scholarly journals Demonstration of electron focusing using electronic lenses in low-dimensional system

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Chengyu Yan ◽  
Michael Pepper ◽  
Patrick See ◽  
Ian Farrer ◽  
David Ritchie ◽  
...  
Keyword(s):  
Dimensional System ◽  
Low Dimensional ◽  
Electron Focusing

scholarly journals Evidence accumulation and change rate inference in dynamic environments

2016 ◽  
Author(s):  
Adrian E Radillo ◽  
Alan Veliz-Cuba ◽  
Kresimir Josic ◽  
Zachary Kilpatrick
Keyword(s):  
Rate Of Change ◽  
Ideal Observer ◽  
Moment Closure ◽  
Dimensional System ◽  
Change Rate ◽  
Observer Model ◽  
Low Dimensional ◽  
State Of The Environment ◽  
Rate Correlation ◽  
Moment Closure Approximation

In a constantly changing world, animals must account for environmental volatility when making decisions. To appropriately discount older, irrelevant information, they need to learn the rate at which the environment changes. We develop an ideal observer model capable of inferring the present state of the environment along with its rate of change. Key to this computation is updating the posterior probability of all possible changepoint counts. This computation can be challenging, as the number of possibilities grows rapidly with time. However, we show how the computations can be simplified in the continuum limit by a moment closure approximation. The resulting low-dimensional system can be used to infer the environmental state and change rate with accuracy comparable to the ideal observer. The approximate computations can be performed by a neural network model via a rate-correlation based plasticity rule. We thus show how optimal observers accumulates evidence in changing environments, and map this computation to reduced models which perform inference using plausible neural mechanisms.

Non-Standard Reduction of Noisy Structural Systems: Shallow Arches

2000 ◽  
Author(s):  
Lalit Vedula ◽  
N. Sri Namachchivaya
Keyword(s):  
Markov Process ◽  
Random Perturbation ◽  
Exit Time ◽  
Stochastic Averaging ◽  
Dimensional System ◽  
Shallow Arches ◽  
Higher Dimensional ◽  
Mean Exit Time ◽  
Stationary Probability Density Function ◽  
Low Dimensional

Abstract The dynamics of a shallow arch subjected to small random external and parametric excitation is invegistated in this work. We develop rigorous methods to replace, in some limiting regime, the original higher dimensional system of equations by a simpler, constructive and rational approximation – a low-dimensional model of the dynamical system. To this end, we study the equations as a random perturbation of a two-dimensional Hamiltonian system. We achieve the model-reduction through stochastic averaging and the reduced Markov process takes its values on a graph with certain glueing conditions at the vertex of the graph. Examination of the reduced Markov process on the graph yields many important results such as mean exit time, stationary probability density function.

scholarly journals Observable for a Large System of Globally Coupled Excitable Units

2019 ◽  
Vol 24 (2) ◽  
pp. 37 ◽  
Author(s):  
Santiago Boari ◽  
Gonzalo Uribarri ◽  
Ana Amador ◽  
Gabriel Mindlin
Keyword(s):  
Order Parameter ◽  
Field Potential ◽  
Dimensional System ◽  
System Of Equations ◽  
In Vivo Electrophysiology ◽  
Excitable Systems ◽  
Global Variable ◽  
Good Proxy ◽  
Low Dimensional

The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system’s order parameter. In this work, we show how to explicitly introduce a variable describing the global synaptic activation of the network into these family of models. This global variable is built by adding realistic synaptic time traces. We propose that this variable can, under certain conditions, be a good proxy for the local field potential of the network. We report experimental, in vivo, electrophysiology data supporting this claim.

Hopf Bifurcation Analysis and Stability for a Ratio-Dependent Predator–Prey Diffusive System with Time Delay

2020 ◽  
Vol 30 (03) ◽  
pp. 2050037
Author(s):  
Longyue Li ◽  
Yingying Mei ◽  
Jianzhi Cao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Periodic Solutions ◽  
Positive Equilibrium ◽  
Dimensional System ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Ratio Dependent ◽  
Low Dimensional

In this paper, we are focused on a new ratio-dependent predator–prey system that introduced the diffusive and time delay effect simultaneously. By analyzing the characteristic equations and the distribution of eigenvalues, we examine the stability and boundary of positive equilibrium states, and the existence of spatially homogeneous and spatially inhomogeneous bifurcating periodic solutions, respectively. Further, we prove that when [Formula: see text], the system has Hopf bifurcation at the positive equilibrium state. By using the center manifold reduction, we simplify the system so that we can convert an infinite-dimensional system into a low-dimensional finite-dimensional system. By using the normal form theory, we obtain explicit expressions for the direction, stability and period of Hopf bifurcation periodic solutions. Finally, we have illustrated the main results in this thesis by numerical examples, our work may provide some useful measures to save time or cost and to control the ecosystem.

THERMOELECTRIC POWER COEFFICIENT IN A QUANTUM WELL

2002 ◽  
Vol 09 (05n06) ◽  
pp. 1765-1768 ◽  
Author(s):  
B. A. PAEZ ◽  
H. MÉNDEZ ◽  
J. C. GIRALDO
Keyword(s):  
Boltzmann Equation ◽  
Quantum Well ◽  
Variational Methods ◽  
Thermoelectric Power ◽  
Computer Code ◽  
Power Coefficient ◽  
Dimensional System ◽  
Scattering Mechanism ◽  
Transport Approximation ◽  
Low Dimensional

Based on the solution of the quantum Boltzmann equation, in the linear transport approximation for an isotropic low-dimensional system, the thermoelectric power coefficient, Q, in a quantum well structure was determined. These calculations are based on variational methods, taking into account especial functions which include important parameters being varied at the time of evaluating the thermoelectric power, e.g. height and width barrier. Values of Q are carried out by using a computer code written in Mathematica, which allows one to depict them easily and in this way to compare different behaviors of Q against temperature according to the scattering mechanism (phonons).

AN ANALYTICAL FRAMEWORK FOR MODELING EVOKED AND EVENT-RELATED POTENTIALS

2004 ◽  
Vol 14 (02) ◽  
pp. 653-666 ◽  
Author(s):  
AXEL HUTT
Keyword(s):  
Auditory Evoked Potentials ◽  
Event Related Potentials ◽  
Analytical Framework ◽  
Multidimensional Data ◽  
Dimensional System ◽  
Segmentation Method ◽  
Neuronal Dynamics ◽  
Related Potentials ◽  
Low Dimensional ◽  
Number Of Segments

The present work reviews briefly a segmentation method and a modeling approach for multivariate quasi-stationary data. The combination of both parts allows the extraction of low-dimensional models from multidimensional data. The segmentation method is applied to event-related potentials and fields and early auditory evoked potentials and extracts ERP- and ERF-components and early auditory waves objectively and independent from the number of segments. Additionally, the early auditory wave Pa is modeled by a two-dimensional system of ordinary differential equations. We find a common topology of wave Pa, which lets us conjecture intrinsic low-dimensional underlying attractors in the corresponding neuronal dynamics.

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