Artificial Systems and Self-Organisation Concepts

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Questions and Answers

Which technologies are contrasted in the table regarding their artificial nature?

  • organic materials and synthetic compounds
  • carbon technology and silicon technology (correct)
  • biological systems and computational models
  • molecular biology and quantum mechanics

What is one of the main applications of the concepts discussed?

  • Enhancing human cognitive abilities through technology
  • Modeling complex biological and socio-economic systems (correct)
  • Developing natural languages for artificial intelligence
  • Creating biological organisms from scratch

Which type of interactions are associated with artificial systems as mentioned in the content?

  • magnetic interactions
  • molecular interactions
  • electric interactions (correct)
  • thermodynamic interactions

Which of the following is categorized under artificial systems in practice?

<p>integrated circuits (D)</p>
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What kind of algorithms are mentioned as relevant in the philosophical context?

<p>Evolutionary algorithms (A)</p>
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What principle of self-organisation refers to the lack of control from external sources?

<p>No external control (B)</p>
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Which of the following is NOT one of the defining principles of self-organisation?

<p>Emergence of new capabilities (D)</p>
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Which principle involves systems responding effectively to changing conditions?

<p>Adaptability (C)</p>
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What does the principle of interaction in self-organisation emphasize?

<p>Dynamic relationships among components (B)</p>
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Which of the following statements best represents a view on emergence?

<p>What emerges is often subjective to the observer. (C)</p>
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Which principle is closely associated with systems achieving higher complexity and order?

<p>Increase in order (D)</p>
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In the context of self-organisation, what is meant by asynchronism?

<p>Different components acting at varied times without direct coordination (C)</p>
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How does self-organisation contribute to systems in nature?

<p>By embedding order and complexity in all components (A)</p>
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What role does momentum play in the training of neural networks?

<p>It contributes to better learning and helps avoid local minima. (A)</p>
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Which of the following statements about adaptive momentum estimation (ADAM) is correct?

<p>ADAM computes averages of past gradients to facilitate learning. (A)</p>
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What does the variable $m_t$ represent in the ADAM algorithm?

<p>The estimate of the 1st moment (mean) of gradients. (D)</p>
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In the context of backpropagation, what is an epoch?

<p>The presentation of all training examples once. (D)</p>
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Which is NOT a suggested value for parameters in the ADAM algorithm?

<p>$eta_3 = 0.8$ (D)</p>
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What is the role of the tangent vector in determining velocity?

<p>It represents the instantaneous rate of change of position. (B)</p>
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Which characteristic is essential for non-linear systems to provide universal computation?

<p>Non-linearity (A)</p>
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What is a limit cycle in the context of dynamical systems?

<p>An oscillatory trajectory that cyclically returns to itself. (B)</p>
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How do Hopfield networks enable the manipulation of attractors?

<p>By controlling the positions of the attractors to match input patterns. (A)</p>
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What is a defining feature of dissipative systems?

<p>They converge to an attractor over time. (B)</p>
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Which best describes the energy-minimization dynamics in neural networks?

<p>They exploit trajectories that reduce energy consumption to compute effectively. (D)</p>
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What is the purpose of storing a set of patterns in an associative memory?

<p>To recall patterns that closely resemble a presented input. (B)</p>
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What effect does noise typically have on neural networks?

<p>It is a characteristic feature that is often present. (D)</p>
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What does the universal approximation theorem assert about a multilayer perceptron (MLP)?

<p>A single hidden layer is sufficient for a MLP to compute a near approximation. (D)</p>
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In the universal approximation theorem, what is the significance of the function ϕ(·)?

<p>It should be non-constant, bounded, and monotonous-increasing. (C)</p>
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What does the error risk bound suggest when using an MLP?

<p>The configuration of hidden layer neurons is related to error risk. (B)</p>
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Which statement is true regarding the function approximation capabilities of an MLP?

<p>Generalization cannot be assured solely on the number of hidden layers. (D)</p>
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What is often a limitation of using a single hidden layer in an MLP for function approximation?

