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جلسه چهارم معادلات دیفرانسیل و سامانه های پویا
Geometric Interpretation (the qualitative theory of) of Dynamical Systems
Phase Portrait
Terminology: Fixed point, Steady State, Equilibrium
Terminology: Nullcline
Fixed points and stability
Linear Stability Analysis
Terminology: Vector fields - Trajectories
A quick guide to sketching phase planes and qualitative Analysis
Classification of Phase Portraits
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Geometric Interpretation (the qualitative theory of) of Dynamical Systems
Phase Portrait
Terminology: Fixed point, Steady State, Equilibrium
Terminology: Nullcline
Fixed points and stability
Linear Stability Analysis
Terminology: Vector fields - Trajectories
A quick guide to sketching phase planes and qualitative Analysis
Classification of Phase Portraits
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Differential Equations 3.pdf
3.7 MB
جلسه چهارم معادلات دیفرانسیل و سامانه های پویا
Geometric Interpretation (the qualitative theory of) of Dynamical Systems
Phase Portrait
Terminology: Fixed point, Steady State, Equilibrium
Terminology: Nullcline
Fixed points and stability
Linear Stability Analysis
Terminology: Vector fields - Trajectories
A quick guide to sketching phase planes and qualitative Analysis
Classification of Phase Portraits
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Geometric Interpretation (the qualitative theory of) of Dynamical Systems
Phase Portrait
Terminology: Fixed point, Steady State, Equilibrium
Terminology: Nullcline
Fixed points and stability
Linear Stability Analysis
Terminology: Vector fields - Trajectories
A quick guide to sketching phase planes and qualitative Analysis
Classification of Phase Portraits
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
درود، میخوام یک بازی فکری-پژوهشی در کانال راه اندازی کنم. فکر کنید که تعدادی آدم فضایی با امکانات مهندسی بالایی به زمین آمدن و از جمعیت پژوهشگران علوم اعصاب میخوان که بهشون 10 گزاره بنیادی درباره ساختار-عملکرد-دینامیک سیستم عصبی/بدن ارائه بدن تا این آدم فضایی ها بتونن چیزی مشابه سیستم های عصبی ارگانیک بسازن. بیش از 10 گزاره نمیشه به اینها داد.
امروز داشتم قدم میزدم و به این پرسش فکر میکردم که چه 10 گزاره ای به اینها خواهم داد و هنوز درباره انتخاب هام مطمئن نیستم. اما ایده ای که به ذهنم رسید این بود که گزاره هایی که اگر برقرار بشن بتونن تعداد بیشتری اصول دیگر رو درباره مغز پدیدار بیارن احتمالا مقدم هستند بر گزاره های سطح بالایی که این قدرت رو ندارن. برای مثال به دو گزاره پایین فکر کنید:
Neural circuits oscillate in different ranges of frequencies.
من میتونم این گزاره رو بدم ولی خب گزاره دیگری وجود داره که اگر بدم این سطح رو هم در بر میگیره در کنار اطلاعات دیگری که میده. این گزاره است:
In the nervous system, inhibitory and excitatory neurons have domain-specific (compartmentalized) synaptic connectivity.
از نظر من برای این هدفی که داریم، گزاره دوم بر گزاره نخست مقدم هست. چون اگر نورون های مهاری-تهییجی مختلف رو به شکل های مختلف به هم وصل کنیم نوسانات ازش به صورت ویژگی ای پدیداری بروز میکنه.
حالا بازی این هست که این گزاره ها رو پیشنهاد کنیم و در طول زمان به گزاره های بنیادی تری برسیم که گستره بیشتری از ویژگی های سیستم عصبی رو در خودشون قرار میدن. به صورتی که اگر سیستم با این ده ویژگی بسازیم بسیاری از ویژگی های دیگر مغز ازش بروز کنه. حالا من چندین گزاره مینویسم. این گزاره ها اولویت بندی نیستن و به عنوان پایه ای هستن که تغییر کنن. میتونید گزاره های خودتون رو پیشنهاد کنید و یا گزاره های جایگزین دربرگیرنده بهتری ارائه بدید.
