scholarly journals Geometric Analysis of Population Rhythms in Synaptically Coupled Neuronal Networks

2000 ◽  
Vol 12 (3) ◽  
pp. 597-645 ◽  
Author(s):  
J. Rubin ◽  
D. Terman
Keyword(s):  
Geometric Analysis ◽  
Geometric Approach ◽  
Multiple Roles ◽  
Network Behavior ◽  
Intrinsic Properties ◽  
Coupled Networks ◽  
Ionic Conductances ◽  
Paroxysmal Discharge ◽  
Inhibitory Coupling ◽  
Cortical Inputs

We develop geometric dynamical systems methods to determine how various components contribute to a neuronal network's emergent population behaviors. The results clarify the multiple roles inhibition can play in producing different rhythms. Which rhythms arise depends on how inhibition interacts with intrinsic properties of the neurons; the nature of these interactions depends on the underlying architecture of the network. Our analysis demonstrates that fast inhibitory coupling may lead to synchronized rhythms if either the cells within the network or the architecture of the network is sufficiently complicated. This cannot occur in mutually coupled networks with basic cells; the geometric approach helps explain how additional network complexity allows for synchronized rhythms in the presence of fast inhibitory coupling. The networks and issues considered are motivated by recent models for thalamic oscillations. The analysis helps clarify the roles of various biophysical features, such as fast and slow inhibition, cortical inputs, and ionic conductances, in producing network behavior associated with the spindle sleep rhythm and with paroxysmal discharge rhythms. Transitions between these rhythms are also discussed.

scholarly journals The geometry of masking in neural populations

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Dario L. Ringach
Keyword(s):  
Visual Cortex ◽  
Cortical Neurons ◽  
Dimensional Space ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Population Level ◽  
Contextual Modulation ◽  
Neural Populations ◽  
Early Visual Cortex ◽  
Low Dimensional

Abstract The normalization model provides an elegant account of contextual modulation in individual neurons of primary visual cortex. Understanding the implications of normalization at the population level is hindered by the heterogeneity of cortical neurons, which differ in the composition of their normalization pools and semi-saturation constants. Here we introduce a geometric approach to investigate contextual modulation in neural populations and study how the representation of stimulus orientation is transformed by the presence of a mask. We find that population responses can be embedded in a low-dimensional space and that an affine transform can account for the effects of masking. The geometric analysis further reveals a link between changes in discriminability and bias induced by the mask. We propose the geometric approach can yield new insights into the image processing computations taking place in early visual cortex at the population level while coping with the heterogeneity of single cell behavior.

GEOMETRIC ANALYSIS OF THE KINEMATIC SENSITIVITY OF PLANAR PARALLEL MECHANISMS

2011 ◽  
Vol 35 (4) ◽  
pp. 477-490 ◽  
Author(s):  
Mohammad Hossein Saadatzi ◽  
Mehdi Tale Masouleh ◽  
Hamid D. Taghirad ◽  
Clément Gosselin ◽  
Philippe Cardou
Keyword(s):  
Physical Meaning ◽  
Performance Index ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Sensitivity Index ◽  
Parallel Mechanisms ◽  
Dimensional Synthesis ◽  
Kinematic Sensitivity

The kinematic sensitivity is a unit-consistent measure that has been recently proposed as a mechanism performance index to compare robot architectures. This paper presents a robust geometric approach for computing this index for the case of planar parallel mechanisms. The physical meaning of the kinematic sensitivity is investigated through different combinations of the Euclidean and infinity norms and by means of several illustrative examples. Finally, this paper opens some avenues to the dimensional synthesis of parallel mechanisms by exploring the meaning of the global kinematic sensitivity index.

Optimal linear attitude estimator and its recursive algorithm via geometric analysis

2012 ◽  
Vol 227 (1) ◽  
pp. 100-109
Author(s):  
Deren Gong ◽  
Xiaowei Shao ◽  
Wei Li ◽  
Dengping Duan
Keyword(s):  
Recursive Algorithm ◽  
Single Point ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Sudden Increase ◽  
Unknown Parameters ◽  
Attitude Error ◽  
Special Cases ◽  
Optimal Linear ◽  
Noisy Measurements

A new optimal linear attitude estimator is proposed for single-point attitude estimation using geometric approach, and a recursive optimal linear attitude estimator is developed through filtering noisy measurements. Dot and cross products are taken in order to eliminate the unknown parameters of relationships between measurements and Gibbs vector. The optimality criterion, which does not coincide with Wahba’s constrained criterion, yields linear attitude estimate. A prior rotation is adopted to avoid singularity which occurs when the principal angle is close to π. The recursive algorithm is achieved for the purpose of improving attitude accuracy using all past measurements. For long-term space missions, memory fading concept is introduced into recursive optimal linear attitude estimator. The optimal relative weighting is obtained through minimizing error propagation, and an efficient modification is proposed to significantly reduce the sudden increase of attitude error of recursive optimal linear attitude estimator in special cases. Numerical simulations show that the estimate of optimal linear attitude estimator is almost identical with that of the famous QUaternion ESTimator, and the accuracy provided by recursive optimal linear attitude estimator is over an order magnitude higher than that of optimal linear attitude estimator or QUaternion ESTimator in most cases.

