Numbers in action

2021 ◽  
Vol 44 ◽  
Author(s):  
David C. Burr ◽  
Giovanni Anobile ◽  
Elisa Castaldi ◽  
Roberto Arrighi

Abstract To understand the number sense, we need to understand its function. We argue that numerosity estimation is fundamental not only for perception, but also preparation and control of action. We outline experiments that link numerosity estimation with action, pointing to a generalized numerosity system that serves both perception and action preparation.


eNeuro ◽  
2018 ◽  
Vol 5 (3) ◽  
pp. ENEURO.0408-17.2018 ◽  
Author(s):  
Tahnée Engelen ◽  
Minye Zhan ◽  
Alexander T. Sack ◽  
Beatrice de Gelder


2021 ◽  
Vol 15 ◽  
pp. 183449092110126
Author(s):  
Cihua Zhou ◽  
Wei Xu ◽  
Yujie Liu ◽  
Zhichao Xue ◽  
Rui Chen ◽  
...  

Enumerating objects in the environment (i.e., “number sense”) is crucial for survival in many animal species, and foundational for the construction of more abstract and complex mathematical knowledge in humans. Perhaps surprisingly, deep convolutional neural networks (DCNNs) spontaneously emerge a similar number sense even without any explicit training for numerosity estimation. However, little is known about how the number sense emerges, and the extent to which it is comparable with human number sense. Here, we examined whether the numerosity underestimation effect, a phenomenon indicating that numerosity perception acts upon the perceptual number rather than the physical number, can be observed in DCNNs. In a typical DCNN, AlexNet, we found that number-selective units at late layers operated on the perceptual number, like humans do. More importantly, this perceptual number sense did not emerge abruptly, rather developed progressively along the hierarchy in the DCNN, shifting from the physical number sense at early layers to perceptual number sense at late layers. Our finding hence provides important implications for the neural implementation of number sense in the human brain and advocates future research to determine whether the representation of numerosity also develops gradually along the human visual stream from physical number to perceptual number.



2018 ◽  
Author(s):  
Leo Poom ◽  
Marcus Lindskog ◽  
Anders Winman ◽  
Ronald van den Berg

ABSTRACTHumans can estimate numerosities – such as the number sheep in a flock – without deliberate counting. A number of biases have been identified in these estimates, which seem primarily rooted in the spatial organization of objects (grouping, symmetry, etc). Most previous studies on the number sense used static stimuli with extremely brief exposure times. However, outside the laboratory, visual scenes are often dynamic and freely viewed for prolonged durations (e.g., a flock of moving sheep). The purpose of the present study is to examine grouping-induced numerosity biases in stimuli that more closely mimic these conditions. To this end, we designed two experiments with limited-dot-lifetime displays (LDDs), in which each dot is visible for a brief period of time and replaced by a new dot elsewhere after its disappearance. The dynamic nature of LDDs prevents subjects from counting even when they are free-viewing a stimulus under prolonged presentation. Subjects estimated the number of dots in arrays that were presented either as a single group or were segregated into two groups by spatial clustering, dot size, dot color, or dot motion. Grouping by color and motion reduced perceived numerosity compared to viewing them as a single group. Moreover, the grouping effect sizes between these two features were correlated, which suggests that the effects may share a common, feature-invariant mechanism. Finally, we find that dot size and total stimulus area directly affect perceived numerosity, which makes it difficult to draw reliable conclusions about grouping effects induced by spatial clustering and dot size. Our results provide new insights into biases in numerosity estimation and they demonstrate that the use of LDDs is an effective method to study the human number sense under prolonged viewing.



2021 ◽  
pp. 1-19
Author(s):  
Álvaro Darriba ◽  
Sandrien Van Ommen ◽  
Yi-Fang Hsu ◽  
Florian Waszak

Abstract Humans live in a volatile environment, subject to changes occurring at different timescales. The ability to adjust internal predictions accordingly is critical for perception and action. We studied this ability with two EEG experiments in which participants were presented with sequences of four Gabor patches, simulating a rotation, and instructed to respond to the last stimulus (target) to indicate whether or not it continued the direction of the first three stimuli. Each experiment included a short-term learning phase in which the probabilities of these two options were very different (p = .2 vs. p = .8, Rules A and B, respectively), followed by a neutral test phase in which both probabilities were equal. In addition, in one of the experiments, prior to the short-term phase, participants performed a much longer long-term learning phase where the relative probabilities of the rules predicting targets were opposite to those of the short-term phase. Analyses of the RTs and P3 amplitudes showed that, in the neutral test phase, participants initially predicted targets according to the probabilities learned in the short-term phase. However, whereas participants not pre-exposed to the long-term learning phase gradually adjusted their predictions to the neutral probabilities, for those who performed the long-term phase, the short-term associations were spontaneously replaced by those learned in that phase. This indicates that the long-term associations remained intact whereas the short-term associations were learned, transiently used, and abandoned when the context changed. The spontaneous recovery suggests independent storage and control of long-term and short-term associations.



2001 ◽  
Vol 24 (5) ◽  
pp. 906-907
Author(s):  
Stefan Vogt ◽  
Heiko Hecht

We share the authors' general approach to the study of perception and action, but rather than singling out a particular level of “late perceptual” and “early motor” processing for sensorimotor interactions, we argue that these can arise at multiple levels during action preparation and execution. Recent data on action-perception transfer are used to illustrate this perspective.