هر هفته بر مبنای پاسخ هایی که ارائه بدید من این گزاره ها رو بروزرسانی میکنم.
1 - The brain operates as a modular network.
2 - The nervous system is composed of a variety of cell types such as different types of neurons and glia, each characterized by unique genetic and molecular identities.
3 - There are two broad categories of neurons, inhibitory and excitatory, which have unique domain-specific (compartmentalized) synaptic connections with each other in different circuits.
4 - Neurons have broadly two modes of activity, a continuous subthreshold voltage fluctuation, and a discrete spiking activity.
5 - Neurons exhibit various patterns of spiking activity, such as bursting and regular spiking, constrained by their refractory periods.
6 - The synaptic connectivity profile between neurons can change (synaptic plasticity) leading to the strengthening or weakening of the direct interaction
7 - To maintain stability, the nervous system regulates synaptic plasticity through homeostatic mechanisms.
8 - Brain activity is predominantly self-organized, driven by the system's intrinsic biophysical properties to spontaneously generate activity, though it can also be influenced by external stimuli.
9 -The brain functions as a control system organized in both hierarchical and heterarchical manners, featuring extensive feedback loops.
10 - The brain is embedded and embodied (brain functionality is integrated with bodily dynamics, demonstrating coordination between neural and physical actions.)
با این هشتگ میتونید پست های بروزرسانی شده رو دنبال کنید.
#NeuralPrinciples #Part1
امروز داشتم قدم میزدم و به این پرسش فکر میکردم که چه 10 گزاره ای به اینها خواهم داد و هنوز درباره انتخاب هام مطمئن نیستم. اما ایده ای که به ذهنم رسید این بود که گزاره هایی که اگر برقرار بشن بتونن تعداد بیشتری اصول دیگر رو درباره مغز پدیدار بیارن احتمالا مقدم هستند بر گزاره های سطح بالایی که این قدرت رو ندارن. برای مثال به دو گزاره پایین فکر کنید:
Neural circuits oscillate in different ranges of frequencies.
من میتونم این گزاره رو بدم ولی خب گزاره دیگری وجود داره که اگر بدم این سطح رو هم در بر میگیره در کنار اطلاعات دیگری که میده. این گزاره است:
In the nervous system, inhibitory and excitatory neurons have domain-specific (compartmentalized) synaptic connectivity.
از نظر من برای این هدفی که داریم، گزاره دوم بر گزاره نخست مقدم هست. چون اگر نورون های مهاری-تهییجی مختلف رو به شکل های مختلف به هم وصل کنیم نوسانات ازش به صورت ویژگی ای پدیداری بروز میکنه.
حالا بازی این هست که این گزاره ها رو پیشنهاد کنیم و در طول زمان به گزاره های بنیادی تری برسیم که گستره بیشتری از ویژگی های سیستم عصبی رو در خودشون قرار میدن. به صورتی که اگر سیستم با این ده ویژگی بسازیم بسیاری از ویژگی های دیگر مغز ازش بروز کنه. حالا من چندین گزاره مینویسم. این گزاره ها اولویت بندی نیستن و به عنوان پایه ای هستن که تغییر کنن. میتونید گزاره های خودتون رو پیشنهاد کنید و یا گزاره های جایگزین دربرگیرنده بهتری ارائه بدید.
هر هفته بر مبنای پاسخ هایی که ارائه بدید من این گزاره ها رو بروزرسانی میکنم.
1 - The brain operates as a modular network.
2 - The nervous system is composed of a variety of cell types such as different types of neurons and glia, each characterized by unique genetic and molecular identities.
3 - There are two broad categories of neurons, inhibitory and excitatory, which have unique domain-specific (compartmentalized) synaptic connections with each other in different circuits.
4 - Neurons have broadly two modes of activity, a continuous subthreshold voltage fluctuation, and a discrete spiking activity.
5 - Neurons exhibit various patterns of spiking activity, such as bursting and regular spiking, constrained by their refractory periods.
6 - The synaptic connectivity profile between neurons can change (synaptic plasticity) leading to the strengthening or weakening of the direct interaction
7 - To maintain stability, the nervous system regulates synaptic plasticity through homeostatic mechanisms.