<p>It can be inefficient in terms of training time. (B)</p>
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What aspects must be maintained for function approximation using neural networks according to the universal approximation theorem?

<p>Boundedness and non-constancy of the output. (A)</p>
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What does the notation $F(x_1, ..., x_{m_0}) = \Sigma_{i=1}^{m_1} \Sigma_{j=1}^{m_0} α_i ϕ(w_{ij} x_j + b_i)$ represent?

<p>The final approximation of function $f$ through neural computation. (C)</p>
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Why might it be necessary to go deeper into an MLP's architecture?

<p>To improve the approximation capability for more complex functions. (A)</p>
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What should the desired outputs fall within for the hyperbolic tangent function when a = 1.7159 and ϵ = 0.7159?

<p>dk = -1.7159 + 0.7159 (B), dk = 1.7159 - 0.7159 (D)</p>
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What is one of the requirements for input normalization in a neural network?

<p>Each input should have average close to zero. (A)</p>
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What is the intended role of PCA in input normalization?

<p>To reduce the dimensionality of the input features. (A)</p>
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What should the initial weight values be in a neural network to avoid saturation?

<p>Values around zero. (D)</p>
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What is the desired outcome of initializing random uniform synaptic weights?

<p>To keep the average of the weights to zero. (B)</p>
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In weight initialization, what variance is ideally suggested for future calculations?

<p>Should equal one for stability. (A)</p>
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What does a learning rate of η signify for neurons with more inputs?

<p>It should be smaller, inversely proportional to the square root of the number of inputs. (C)</p>
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What is the effect of having non-correlated inputs during training?

<p>Ensures synaptic weights learn at a similar speed. (D)</p>
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What is one common strategy for weight initialization related to the hyperbolic tangent function?

<p>Setting weight variance to one. (C)</p>
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What does the maximum induced local field variance depend on?

<p>Weights and inputs covariance. (B)</p>
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How can learning speed be affected by using information about the function?

<p>It enhances efficiency and consistency of backpropagation. (C)</p>
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What is the advantage of having small initial weights during training?

<p>Prevents saturation and maintains learning dynamics. (D)</p>
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What condition ideally applies to the average of inputs for effective weight training?

<p>Average should be null. (C)</p>
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What is essential about the weights in relation to the number of synapses of a neuron?

<p>Weight variance is inversely proportional to the number of synapses. (B)</p>
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Flashcards

Philosophy

The study of the fundamental nature of reality, knowledge, and existence.

Artificial Life (ALife)

The process of applying scientific principles and engineering techniques to create non-biological systems that mimic the behavior of natural systems.

Software Artificial Life

An approach to creating artificial life by simulating biological processes within a computer program.

Hardware Artificial Life

An approach to creating artificial life by building physical robots that interact with the real world.

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Ethology

The study of the evolution of behaviors and strategies in animals, often through the use of computer simulations.

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Momentum in Backpropagation

A technique used in backpropagation to improve learning and escape local minima. It involves adding a fraction of the previous weight change to the current weight change. It is like pushing a heavy ball with momentum, allowing it to overcome obstacles.

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Variable Learning Rates (ηji)

A learning rate in backpropagation that is not constant but varies for each synapse. This allows different parts of the network to learn at different speeds, potentially leading to faster convergence.

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Adaptive Momentum Estimation (ADAM)

A backpropagation technique that adaptively adjusts the learning rate for each synapse based on past gradients. It combines the benefits of momentum (smooth learning) and adaptive learning rates. It is like a heavy ball with friction, making it more stable.

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Epoch

The complete presentation of all training examples once in backpropagation.

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Sequential Training

A training method in backpropagation where each training example is presented sequentially to the network. This approach is often used in online learning.

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Adaptability in Self-Organisation

A system's ability to change and adapt in response to its environment.

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Increase in Order in Self-Organisation

Self-organisation occurs when a system exhibits increasing complexity and order without external control or intervention.

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No External Control in Self-Organisation

The absence of external control in a self-organising system, meaning it is driven by internal interactions.

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Interaction in Self-Organisation

A key principle in self-organisation where components interact and influence each other's behaviour.