Author(s):  
Ian G. Colditz

The relationship of the animal with its environment has been of longstanding interest in philosophy and science. Here I provide a brief introduction to concepts that place an emphasis on mutualism as the basis of organism - environment interaction, in contrast to the long standing view that the environment exerts an instrumental role in shaping the organism. Two influential theories have been von Uexküll’s theory of umwelt and Gibson’s theory of affordances. The former envisioned the animal as immersed in its surroundings (umwelt) to form a functional unit. In a similar manner, the latter theory describes a unity between 1) environmental information that provides the animal with opportunities for action (affordances) and 2) the ability of the animal to perceive and engage with those affordances. These views have influenced more recent ecological models of the organism as the functional unit of biology and have also influenced models of immune function. In ecological models, agency is seen as the ability of the organism to predict and control its engagement with the environment in order to maintain its integrity. The predominant contemporary model of neural function in which perception and action are understood to operate through Bayes-like active inference complements the concept of agency as proposed by the mutualism models. However, it is suggested that rather than a constant mutualism, encounters between organism and environment range over a dynamic spectrum from dualism to mutualism. It is also suggested that along this spectrum, agency emerges when the balance of instrumentality shifts from the environment to the organism, and that the balance of this relationship can further progress towards a felicitous mutualism. Meaning emerges between environmental information and an agent as opportunity for action. Implications for opportunities to foster agency in animals within our care is noted.



Author(s):  
R. R. Dils ◽  
P. S. Follansbee

Electric fields have been applied across oxides growing on a high temperature alloy and control of the oxidation of the material has been demonstrated. At present, three-fold increases in the oxidation rate have been measured in accelerating fields and the oxidation process has been completely stopped in a retarding field.The experiments have been conducted with an iron-base alloy, Pe 25Cr 5A1 0.1Y, although, in principle, any alloy capable of forming an adherent aluminum oxide layer during oxidation can be used. A specimen is polished and oxidized to produce a thin, uniform insulating layer on one surface. Three platinum electrodes are sputtered on the oxide surface and the specimen is reoxidized.



Author(s):  
D. M. DePace

The majority of blood vessels in the superior cervical ganglion possess a continuous endothelium with tight junctions. These same features have been associated with the blood brain barrier of the central nervous system and peripheral nerves. These vessels may perform a barrier function between the capillary circulation and the superior cervical ganglion. The permeability of the blood vessels in the superior cervical ganglion of the rat was tested by intravenous injection of horseradish peroxidase (HRP). Three experimental groups of four animals each were given intravenous HRP (Sigma Type II) in a dosage of.08 to.15 mg/gm body weight in.5 ml of.85% saline. The animals were sacrificed at five, ten or 15 minutes following administration of the tracer. Superior cervical ganglia were quickly removed and fixed by immersion in 2.5% glutaraldehyde in Sorenson's.1M phosphate buffer, pH 7.4. Three control animals received,5ml of saline without HRP. These were sacrificed on the same time schedule. Tissues from experimental and control animals were reacted for peroxidase activity and then processed for routine transmission electron microscopy.



Author(s):  
G. Mazzocchi ◽  
P. Rebuffat ◽  
C. Robba ◽  
P. Vassanelli ◽  
G. G. Nussdorfer

It is well known that the rat adrenal zona glomerulosa steroidogenic activity is controlled by the renin-angiotensin system. The ultrastructural changes in the rat zona glomerulosa cells induced by renovascular hypertension were described previously, but as far as we are aware no correlated biochemical and morphometric investigations were performed.Twenty adult male albino rats were divided into 2 experimental groups. One group was subjected to restriction of blood flow to the left kidney by the application of a silver clip about the left renal artery. The other group was sham-operated and served as a control. Renovascular hypertension developed in about 10 days: sistolic blood pressure averaged 165 ± 6. 4 mmHg, whereas it was about 110 ± 3. 8 mmHg in the control animals. The hypertensive and control rats were sacrificed 20 days after the operation. The blood was collected and plasma renin activity was determined by radioimmunological methods. The aldosterone concentration was radioimmunologically assayed both in the plasma and in the homogenate of the left capsular adrenal gland.



Author(s):  
Henry I. Smith ◽  
D.C. Flanders

Scanning electron beam lithography has been used for a number of years to write submicrometer linewidth patterns in radiation sensitive films (resist films) on substrates. On semi-infinite substrates, electron backscattering severely limits the exposure latitude and control of cross-sectional profile for patterns having fundamental spatial frequencies below about 4000 Å(l),Recently, STEM'S have been used to write patterns with linewidths below 100 Å. To avoid the detrimental effects of electron backscattering however, the substrates had to be carbon foils about 100 Å thick (2,3). X-ray lithography using the very soft radiation in the range 10 - 50 Å avoids the problem of backscattering and thus permits one to replicate on semi-infinite substrates patterns with linewidths of the order of 1000 Å and less, and in addition provides means for controlling cross-sectional profiles. X-radiation in the range 4-10 Å on the other hand is appropriate for replicating patterns in the linewidth range above about 3000 Å, and thus is most appropriate for microelectronic applications (4 - 6).



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