Glossary¶

Key terms used throughout LZGraphs documentation.

CDR3 (Complementary Determining Region 3): The hypervariable region of a T-cell or B-cell receptor that primarily determines antigen specificity. LZGraphs models the statistical structure of CDR3 sequences.
DAG (Directed Acyclic Graph): A graph with directed edges and no cycles. LZGraphs with positional encoding (AAP and NDP variants) are inherently DAGs because node positions increase monotonically along any path.
Dynamic Range: The ratio between the most and least probable sequences in the graph, typically expressed in orders of magnitude. Immune repertoire graphs commonly span 100–300 orders of magnitude.
Edge Weight: The conditional transition probability from one node to another. In LZGraphs 3.0+, edge weights are renormalized at each step to strictly enforce LZ76 dictionary constraints.
Effective Diversity (N_eff): The number of equiprobable sequences that would produce the same Shannon entropy as the graph's actual distribution. Computed as exp(H) where H is the entropy.
Entropy (Shannon entropy): A measure of uncertainty in the generative distribution: H = −Σ P(x) log P(x). Higher entropy means a more uniform (less concentrated) distribution.
Hill Number (D^(α)): A family of diversity measures parameterized by order α. D⁽⁰⁾ = richness (total producible sequences), D⁽¹⁾ = effective diversity, D⁽²⁾ = inverse Simpson index (collision diversity). Higher α gives more weight to common sequences.
LZ76 Decomposition (Lempel-Ziv 1976): An algorithm that parses a string into the shortest sequence of subpatterns where each new subpattern extends a previously seen one by exactly one character. For example, CASSLE → [C, A, S, SL, E].
LZPGEN (Probability of GENeration): The probability that the graph's generative model produces a specific sequence. Computed using an LZ-constrained random walk model starting from the root node (@).
Node: A vertex in the LZGraph representing a subpattern at a specific position. Node format depends on the graph variant: - AAP: {subpattern}_{position} (e.g., SL_6) - NDP: {subpattern}{reading_frame}_{position} (e.g., TG2_4) - Naive: just the subpattern (e.g., SL)
Occupancy Model: A statistical model used to predict repertoire richness and overlap at arbitrary sequencing depths. LZGraphs uses a Poisson occupancy model with Taylor expansion and Wynn acceleration for high precision.
Path Count: The total number of unique sequences that can be generated by the graph. Because repertoire space is massive, this is usually an astronomically large number.
Posterior Graph: A graph created by the posterior() method that blends a population-level prior with an individual's observed sequences.
Reading Frame: In the NDP variant, the codon position (0, 1, or 2) of each nucleotide subpattern. This encodes the relationship between the nucleotide sequence and the underlying amino acid sequence.
Repertoire: The full set of T-cell or B-cell receptor sequences in a sample. LZGraphs models the statistical structure of repertoires.
Sharing Spectrum: The distribution describing how many distinct sequences are shared by exactly k donors in a cohort. Predicted by predict_sharing().
Simulation: The process of generating new sequences by performing random walks on the graph. In LZGraphs, all simulated sequences are guaranteed to be valid LZ76 decompositions.
Terminal Node: A node that contains the terminal sentinel $. These nodes represent valid endings for a sequence.
V gene / J gene: Variable and Joining gene segments. When provided during graph construction, these enable gene-aware analysis and constrained sequence generation.