habour Laboratory, 2020-05-11) Kamugisha Mbabazi Fulgensia; Gavamukulya Yahaya; Awichi Richard; Olupot-Olupot Peter; Rwahwire Samson; Biira Saphina; Luboobi Livingstone S.
The human–infecting corona virus disease (COVID–19) caused by the novel severe acute respiratory syndrome corona virus 2 (SARS–CoV–2) was declared a global pandemic on March 11th, 2020. Current human deaths due to the infection have raised the threat globally with only 1 African country free of Virus (Lesotho) as of May 6th, 2020. Different countries have adopted different interventions at different stages of the outbreak, with social distancing being the first option while lock down the preferred option for flattening the curve at the peak of the pandemic. Lock down is aimed at adherence to social distancing, preserve the health system and improve survival. We propose a Susceptible–Exposed–Infected–Expected recoveries (SEIR) mathematical model to study the impact of a variety of prevention and control strategies Uganda has applied since the eruption of the pandemic in the country. We analyze the model using available data to find the infection–free, endemic/infection steady states and the basic reproduction number. In addition, a sensitivity analysis done shows that the transmission rate and the rate at which persons acquire the virus, have a positive influence on the basic reproduction number. On other hand the rate of evacuation by rescue ambulance greatly reduces the reproduction number. The results have potential to inform the impact and effect of early strict interventions including lock down in resource limited settings and social distancing.