scholarly journals A random-matrix theory of the number sense

2018 ◽  
Vol 373 (1740) ◽  
pp. 20170253 ◽  
Author(s):  
T. Hannagan ◽  
A. Nieder ◽  
P. Viswanathan ◽  
S. Dehaene
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Number Sense ◽  
Fine Tuning ◽  
Tuning Curves ◽  
Self Organized ◽  
Human Adults ◽  
Brain States ◽  
Von Mises

Number sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit very similar neurons tuned to specific numerosities. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We introduce a random-matrix theory of self-organized neural states where numbers are coded by vectors of activation across multiple units, and where the vector codes for successive integers are obtained through multiplication by a fixed but random matrix. This cortical implementation of the ‘von Mises' algorithm explains many otherwise disconnected observations ranging from neural tuning curves in monkeys to looking times in neonates and cortical numerotopy in adults. The theory clarifies the origin of Weber–Fechner's Law and yields a novel and empirically validated prediction of multi-peak number neurons. Random matrices constitute a novel mechanism for the emergence of brain states coding for quantity. This article is part of a discussion meeting issue ‘The origins of numerical abilities’.

scholarly journals A random-matrix theory of the number sense

2017 ◽  
Author(s):  
T. Hannagan ◽  
A. Nieder ◽  
P. Viswanathan ◽  
S. Dehaene
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Number Sense ◽  
Fine Tuning ◽  
Tuning Curves ◽  
Human Adults ◽  
Brain States ◽  
Von Mises ◽  
Multiple Units

AbstractNumber sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit number-selective neuronal activity. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We introduce a random matrix theory of self-organised neural states where numbers are coded by vectors of activation across multiple units, and where the vector codes for successive integers are obtained through multiplication by a fixed but random matrix. This cortical implementation of the “von Mises” algorithm explains many otherwise disconnected observations ranging from neural tuning curves in monkeys to looking times in neonates and cortical numerotopy in adults. The theory clarifies the origin of Weber-Fechner’s law and yields a novel and empirically validated prediction of multi-peak number neurons. Random matrices constitute a novel mechanism for the emergence of brain states coding for quantity.

scholarly journals Facial erythema detects diabetic neuropathy using the fusion of machine learning, random matrix theory and self organized criticality

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Esmaeil S. Nadimi ◽  
Tomas Majtner ◽  
Knud B. Yderstraede ◽  
Victoria Blanes-Vidal
Keyword(s):  
Diabetic Neuropathy ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Decay Rates ◽  
Control Group ◽  
Facial Erythema ◽  
Self Organized ◽  
Optimal Ensemble ◽  
Self Organized Criticality

Abstract Rubeosis faciei diabeticorum, caused by microangiopathy and characterized by a chronic facial erythema, is associated with diabetic neuropathy. In clinical practice, facial erythema of patients with diabetes is evaluated based on subjective observations of visible redness, which often goes unnoticed leading to microangiopathic complications. To address this major shortcoming, we designed a contactless, non-invasive diagnostic point-of-care-device (POCD) consisting of a digital camera and a screen. Our solution relies on (1) recording videos of subject’s face (2) applying Eulerian video magnification to videos to reveal important subtle color changes in subject’s skin that fall outside human visual limits (3) obtaining spatio-temporal tensor expression profile of these variations (4) studying empirical spectral density (ESD) function of the largest eigenvalues of the tensors using random matrix theory (5) quantifying ESD functions by modeling the tails and decay rates using power law in systems exhibiting self-organized-criticality and (6) designing an optimal ensemble of learners to classify subjects into those with diabetic neuropathy and those of a control group. By analyzing a short video, we obtained a sensitivity of 100% in detecting subjects diagnosed with diabetic neuropathy. Our POCD paves the way towards the development of an inexpensive home-based solution for early detection of diabetic neuropathy and its associated complications.

SSA, Random Matrix Theory, and Noise-Reduced Correlations

2016 ◽  
Author(s):  
Jan W Dash ◽  
Xipei Yang ◽  
Mario Bondioli ◽  
Harvey J. Stein
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory

History—an overview

2018 ◽  
Author(s):  
Oriol Bohigas ◽  
Hans A. Weidenmüller
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
The Past ◽  
History Of ◽  
And Mathematics

An overview of the history of random matrix theory (RMT) is provided in this chapter. Starting from its inception, the authors sketch the history of RMT until about 1990, focusing their attention on the first four decades of RMT. Later developments are partially covered. In the past 20 years RMT has experienced rapid development and has expanded into a number of areas of physics and mathematics.

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