Canonical Forms in Interactive Exercise Assistants

Interactive exercise assistants support students in practicing exercises, and acquiring procedural skills. Many mathematical topics can be practiced in such assistants. Ideally, an interactive exercise assistant not only validates final answers, but also comments on intermediate steps submitted by a student, provides hints on how to proceed, and presents worked-out examples. For these purposes, fine control over the symbolic simplification procedures of the underlying mathematical machinery is needed. In this paper, we introduce views for mathematical expressions. A view defines an equivalence relation by choosing a canonical form of mathematical expressions. We use views to track and recognize intermediate answers, to help in presenting expressions to a user, and to control the granularity of the steps in worked-out examples. We develop the concept of a view, discuss the laws it satisfies, and show how views are composed, which means that they can be used for multiple exercise classes.

Economic evaluations in paediatric dentistry clinical trials

Economic evaluations play an important role in identifying the cost‐effectiveness of alternative healthcare programmes, informing decisions surrounding funding and the allocation of resources. This paper outlines the basic principles of economic evaluation and how it can be conducted alongside a clinical trial. Furthermore, it considers the ways in which evidence from these studies can be used, and the challenges researchers are faced with when conducting economic evaluations in the field of children’s oral health

Processing deficits for familiar and novel faces in patients with left posterior fusiform lesions

Pure alexia (PA) arises fromdamage to the left posterior fusiformgyrus (pFG) and the striking reading disorder that defines this condition has meant that such patients are often cited as evidence for the specialisation of this regiontoprocessing of writtenwords.There is,however, an alternative view that suggests this region is devoted to processing of high acuity foveal input, which is particularly salient for complex visual stimuli like letter strings. Previous reports have highlighted disrupted processing of non-linguistic visual stimuli after damage to the left pFG, both for familiar and unfamiliar objects and also for novel faces. This study explored the nature of face processing deficits in patients with left pFG damage. Identification of famous faces was found to be compromised in both expressive and receptive tasks. Discrimination of novel faces was also impaired, particularly for those that varied in terms of second-order spacing information, and this deficit was most apparent for the patients with the more severe reading deficits. Interestingly, discrimination of faces that varied in terms of feature identity was considerably better in these patients and it was performance in this condition that was related to the size of the length effects shown in reading. This finding complements functional imaging studies showing left pFG activation for faces varying only in spacing and frontal activation for faces varying only on features. These results suggest that the sequential part-based processing strategy that promotes the length effect inthe reading of these patients also allows themto discriminate between faces on the basis of feature identity, but processing of second-order configural information is most compromised due to their left pFG lesion. This study supports a view in which the left pFG is specialised for processing of high acuity foveal visual information that supports processing of both words and faces.variou

Pragmatic financialisation: the role of the Japanese Post Office

The Japanese Post Office, one of the world’s largest financial institutions, was finally privatised in 2015, marking an appropriate time to examine financialisation in Japan. Literature on financialisation and changes in Japanese capitalism assumes convergence on Anglo-American capitalism with a diminishing of state power. The main argument of this paper is that financialisation is instead a more contingent process. This is put forth through an examination of how this process has been mediated by the Japanese state through the workings of the Japanese Post Office. The state has frequently shaped the direction of financialisation by intervening in the routing of household funds via the postal savings system in order to achieve its objectives in different circumstances, particularly evident in the protracted and contested nature of the post bank’s privatisation. Financialisation is thus not preordained; instead its path is hewn by crisis, catastrophe, demographics and the agency of domestic social actors

Mouse Chromosome 11

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46996/1/335_2004_Article_BF00648429.pd

Reductio ad Absurdum: Planning Proofs by Contradiction

Sometimes it is pragmatically useful to prove a theorem by contradiction rather than finding a direct proof. Some reductio ad absurdum arguments have made mathematical history and the general issue if and how a proof by contradiction can be replaced by a direct proof touches upon deep foundational issues such as the legitimacy of tertium non datur arguments in classical vs. intuitionistic foundations. In this paper we are interested in the pragmatic issue when and how to use this proof strategy in everyday mathematics in general and in particular in automated proof planning. Proof planning is a general technique in automated theorem proving that captures and makes explicit proof patterns and mathematical search control. So, how can we proof plan an argument by reductio ad absurdum and when is it useful to do so? What are the methods and decision involved