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Asynchronism in Self-Organisation

The property of a self-organising system where components act asynchronously, not needing to be coordinated or synchronized.

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Emergence as Observer-Dependent

The perspective that emergent phenomena are subjective and depend on the observer's interpretation.

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Syntactic Emergence

A situation where emergent behaviour is not a result of the system acquiring new capabilities or changing its model.

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Emergence Within the System

Emergence occurring within the system itself, arising from its internal interactions and dynamics.

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Dissipative Systems

A dynamical system where trajectories converge to a lower dimensional state over time.

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Point Attractors

Attractors in dynamical systems that correspond to a point in the state space.

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Limit Cycle Attractors

Attractors in dynamical systems that correspond to a closed loop or periodic orbit.

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Chaotic Attractors

Attractors in dynamical systems that correspond to a chaotic or unpredictable behavior.

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Hyperbolic Attractors

Attractors in dynamical systems that correspond to a region in the state space where the system exhibits exponential divergence of trajectories.

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Basin of Attraction

The set of initial conditions that lead to a particular attractor.

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Hopfield Networks

Neural networks that exploit the energy-minimization dynamics to perform useful computation.

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Recurrent Neural Network (RNN)

A type of neural network that exhibit dissipative dynamics, converging to attractor states over time.

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Rule of Thumb for Neural Network Size

A rule of thumb stating that the number of training examples (N) should be significantly larger than the number of free parameters (weights and biases) in a neural network (W). This ensures that the network does not overfit, meaning it can learn general patterns from the data and generalize well to unseen examples.

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Universal Approximation Theorem

A mathematical theorem that states that a single-layer feedforward neural network with a sufficient number of neurons can approximate any continuous function with arbitrary accuracy. This means that given a training set, the network can learn the underlying function that maps the inputs to the outputs.

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Generalization in Neural Networks

The ability of a neural network to generalize well to unseen data. If the network overfits, it will perform well on the training data but poorly on new data. Conversely, a network with good generalization ability will perform well on both seen and unseen data.

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Backpropagation

The process of adjusting the weights and biases of a neural network to minimize the difference between the predicted output and the actual target output for a given input. This is achieved through iterative training using gradient descent.

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Training Set

The set of input-output pairs used to train a neural network. The network's goal is to learn the underlying function that maps the inputs to the outputs.

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Free Parameters

The number of adjustable parameters in a neural network. This includes the weights and biases of the neurons.

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Multilayer Perceptron (MLP)

A type of neural network that uses multiple layers of neurons, connected in a hierarchical structure. Each layer processes the output of the previous layer to extract increasingly complex features from the input data.

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Error in Neural Networks

The difference between the predicted output of a neural network and the actual target output for a given input. This difference is used to calculate the loss function and guide the backpropagation algorithm.

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Desired output range in backpropagation

The desired outputs (dk) should be within the linear zone of the activation function (phi), at a distance of epsilon from the limiting values of phi. For the hyperbolic tangent, this means dk is equal to a minus epsilon for positive values and minus a plus epsilon for negative values.

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Input Normalisation in Backpropagation

Normalise the input data so that each input variable has an average of zero or close to it. This prevents all weights in the input layer from varying together and helps avoid correlations between inputs.

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Initialisation of Weights in Backpropagation

Initialise synaptic weights in a way that avoids saturation (very large weights) and saddle points (very small weights). Assuming null average inputs and unit variance, a good strategy is to initialize weights randomly with a small variance.

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Local Field Average in Backpropagation

The average of the local field (vj) is zero when inputs have zero average and weights are initialized with zero average.

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Local Field Variance in Backpropagation

The variance of the local field (vj) is equal to the variance of the weights multiplied by the number of synapses of a neuron.

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Weight Initialisation for Hyperbolic Tangent

For an activation function like the hyperbolic tangent, a good strategy for initialising synaptic weights is to set the variance of the local field (σv) to 1. This ensures that the weights fall within the linear zone of the sigmoid.