8 - Brain activity is predominantly self-organized, driven by the system's intrinsic biophysical properties to spontaneously generate activity, though it can also be influenced by external stimuli.
9 -The brain functions as a control system organized in both hierarchical and heterarchical manners, featuring extensive feedback loops.
10 - The brain is embedded and embodied (brain functionality is integrated with bodily dynamics, demonstrating coordination between neural and physical actions.)
با این هشتگ میتونید پست های بروزرسانی شده رو دنبال کنید.
#NeuralPrinciples #Part1
NeuroSyntax
درود، میخوام یک بازی فکری-پژوهشی در کانال راه اندازی کنم. فکر کنید که تعدادی آدم فضایی با امکانات مهندسی بالایی به زمین آمدن و از جمعیت پژوهشگران علوم اعصاب میخوان که بهشون 10 گزاره بنیادی درباره ساختار-عملکرد-دینامیک سیستم عصبی/بدن ارائه بدن تا این آدم فضایی…
من از چت جی پی تی 4 همین سوال بالا رو پرسیدم و ازش خواستم که 10 مبانی عصبی خودش رو بهم بده. این پاسخ چت جی پی تی هست:
Creating a system that approximates the dynamics and function of the brain involves understanding and implementing core principles that underlie its operation. Here are ten neural principles that could guide the aliens in constructing such a system:
1. Neural Plasticity: The system must be capable of adapting its connections and functions based on experience, akin to synaptic plasticity in the human brain, allowing for learning and memory formation.
2. Modularity: Organize the system into modules or networks that specialize in different functions (e.g., vision, language, motor control), but ensure these modules can interact seamlessly to produce coherent behavior.
3. Parallel Processing: Design the system to process multiple streams of information simultaneously, enabling rapid responses to complex environments, much like the brain's parallel processing capabilities.
4. Energy Efficiency: The system should optimize for low energy consumption while maintaining high computational power, mirroring the brain's ability to perform complex computations with minimal energy.
5. Neurogenesis: Incorporate mechanisms for the creation of new processing units or the enhancement of existing ones in response to new information or tasks, inspired by the concept of neurogenesis in the human brain.
6. Excitatory and Inhibitory Balance: Ensure the system maintains a balance between excitatory and inhibitory signals, critical for stable yet flexible operation, preventing runaway activity or total inactivity.
7. Feedback Loops: Implement feedback mechanisms that allow the system to self-regulate and adapt to changing conditions, similar to the feedback loops found in neural circuits for homeostasis and learning.
8. Sensory Integration: The system should be able to integrate sensory information from multiple modalities (e.g., visual, auditory, tactile) to form a unified perception of the environment.
9. Error Correction: Design the system with the ability to detect and correct errors in its processing, a principle central to human learning and decision-making processes.
10. Spontaneous Activity: Include a mechanism for spontaneous activity that does not require external input, facilitating creativity, and problem-solving by generating internal models of the world.
These principles, drawn from current understanding of neuroscience, would provide a foundation for designing a system that approximates the complexity and functionality of the human brain. Each principle captures an essential aspect of neural function, from the structural and functional adaptability of the brain to its efficient, integrated, and self-regulating computational capabilities.
#NeuralPrinciples #Part2 #chatgpt
Creating a system that approximates the dynamics and function of the brain involves understanding and implementing core principles that underlie its operation. Here are ten neural principles that could guide the aliens in constructing such a system:
1. Neural Plasticity: The system must be capable of adapting its connections and functions based on experience, akin to synaptic plasticity in the human brain, allowing for learning and memory formation.
2. Modularity: Organize the system into modules or networks that specialize in different functions (e.g., vision, language, motor control), but ensure these modules can interact seamlessly to produce coherent behavior.
3. Parallel Processing: Design the system to process multiple streams of information simultaneously, enabling rapid responses to complex environments, much like the brain's parallel processing capabilities.
4. Energy Efficiency: The system should optimize for low energy consumption while maintaining high computational power, mirroring the brain's ability to perform complex computations with minimal energy.
