Search results for " Representation."
showing 10 items of 791 documents
A Note on Locally ??-compact Spaces
1995
: The local version of the concept of ℰτ-compactness (where ℰ is a class of Hausdorff spaces and ℰ is a cardinal) introduced by the first author as a generalization of Her-rlich's concept of ℰ-compactness (and hence, also of Mrowka's E-compactness) is defined and the corresponding theory is initiated. An essential part of the theory is developed under the additional assumption that all spaces from ℰ are absolute extensors for spaces under consideration. The theory contains as a special case the classical theory of local compactness.
Unitary units and skew elements in group algebras
2003
Let FG be the group algebra of a group G over a field F and let * denote the canonical involution of FG induced by the map g→g −1 ,gG. Let Un(FG)={uFG|uu * =1} be the group of unitary units of FG. In case char F=0, we classify the torsion groups G for which Un(FG) satisfies a group identity not vanishing on 2-elements. Along the way we actually prove that, in characteristic 0, the unitary group Un(FG) does not contain a free group of rank 2 if FG − , the Lie algebra of skew elements of FG, is Lie nilpotent. Motivated by this connection we characterize most groups G for which FG − is Lie nilpotent and char F≠2.
Invariant deformation theory of affine schemes with reductive group action
2015
We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we device an algorithm to compute the universal deformation of $X$ in terms of generators and relations up to a given order. In many situations, our algorithm even computes an algebraization of the universal deformation. As an application, we determine new families of examples of the invariant Hilbert scheme of Alexeev and Brion, where $G$ is a classical group acting on a classical representation, and describe their singularities.
Space counts! Brain correlates of spatial and numerical representations in synaesthesia
2018
Over-learned semantic representations, such as numbers, are strongly associated with space in normal cognition, and in the phenomenon called number-space synaesthesia. In number-space synaesthesia, numbers are linked to spatial locations in an idiosyncratic way. Synaesthetes report numbers as belonging to a specific location, or feelings that a specific location is the right location for that number. What does really differentiate synaesthetes from non-synaesthetes with respect to their number-space representation? Here we present a number-space synaesthete, MkM, whose number-space representation dramatically differs from that of controls. We examined the impact of spatial distance with res…
Right-handers and left-handers have different representations of their own hand
1998
The visual control of our own hand when dealing with an object and the observation of interactions between other people's hand and objects can be involved in the construction of internal representations of our own hand, as well as in hand recognition processes. Therefore, a different effect on handedness recognition is expected when subjects are presented with hands holding objects with either a congruent or an incongruent type of grip. Such an experiment was carried out on right-handed and left-handed subjects. We expected that the different degree of lateralisation in motor activities observed in the two populations [J. Herron, Neuropsychology of left- handedness, Academic Press, New York…
What Will You Do Next? A Cognitive Model for Understanding Others’ Intentions Based on Shared Representations
2013
Goal-directed action selection is the problem of what to do next in order to progress towards goal achievement. This problem is computationally more complex in case of joint action settings where two or more agents coordinate their actions in space and time to bring about a common goal: actions performed by one agent influence the action possibilities of the other agents, and ultimately the goal achievement. While humans apparently effortlessly engage in complex joint actions, a number of questions remain to be solved to achieve similar performances in artificial agents: How agents represent and understand actions being performed by others? How this understanding influences the choice of ag…
Graphic syntax and representational development
2008
International audience; This chapter focuses specifically on the relationships between syntax and cognitive development, particularly representational development. Vinter, Picard and Fernandes promote the take-home message that changes in drawing behaviour during development result from changes in the size of the cognitive units or mental representations used to plan behaviour, and in the capacity to manage part-whole relationships. This hypothesis is first illustrated by reviewing studies in which children's adherence to the graphic rules when they copy elementary or complex figures is assessed. The authors also examine children's syntactical behaviour at a more global level, characterizin…
Demonstration Tasks for Assessment
2017
International audience; Learning from animations is conventionally measured using static assessment tools such as multiple choice tests or extended answer questions. These tools tend to rely heavily on textual information both for presenting the assessment items and as the medium for learner response. However, such assessments are not well aligned with the defining dynamic, pictorial characteristics of animated learning materials. This chapter considers the potential of demonstration tasks to offer more appropriate assessments of learning from animation. In these tasks, learners interact with a manipulable model of the animation’s subject matter to provide an explanatory account of how it c…
The Third Way of Cognitive Science and the Middle Way of Buddhism
2013
Even though cognitive science may not be established as a mature science, being rather a loose affiliation of disciplines which make human cognition a scientific theme, it has already had significant impact in the field of epistemology. Since the late 1970s, research conducted on aspects of cognition ranging from perception to language has laid the groundwork for a fundamental epistemological shift in cognitive science, which bears directly on the Western philosophical dilemma of whether reality is objective (and independent of our cognition) or subjective (and so our mind’s projection). My aim here is to trace some major developments in the history of cognitive science leading to the emerg…
Commentary on Jakab's “Ineffability of Qualia”
2000
Zoltan Jakab has presented an interesting conceptual analysis of the ineffability of qualia in a functionalist and classical cognitivist framework. But he does not want to commit himself to a certain metaphysical thesis on the ontology of consciousness or qualia. We believe that his strategy has yielded a number of highly relevant and interesting insights, but still suffers from some minor inconsistencies and a certain lack of phenomenological and empirical plausibility. This may be due to some background assumptions relating to the theory of mental representation employed. Jakab's starting assumption is that there is no linguistic description of a given experience such that understanding t…