scholarly journals Mapping internal states to formal systems: modeling human numerosity estimation

2019 ◽  
Author(s):  
Erik Brockbank ◽  
Edward Vul ◽  
David Barner
Keyword(s):  
Mapping Function ◽  
Individual Variability ◽  
Modern World ◽  
Internal Variables ◽  
Limited Data ◽  
Formal Systems ◽  
Sensory Experiences ◽  
Internal States ◽  
Human Estimation ◽  
Numerosity Estimation

Whether estimating the size of a crowd, thinking about how heavy something will be before trying to lift it, or reviewing a restaurant on a five-star scale, the modern world frequently requires us to navigate between subjective sensory experiences and shared formal systems. This entails mapping internal variables onto a common scale. Here we ask how people manage this in the case of estimating number. We present people with arrays of dots and ask them to report how many dots there are. In Experiment 1, we test predictions made by existing models of how people map from internal representations of numerosity to verbal estimates. We find that people’s estimates do not have a stable coefficient of variation at higher magnitudes, as has previously been suggested, and that the likely cause of this is a “drift” in people’s estimate calibration over many trials. Building on these results, we present a model of the mapping function from subjective numerosity to formal number estimates which relies only on a limited set of previous estimates and a rough sensitivity to the distribution of numbers in the world. Our model is able to generate an accurate mapping with limited data, as well as reproduce the notable aspects of human estimation described in our experimental results, namely humanlike patterns of underestimation, individual variability, and dynamic miscalibration at higher magnitudes.

scholarly journals Mapping visual features onto numbers

2019 ◽  
Author(s):  
Erik Brockbank ◽  
Edward Vul
Keyword(s):  
Visual Cues ◽  
Mapping Function ◽  
Modern Society ◽  
Number Line ◽  
Internal Variables ◽  
Formal Systems ◽  
Subjective Estimate ◽  
Common Scale ◽  
Changes Over Time ◽  
Line P

Modern society frequently requires that we express our subjective senses in objective, shared formal systems; this entails mapping multiple internal variables onto a common scale. Here we ask whether we accomplish this feat in the case of estimating number by learning a single mapping between explicit numbers and one integrated subjective estimate of numerosity, or if we separately map different perceptual features onto numbers. We present people with arrays of dots and ask them to report how many dots there are; we rely on the systematic under/overestimation of number at higher quantities to estimate error in the mapping function. By comparing how this error changes over time, as the mapping fluctuates for different visual cues to numerosity, we can evaluate whether these cues share a single mapping, or are mapped onto number individually. We find that area, size, and density all share a common mapping, indicating that people obtain a unified subjective estimate of numerosity before mapping it onto the formal number line.

scholarly journals Variability in the macro- and microstructure of the human brain and its importance to the investigation of neurological disorders

2019 ◽  
Author(s):  
András Király
Keyword(s):  
Human Brain ◽  
Hemispheric Asymmetry ◽  
Mapping Function ◽  
Individual Variability ◽  
Optimal Choice ◽  
Brain Morphology ◽  
Coordinate Space ◽  
Coordinate Frame ◽  
Standard Space ◽  
The Brain

The exact shape of every human brain - including its micro- and macroscopic features - is as unique as a human fingerprint, resulting in inter-individual anatomical variability. In the past two decades, the understanding of this variability advanced dramatically not only at the level of sulcal/gyral patterns, anatomical features (e.g. cortical thickness, volume and shape) and extent of cytoarchitectonic areas defined at the microscopic level, but also in the anatomical and functional connectivity of the brain. The core concept within the field of brain mapping is the use of a standardized 3D coordinate frame for data analysis and reporting of findings from neuroimaging experiments. This simple construct allows brain researchers to combine (even structural or functional) data from many subjects to create group-averaged signals. Also, where the signal is robust enough to be detected in individuals, it allows for the exploration of inter-individual variance in the location of that signal. Spatial standardization requires two basic components: (i) the specification of the 3D standard coordinate space, and (ii) a mapping function that transforms a 3D brain image from “native” space to that standard space. The first component is usually expressed by the choice of a representative 3D MR image that serves as target (template or atlas). The native image is re-sampled to standard space under the mapping function that may have few or many degrees of freedom, depending upon the experimental design. The optimal choice of atlas template and mapping function depends upon considerations of age, gender, hemispheric asymmetry, anatomical correspondence, spatial normalization methodology and disease-specificity (1). In our studies we investigated some of these aspects, e.g. 1) how gender and normal aging influences brain morphology, 2) how normal hemispheric asymmetry plays a role in lateralized neurological diseases, such as cluster headache, 3) how progressive neurodegenerative disorders, such as Huntington’s disease affect the brain structure, or 4) how we can deal with inter-individual variability in case of neurosurgical interventions, such as thalamotomy in the therapy of medication resistant tremor.

scholarly journals Behind the scenes of streamflow model performance

2020 ◽  
Author(s):  
Laurène J. E. Bouaziz ◽  
Guillaume Thirel ◽  
Tanja de Boer-Euser ◽  
Lieke A. Melsen ◽  
Joost Buitink ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Root Zone ◽  
Model Performance ◽  
Remotely Sensed ◽  
Decision Makers ◽  
Internal Variables ◽  
Hydrological Models ◽  
Process Representation ◽  
Snow Storage ◽  
Internal States

