1,121 research outputs found
Memory Structure and Cognitive Maps
A common way to understand memory structures in the cognitive sciences is as a cognitive map​.
Cognitive maps are representational systems organized by dimensions shared with physical space. The
appeal to these maps begins literally: as an account of how spatial information is represented and used
to inform spatial navigation. Invocations of cognitive maps, however, are often more ambitious;
cognitive maps are meant to scale up and provide the basis for our more sophisticated memory
capacities. The extension is not meant to be metaphorical, but the way in which these richer mental
structures are supposed to remain map-like is rarely made explicit. Here we investigate this missing
link, asking: how do cognitive maps represent non-spatial information?​ We begin with a survey of
foundational work on spatial cognitive maps and then provide a comparative review of alternative,
non-spatial representational structures. We then turn to several cutting-edge projects that are engaged
in the task of scaling up cognitive maps so as to accommodate non-spatial information: first, on the
spatial-isometric approach​ , encoding content that is non-spatial but in some sense isomorphic to
spatial content; second, on the ​ abstraction approach​ , encoding content that is an abstraction over
first-order spatial information; and third, on the ​ embedding approach​ , embedding non-spatial
information within a spatial context, a prominent example being the Method-of-Loci. Putting these
cases alongside one another reveals the variety of options available for building cognitive maps, and the
distinctive limitations of each. We conclude by reflecting on where these results take us in terms of
understanding the place of cognitive maps in memory
An Algebraic Framework for Discrete Tomography: Revealing the Structure of Dependencies
Discrete tomography is concerned with the reconstruction of images that are
defined on a discrete set of lattice points from their projections in several
directions. The range of values that can be assigned to each lattice point is
typically a small discrete set. In this paper we present a framework for
studying these problems from an algebraic perspective, based on Ring Theory and
Commutative Algebra. A principal advantage of this abstract setting is that a
vast body of existing theory becomes accessible for solving Discrete Tomography
problems. We provide proofs of several new results on the structure of
dependencies between projections, including a discrete analogon of the
well-known Helgason-Ludwig consistency conditions from continuous tomography.Comment: 20 pages, 1 figure, updated to reflect reader inpu
A multigrid method for the Helmholtz equation with optimized coarse grid corrections
We study the convergence of multigrid schemes for the Helmholtz equation,
focusing in particular on the choice of the coarse scale operators. Let G_c
denote the number of points per wavelength at the coarse level. If the coarse
scale solutions are to approximate the true solutions, then the oscillatory
nature of the solutions implies the requirement G_c > 2. However, in examples
the requirement is more like G_c >= 10, in a trade-off involving also the
amount of damping present and the number of multigrid iterations. We conjecture
that this is caused by the difference in phase speeds between the coarse and
fine scale operators. Standard 5-point finite differences in 2-D are our first
example. A new coarse scale 9-point operator is constructed to match the fine
scale phase speeds. We then compare phase speeds and multigrid performance of
standard schemes with a scheme using the new operator. The required G_c is
reduced from about 10 to about 3.5, with less damping present so that waves
propagate over > 100 wavelengths in the new scheme. Next we consider extensions
of the method to more general cases. In 3-D comparable results are obtained
with standard 7-point differences and optimized 27-point coarse grid operators,
leading to an order of magnitude reduction in the number of unknowns for the
coarsest scale linear system. Finally we show how to include PML boundary
layers, using a regular grid finite element method. Matching coarse scale
operators can easily be constructed for other discretizations. The method is
therefore potentially useful for a large class of discretized high-frequency
Helmholtz equations.Comment: Coarse scale operators are simplified and only standard smoothers
used in v3; 5 figures, 12 table
De invloed van het ruwvoederrantsoen op het cellulose - afbrekend vermogen van de pensflora in een kunstpens
Predicting lymphatic filariasis transmission and elimination dynamics using a multi-model ensemble framework
Mathematical models of parasite transmission provide powerful tools for assessing the impacts of interventions. Owing to complexity and uncertainty, no single model may capture all features of transmission and elimination dynamics. Multi-model ensemble modelling offers a framework to help overcome biases of single models. We report on the development of a first multi-model ensemble of three lymphatic filariasis (LF) models (EPIFIL, LYMFASIM, and TRANSFIL), and evaluate its predictive performance in comparison with that of the constituents using calibration and validation data from three case study sites, one each from the three major LF endemic regions: Africa, Southeast Asia and Papua New Guinea (PNG). We assessed the performance of the respective models for predicting the outcomes of annual MDA strategies for various baseline scenarios thought to exemplify the current endemic conditions in the three regions. The results show that the constructed multi-model ensemble outperformed the single models when evaluated across all sites. Single models that best fitted calibration data tended to do less well in simulating the out-of-sample, or validation, intervention data. Scenario modelling results demonstrate that the multi-model ensemble is able to compensate for variance between single models in order to produce more plausible predictions of intervention impacts. Our results highlight the value of an ensemble approach to modelling parasite control dynamics. However, its optimal use will require further methodological improvements as well as consideration of the organizational mechanisms required to ensure that modelling results and data are shared effectively between all stakeholders
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