Algorithmic Complexity and Big O Notation

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Questions and Answers

Which of the following is LEAST likely to occur as a direct result of synaptic fatigue within a neural circuit?

  • A progressive decrease in the amplitude of excitatory post-synaptic potentials (EPSPs) in the post-synaptic neuron.
  • Enhanced responsiveness of the post-synaptic neuron to subsequent stimuli due to prolonged hyperpolarization. (correct)
  • Reduced probability of neurotransmitter release from the pre-synaptic neuron following repeated stimulation.
  • Increased reliance on recruitment of additional neurons to maintain a consistent level of output signal.

A drug that selectively impairs the function of the presynaptic region would most likely disrupt which aspect of synaptic transmission?

  • The synthesis and release of neurotransmitters. (correct)
  • The responsiveness of the post-synaptic receptors to neurotransmitters.
  • The reuptake or degradation of neurotransmitters in the synaptic cleft.
  • The ability of the post-synaptic neuron to generate action potentials.

Which of the following scenarios would most directly compromise the 'one-way conduction' property of a synapse?

  • Retrograde signaling from the post-synaptic to the pre-synaptic neuron influencing neurotransmitter release. (correct)
  • Receptor desensitization on the post-synaptic neuron.
  • Spatial summation of inhibitory post-synaptic potentials (IPSPs) at the axon hillock.
  • Enzymatic degradation of neurotransmitters within the synaptic cleft.

In the context of synaptic transmission, what is the functional significance of 'occlusion'?

<p>The phenomenon where the effect of one stimulus is blocked by the presence of another stimulus, suggesting a shared pathway. (D)</p> Signup and view all the answers

Long-term depression (LTD) is a form of synaptic plasticity that results in:

<p>A persistent weakening of synaptic connections. (D)</p> Signup and view all the answers

Which of the following mechanisms contributes most directly to the termination of neurotransmitter signaling at a chemical synapse?

<p>The diffusion, degradation, or reuptake of neurotransmitters from the synaptic cleft. (B)</p> Signup and view all the answers

How does the presence of a 'subliminal fringe' influence neuronal communication within a network?

<p>It allows for the modulation of neuronal excitability without necessarily triggering immediate action potentials, affecting network dynamics. (C)</p> Signup and view all the answers

What is the primary distinction between electrical and chemical synapses in terms of signal transmission speed and direction?

<p>Electrical synapses are faster and bidirectional, while chemical synapses are slower and primarily unidirectional. (A)</p> Signup and view all the answers

Convergence and divergence are key features of neural circuits. If a single neuron receives input from multiple pre-synaptic neurons, and then sends signals to numerous other post-synaptic neurons, what function does this arrangement MOST likely facilitate?

<p>Integration and distribution of information across a wider network. (A)</p> Signup and view all the answers

Following a period of heightened activity, a neuron exhibits 'after discharge'. Which of the following best describes the underlying mechanism contributing to this phenomenon?

<p>The persistent influx of calcium ions into the pre-synaptic terminal, leading to sustained neurotransmitter release. (C)</p> Signup and view all the answers

Flashcards

Synapse

A junction between two nerve cells, consisting of a presynaptic region, a synaptic cleft, and a postsynaptic region.

Electrical Synapse

Allows direct electrical signaling between neurons through gap junctions.

Chemical Synapse

Involves the release of neurotransmitters across the synaptic cleft for neuron communication.

Presynaptic Region

The region of the neuron that releases neurotransmitters into the synapse.

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Synaptic Cleft

The space between the presynaptic and postsynaptic neurons.

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Postsynaptic Region

The region of the neuron that receives neurotransmitters.

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Synaptic Events

Includes neurotransmitter release, postsynaptic electrical events, and termination of neurotransmitter action.

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NT Release

The release of neurotransmitters (NT) from the presynaptic neuron into the synaptic cleft.

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Postsynaptic Electrical Events

The change in the postsynaptic neuron's electrical potential due to neurotransmitter binding.

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Termination of NT

Mechanisms to stop neurotransmitter signaling, such as reuptake or degradation.

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Study Notes

  • Algorithmic complexity measures resources needed for an algorithm to solve a problem.
    • Resources include time and space.

Time Complexity

  • Time complexity is the amount of time required by an algorithm relative to the input size.

Space Complexity

  • Space complexity is the amount of memory space required in relation to the input size.

Big O Notation

  • Big O notation describes the limiting behavior of a function.
  • Classifies algorithms based on how their time or space requirements grow as input size increases.
  • Describes the upper bound of time or space complexity.
  • Represents the worst-case scenario for an algorithm's performance.

Common Time Complexities

  • O(1) Constant: Time is the same regardless of input size, like accessing an array element by index.
  • O(log n) Logarithmic: Time increases logarithmically as input size increases, such as in binary search.
  • O(n) Linear: Time increases linearly with input size, like in a simple search.
  • O(n log n) Linearithmic: Time increases linearly with a logarithmic factor, seen in merge sort and quicksort.
  • O(n^2) Quadratic: Time increases quadratically as input size increases, seen in bubble sort and selection sort.
  • O(n^3) Cubic: The time increases cubically as the input size increases, like with matrix multiplication.
  • O(2^n) Exponential: Time doubles with each addition to input size, such as in recursive Fibonacci.
  • O(n!) Factorial: Time increases factorially as input size increases, like with the traveling salesman problem (brute force).

Impact

  • Understanding algorithmic complexity helps choose efficient algorithms, leading to better performance with large datasets.
  • Allows predicting how well an algorithm will scale as the input size grows
  • Developers can optimize time-consuming parts of an algorithm by analyzing its complexity.

Example: Searching an Array

  • Linear Search: O(n) checks each element one by one.
  • Binary Search: O(log n) repeatedly divides the search interval in half.
  • For a large array, binary search outperforms linear search due to lower time complexity.

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