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Optimal Weight Variance in Backpropagation

The optimal variance of the weights (σw) is equal to the reciprocal of the number of synapses of a neuron. This strategy ensures that the weights fall within the linear zone of the activation function, allowing the network to learn effectively.

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Learning Clues in Backpropagation

Use knowledge about the function being learned to accelerate backpropagation. For example, exploit any invariant or symmetry properties of the problem.

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Learning Rate in Backpropagation

The learning rate (η) should be smaller in the last layers of a neural network, as these layers typically have higher local gradients. Also, neurons with more inputs should have smaller learning rates, in inverse proportion to the square root of the number of inputs.

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Backpropagation Algorithm

The backpropagation algorithm is a method for training artificial neural networks by updating the weights of the network based on the error between the network's output and the desired output.

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Activation Function

The activation function is a function that introduces non-linearity into a neural network, allowing it to learn complex patterns.

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Sigmoid Function

A sigmoid function is a type of activation function that squashes the output of a neuron to a range between 0 and 1.

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Hyperbolic Tangent

The hyperbolic tangent (tanh) is a sigmoid function that squashes the output of a neuron to a range between -1 and 1.

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Local Field in a Neuron

The local field is the weighted sum of inputs to a neuron, before the activation function is applied.

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Synaptic Weights

Synaptic weights are the parameters of a neural network that determine the strength of the connection between neurons.

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Study Notes

Dynamical Systems

  •  Dynamical systems involve deterministic equations that represent the time evolution of a system
  •  Deterministic systems evolve according to a set rule with no randomness
  •  Dynamical systems can exhibit unpredictable behavior, especially when they display chaotic traits
  •  Real-world systems often have many interconnected parameters that evolve over time
  •  A trajectory (or orbit) showcases the system's path in phase space, which represents all possible states of the system

Continuous vs. Discrete Dynamical Systems

  •  Continuous dynamical systems evolve continuously over time, without discrete steps
  •  Continuous systems are often modeled using equations like dx/dt = f(x) where the change in a variable (x) is over time (t).
  •  Continuous systems usually have smooth, gradual change over time.
  •  Discrete dynamical systems evolve in steps (discrete steps), with the time variable n representing discrete time intervals
  •  Discrete systems are expressed as xn+1 = M(xn)

Chaos and Sensitive Dependence on Initial Conditions

  •  Chaos can exist in deterministic systems, where small changes in initial conditions lead to significantly different outcomes over time, making long-term prediction impossible.
  •  The Lyapunov exponent quantifies how sensitive initial conditions are, determining chaotic behavior. A positive exponent indicates chaotic behaviour

Bifurcations and Attractors

  •  Bifurcation: points where the behavior of a system changes dramatically as a parameter (e.g., r in the logistic map) changes; this transition between different types of behavior can include fixed points to cyclical, repeating orbits.
  •  Attractor: A stable state (or a cyclical pattern) and it's a region of the phase space to which orbits evolve.
  •  Types of attractors (e.g., fixed points & limit cycles); as parameters shift, systems can transition from one to another

Stability of Fixed Points

  •  Fixed point: a state where the system's state does not change over time (dx/dt = 0).
  •  Stability depends on the derivative of the system at the fixed point: a value less than 1 indicates stability (attracting nearby points) ; a value greater than 1 indicates instability (repellling nearby points); and a value equals to 1 represents meta-stability

Conservative vs. Dissipative Systems

  •  Conservative Systems: preserve total 'volume' in phase space, with no dissipation and conserving the total energy of the system.
  •  Dissipative systems: lose "volume" in phase space, typically due to energy loss.

Chaotic Systems and Fractals

  •  Chaotic systems exhibit sensitive dependence on initial conditions, leading to divergence with minute differences
  •  Strange attractors (in chaotic systems): have fractal dimensions and irregular patterns; these are key properties of fractals

Symbolic Dynamics and Phase Space Partitioning

  •  Symbolic dynamics: partitioning phase space to regions then labeling each region with a symbol
  •  Symbolic sequences represent the system's trajectory through the phase space.
  •  Phase Space: the phase space is the set of all possible states or values of a system in a multi-dimensional space.

