Numerical Representations for Nontransitive Preferences

2011 ◽  
Author(s):  
Carmen Vázquez Pampín ◽  
Carmen Quinteiro Sandomingo
Keyword(s):  
Nontransitive Preferences ◽  
Numerical Representations

Analog Numerical Representations in Rhesus Monkeys: Evidence for Parallel Processing

2004 ◽  
Vol 16 (5) ◽  
pp. 889-901 ◽  
Author(s):  
Andreas Nieder ◽  
Earl K. Miller
Keyword(s):  
Rhesus Monkeys ◽  
Neuronal Response ◽  
Weber Fraction ◽  
Discrimination Performance ◽  
Model Organisms ◽  
Response Latencies ◽  
Numerosity Discrimination ◽  
Numerical Information ◽  
Match To Sample ◽  
Numerical Representations

Monkeys have been introduced as model organisms to study neural correlates of numerical competence, but many of the behavioral characteristics of numerical judgments remain speculative. Thus, we analyzed the behavioral performance of two rhesus monkeys judging the numerosities 1 to 7 during a delayed match-to-sample task. The monkeys showed similar discrimination performance irrespective of the exact physical appearance of the stimuli, confirming that performance was based on numerical information. Performance declined smoothly with larger numerosities, and reached discrimination threshold at numerosity “4.” The nonverbal numerical representations in monkeys were based on analog magnitudes, object tracking process (“subitizing”) could not account for the findings because the continuum of small and large numbers shows a clear Weber fraction signature. The lack of additional scanning eye movements with increasing set sizes, together with indistinguishable neuronal response latencies for neurons with different preferred numerosities, argues for parallel encoding of numerical information. The slight but significant increase in reaction time with increasing numerosities can be explained by task difficulty and consequently time-consuming decision processes. The behavioral results are compared to single-cell recordings from the prefrontal cortex in the same subjects. Models for numerosity discrimination that may account for these results are discussed.

scholarly journals Numerosity representations in crows obey the Weber–Fechner law

2016 ◽  
Vol 283 (1827) ◽  
pp. 20160083 ◽  
Author(s):  
Helen M. Ditz ◽  
Andreas Nieder
Keyword(s):  
Weber Fraction ◽  
Discrimination Performance ◽  
Brain Structures ◽  
Number System ◽  
Number Line ◽  
Just Noticeable Difference ◽  
Match To Sample ◽  
Close Phylogenetic Relationship ◽  
The One ◽  
Numerical Representations

The ability to estimate number is widespread throughout the animal kingdom. Based on the relative close phylogenetic relationship (and thus equivalent brain structures), non-verbal numerical representations in human and non-human primates show almost identical behavioural signatures that obey the Weber–Fechner law. However, whether numerosity discriminations of vertebrates with a very different endbrain organization show the same behavioural signatures remains unknown. Therefore, we tested the numerical discrimination performance of two carrion crows ( Corvus corone ) to a broad range of numerosities from 1 to 30 in a delayed match-to-sample task similar to the one used previously with primates. The crows' discrimination was based on an analogue number system and showed the Weber-fraction signature (i.e. the ‘just noticeable difference’ between numerosity pairs increased in proportion to the numerical magnitudes). The detailed analysis of the performance indicates that numerosity representations in crows are scaled on a logarithmically compressed ‘number line’. Because the same psychophysical characteristics are found in primates, these findings suggest fundamentally similar number representations between primates and birds. This study helps to resolve a classical debate in psychophysics: the mental number line seems to be logarithmic rather than linear, and not just in primates, but across vertebrates.

scholarly journals A SELF-ADAPTABLE DISTRIBUTED CBR VERSION OF THE EQUIVOX SYSTEM

2016 ◽  
Vol 28 (04) ◽  
pp. 1650028
Author(s):  
Julien Henriet ◽  
Christophe Lang ◽  
Ronnie Muthada Pottayya ◽  
Karla Breschi
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Three Dimensional ◽  
Multi Agent System ◽  
Accidental Exposure ◽  
Interpolation Accuracy ◽  
Multi Agent ◽  
Artificial Neural Network Ann ◽  
Numerical Representations ◽  
Voxel Phantoms

