Ⅰ.Context
In a synthetic bio-neural network, information is transmitted between N neurons through chemical and electrical signals. Your objective is to find the minimum Metabolic Cost to trnasmit a signal from a Source_Neuron to a Target_Neuron.
Ⅱ.Neuron Structure and Genetic Coding
Each neuron i is identified by a unique Protein Code (a string consisting of bases A, C, G, T).
  • Genetic Distance (G): The base cost to jump from neuron u to neuron v is defined as the Levenshtein Distance (minimum number of edits: insertions, deletions, or substitutions) between their Protein Code strings.
Ⅲ.Polarization States and Transitions
At any time step T, a neuron exists in one of three Polarization States: P ∈ {0,1,2}. When a signal jumps from u to v, the state of the signal evolves based on a 3x3 Transition Matrix M:
  • If is even:
  • If is odd:
  • (Note: Matrix M is 1-indexed in logic, e.g., ).
Ⅳ.Sypnatic Barriers (Constraints)
A connection from neuron u to v is only valid if all the following conditions are met:
  1. Chemotaxis Condition: The Protein Code of v must contain at least one sub-sequence of length 2 that exists within the Protein Code of u. (e.g., if u is AGCT, v must contain AG, GC, or CT).
  2. Energy Limit: The total accumulated cost from the source must not exceed .
  3. Temporal Gating: A neuron i enters a "refractory period" (disabled) if the current time step T is a multiple of its Stability Index . (i.e., if mod() == 0, the neuron cannot be entered).
Ⅴ.Metabolic Cost Calculation
The total cost to transition from u to v at time T with the current signal state is:
Where:
  • is a weight vector correspoding to the 3 polarization states.
  • Interference(T) = (simulating temporal electromagnetic noise).
Ⅵ.Input / Output Requirements
Input: * neurons: A struct array containing .code(string) and .S(integer).
  • M: A 3x3 state transition matrix.
  • W_state: A 1x3 weight vector.
  • E_max: Maximum energy allowed (scalar).
  • start_id, target_id: Indices of the start and neurons.
Output: * The minimum metabolic cost (scalar). Return -1 if the target is unreachable.
  • (Optional) The path taken (sequence of neuron IDs).
Solve

Solution Stats

1 Solutions

1 Solvers

Last Solution submitted on Mar 20, 2026

Last 200 Solutions

Solution Comments

Show comments

Problem Recent Solvers1

Hoang Minh Tri

Suggested Problems

More from this Author19

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!