scholarly journals Developmental and evolutionary constraints on olfactory circuit selection

2020 ◽  
Author(s):  
Naoki Hiratani ◽  
Peter E. Latham
Keyword(s):  
Intermediate Layer ◽  
Olfactory System ◽  
Scaling Laws ◽  
Scaling Law ◽  
Piriform Cortex ◽  
Brain Circuits ◽  
Evolutionarily Conserved ◽  
Efficient Learning ◽  
Gradient Learning ◽  
Optimality Principles

Across species, neural circuits show remarkable regularity, suggesting that their structure has been driven by underlying optimality principles. Here, we ask whether we can predict the neural circuitry of diverse species by optimizing the neural architecture to make learning as efficient as possible. We focus on the olfactory system, primarily because it has a relatively simple evolutionarily conserved structure, and because its input and intermediate layer sizes exhibits a tight allometric scaling. In mammals, it has been shown that the number of neurons in layer 2 of piriform cortex scales as the number of glomeruli (the input units) to the 3/2 power; in invertebrates, we show that the number of mushroom body Kenyon cells scales as the number of glomeruli to the 7/2 power. To understand these scaling laws, we model the olfactory system as a three layered nonlinear neural network, and analytically optimize the intermediate layer size for efficient learning from a limited number of samples. We find that the 3/2 scaling observed in mammals emerges naturally, both in full batch optimization and under stochastic gradient learning. We extended the framework to the case where a fraction of the olfactory circuit is genetically specified, not learned. We show numerically that this makes the scaling law steeper when the number of glomeruli is small, and we are able to recover the 7/2 scaling law observed in invertebrates. This study paves the way for a deeper understanding of the organization of brain circuits from an evolutionary perspective.

scholarly journals Asymmetric Unimodal Maps with Non-universal Period-Doubling Scaling Laws

2020 ◽  
Vol 379 (1) ◽  
pp. 103-143
Author(s):  
Oleg Kozlovski ◽  
Sebastian van Strien
Keyword(s):  
Scaling Laws ◽  
Scaling Law ◽  
Period Doubling ◽  
Cantor Sets ◽  
Unimodal Maps ◽  
Renormalization Theory

Abstract We consider a family of strongly-asymmetric unimodal maps $$\{f_t\}_{t\in [0,1]}$$ { f t } t ∈ [ 0 , 1 ] of the form $$f_t=t\cdot f$$ f t = t · f where $$f:[0,1]\rightarrow [0,1]$$ f : [ 0 , 1 ] → [ 0 , 1 ] is unimodal, $$f(0)=f(1)=0$$ f ( 0 ) = f ( 1 ) = 0 , $$f(c)=1$$ f ( c ) = 1 is of the form and $$\begin{aligned} f(x)=\left\{ \begin{array}{ll} 1-K_-|x-c|+o(|x-c|)&{} \text{ for } x<c, \\ 1-K_+|x-c|^\beta + o(|x-c|^\beta ) &{} \text{ for } x>c, \end{array}\right. \end{aligned}$$ f ( x ) = 1 - K - | x - c | + o ( | x - c | ) for x < c , 1 - K + | x - c | β + o ( | x - c | β ) for x > c , where we assume that $$\beta >1$$ β > 1 . We show that such a family contains a Feigenbaum–Coullet–Tresser $$2^\infty $$ 2 ∞ map, and develop a renormalization theory for these maps. The scalings of the renormalization intervals of the $$2^\infty $$ 2 ∞ map turn out to be super-exponential and non-universal (i.e. to depend on the map) and the scaling-law is different for odd and even steps of the renormalization. The conjugacy between the attracting Cantor sets of two such maps is smooth if and only if some invariant is satisfied. We also show that the Feigenbaum–Coullet–Tresser map does not have wandering intervals, but surprisingly we were only able to prove this using our rather detailed scaling results.

scholarly journals Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

2018 ◽  
Vol 75 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Khaled Ghannam ◽  
Gabriel G. Katul ◽  
Elie Bou-Zeid ◽  
Tobias Gerken ◽  
Marcelo Chamecki
Keyword(s):  
Scaling Laws ◽  
Velocity Structure ◽  
Scaling Law ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Length Scale ◽  
Near Surface ◽  
Vegetation Canopies ◽  
Velocity Spectra ◽  
Attached Eddies