5. Neurogenesis: Incorporate mechanisms for the creation of new processing units or the enhancement of existing ones in response to new information or tasks, inspired by the concept of neurogenesis in the human brain.
6. Excitatory and Inhibitory Balance: Ensure the system maintains a balance between excitatory and inhibitory signals, critical for stable yet flexible operation, preventing runaway activity or total inactivity.
7. Feedback Loops: Implement feedback mechanisms that allow the system to self-regulate and adapt to changing conditions, similar to the feedback loops found in neural circuits for homeostasis and learning.
8. Sensory Integration: The system should be able to integrate sensory information from multiple modalities (e.g., visual, auditory, tactile) to form a unified perception of the environment.
9. Error Correction: Design the system with the ability to detect and correct errors in its processing, a principle central to human learning and decision-making processes.
10. Spontaneous Activity: Include a mechanism for spontaneous activity that does not require external input, facilitating creativity, and problem-solving by generating internal models of the world.
These principles, drawn from current understanding of neuroscience, would provide a foundation for designing a system that approximates the complexity and functionality of the human brain. Each principle captures an essential aspect of neural function, from the structural and functional adaptability of the brain to its efficient, integrated, and self-regulating computational capabilities.
#NeuralPrinciples #Part2 #chatgpt
پاسخ Gemini - قسمت 1
Here are 10 principles that neuroscientists might suggest to the aliens to approximate the dynamics and function of the brain:
1. Distributed Processing: Information isn't stored in single locations but spread across interconnected networks of neurons. This allows for parallel processing, fault tolerance, and emergent properties.
2. Neuronal Diversity: Different types of neurons with distinct properties (excitatory, inhibitory) enable diverse computations and flexible information flow.
3. Hebbian Learning: Synaptic connections strengthen with use ("fire together, wire together"), allowing the network to learn and adapt to experience.
4. Competitive Learning: Neurons compete for limited resources, leading to the selection of strong signals and pruning of weak ones, enhancing signal processing and efficiency.
5. Homeostatic Regulation: The system maintains internal stability through feedback loops, adjusting activity levels and resource allocation to keep functioning within optimal ranges.
6. Noise and Stochasticity: Randomness plays a role in neural activity, contributing to exploration, flexibility, and preventing the system from getting stuck in local minima.
7. Hierarchical Organization: Information is processed at multiple scales, with higher levels integrating outputs from lower ones, enabling complex decision-making and flexible behavior.
8. Local vs. Global Connectivity: Neurons interact with nearby neighbors and distant regions, facilitating both specialized processing and long-range communication.
9. Plasticity and Remodeling: The system can change its structure and function over time, based on experience and learning, enabling adaptation and memory formation.
10. Dynamical Systems: The brain's behavior is best understood through the lens of complex, non-linear dynamics, where small changes can have large cascading effects, leading to emergent phenomena.
These are just a few possibilities, and different neuroscientists might prioritize different principles or propose alternative ones. It's important to remember that the brain is incredibly complex, and these principles represent simplified models that capture some aspects of its behavior, but not all.
Furthermore, the aliens' ability to build anything based on the instructions is a hypothetical scenario. In reality, translating these principles into a functional system would require overcoming significant engineering challenges and might not perfectly capture the intricacies of the biological brain.
#NeuralPrinciples #Part3 #gemini
Here are 10 principles that neuroscientists might suggest to the aliens to approximate the dynamics and function of the brain:
1. Distributed Processing: Information isn't stored in single locations but spread across interconnected networks of neurons. This allows for parallel processing, fault tolerance, and emergent properties.
2. Neuronal Diversity: Different types of neurons with distinct properties (excitatory, inhibitory) enable diverse computations and flexible information flow.
3. Hebbian Learning: Synaptic connections strengthen with use ("fire together, wire together"), allowing the network to learn and adapt to experience.
4. Competitive Learning: Neurons compete for limited resources, leading to the selection of strong signals and pruning of weak ones, enhancing signal processing and efficiency.
5. Homeostatic Regulation: The system maintains internal stability through feedback loops, adjusting activity levels and resource allocation to keep functioning within optimal ranges.
