Search results for "reduction theory"
showing 7 items of 7 documents
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
Temporal Binding in Multisensory and Motor-Sensory Contexts: Toward a Unified Model
2021
Our senses receive a manifold of sensory signals at any given moment in our daily lives. For a coherent and unified representation of information and precise motor control, our brain needs to temporally bind the signals emanating from a common causal event and segregate others. Traditionally, different mechanisms were proposed for the temporal binding phenomenon in multisensory and motor-sensory contexts. This paper reviews the literature on the temporal binding phenomenon in both multisensory and motor-sensory contexts and suggests future research directions for advancing the field. Moreover, by critically evaluating the recent literature, this paper suggests that common computational prin…
Uncertainty in urban flood damage assessment due to urban drainage modelling and depth-damage curve estimation
2010
Due to the increased occurrence of flooding events in urban areas, many procedures for flood damage quantification have been defined in recent decades. The lack of large databases in most cases is overcome by combining the output of urban drainage models and damage curves linking flooding to expected damage. The application of advanced hydraulic models as diagnostic, design and decision-making support tools has become a standard practice in hydraulic research and application. Flooding damage functions are usually evaluated by a priori estimation of potential damage (based on the value of exposed goods) or by interpolating real damage data (recorded during historical flooding events). Hydrau…
Epistemic cooperation scripts in online learning environments: Fostering learning by reducing uncertainty in discourse?
2005
Using online learning environments in higher education offers innovative possibilities to support collaborative learning. However, online learning creates new kinds of problems for participants who have not previously worked with each other. One of these problems is uncertainty which occurs when participants do not know each other. According to the uncertainty reduction theory, low uncertainty level increases the amount of discourse and decreases the amount of information seeking. Therefore, uncertainty may influence online discourse and learning. This study investigates the effects of an epistemic cooperation script with respect to the amount of discourse, information seeking and learning …
Micropollutants throughout an integrated urban drainage model: Sensitivity and uncertainty analysis
2017
Abstract The paper presents the sensitivity and uncertainty analysis of an integrated urban drainage model which includes micropollutants. Specifically, a bespoke integrated model developed in previous studies has been modified in order to include the micropollutant assessment (namely, sulfamethoxazole – SMX). The model takes into account also the interactions between the three components of the system: sewer system (SS), wastewater treatment plant (WWTP) and receiving water body (RWB). The analysis has been applied to an experimental catchment nearby Palermo (Italy): the Nocella catchment. Overall, five scenarios, each characterized by different uncertainty combinations of sub-systems (i.e…
Integral binary Hamiltonian forms and their waterworlds
2018
We give a graphical theory of integral indefinite binary Hamiltonian forms $f$ analogous to the one by Conway for binary quadratic forms and the one of Bestvina-Savin for binary Hermitian forms. Given a maximal order $\mathcal O$ in a definite quaternion algebra over $\mathbb Q$, we define the waterworld of $f$, analogous to Conway's river and Bestvina-Savin's ocean, and use it to give a combinatorial description of the values of $f$ on $\mathcal O\times\mathcal O$. We use an appropriate normalisation of Busemann distances to the cusps (with an algebraic description given in an independent appendix), and the $\operatorname{SL}_2(\mathcal O)$-equivariant Ford-Voronoi cellulation of the real …
Uncertainty-reducing cooperation scripts in online learning environments
2004
Online learning courses can create new interaction situations for participants who have not previously worked with each other. Initially, there is some degree of uncertainty between participants in these interaction situations. According to the uncertainty reduction theory, low uncertainty increases theamount of discourse and decreases information seeking. Thus, uncertainty may influence online discourseand learning. However, the relation of uncertainty reduction to learning outcomes has not yet been investigated systematically. Cooperation scripts may reduce uncertainty, and therefore enhance learning.A cooperation script, which aims to reduce uncertainty at a cognitive level, was chosen f…