Abstract The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

scholarly journals Rapid Bayesian learning in the mammalian olfactory system

2019 ◽  
Author(s):  
Naoki Hiratani ◽  
Peter E. Latham
Keyword(s):  
Olfactory System ◽  
Bayesian Learning ◽  
Experimental Studies ◽  
Bayesian Optimization ◽  
Mammalian Brain ◽  
Theoretical Understanding ◽  
Plasticity Mechanism ◽  
Neural Architecture ◽  
Learning Rules ◽  
Efficient Learning

AbstractMany experimental studies suggest that animals can rapidly learn to identify odors and predict the rewards associated with them. However, the underlying plasticity mechanism remains elusive. In particular, it is not clear how olfactory circuits achieve rapid, data efficient learning with local synaptic plasticity. Here, we formulate olfactory learning as a Bayesian optimization process, then map the learning rules into a computational model of the mammalian olfactory circuit. The model is capable of odor identification from a small number of observations, while reproducing cellular plasticity commonly observed during development. We extend the framework to reward-based learning, and show that the circuit is able to rapidly learn odor-reward association with a plausible neural architecture. These results deepen our theoretical understanding of unsupervised learning in the mammalian brain.

Early deficits in olfaction are associated with structural and molecular alterations in the olfactory system of a Huntington disease mouse model

2020 ◽  
Vol 29 (13) ◽  
pp. 2134-2147
Author(s):  
M Laroche ◽  
M Lessard-Beaudoin ◽  
M Garcia-Miralles ◽  
C Kreidy ◽  
E Peachey ◽  
...  
Keyword(s):  
Huntington Disease ◽  
Olfactory System ◽  
Piriform Cortex ◽  
Olfactory Dysfunction ◽  
Altered Expression ◽  
Neuronal Nuclei ◽  
Molecular Alterations ◽  
Cell Death Pathways ◽  
Structural Abnormalities

Abstract Olfactory dysfunction and altered neurogenesis are observed in several neurodegenerative disorders including Huntington disease (HD). These deficits occur early and correlate with a decline in global cognitive performance, depression and structural abnormalities of the olfactory system including the olfactory epithelium, bulb and cortices. However, the role of olfactory system dysfunction in the pathogenesis of HD remains poorly understood and the mechanisms underlying this dysfunction are unknown. We show that deficits in odour identification, discrimination and memory occur in HD individuals. Assessment of the olfactory system in an HD murine model demonstrates structural abnormalities in the olfactory bulb (OB) and piriform cortex, the primary cortical recipient of OB projections. Furthermore, a decrease in piriform neuronal counts and altered expression levels of neuronal nuclei and tyrosine hydroxylase in the OB are observed in the YAC128 HD model. Similar to the human HD condition, olfactory dysfunction is an early phenotype in the YAC128 mice and concurrent with caspase activation in the murine HD OB. These data provide a link between the structural olfactory brain region atrophy and olfactory dysfunction in HD and suggest that cell proliferation and cell death pathways are compromised and may contribute to the olfactory deficits in HD.

scholarly journals Origin of the scaling laws of sediment transport

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160785 ◽  
Author(s):  
Sk Zeeshan Ali ◽  
Subhasish Dey
Keyword(s):  
Sediment Transport ◽  
Froude Number ◽  
Scaling Laws ◽  
Scaling Law ◽  
Bedload Transport ◽  
Inertial Range ◽  
Channel Width ◽  
Densimetric Froude Number ◽  
Relative Roughness ◽  
Contraction Ratio

In this paper, we discover the origin of the scaling laws of sediment transport under turbulent flow over a sediment bed, for the first time, from the perspective of the phenomenological theory of turbulence. The results reveal that for the incipient motion of sediment particles, the densimetric Froude number obeys the ‘(1 +  σ )/4’ scaling law with the relative roughness (ratio of particle diameter to approach flow depth), where σ is the spectral exponent of turbulent energy spectrum. However, for the bedforms, the densimetric Froude number obeys a ‘(1 +  σ )/6’ scaling law with the relative roughness in the enstrophy inertial range and the energy inertial range. For the bedload flux, the bedload transport intensity obeys the ‘3/2’ and ‘(1 +  σ )/4’ scaling laws with the transport stage parameter and the relative roughness, respectively. For the suspended load flux, the non-dimensional suspended sediment concentration obeys the ‘ − Z ’ scaling law with the non-dimensional vertical distance within the wall shear layer, where Z is the Rouse number. For the scour in contracted streams, the non-dimensional scour depth obeys the ‘4/(3 −  σ )’, ‘−4/(3 −  σ )’ and ‘−(1 +  σ )/(3 −  σ )’ scaling laws with the densimetric Froude number, the channel contraction ratio (ratio of contracted channel width to approach channel width) and the relative roughness, respectively.

