scholarly journals A Thermodynamic Model of Mesoscale Neural Field Dynamics: Derivation and Linear Analysis

2020 ◽  
Author(s):  
Y. Qin ◽  
A.P. Maurer ◽  
A. Sheremet
Keyword(s):  
Thermodynamic Model ◽  
Refractory Period ◽  
Type Systems ◽  
Gamma Oscillations ◽  
Linear Analysis ◽  
Oscillatory Behavior ◽  
Single Type ◽  
Activity Levels ◽  
State Variables ◽  
Refractory State

ABSTRACTMotivated by previous research suggesting that mesoscopic collective activity has the defining characteristics of a turbulent system, we postulate a thermodynamic model based on the fundamental assumption that the activity of a neuron is characterized by two distinct stages: a sub-threshold stage, described by the value of mean membrane potential, and a transitional stage, corresponding to the firing event. We therefore distinguish between two types of energy: the potential energy released during a spike, and the internal kinetic energy that triggers a spike. Formalizing these assumptions produces a system of integro-differential equations that generalizes existing models [Wilson and Cowan, 1973, Amari, 1977], with the advantage of providing explicit equations for the evolution of state variables. The linear analysis of the system shows that it supports single- or triple-point equilibria, with the refractoriness property playing a crucial role in the generation of oscillatory behavior. In single-type (excitatory) systems this derives from the natural refractory state of a neuron, producing “refractory oscillations” with periods on the order of the neuron refractory period. In dual-type systems, the inhibitory component can provide this functionality even if neuron refractory period is ignored, supporting mesoscopic-scale oscillations at much lower activity levels. Assuming that the model has any relevance for the interpretation of LFP measurements, it provides insight into mesocale dynamics. As an external forcing, theta may play a major role in modulating key parameters of the system: internal energy and excitability (refractoriness) levels, and thus in maintaining equilibrium states, and providing the increased activity necessary to sustain mesoscopic collective action. Linear analysis suggest that gamma oscillations are associated with the theta trough because it corresponds to higher levels of forced activity that decreases the stability of the equilibrium state, facilitating mesoscopic oscillations.

scholarly journals A Novel Two-Zone Thermodynamic Model for Spark-Ignition Engines Based on an Idealized Thermodynamic Process

Energies ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3801
Author(s):  
Yuanfeng Wang
Keyword(s):  
Thermodynamic Model ◽  
Spark Ignition ◽  
Zone Model ◽  
Spark Ignition Engines ◽  
The Novel ◽  
State Variables ◽  
Algebraic Equations ◽  
Thermodynamic Process ◽  
Governing Equations ◽  
Computationally Intensive

The thermodynamic model is a valuable simulation tool for developing combustion engines. The most widely applied thermodynamic models of spark-ignition engines are the single-zone model and the two-zone model. Compared to the single-zone model, the two-zone model offers more detailed in-cylinder thermodynamic conditions, but its governing equations are numerically stiffer, therefore it is restricted when applied in computationally intensive scenarios. To reduce the two-zone model’s stiffness, this paper isolates an idealized thermodynamic process in the unburned zone and describes this idealized thermodynamic process by an algebraic equation. Assisted with this idealized thermodynamic process, this paper builds a novel two-zone model for spark-ignition engines, whose governing equations are simplified to a set of two ordinary differential equations accompanied by a set of three algebraic equations. Benchmarked against the single-zone model and conventional two-zone model, the novel two-zone model is formed and validated by experimental results, and its stiffness is quantitatively evaluated by linearizing its governing equations at simulation steps. The results show that the novel two-zone model inherits the conventional two-zone model’s ability to estimate both zones’ state variables highly accurately while its simplified structure reduces its stiffness down to the level of the single-zone model, accelerating the computation speed.

OBSERVATION OF NONLINEAR VERTICUM-TYPE SYSTEMS APPLIED TO ECOLOGICAL MONITORING

2012 ◽  
Vol 05 (06) ◽  
pp. 1250051 ◽  
Author(s):  
S. MOLNÁR ◽  
M. GÁMEZ ◽  
I. LÓPEZ
Keyword(s):  
Design Method ◽  
Type System ◽  
Type Systems ◽  
Ecological Monitoring ◽  
Observer Design ◽  
Observation System ◽  
State Variables ◽  
Rank Condition ◽  
Decomposition Approach ◽  
Observation Systems