Real-World Applications

  •  Dynamical systems provide modeling for a wide range of real-world contexts including human health, geological systems, living systems (e.g., the evolution of living organisms over time
  •  Real world systems have complex dynamics due to many interacting variables

Summary and Reflections

  •  Deterministic chaos theory demonstrates complex behaviors, particularly in systems with numerous interdependent variables
  •  System transitions from stable states to periodic orbits and chaos are important and are characteristic signs of a chaotic system.
  •  Sensitive dependence on initial conditions, and strange attractor behaviour are hallmarks of chaotic systems.

Fractality in Chaos

  •  Fractality in chaos: Chaotic systems and attractors often exhibit self-similarity at different scales
  •  Practical implications are vast, applying chaos theory to wider fields like biology, physics, economics, and engineering to understand complex and non-linear behaviours over time

Dynamical Systems II (Fractal Dimensions)

  •  Dynamical Systems: the study of systems that change over time, governed by rules and equations.
- Fractal Dimension: a metric used to quantify the complexity of fractals due to their irregular and self-similar structures at various scales. 
- Iterated Function Systems (IFS): a collection of functions used iteratively to generate fractal patterns.
- Logistic Function: a simple nonlinear function used extensively in modeling population dynamics, expressed as xn+1=f(xn)=rxn(1-xn), typically with the parameter (r) between 2 and 4

Entropy, Complexity, and Information

  •  Entropy: a measure of randomness or disorder in a system

  •  Complexity: amount of information needed to describe a system's behavior
  •  Randomness: when all possibilities are equally probable; systems with high entropy tend to be hard to predict

Fractals

  •  Fractals: geometric objects with self-similarity; appearing identical at different scales — they can have a fractal dimension.

Methods for Calculating Fractal Dimensions

  •  Self-Similarity Method: based on the concept that fractals are scaled versions of themselves at different scales; the fractal dimension arises from the relationship between the number of parts N and the scale E(or the scale rate)
  •  Geometric method: method used for computing the length or area of a fractal at differing scales or sizes of a box for each scale rate to find the relationships for estimating the fractal dimension.
  •  Box Counting Method: counting the number of boxes required to cover a fractal, which is used to calculate and estimate the fractal dimension; this method uses boxes of varying sizes
  •  Fractal Dimensions can also be estimated using other methods including the Minkowski-Bouligand, Hausdorff, Rényi

L-Systems

  •  An L-system is method for creating a system of rules that define how a string of symbols evolves over time.
  •  Commonly employed for modeling processes of growth and development in various systems including the development of biological organisms and their growth patterns.
- Typical components include; an alphabet of symbols representing parts of the organism; an initial state or the axiom; production rules defining the rewriting of the symbols; and ending or stopping process

Applications of Fractals and Dynamical Systems

  •  Fractals and dynamical systems are used to model many natural occurrences and complex problems
  •  Examples of practical applications include biological structures and systems, computer graphics, and other disciplines

Computational Artificial Life (ALife)

  •  Investigates life by recreating underlying principles found in biological systems, using computers to create a new kind of environment for studying computational models

ALife illustrative example

  •  Morphological and neural control under evolution
  •  Sensory inputs
  •  Evolutionary pressures (to move/capture)
  •  Self-propelling beings: a major problem in the development

ALife Research Questions (RQ's)

  •  Evolution of complexity: Is there a rational reason behind the increase in complexity?
  •  Origins of life: Exploring pre-biotic systems
  •  Major transitions: Exploring transitions in evolution (prokaryotes to eukaryotes, single cells to multi-cellular life)
  •  Cultural Evolution vs. Biological Evolution: How are each intertwined?
  •  Fundamental Intelligence requirements: What factors are fundamental for intelligence?

Course Logistics

  •  Assessment: comprised of 3 parts, including a project (70%), Flash Test (20%), and reports from TP exercises (10%)

Historical notes on ALife

  •  Citations include works by Christoph Adami, Cristopher Langton, Steven Levy, Claus Emmeche, Erwin Schrödinger and many more regarding the history of Artificial Life

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