Abstract. Streamflow is often the only variable used to constrain hydrological models. In a previous international comparison study, eight research groups followed an identical protocol to calibrate a total of twelve hydrological models using observed streamflow of catchments within the Meuse basin. In the current study, we hypothesize that these twelve process-based models with similar streamflow performance have similar representations of internal states and fluxes. We test our hypothesis by comparing internal states and fluxes between models and we assess their plausibility using remotely-sensed products of evaporation, snow cover, soil moisture and total storage anomalies. Our results indicate that models with similar streamflow performance represent internal states and fluxes differently. Substantial dissimilarities between models are found for annual and seasonal evaporation and interception rates, the number of days per year with water stored as snow, the mean annual maximum snow storage and the size of the root-zone storage capacity. Relatively small root-zone storage capacities for several models lead to drying-out of the root-zone storage and significant reduction of evaporative fluxes each summer, which is not suggested by remotely-sensed estimates of evaporation and root-zone soil moisture. These differences in internal process representation imply that these models cannot all simultaneously be close to reality. Using remotely-sensed products, we could evaluate the plausibility of model representations only to some extent, as many of these internal variables remain unknown, highlighting the need for experimental research. We also encourage modelers to rely on multi-model and multi-parameter studies to reveal to decision-makers the uncertainties inherent to the heterogeneity of catchments and the lack of evaluation data.

The Role of Internal Variables on the Control of Viscoelastic Structures

2002 ◽  
Author(s):  
Luciano A. Silva ◽  
Eric M. Austin ◽  
Daniel J. Inman
Keyword(s):  
Complex Modulus ◽  
Viscoelastic Behavior ◽  
Internal Variable ◽  
Material Behavior ◽  
Internal Variables ◽  
Affect Control ◽  
Standard Observer ◽  
Full State ◽  
Internal States ◽  
Maxwell Models

Scientists have used internal variables to model time-dependent material behavior for many years. Since the 1980s they have been employed to predict transient response of structures that include viscoelastic materials. The potentially large number of extra states introduced by the internal variables can be problematic when designing control systems, so the purpose of this paper is to explore how internal variables affect control system design. Practical designs are based on output feedback of a limited number of the physical states, but this brings up the question of whether it is advantageous to recreate the full state vector (including internal states) using a standard observer. Internal variables based on Maxwell models are used to address observability and controllability as well as full- and partial-state feedback on a single-degree-of-freedom system. Comparisons are also made between complex-modulus and internal-variable representations of viscoelastic behavior.

Inter-individual variation shapes the human microbiome

2019 ◽  
Vol 42 ◽  
Author(s):  
Emily F. Wissel ◽  
Leigh K. Smith
Keyword(s):  
Individual Differences ◽  
Individual Variation ◽  
Human Microbiome ◽  
Individual Variability ◽  
Microbiota Composition ◽  
Target Article ◽  
Microbiome Research

Abstract The target article suggests inter-individual variability is a weakness of microbiota-gut-brain (MGB) research, but we discuss why it is actually a strength. We comment on how accounting for individual differences can help researchers systematically understand the observed variance in microbiota composition, interpret null findings, and potentially improve the efficacy of therapeutic treatments in future clinical microbiome research.

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

Humanitarianism in the Modern World

2020 ◽  
Author(s):  
Norbert Götz ◽  
Georgina Brewis ◽  
Steffen Werther
Keyword(s):  
Modern World

EURRECA’s Approach for Estimating Micronutrient Requirements

2011 ◽  
Vol 81 (4) ◽  
pp. 256-263 ◽  
Author(s):  
Christophe Matthys ◽  
Pieter van ‘t Veer ◽  
Lisette de Groot ◽  
Lee Hooper ◽  
Adriënne E.J.M. Cavelaars ◽  
...  
Keyword(s):  
Reference Values ◽  
Policy Decision ◽  
Individual Variability ◽  
The Body ◽  
Decision Makers ◽  
Nutrient Requirements ◽  
Factorial Approach ◽  
Dietary Reference Values ◽  
Health Policy Decision ◽  
Quantitative Integration

In Europe, micronutrient dietary reference values have been established by (inter)national committees of experts and are used by public health policy decision-makers to monitor and assess the adequacy of diets within population groups. The approaches used to derive dietary reference values (including average requirements) vary considerably across countries, and so far no evidence-based reason has been identified for this variation. Nutrient requirements are traditionally based on the minimum amount of a nutrient needed by an individual to avoid deficiency, and is defined by the body’s physiological needs. Alternatively the requirement can be defined as the intake at which health is optimal, including the prevention of chronic diet-related diseases. Both approaches are confronted with many challenges (e. g., bioavailability, inter and intra-individual variability). EURRECA has derived a transparent approach for the quantitative integration of evidence on Intake-Status-Health associations and/or Factorial approach (including bioavailability) estimates. To facilitate the derivation of dietary reference values, EURopean micronutrient RECommendations Aligned (EURRECA) is developing a process flow chart to guide nutrient requirement-setting bodies through the process of setting dietary reference values, which aims to facilitate the scientific alignment of deriving these values.

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