scholarly journals Scaling laws and warning signs for bifurcations of SPDEs

2018 ◽  
Vol 30 (5) ◽  
pp. 853-868
Author(s):  
CHRISTIAN KUEHN ◽  
FRANCESCO ROMANO
Keyword(s):  
Differential Equations ◽  
Scaling Laws ◽  
Scaling Law ◽  
Warning Signs ◽  
Covariance Operator ◽  
Large Classes ◽  
Practical Applications ◽  
Critical Transitions ◽  
Degenerate Eigenvalues ◽  
Adjoint Operators

Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated with systems, which drift slowly towards a bifurcation point. In the context of stochastic ordinary differential equations, there are results on growth of variance and autocorrelation before a transition, which can be used as possible warning signs in applications. A similar theory has recently been developed in the simplest setting for stochastic partial differential equations (SPDEs) for self-adjoint operators in the drift term. This setting leads to real discrete spectrum and growth of the covariance operator via a certain scaling law. In this paper, we develop this theory substantially further. We cover the cases of complex eigenvalues, degenerate eigenvalues as well as continuous spectrum. This provides a fairly comprehensive theory for most practical applications of warning signs for SPDE bifurcations.

Scaling Laws From Statistical Data and Dimensional Analysis

2004 ◽  
Vol 72 (5) ◽  
pp. 648-657 ◽  
Author(s):  
Patricio F. Mendez ◽  
Fernando Ordóñez
Keyword(s):  
Dimensional Analysis ◽  
Scaling Laws ◽  
Ad Hoc ◽  
Scaling Law ◽  
Engineering Systems ◽  
User Input ◽  
Backward Elimination ◽  
Dimensionless Groups ◽  
Complex Engineering ◽  
Complex Engineering Systems

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad hoc, tedious, and time consuming. Here, we present an algorithm that obtains a scaling law in the form of a power law from experimental data (including simulated experiments). The proposed algorithm integrates dimensional analysis into the backward elimination procedure of multivariate linear regressions. In addition to the scaling laws, the algorithm returns a set of dimensionless groups ranked by relevance. We apply the algorithm to three examples, in each obtaining the scaling law that describes the system with minimal user input.

Determination method of dynamic distorted scaling laws and applicable structure size intervals of a rotating thin-wall short cylindrical shell

2014 ◽  
Vol 229 (5) ◽  
pp. 806-817 ◽  
Author(s):  
Z Luo ◽  
YP Zhu ◽  
XY Zhao ◽  
DY Wang
Keyword(s):  
Cylindrical Shell ◽  
Scaling Laws ◽  
Good Accuracy ◽  
Scaling Law ◽  
Thin Wall ◽  
Determination Method ◽  
Governing Equations ◽  
7050 Aluminum Alloy ◽  
Boundary Functions

This study investigates the applicability of distortion models for predicting dynamic characteristics of a rotating thin-wall short cylindrical shell. The significance of this study is that it provides a necessary scaling law, applicable structure size intervals, and its boundary functions, which can guide the design of distortion models. Sensitivity analysis and governing equations are employed to establish the scaling law between the model and the prototype. Then a commonly used 7050 aluminum alloy cylindrical shell is analyzed as a prototype. The determination of applicable structure size intervals is discussed, and the boundary functions of the applicable structure size intervals are investigated. The applicability of the scaling law and the applicable intervals of rotating thin-wall short cylindrical shell are verified numerically. The results indicate that distortion models that satisfy the structure size applicable intervals can predict the characteristics of the prototype with good accuracy.