NON-UNIFORM RATIONAL B-SPLINE BASED ISO-GEOMETRIC ANALYSIS FOR A CLASS OF HYDRODYNAMIC PROBLEMS

2021 ◽  
Vol 162 (A2) ◽  
Author(s):  
M Goel ◽  
R Sharma ◽  
S K Bhattacharyya ◽  
Tae-wan Kim
Keyword(s):  
Boundary Value Problems ◽  
Potential Function ◽  
Computational Efficiency ◽  
Boundary Value ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Panel Method ◽  
B Spline ◽  
Computational Performance ◽  
Wide Range

Herein, we present the design and development of a ‘Non-uniform Rational B-spline (NURBS)’ based iso-geometric approach for the analysis of a number of ‘Boundary Value Problems (BVPs)’ relevant in hydrodynamics. We propose a ‘Potential Function’ based ‘Boundary Element Method (BEM)’ and show that it holds the advantage of being computationally efficient over the other known numerical methods for a wide range of external flow problems. The use of NURBS is consistent, as inspired by the ‘iso-geometric analysis’, from geometric formulation for the body surface to the potential function representation to interpolation. The control parameters of NURBS are utilised and they have been explored to arrive at some preferable values and parameters for parameterization and the knot vector selection. Also, the present paper investigates the variational strength panel method, and its computational performance is analyzed in comparison with the constant strength panel method. The two variations have been considered, e.g. linear and quadratic. Finally, to illustrate the effectiveness and efficiency of the proposed NURBS based iso-geometric approach for the analysis of boundary value problems, five different problems (i.e. flow over a sphere, effect of the knot vector selection on analysis, flow over a rectangular wing section of NACA 0012 aerofoil section, performance of DTMB 4119 propeller (un-skewed), performance of DTNSDRC 4382 propeller (skewed)) are considered. The results show that in the absence of predominant viscous effects, a ‘Potential Function’ based BEM with NURBS representation performs well with very good computational efficiency and with less complexity as compared to the results available from the existing approaches and commercial software programs, i.e. low maximum errors close to 110−3 , faster convergence with even up to 75 % reduction in the number of panels and improvements in the computational efficiency up to 32.5 % even with low number of panels.

A feature-geometric approach to verbal inflection in Onondaga

2020 ◽  
pp. 17-38
Author(s):  
Gabriela Alboiu ◽  
Michael Barrie
Keyword(s):  
Geometric Analysis ◽  
Geometric Approach ◽  
Verbal Morphology ◽  
Central Concept ◽  
Verbal Inflection ◽  
Crucial Ingredient ◽  
Generative Approach

Iroquoian inflectional verbal morphology is well-documented in the descriptive literature, but has received less attention from a generative perspective, a fact this chapter sets to remedy. Most generative analyses rely on the notion of tense as a central category and assume a universal projection of a T(ense) Phrase in tensed/finite clauses. Onondaga (Northern Iroquoian), however, typically makes very little use of tense as a grammatical concept, despite the fact that it only allows for finite clauses. Instead, this language capitalizes on the notions of aspect and mood, thereby rendering the standard generative approach inappropriate. Consequently, this chapter argues that a feature geometric analysis, which does not rely on tense as a central concept, is better suited for analysing the Onondaga verbal inflectional domain where it is aspect that serves as the crucial ingredient in activating Infl.

scholarly journals Intrinsic properties of rat striatal output neurones and time‐dependent facilitation of cortical inputs in vivo

2000 ◽  
Vol 527 (2) ◽  
pp. 345-354 ◽  
Author(s):  
Séverine Mahon ◽  
Bruno Delord ◽  
Jean‐Michel Deniau ◽  
Stéphane Charpier
Keyword(s):  
Time Dependent ◽  
Intrinsic Properties ◽  
Cortical Inputs

Non-Uniform Rational B-Spline Based Iso-Geometric Analysis for a Class of Hydrodynamic Problems