Three dimensional (3D) voxel phantoms are numerical representations of human bodies, used by physicians in very different contexts. In the controlled context of hospitals, where from 2 to 10 subjects may arrive per day, phantoms are used to verify computations before therapeutic exposure to radiation of cancerous tumors. In addition, 3D phantoms are used to diagnose the gravity of accidental exposure to radiation. In such cases, there may be from 10 to more than 1000 subjects to be diagnosed simultaneously. In all of these cases, computation accuracy depends on a single such representation. In this paper, we present EquiVox which is a tool composed of several distributed functions and enables to create, as quickly and as accurately as possible, 3D numerical phantoms that fit anyone, whatever the context. It is based on a multi-agent system. Agents are convenient for this kind of structure, they can interact together and they may have individual capacities. In EquiVox, the phantoms adaptation is a key phase based on artificial neural network (ANN) interpolations. Thus, ANNs must be trained regularly in order to take into account newly capitalized subjects and to increase interpolation accuracy. However, ANN training is a time-consuming process. Consequently, we have built Equivox to optimize this process. Thus, in this paper, we present our architecture, based on agents and ANN, and we put the stress on the adaptation module. We propose, next, some experimentations in order to show the efficiency of the EquiVox architecture.

An Adjoint Based Approach for Optimal Design of Morphing SMP

2013 ◽  
Author(s):  
Shuang Wang ◽  
John C. Brigham
Keyword(s):  
Shape Change ◽  
Mechanical Energy ◽  
Optimization Methods ◽  
Design Parameters ◽  
Optimization Strategy ◽  
Thermally Activated ◽  
Gradient Based ◽  
Nonlinear Optimization Methods ◽  
Numerical Representations ◽  
Objective Functional

This work presents a strategy to identify the optimal localized activation and actuation for a morphing thermally activated SMP structure or structural component to obtain a targeted shape change or set of shape features, subject to design objectives such as minimal total required energy and time. This strategy combines numerical representations of the SMP structure’s thermo-mechanical behavior subject to activation and actuation with gradient-based nonlinear optimization methods to solve the morphing inverse problem that includes minimizing cost functions which address thermal and mechanical energy, morphing time, and damage. In particular, the optimization strategy utilizes the adjoint method to efficiently compute the gradient of the objective functional(s) with respect to the design parameters for this coupled thermo-mechanical problem.

From Seeing and Reaching to Hearing and Speaking

2021 ◽  
pp. 404-479
Author(s):  
Stephen Grossberg
Keyword(s):  
Speech Production ◽  
Arm Movement ◽  
Noisy Environments ◽  
Multiple Sources ◽  
Speaker Normalization ◽  
Cocktail Party Problem ◽  
Item Order ◽  
Number Systems ◽  
Numerical Representations ◽  
Representations Of Space

This far-ranging chapter provides unified explanations of data about audition, speech, and language, and the general cognitive processes that they specialize. The ventral What stream and dorsal Where cortical stream in vision have analogous ventral sound-to-meaning and dorsal sound-to-action streams in audition. Circular reactions for learning to reach using vision are homologous to circular reactions for learning to speak using audition. VITE circuits control arm movement properties of synergy, synchrony, and speed. Volitional basal ganglia GO signals choose which limb to move and how fast it moves. VAM models use a circular reaction to calibrate VITE circuit signals. VITE is joined with the FLETE model to compensate for variable loads, unexpected perturbations, and obstacles. Properties of cells in cortical areas 4 and 5, spinal cord, and cerebellum are quantitatively simulated. Motor equivalent reaching using clamped joints or tools arises from circular reactions that learn representations of space around an actor. Homologous circuits model motor-equivalent speech production, including coarticulation. Stream-shroud resonances play the role for audition that surface-shroud resonances play in vision. They support auditory consciousness and speech production. Strip maps and spectral-pitch resonances cooperate to solve the cocktail party problem whereby humans track voices of speakers in noisy environments with multiple sources. Auditory streaming and speaker normalization use networks with similar designs. Item-Order-Rank working memories and Masking Field networks temporarily store sequences of events while categorizing them into list chunks. Analog numerical representations and place-value number systems emerge from phylogenetically earlier Where and What stream spatial and categorical processes.

Sign in / Sign up

Export Citation Format

Share Document