6. Noise and Stochasticity: Randomness plays a role in neural activity, contributing to exploration, flexibility, and preventing the system from getting stuck in local minima.
7. Hierarchical Organization: Information is processed at multiple scales, with higher levels integrating outputs from lower ones, enabling complex decision-making and flexible behavior.
8. Local vs. Global Connectivity: Neurons interact with nearby neighbors and distant regions, facilitating both specialized processing and long-range communication.
9. Plasticity and Remodeling: The system can change its structure and function over time, based on experience and learning, enabling adaptation and memory formation.
10. Dynamical Systems: The brain's behavior is best understood through the lens of complex, non-linear dynamics, where small changes can have large cascading effects, leading to emergent phenomena.
These are just a few possibilities, and different neuroscientists might prioritize different principles or propose alternative ones. It's important to remember that the brain is incredibly complex, and these principles represent simplified models that capture some aspects of its behavior, but not all.
Furthermore, the aliens' ability to build anything based on the instructions is a hypothetical scenario. In reality, translating these principles into a functional system would require overcoming significant engineering challenges and might not perfectly capture the intricacies of the biological brain.
#NeuralPrinciples #Part3 #gemini
پاسخ Gemini - قسمت 2
Ten Neural Principles for Aliens to Create a Brain-Like System
1. Modularity: The brain is composed of specialized modules that perform specific functions, such as vision, hearing, and motor control. These modules can operate independently but also communicate with each other to create complex behaviors.
2. Hierarchy: The brain has a hierarchical organization, with higher-level modules controlling and coordinating the activities of lower-level modules. This allows for efficient processing of information and decision-making.
3. Plasticity: The brain is highly plastic, meaning that it can change and adapt in response to new experiences and learning. This allows the brain to learn new skills and knowledge throughout life.
4. Connectivity: The brain is densely interconnected, with billions of neurons communicating with each other through synapses. This connectivity allows for the rapid and efficient transmission of information across the brain.
5. Feedback: The brain uses feedback loops to regulate its own activity and to learn from its mistakes. This allows the brain to constantly adjust and improve its performance.
6. Redundancy: The brain has built-in redundancy, with multiple pathways and mechanisms for performing the same function. This redundancy helps to ensure that the brain can continue to function even if some parts are damaged.
7. Energy efficiency: The brain is remarkably energy efficient, consuming only about 20 watts of power. This is due to the use of specialized neurons and circuits that minimize energy consumption.
8. Parallel processing: The brain can process information in parallel, allowing it to perform multiple tasks simultaneously. This parallel processing capability is essential for the brain's ability to handle the vast amount of information it receives.
9. Self-organization: The brain has the ability to self-organize, meaning that it can create new connections and pathways without external instruction. This self-organization allows the brain to adapt to changing circumstances and to learn new things.
10. Emergence: The brain's complex behaviors and functions emerge from the interactions of its individual components. These emergent properties cannot be predicted from the behavior of the individual components alone.
#NeuralPrinciples #Part4 #gemini
Ten Neural Principles for Aliens to Create a Brain-Like System
1. Modularity: The brain is composed of specialized modules that perform specific functions, such as vision, hearing, and motor control. These modules can operate independently but also communicate with each other to create complex behaviors.
2. Hierarchy: The brain has a hierarchical organization, with higher-level modules controlling and coordinating the activities of lower-level modules. This allows for efficient processing of information and decision-making.
3. Plasticity: The brain is highly plastic, meaning that it can change and adapt in response to new experiences and learning. This allows the brain to learn new skills and knowledge throughout life.
4. Connectivity: The brain is densely interconnected, with billions of neurons communicating with each other through synapses. This connectivity allows for the rapid and efficient transmission of information across the brain.
5. Feedback: The brain uses feedback loops to regulate its own activity and to learn from its mistakes. This allows the brain to constantly adjust and improve its performance.
6. Redundancy: The brain has built-in redundancy, with multiple pathways and mechanisms for performing the same function. This redundancy helps to ensure that the brain can continue to function even if some parts are damaged.