2020 ◽  
Vol 162 (A2) ◽  
Author(s):  
M Goel ◽  
R Sharma ◽  
S K Bhattacharyya ◽  
Tae-wan Kim
Keyword(s):  
Boundary Value Problems ◽  
Potential Function ◽  
Computational Efficiency ◽  
Boundary Value ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Panel Method ◽  
B Spline ◽  
Computational Performance ◽  
Wide Range

Herein, we present the design and development of a ‘Non-uniform Rational B-spline (NURBS)’ based iso-geometric approach for the analysis of a number of ‘Boundary Value Problems (BVPs)’ relevant in hydrodynamics. We propose a ‘Potential Function’ based ‘Boundary Element Method (BEM)’ and show that it holds the advantage of being computationally efficient over the other known numerical methods for a wide range of external flow problems. The use of NURBS is consistent, as inspired by the ‘iso-geometric analysis’, from geometric formulation for the body surface to the potential function representation to interpolation. The control parameters of NURBS are utilised and they have been explored to arrive at some preferable values and parameters for parameterization and the knot vector selection. Also, the present paper investigates the variational strength panel method, and its computational performance is analyzed in comparison with the constant strength panel method. The two variations have been considered, e.g. linear and quadratic. Finally, to illustrate the effectiveness and efficiency of the proposed NURBS based iso-geometric approach for the analysis of boundary value problems, five different problems (i.e. flow over a sphere, effect of the knot vector selection on analysis, flow over a rectangular wing section of NACA 0012 aerofoil section, performance of DTMB 4119 propeller (un-skewed), performance of DTNSDRC 4382 propeller (skewed)) are considered. The results show that in the absence of predominant viscous effects, a ‘Potential Function’ based BEM with NURBS representation performs well with very good computational efficiency and with less complexity as compared to the results available from the existing approaches and commercial software programs, i.e. low maximum errors close to 110−3 , faster convergence with even up to 75 % reduction in the number of panels and improvements in the computational efficiency up to 32.5 % even with low number of panels.

Microchemistry of ZnO Varistors

1992 ◽  
Vol 50 (2) ◽  
pp. 1694-1695
Author(s):  
K. K. Soni ◽  
J. Hwang ◽  
V. P. Dravid ◽  
T. O. Mason ◽  
R. Levi-Setti
Keyword(s):  
Grain Boundaries ◽  
Multiple Roles ◽  
Grain Boundary Engineering ◽  
Ion Microprobe ◽  
Dopant Distribution ◽  
Important Ingredient ◽  
Zno Varistor ◽  
Zno Varistors ◽  
Zno Powder ◽  
The University

ZnO varistors are made by mixing semiconducting ZnO powder with powders of other metal oxides e.g. Bi2O3, Sb2O3, CoO, MnO2, NiO, Cr2O3, SiO2 etc., followed by conventional pressing and sintering. The non-linear I-V characteristics of ZnO varistors result from the unique properties that the grain boundaries acquire as a result of dopant distribution. Each dopant plays important and sometimes multiple roles in improving the properties. However, the chemical nature of interfaces in this material is formidable mainly because often trace amounts of dopants are involved. A knowledge of the interface microchemistry is an essential component in the ‘grain boundary engineering’ of materials. The most important ingredient in this varistor is Bi2O3 which envelopes the ZnO grains and imparts high resistance to the grain boundaries. The solubility of Bi in ZnO is very small but has not been experimentally determined as a function of temperature.In this study, the dopant distribution in a commercial ZnO varistor was characterized by a scanning ion microprobe (SIM) developed at The University of Chicago (UC) which offers adequate sensitivity and spatial resolution.

Liquid crystalline ordering of paired helical filaments in neurofibrillary tangles of Alzheimer's disease

1986 ◽  
Vol 44 ◽  
pp. 348-349
Author(s):  
D.F. Clapin ◽  
V.J.A. Montpetit
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Neurofibrillary Tangles ◽  
Liquid Crystalline ◽  
Amyloid Fibrils ◽  
Geometric Analysis ◽  
Paired Helical Filaments ◽  
Microscopic Level ◽  
Light Microscopic Level ◽  
Regular Spacing

Alzheimer's disease is characterized by the accumulation of abnormal filamentous proteins. The most important of these are amyloid fibrils and paired helical filaments (PHF). PHF are located intraneuronally forming bundles called neurofibrillary tangles. The designation of these structures as "tangles" is appropriate at the light microscopic level. However, localized domains within individual tangles appear to demonstrate a regular spacing which may indicate a liquid crystalline phase. The purpose of this paper is to present a statistical geometric analysis of PHF packing.

A Geometric Approach to Homology Theory

1976 ◽  
Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson
Keyword(s):  
Geometric Approach ◽  
Homology Theory
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