Ordinal Context Research Articles

Representing Context and Priority in Working Memory.

The ability to prioritize among contents in working memory (WM) is critical for successful control of thought and behavior. Recent work has demonstrated that prioritization in WM can be implemented by representing different states of priority in different representational formats. Here, we explored the mechanisms underlying WM prioritization by simulating the double serial retrocuing task with recurrent neural networks. Visualization of stimulus representational dynamics using principal component analysis revealed that the network represented trial context (order of presentation) and priority via different mechanisms. Ordinal context, a stable property lasting the duration of the trial, was accomplished by segregating representations into orthogonal subspaces. Priority, which changed multiple times during a trial, was accomplished by separating representations into different strata within each subspace. We assessed the generality of these mechanisms by applying dimensionality reduction and multiclass decoding to fMRI and EEG data sets and found that priority and context are represented differently along the dorsal visual stream and that behavioral performance is sensitive to trial-by-trial variability of priority coding, but not context coding.

Strategic control of location and ordinal context in visual working memory.

Working memory (WM) requires encoding stimulus identity and context (e.g. where or when stimuli were encountered). To explore the neural bases of the strategic control of context binding in WM, we acquired fMRI while subjects performed delayed recognition of 3 orientation patches presented serially and at different locations. The recognition probe was an orientation patch with a superimposed digit, and pretrial instructions directed subjects to respond according to its location ("location-relevant"), to the ordinal position corresponding to its digit ("order-relevant"), or to just its orientation (relative to all three samples; "context-irrelevant"). Delay period signal in PPC was greater for context-relevant than for "context-irrelevant" trials, and multivariate decoding revealed strong sensitivity to context binding requirements (relevant vs. "irrelevant") and to context domain ("location-" vs. "order-relevant") in both occipital cortex and PPC. At recognition, multivariate inverted encoding modeling revealed markedly different patterns in these 2 regions, suggesting different context-processing functions. In occipital cortex, an active representation of the location of each of the 3 samples was reinstated regardless of the trial type. The pattern in PPC, by contrast, suggested a trial type-dependent filtering of sample information. These results indicate that PPC exerts strategic control over the representation of stimulus context in visual WM.

Permutation tests for experimental data

This article surveys the use of nonparametric permutation tests for analyzing experimental data. The permutation approach, which involves randomizing or permuting features of the observed data, is a flexible way to draw statistical inferences in common experimental settings. It is particularly valuable when few independent observations are available, a frequent occurrence in controlled experiments in economics and other social sciences. The permutation method constitutes a comprehensive approach to statistical inference. In two-treatment testing, permutation concepts underlie popular rank-based tests, like the Wilcoxon and Mann–Whitney tests. But permutation reasoning is not limited to ordinal contexts. Analogous tests can be constructed from the permutation of measured observations—as opposed to rank-transformed observations—and we argue that these tests should often be preferred. Permutation tests can also be used with multiple treatments, with ordered hypothesized effects, and with complex data-structures, such as hypothesis testing in the presence of nuisance variables. Drawing examples from the experimental economics literature, we illustrate how permutation testing solves common challenges. Our aim is to help experimenters move beyond the handful of overused tests in play today and to instead see permutation testing as a flexible framework for statistical inference.

Assessing Deprivation with Ordinal Variables: Depth Sensitivity and Poverty Aversion

The challenges associated with poverty measurement within an axiomatic framework, especially with cardinal variables, have received due attention during the last four decades. However, there is a dearth of literature studying how to meaningfully assess poverty with ordinal variables, capturing the depth of deprivations. In this paper, we first propose a class of additively decomposable ordinal poverty measures and provide an axiomatic characterisation using a set of basic foundational properties. Then, in a novel effort, we introduce a set of properties operationalising prioritarianism in the form of different degrees of poverty aversion in the ordinal context and characterise corresponding subclasses of measures. Moreover, for all the characterised classes and subclasses of measures, we develop stochastic dominance conditions, some of which are in themselves novel contributions to the stochastic dominance literature. Finally, we demonstrate the efficacy of our methods using an empirical illustration scrutinising the change in sanitation deprivation in Bangladesh.

Scale-Invariant Measurement of Inequality and Welfare in Ordinal Achievements: An Application to Subjective Well-Being and Education in OECD Countries

Designing well-being policies often requires the use of qualitative data. In fact many dimensions of well-being have to be appraised through the use of an ordered status: that is the case with health, happiness and educational attainments. While it is important to look at the mean levels achieved by society, distributional features are also salient aspects for any evaluation exercises, as it is likely that strong disparities in achievements among the population will prevail in those dimensions. Nonetheless, standards tools for inequality analysis, essentially mean-based and thus scale-dependent, are not applicable in this context, as any choice of scale in an ordinal framework is likely to be arbitrary and subject to change. Relying on the median-based approach developed by Allison and Foster (J Health Econ 23:505–524, 2004) for the measurement of self-reported health status inequality, this paper applies scale-invariant measures to subjective well-being and educational attainments in OECD countries using the 2010 round of the Gallup World Poll. This scale-invariant approach, applied to the case of three-category ordinal variables with identical median states, generates an unambiguous inequality and welfare ordering. This ranking is further completed by the computation of a scale-invariant inequality index. Both these measures aim to provide a robust picture of inequality and welfare in an ordinal context.

One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers

We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also measured by asking the children to assess the correctness of a cartoon character’s counting in both contexts. In general, the children performed cardinal tasks significantly better than ordinal ones. Tasks requiring the production of the number for a given quantity or position were solved more accurately than those testing the ability to select a set of n objects or the object in the nth position. Different profiles were obtained for the principles; those principles shared by the two contexts were mastered earlier in the cardinal context. Regarding order (ir)relevance, older children adhered to rigid ways of counting, producing better results in the ordinal context and incorrect rejections in the cardinal trials. Altogether, our data indicate that the acquisitions of cardinal and ordinal meanings of numbers are related, and cardinality precedes the development of ordinality.

A new version of 2-tuple fuzzy linguistic representation model for computing with words

In this paper, we provide a new (proportional) 2-tuple fuzzy linguistic representation model for computing with words (CW), which is based on the concept of symbolic proportion. This concept motivates us to represent the linguistic information by means of 2-tuples, which are composed by two proportional linguistic terms. For clarity and generality, we first study proportional 2-tuples under ordinal contexts. Then, under linguistic contexts and based on canonical characteristic values (CCVs) of linguistic labels, we define many aggregation operators to handle proportional 2-tuple linguistic information in a computational stage for CW without any loss of information. Our approach for this proportional 2-tuple fuzzy linguistic representation model deals with linguistic labels, which do not have to be symmetrically distributed around a medium label and without the traditional requirement of having equal distance between them. Moreover, this new model not only provides a space to allow a continuous interpolation of a sequence of ordered linguistic labels, but also provides an opportunity to describe the initial linguistic information by members of a continuous linguistic scale domain which does not necessarily require the ordered linguistic terms of a linguistic variable being equidistant. Meanwhile, under the assumption of equally informative (which is defined by a condition based on the concept of CCV), we show that our model reduces to Herrera and Mart/spl inodot//spl acute/nez's (translational) 2-tuple fuzzy linguistic representation model.

Coordinatization of ordinal structures

Dependencies between attributes in ordinal data contexts are algebraically described. Suitable conditions are analysed which allow coordinatizations of ordinal contexts (ordinal structures) by ordered n-quasigroups, ordered abelian groups, and ordered fields. The presented development offers a new approach to conjoint measurement.