An allele that increases the rate of mutations. In an asexual lineage it can hitchhike with a beneficial change, despite also increasing the production of harmful changes; genetic recombination can weaken that association.

Diversification of specified sequence positions across a defined set of residues. It focuses screening but can exclude important effects at unchosen sites.

The number or distribution of sequence changes per variant in a mutagenized library. Higher load explores more distant combinations while commonly reducing functional recovery.

Random-restart optimization repeatedly runs a local optimization algorithm from independently sampled starting points and retains the best result. It exploits multiple basins of attraction without requiring the local solver itself to escape a local extremum.

If each restart has probability $p$ of entering a desired basin, independent restarts miss it with probability $(1-p{)}^N$ after $N$ attempts. This formula quantifies the benefit only for the specified starting distribution and basin; neither $p>0$ nor a finite run certifies a global extremum. Recording the starting distribution and stopping rule makes computational comparisons reproducible.

A fivefold-twinned particle with five approximately tetrahedral domains sharing an axis. Five ideal fcc tetrahedral wedge angles leave an angular deficit of about $7.36^{\circ }$, accommodated by strain and defects.

A multiply twinned particle containing twenty approximately tetrahedral domains around a common centre. Its idealized exterior has twenty triangular facets; surface-energy reduction competes with strain and twin-boundary costs.

An ideal column model with the same adsorption-to-desorption ratio at every height. With $x=Kp$, the stationary height distribution is $P(j)=(1-x)x^j$ for $0\le x<1$, and its mean is $x/(1-x)$. Unlimited height makes the mean diverge as $x\to 1^{-}$; at $x\ge 1$ no normalized equilibrium height distribution exists.

The 2019 and 2021 NE2 papers match Engineering 4I10 papers with public worked cribs: 2019 crib and 2021 crib. The 2020 NE1 cover explicitly crosslists Engineering 4M16; Engineering advertises student access to examination cribs for all years in its library. These three papers are skipped for new solutions. Student-answer availability for the other held papers remains unverified.

Stochastic methods for quantum many-particle expectation values or ground-state projection. Variational and diffusion approaches can include correlations beyond a single Slater determinant; fermion signs or nodal constraints and finite-system extrapolation require explicit control.

The lowest-energy unoccupied orbital of a specified reference electron configuration. In a fixed-orbital approximation, adding one electron occupies this orbital; orbital relaxation and electron correlation can alter that picture.

Orbital degeneracy means distinct spatial orbitals have equal energy within the specified model or symmetry. Two electrons in degenerate orbitals need not pair; exchange can favor a triplet state.

The occupied molecular orbital of greatest energy in a specified reference electron configuration. A fixed-orbital model removes an electron from this level first; relaxation and electron correlation can modify the resulting energy.

An energy-level scheme showing the occupied molecular orbitals and their relation to atomic orbitals. Occupancies must account for degeneracy and spin.

A molecular orbital with little or no net bonding interaction between the atoms in the stated orbital model. A symmetry-isolated atomic orbital can be exactly nonbonding in a minimal basis: the out-of-plane nitrogen $2p_z$ orbital in planar Ammonia has no matching hydrogen symmetry orbital. A mainly localized lone pair can acquire bonding admixture when a distortion permits additional mixing.

A spatial molecular orbital occupied by one electron. In an open-shell molecule, its empty opposite-spin slot can accept another electron even though the spatial orbital is occupied.