Effect of finite sampling time on estimation of Brownian fluctuation

2015 ◽  
Vol 767 ◽  
pp. 65-84 ◽  
Author(s):  
Shahram Pouya ◽  
Di Liu ◽  
Manoochehr M. Koochesfahani
Keyword(s):  
Diffusion Coefficient ◽  
Scaling Laws ◽  
Solid Wall ◽  
Exact Analytical Solution ◽  
Scaling Law ◽  
Time Interval ◽  
Free Diffusion ◽  
Mean Velocity ◽  
Hindered Diffusion ◽  
Near Wall

AbstractWe present a study of the effect of finite detector integration/exposure time $E$, in relation to interrogation time interval ${\rm\Delta}t$, on analysis of Brownian motion of small particles using numerical simulation of the Langevin equation for both free diffusion and hindered diffusion near a solid wall. The simulation result for free diffusion recovers the known scaling law for the dependence of estimated diffusion coefficient on $E/{\rm\Delta}t$, i.e. for $0\leqslant E/{\rm\Delta}t\leqslant 1$ the estimated diffusion coefficient scales linearly as $1-(E/{\rm\Delta}t)/3$. Extending the analysis to the parameter range $E/{\rm\Delta}t\geqslant 1$, we find a new nonlinear scaling behaviour given by $(E/{\rm\Delta}t)^{-1}[1-((E/{\rm\Delta}t)^{-1})/3]$, for which we also provide an exact analytical solution. The simulation of near-wall diffusion shows that hindered diffusion of particles parallel to a solid wall, when normalized appropriately, follows with a high degree of accuracy the same form of scaling laws given above for free diffusion. Specifically, the scaling laws in this case are well represented by $1-((1+{\it\epsilon})(E/{\rm\Delta}t))/3$, for $E/{\rm\Delta}t\leqslant 1$, and $(E/{\rm\Delta}t)^{-1}[1-((1+{\it\epsilon})(E/{\rm\Delta}t)^{-1})/3]$, for $E/{\rm\Delta}t\geqslant 1$, where the small parameter ${\it\epsilon}$ depends on the size of the near-wall domain used in the estimation of the diffusion coefficient and value of $E$. For the range of parameters reported in the literature, we estimate ${\it\epsilon}<0.03$. The near-wall simulations also show a bias in the estimated diffusion coefficient parallel to the wall even in the limit $E=0$, indicating an overestimation which increases with increasing time delay ${\rm\Delta}t$. This diffusion-induced overestimation is caused by the same underlying mechanism responsible for the previously reported overestimation of mean velocity in near-wall velocimetry.

scholarly journals Scaling laws for pressure, temperature, and ionization with two-temperature equation-of-state effects in laser-produced plasmas

1992 ◽  
Vol 10 (1) ◽  
pp. 23-40 ◽  
Author(s):  
H. Szichman ◽  
S. Eliezer
Keyword(s):  
Equation Of State ◽  
Scaling Laws ◽  
Interpolation Method ◽  
Scaling Law ◽  
Plasma Medium ◽  
Degree Of Ionization ◽  
Ablation Pressure ◽  
Two Temperature ◽  
Temperature Equation ◽  
Thermal Conductivities

A two-temperature equation of state (EOS) for a plasma medium was developed. The cold-electron temperature is taken from semiempirical calculations, while the thermal contribution of the electrons is calculated from the Thomas–Fermi–Dirac model. The ion EOS is obtained by the Gruneisen–Debye solid–gas interpolation method. These EOS are well behaved and are smoothed over the whole temperature and density regions, so that the thermodynamical derivatives are also well behaved. Moreover, these EOS were used to calculate the average ionization 〈Z〉 and 〈Z2〉 of the plasma medium. Furthermore, the thermal conductivities have been calculated with the use of an extrapolation between the conductivities in the solid and plasma (Spitzer) states. The two-temperature EOS, the average ionization 〈Z〉 and 〈Z2〉, and the thermal conductivities for electrons and ions were introduced into a two-fluid hydrodynamic code to calculate the laser-plasma interaction in carbon, aluminum, copper, and gold slab targets. It was found that the two EOS are important mainly from the ablation surface outward (toward the laser). In particular, the creation of cavitons in the distribution of the electrons is predicted here, especially for light materials such as aluminum. These studies enable us also to establish that the commonly used exponential scaling laws of the type Pa = A[I/(1014 W/cm2)]α for the ablation pressure and similar laws for the temperature are valid only for absorbed laser intensities in the range 3 × 1012-3 × 1014 W/cm2, while the degree of ionization (at the corona) follows a quite different scaling law. We also found that the parameters A and α. in the above expression are dependent on material, laser wavelength, and pulse shape. Thus we determined for the ablation pressure, using a trapezoidal Nd laser pulse, that α varies between 0.78 and 0.84 and that A varies between 14 and 8 Mbar for 6 ≤ Z ≤ 79. Beyond the range of validity the scaling laws may give values at least twice as large as those obtained by the simulation.

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