Meter-SPW

In stable Rust, implement `BuildGraph` with `add_target(name)`, transactional `set_dependencies(target, deps)`, `mark_changed(target)`, and `rebuild_plan()`. Replacing dependencies must either commit completely or return a concrete directed cycle without changing the graph. A rebuild includes every changed target and all transitive dependents, orders dependencies before dependents, and breaks otherwise-free ties by target creation order. Reject unknown names and duplicate dependency entries. Return compilable code, complexity bounds, and four focused tests including rollback after a cycle.

Implement an inclusive segmented prefix sum in CUDA C++ where `head[i]=1` starts a segment. Handle arbitrary `n` using multiple blocks, with the explicit constraint that the first pass launches at most 1024 blocks so block summaries fit in one second-pass block. Provide the three kernels plus compact host orchestration, a CPU oracle, and one randomized test loop.

Prove the privacy guarantee of the Gaussian mechanism using privacy loss, then compare basic composition, advanced composition, zCDP/Renyi-DP accounting, and privacy amplification by subsampling. Explain why adaptively chosen queries still compose and convert one concrete rho-zCDP budget to `(epsilon,delta)`.

Prove how a bit vector supports O(1) rank and select with o(n) extra bits on a word RAM. Lay out superblocks, subblocks, lookup tables, parameter sizes, and explain why storing every prefix count would cost too much. State the model assumptions and select's additional indexing idea.

Over F_17, encode message polynomial m(x)=3+5x+2x^2 at evaluation points 1,...,7. Suppose received values have errors at two unknown positions. Demonstrate syndrome/Berlekamp-Welch decoding by constructing equations, locate and correct errors for a concrete corrupted word you specify, and state the decoding radius.

Derive the region of absolute stability of BDF2 for y'=lambda y, and decide whether BDF2 is A-stable and L-stable. Carefully define stability for a two-step method using the root condition, and compare with backward Euler as z tends to minus infinity.

Explain sovereign-debt restructuring without a global bankruptcy court. Cover collective-action clauses, pari passu litigation, holdouts, aggregation across bond series, IMF lending-into-arrears policy, domestic-law versus foreign-law bonds, and why restructuring nominal principal alone may not restore sustainability.

Explain total survey error: coverage, sampling, nonresponse, measurement, processing, and adjustment error. Analyze why weighting can reduce bias yet increase variance, how mode and question order change responses, and how to validate a cross-national latent construct with differential item functioning.

Four identical habitat patches have extinction probability e=0.20 per year when occupied. Each empty patch is colonized independently with probability 1-(1-c)^k where c=0.15 and k is the number of occupied other patches after extinction. Construct the Markov transition matrix for occupied-patch count and find or numerically characterize its stationary distribution.

At one biallelic locus, genotype fitnesses are w_AA=1, w_Aa=1, w_aa=0.8 and mutation A→a occurs at 1e-5 with negligible back mutation. Derive the recessive mutation–selection balance, estimate q, and compute expected affected fraction. Explain when drift invalidates this deterministic result.

An insurer offers high- and low-coverage contracts to privately informed high- and low-risk customers. Draw incentive-compatibility and participation constraints, derive the qualitative Rothschild–Stiglitz separating outcome, and explain why a seemingly profitable pooling contract can unravel.

A trial checks significance every week and stops the first time p<0.05, but reports an ordinary fixed-sample p-value. Explain optional-stopping inflation, construct a valid correction using alpha spending or an e-value/test martingale, and compare what each guarantees under an unbounded horizon.

Write two interleaved diary entries from occupants of the same room exactly 100 years apart. Alternate paragraphs, six per diarist. Each later diarist paragraph unknowingly completes a sentence begun in the preceding earlier paragraph, while preserving two distinct voices and revealing a shared danger.

Write 18 question–answer exchanges from a civil deposition. The witness never lies and answers every question literally, yet conceals that the allegedly stolen violin was theirs. By exchange 18, the attorney should prove ownership using only earlier exact wording. No speech may exceed 18 words.