In this paper the concept of a nonlinear verticum-type observation system is introduced. These systems are composed from several "subsystems" connected sequentially in a particular way: a part of the state variables of each "subsystem" also appears in the next "subsystem" as an "exogenous variable" which can also be interpreted as a control generated by an "exosystem". Therefore, these "subsystems" are not observation systems, but formally can be considered as control-observation systems. The problem of observability of such systems can be reduced to rank conditions on the "subsystems". Indeed, under the condition of Lyapunov stability of an equilibrium of the "large", verticum-type system, it is shown that the Kalman rank condition on the linearization of the "subsystems" implies the observability of the original, nonlinear verticum-type system. For an illustration of the above linearization result, a stage-structured fishery model with reserve area is considered. Observability for this system is obtained by applying the above linearization and decomposition approach. Furthermore, it is also shown that, applying an appropriate observer design method to each subsystem, from the observation of the biomass densities of the adult (harvested) stage, in both areas, the biomass densities of the pre-recruit stage can be efficiently estimated.

Delay Differential Equations in the Dynamics of Gene Copying

2007 ◽  
Author(s):  
Anael Verdugo ◽  
Richard H. Rand
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Messenger Rna ◽  
Critical Time ◽  
Linear Analysis ◽  
State Variables ◽  
State Dependent ◽  
Delay Differential ◽  
Approximate Expressions ◽  
Biological Literature

We analyze a model of gene transcription and protein synthesis which has been previously presented in the biological literature. The model takes the form of an ODE (ordinary differential equation) coupled to a DDE (delay differential equation), the state variables being concentrations of messenger RNA and protein. The delay is assumed to depend on the concentration of mRNA and is therefore state-dependent. Linear analysis gives a critical time delay beyond which a periodic motion is born in a Hopf bifurcation. Lindstedt’s method is applied to the nonlinear system, resulting in closed form approximate expressions for the amplitude and frequency of oscillation.

Mechanisms underlying pattern generation in lobster stomatogastric ganglion as determined by selective inactivation of identified neurons. IV. Network properties of pyloric system

1982 ◽  
Vol 48 (6) ◽  
pp. 1416-1432 ◽  
Author(s):  
J. P. Miller ◽  
A. I. Selverston
Keyword(s):  
Motor Pattern ◽  
Neuronal Cell ◽  
Rhythmic Activity ◽  
Stomatogastric Ganglion ◽  
Oscillatory Behavior ◽  
Pattern Generation ◽  
Membrane Properties ◽  
Identified Neurons ◽  
Activity Levels ◽  
Network Properties

1. In three preceding papers in this series (6, 33, 45), the functional roles, intrinsic cellular properties, and synaptic connections of identified neurons in the lobster stomatogastric ganglion were investigated using the dye-sensitized photoinactivation technique. In this paper, we investigate the network properties of the pyloric system. 2. The relative strengths of the synaptic interactions between all possible motor neuron pairs were measured from the neuronal cell bodies. 3. Experiments were performed to determine the minimal subset of the pyloric neurons that could generate rhythmic activity due to network interactions alone. With the endogenously bursting anterior burster (AB) cell excluded from consideration, the minimum number of elements was found to be two. These two elements behaved as a classical "half-center" oscillator when their overall activity levels were appropriately adjusted. 4. Two cells in the commissural ganglia supply the pyloric system with rhythmic excitatory input phase locked to ongoing pyloric activity. The rhythmicity of that input is shown to be functionally irrelevant. The inputs can exert their effects on pyloric system activity through tonic firing. 5. A qualitative explanation of three important aspects of the pyloric motor pattern is presented, based on the intrinsic properties of pyloric neurons and the systematic properties of the network they form. The existence of the pattern results from oscillatory membrane properties of the individual neurons in combination with the multiple reciprocally inhibitory interactions within the network. The phase relationships derive from the synaptic connectivity and depend on relative synaptic strengths, postinhibitory rebound, rebound delay, and the kinetics of the plateau and bursting pacemaker-potential generation mechanisms. The overall pattern frequency is determined by the AB interneuron via its intrinsic oscillatory behavior and strong synapses with the rest of the pyloric neurons.