7. Energy efficiency: The brain is remarkably energy efficient, consuming only about 20 watts of power. This is due to the use of specialized neurons and circuits that minimize energy consumption.
8. Parallel processing: The brain can process information in parallel, allowing it to perform multiple tasks simultaneously. This parallel processing capability is essential for the brain's ability to handle the vast amount of information it receives.
9. Self-organization: The brain has the ability to self-organize, meaning that it can create new connections and pathways without external instruction. This self-organization allows the brain to adapt to changing circumstances and to learn new things.
10. Emergence: The brain's complex behaviors and functions emerge from the interactions of its individual components. These emergent properties cannot be predicted from the behavior of the individual components alone.
#NeuralPrinciples #Part4 #gemini
NeuroSyntax pinned «درود، میخوام یک بازی فکری-پژوهشی در کانال راه اندازی کنم. فکر کنید که تعدادی آدم فضایی با امکانات مهندسی بالایی به زمین آمدن و از جمعیت پژوهشگران علوم اعصاب میخوان که بهشون 10 گزاره بنیادی درباره ساختار-عملکرد-دینامیک سیستم عصبی/بدن ارائه بدن تا این آدم فضایی…»
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جلسه پنجم معادلات دیفرانسیل و سامانه های پویا
Potentials vs. Phase Portrait
Solving nonhomogeneous ODEs using the method of undetermined coefficients
Example: Modeling a single neuron
* Integrate and fire model
* Solving, plotting, and interpretations
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Potentials vs. Phase Portrait
Solving nonhomogeneous ODEs using the method of undetermined coefficients
Example: Modeling a single neuron
* Integrate and fire model
* Solving, plotting, and interpretations
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Differential Equations 4.pdf
3.5 MB
جلسه پنجم معادلات دیفرانسیل و سامانه های پویا
Potentials vs. Phase Portrait
Solving nonhomogeneous ODEs using the method of undetermined coefficients
Example: Modeling a single neuron
* Integrate and fire model
* Solving, plotting, and interpretations
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Potentials vs. Phase Portrait
Solving nonhomogeneous ODEs using the method of undetermined coefficients
Example: Modeling a single neuron
* Integrate and fire model
* Solving, plotting, and interpretations
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
آیا دوره معادلات دیفرانسیل و سیستم های پویا را دنبال میکنید؟
Anonymous Poll
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54%
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جلسه ششم معادلات دیفرانسیل و سامانه های پویا
A primer on integrals
Solving nonhomogenous ODEs using the method of variation of parameters
Analyzing the toggle switch model
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
A primer on integrals
Solving nonhomogenous ODEs using the method of variation of parameters
Analyzing the toggle switch model
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Differential Equations 5.pdf
1.9 MB
جلسه ششم معادلات دیفرانسیل و سامانه های پویا
A primer on integrals
Solving nonhomogenous ODEs using the method of variation of parameters
Analyzing the toggle switch model
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
A primer on integrals
Solving nonhomogenous ODEs using the method of variation of parameters
Analyzing the toggle switch model
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Media is too big
VIEW IN TELEGRAM
جلسه هفتم معادلات دیفرانسیل و سامانه های پویا - قسمت اول
Integration as the area under the curve
Integration as the antiderivative
Fundamental Theorem of Calculus
Elementary functions
Closed-form and analytical solutions
Numerical Integration
Forward and Backward Euler's formula for integration
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Integration as the area under the curve
Integration as the antiderivative
Fundamental Theorem of Calculus
Elementary functions
Closed-form and analytical solutions
Numerical Integration
Forward and Backward Euler's formula for integration
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Media is too big
VIEW IN TELEGRAM
جلسه هفتم معادلات دیفرانسیل و سامانه های پویا - قسمت دوم
Integration as the area under the curve
Integration as the antiderivative
Fundamental Theorem of Calculus
Elementary functions
Closed-form and analytical solutions
Numerical Integration
Forward and Backward Euler's formula for integration
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Integration as the area under the curve
Integration as the antiderivative
Fundamental Theorem of Calculus
