One More Step Towards Well-Composedness of Cell Complexes over nD Pictures

An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident to v is face-connected. In previous work we proved that if an nD picture I is digitally well composed (DWC) then the cubical complex Q(I) associated to I is wWC. If I is not DWC, we proposed a combinatorial algorithm to “locally repair” Q(I) obtaining an nD pure simplicial complex PS(I) homotopy equivalent to Q(I) which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex PS(¯I) which decomposes the complement space of |PS(I)| and prove that PS(¯I) is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the nD repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an (n − 1)- manifold.Ministerio de Economía y Competitividad MTM2015-67072-

Strong Euler well-composedness

In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an (n−1)-dimensional ball. Working in the particular setting of cubical complexes canonically associated with nD pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension n ≥ 2 and that the converse is not true when n ≥ 4Ministerio de Ciencia, Innovación y Universidades PID2019-107339GB-I00Junta de Andalucía P20_0114

On the Topological Disparity Characterization of Square-Pixel Binary Image Data by a Labeled Bipartite Graph

Given an nD digital image I based on cubical n-xel, to fully characterize the degree of internal topological dissimilarity existing in I when using different adjacency relations (mainly, comparing 2n or 2n −1 adjacency relations) is a relevant issue in current problems of digital image processing relative to shape detection or identification. In this paper, we design and implement a new self-dual representation for a binary 2D image I, called {4, 8}-region adjacency forest of I ({4, 8}-RAF, for short), that allows a thorough analysis of the differences between the topology of the 4-regions and that of the 8-regions of I. This model can be straightforwardly obtained from the classical region adjacency tree of I and its binary complement image Ic, by a suitable region label identification. With these two labeled rooted trees, it is possible: (a) to compute Euler number of the set of foreground (resp. background) pixels with regard to 4-adjacency or 8-adjacency; (b) to identify new local and global measures and descriptors of topological dissimilarity not only for one image but also between two or more images. The parallelization of the algorithms to extract and manipulate these structures is complete, thus producing efficient and unsophisticated codes with a theoretical computing time near the logarithm of the width plus the height of an image. Some toy examples serve to explain the representation and some experiments with gray real images shows the influence of the topological dissimilarity when detecting feature regions, like those returned by the MSER (maximally stable extremal regions) method.Ministerio de Economía, Industria y Competitividad PID2019-110455GB-I00 (Par-HoT)Junta de Andalucía US-138107

Surface-Based Computation of the Euler Characteristic in the BCC Grid

As opposed to the 3D cubic grid, the body-centered cubic (BCC) grid has some favorable topological properties: each set of voxels in the grid is a 3-manifold, with 2-manifold boundary. Thus, the Euler characteristic of an object O in this grid can be computed as half of the Euler characteristic of its boundary ∂O . We propose three new algorithms to compute the Euler characteristic in the BCC grid with this surface-based approach: one based on (critical point) Morse theory and two based on the discrete Gauss–Bonnet theorem. We provide a comparison between the three new algorithms and the classic approach based on counting the number of cells, either of the 3D object or of its 2D boundary surface

The effects of a structured teaching method on mathematics anxiety and achievement of grade eight learners

The hypothesis that a structured, sequenced, approach to mathematics learning, based on the application of learnt facts, decreases mathematics anxiety and increases mathematics achievement is tested. A literature study and an empirical investigation were conducted with respect to the relationships between maths anxiety, maths achievement and teaching methods. A qualitative research design which focussed on the cross-case analysis of different case studies was used. The qualitative case study involves multiple methods such as interviews, observations and a pretest, posttest design. It analyses and compares the effects of the Kuman method, used as the intervention programme, on maths anxiety and maths achievement of an experimental group and a control group. The results of this research indicate that learners on the intervention programme who showed a decrease in anxiety, showed an increase in achievement. This has implications for the teaching methods used in South Africa.Teacher EducationM. Ed. (Specialisation in Guidance and Counselling

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Adapting to western norms of academic argumentation and debate.

The thesis explores the learning experiences of East Asian masters students in dealing with Western academic norms of critical thinking and evaluation in classroom debate and assignment writing. This is a relatively new area of research, which is becoming increasingly important as the numbers of international postgraduate students in the U. K. continue to grow. Previous research has shown that differences in expectations have resulted in misunderstanding and some confusion for both lecturers and students. However, little research has yet been done in the U. K. on the process of adjustment during this learning experience. A grounded theory, case study approach is followed, as one of the aims is for students to tell their own stories, and for theoretical concepts to be developed which reflect the perceptions and interpretations of the students. Sixty seven in-depth interviews were conducted with East Asian students across three case sites: two universities in the U. K. and a third university in China. Eleven British lecturers, five Chinese lecturers and six British students were also interviewed, for triangulation purposes. Although there is no claim to generalisation, the potential for transferability of the findings is increased by also including a vignette questionnaire, involving a further 268 students across the three sites. The thesis takes a cultural approach, and a theoretical model is developed which identifies five learning stages, with various entry and exit routes. The data suggest that the majority of East Asian students reject full academic acculturation into Western norms of argumentation, which is characterised by rigorous, `strong' critical thinking, polarised, linear logic, and `wrestling debate'. Instead, many of them opt for a `Middle Way', which synthesises those elements of Western academic norms that are perceived to be culturally acceptable, with the traditional cultural academic values held by many East Asian students. The Middle Way emphasises a more holistic, empathetic `constructive reasoning', which bridges U. K. and East Asian traditions of academic argumentation and debate. The thesis offers a significant contribution to conventional literature on the academic experiences of East Asian masters students, as it draws attention to the complexity of the adaptation process

Cultural Dynamics in a Globalized World

The book contains essays on current issues in arts and humanities in which peoples and cultures compete as well as collaborate in globalizing the world while maintaining their uniqueness as viewed from cross- and inter-disciplinary perspectives. The book covers areas such as literature, cultural studies, archaeology, philosophy, history, language studies, information and literacy studies, and area studies. Asia and the Pacific are the particular regions that the conference focuses on as they have become new centers of knowledge production in arts and humanities and, in the future, seem to be able to grow significantly as a major contributor of culture, science and arts to the globalized world. The book will help shed light on what arts and humanities scholars in Asia and the Pacific have done in terms of research and knowledge development, as well as the new frontiers of research that have been explored and opening up, which can connect the two regions with the rest of the globe