Modified Extended Thermodynamic Model for Material Damping

1999 ◽  
Author(s):  
Xia Lu ◽  
S. Hanagud
Keyword(s):  
Thermodynamic Model ◽  
Mechanical Energy ◽  
Viscous Damping ◽  
Material Damping ◽  
State Variables ◽  
Longitudinal Vibrations ◽  
Equilibrium Stress ◽  
Classical State ◽  
Extended Thermodynamic ◽  
Non Equilibrium

Abstract During the process of damping of a structure, the mechanical energy is converted to thermal energy. Yet, the most commonly used model for material damping is the linear viscous damping. There are many attempts to develop thermodynamic models for damping. To adequately describe damping, we need more variables than the classical state variables. A simple thermodynamic model that is based on the framework of extended non-equilibrium thermodynamics is presented. Heat flux, non-equilibrium stress field and the associated non-equilibrium internal energy are used as additional variables. Longitudinal vibrations of a uniform rod are studied to present the flexibility of thermodynamic modeling for material damping.

scholarly journals The Refractory Period Matters: Unifying Mechanisms of Macroscopic Brain Waves

2021 ◽  
pp. 1-19
Author(s):  
Corey Weistuch ◽  
Lilianne R. Mujica-Parodi ◽  
Ken Dill
Keyword(s):  
General Model ◽  
Refractory Period ◽  
Mean Field ◽  
Single Type ◽  
Brain Oscillations ◽  
Brain Waves ◽  
Large Populations ◽  
The Relationship

The relationship between complex brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize maximum caliber, a dynamical inference principle, to build a minimal yet general model of the collective (mean field) dynamics of large populations of neurons. In agreement with previous experimental observations, we describe a simple, testable mechanism, involving only a single type of neuron, by which many of these complex oscillatory patterns may emerge. Our model predicts that the refractory period of neurons, which has often been neglected, is essential for these behaviors.

Hope, exploration, and equilibrated action schemes

2019 ◽  
Vol 42 ◽  
Author(s):  
Davood G. Gozli ◽  
Ci Jun Gao
Keyword(s):  
Single Type ◽  
Reward Seeking ◽  
Stable Scheme

AbstractThe concepts want, hope, and exploration cannot be organized in relation to a single type of motive (e.g., motive for food). They require, in addition, the motive for acquiring and maintaining a stable scheme that enables reward-directed activity. Facing unpredictability, the animal has to seek not only reward, but also a new equilibrated state within which reward seeking is possible.

Improvement of cytoprotective and antioxidant activity of Rosa canina L. and Salix alba L. by controlled differential sieving process against H2O2-induced oxidative stress in mouse primary splenocytes

2017 ◽  
Vol 87 (3-4) ◽  
pp. 191-200 ◽  
Author(s):  
Nidhal Soualeh ◽  
Aliçia Stiévenard ◽  
Elie Baudelaire ◽  
Rachid Soulimani ◽  
Jaouad Bouayed
Keyword(s):  
Antioxidant Activity ◽  
Antioxidant Activities ◽  
Biological Activities ◽  
Good Alternative ◽  
Activity Levels ◽  
Salix Alba ◽  
Rosa Canina ◽  
Free Process ◽  
Plant Powders ◽  
Sieving Process

Abstract. In this study, cytoprotective and antioxidant activities of Rosa canina (RC) and Salix alba (SA), medicinal plants, were studied on mouse primary splenocytes by comparing Controlled Differential Sieving process (CDSp), which is a novel green solvent-free process, versus a conventional technique, employing hydroethanolic extraction (HEE). Thus, preventive antioxidant activity of three plant powders of homogeneous particle sizes, 50–100 µm, 100–180 µm and 180–315 µm, dissolved directly in the cellular buffer, were compared to those of hydroethanolic (HE) extract, at 2 concentrations (250 and 500 µg/mL) in H2O2-treated spleen cells. Overall, compared to HE extract, the superfine powders, i. e., fractions < 180 µm, at the lowest concentration, resulted in greater reactive oxygen species (ROS) elimination, increased glutathione peroxidase (GPx) activity and lower malondialdehyde (MDA) production. Better antioxidant and preventive effects in pre-treated cells were found with the superfine powders for SA (i. e., 50–100 µm and 100–180 µm, both p < 0.001), and with the intermediate powder for RC (i. e., 100–180 µm, p < 0.05) versus HE extract. The activity levels of catalase (CAT) and superoxide dismutase (SOD) in pretreated splenocytes exposed to H2O2, albeit reduced, were near to those in unexposed cells, suggesting that pretreatment with the fine powders has relatively restored the normal levels of antioxidant-related enzymes. These findings supported that CDSp improved the biological activities of plants, avoiding the use of organic solvents and thus it could be a good alternative to conventional extraction techniques.

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