Elementary functions
Closed-form and analytical solutions
Numerical Integration
Forward and Backward Euler's formula for integration
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Differential Equations 7.pdf
2.7 MB
اسلاید های جلسه هفتم معادلات دیفرانسیل و سامانه های پویا
Integration as the area under the curve
Integration as the antiderivative
Fundamental Theorem of Calculus
Elementary functions
Closed-form and analytical solutions
Numerical Integration
Forward and Backward Euler's formula for integration
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Integration as the area under the curve
Integration as the antiderivative
Fundamental Theorem of Calculus
Elementary functions
Closed-form and analytical solutions
Numerical Integration
Forward and Backward Euler's formula for integration
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Media is too big
VIEW IN TELEGRAM
جلسه هشتم معادلات دیفرانسیل و سامانه های پویا
Numerical Simulation of dynamical systems
More detailed analysis of forward and backward Euler's scheme
Difficulties of Backward Euler's integrator
2nd and 4th Runge Kutta Integrators
A short primer on graph theory and graph visualization
Diffusion/Signal Propagation in complex/timed networks
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Numerical Simulation of dynamical systems
More detailed analysis of forward and backward Euler's scheme
Difficulties of Backward Euler's integrator
2nd and 4th Runge Kutta Integrators
A short primer on graph theory and graph visualization
Diffusion/Signal Propagation in complex/timed networks
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Differential Equations 8.pdf
4.5 MB
اسلاید های جلسه هشتم معادلات دیفرانسیل و سامانه های پویا
Numerical Simulation of dynamical systems
More detailed analysis of forward and backward Euler's scheme
Difficulties of Backward Euler's integrator
2nd and 4th Runge Kutta Integrators
A short primer on graph theory and graph visualization
Diffusion/Signal Propagation in complex/timed networks
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Numerical Simulation of dynamical systems
More detailed analysis of forward and backward Euler's scheme
Difficulties of Backward Euler's integrator
2nd and 4th Runge Kutta Integrators
A short primer on graph theory and graph visualization
Diffusion/Signal Propagation in complex/timed networks
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Media is too big
VIEW IN TELEGRAM
جلسه نهم معادلات دیفرانسیل و سامانه های پویا
Dynamical Processes on Complex Networks
Oscillators
Synchronization
Kuramoto model of coupled oscillators
The impact of network topology on the tendency of the networks to globally synchronize
- KNN networks
- Random Networks - Erdős-Rényi
Partial Synchronization, Chimera States
- Networks with subpopulations (communities)
Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Dynamical Processes on Complex Networks
Oscillators
Synchronization
Kuramoto model of coupled oscillators
The impact of network topology on the tendency of the networks to globally synchronize
- KNN networks
- Random Networks - Erdős-Rényi
Partial Synchronization, Chimera States
- Networks with subpopulations (communities)
Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Differential Equations 9.pdf
6.4 MB
اسلاید های جلسه نهم معادلات دیفرانسیل و سامانه های پویا
Dynamical Processes on Complex Networks
Oscillators
Synchronization
Kuramoto model of coupled oscillators
The impact of network topology on the tendency of the networks to globally synchronize
- KNN networks
- Random Networks - Erdős-Rényi
Partial Synchronization, Chimera States
- Networks with subpopulations (communities)
Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
Dynamical Processes on Complex Networks
Oscillators
Synchronization
Kuramoto model of coupled oscillators
The impact of network topology on the tendency of the networks to globally synchronize
- KNN networks
- Random Networks - Erdős-Rényi
Partial Synchronization, Chimera States
- Networks with subpopulations (communities)
Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
#CODAC
COmplex Dynamics And Control
#neurosyntax
#ComplexityDynamicsControl
NeuroSyntax
Differential Equations 9.pdf
https://www.complexity-explorables.org/
این وبسایت مجموعه بسیاری جالبی از شبیه سازی سیستم های پیچیده مختلف هست.
#neurosyntax
این وبسایت مجموعه بسیاری جالبی از شبیه سازی سیستم های پیچیده مختلف هست.
#neurosyntax
www.complexity-explorables.org
Complexity Explorables
A collection of interactive explorable explanations of complex systems in biology, physics, mathematics, social sciences, epidemiology, ecology and other fields....