Md. Asif Uddin

    Chapter 8 VII.8

    Phylogenetics and Evolutionary Graphs

    A phylogeny is a tree inferred from distances or characters, and the processes that break tree-likeness are exactly the ones that matter most.

    Evolution drawn as a tree, and the cases where a tree is the wrong object.

    How this chapter is built

    M3Load-bearing

    The content is mathematics. Understanding is demonstrated by computation, not recall.

    basics2/11what the words mean
    concept2/2what to picture
    theory0/4why it works, and when it does not
    mathematics0/15derive it, then compute it
    practice0/9build it, break it, read the papers

    Five strands, not one. Mathematics is the spine; the other four are the body. A chapter cannot pay its way out of teaching with problems, nor out of problems with teaching.

    Before you start

    The problem

    Ancestry is unobserved and must be inferred from present-day sequences. The tree is the natural object, its inference is an optimisation with a stated criterion, and recombination and horizontal transfer are why the object is sometimes a network instead.

    Five architectures, one questionFive convolutional architectures in order, with their depth in layers. Each is an answer to the same problem: how to add depth without the optimisation failing. ResNet's residual connection is the step that made depth cheap.how do you get deeper?5 layersLeNet1998it works at all8 layersAlexNet2012ReLU, dropout, GPUs19 layersVGG2014only 3×3, stacked152 layersResNet2015an additive path home66 layersEfficientNet2019scale the three axes togetherDepth axis is logarithmic. Before ResNet the fight was optimisation; after it, tuning.
    Fig. 8 — Five architectures asking one question: how to get deeper without the optimisation failing. The depth axis is logarithmic.

    Apparatus

    The mathematics this chapter leans on, held in Book 0 so it can be assumed here without being taught here. Not a gate — follow a link when a step stops making sense.

    Graphs, vertices and edges 0.GR.01 · Trees and spanning trees 0.GR.04 · Complexity: P, NP, and why some problems are hard 0.GR.08 · Estimators, bias and variance 0.ST.01 · The bootstrap 0.ST.05

    Notation

    • 𝒟A dataset, as a set of examples
    • θ̂An estimate, as against the quantity it estimates
    • 𝔼Expectation

    Propositions

    Not yet written. The topics above are the plan for this chapter; each will become a proposition with its own figure.

    Worked problems

    0/5 problems0/4 variants0/10 exercisesowes 15 more

    Not yet written. At M3 this chapter owes 5 worked problems across 4 distinct variants, and 10 exercises, every one with a published solution. The build enforces that from the day the chapter is marked published.