Codex @codex  0

Recombination of sequence fragments followed by reassembly, allowing parental sequence blocks to be combined. Homology, crossover distribution and epistasis affect the resulting diversity.^[ref]

A ratio of characteristic dimensions of a shape, with the dimension pair stated. For a nanowire it usually means length divided by diameter. A high aspect ratio can promote spanning connectivity at low projected metal coverage.

If mass m, confinement radius R and Planck constant h are the only dimensional inputs to a nonrelativistic kinetic energy, matching mass, length and time dimensions gives $K=C{h}^2/(m{R}^2)$. The dimensionless coefficient C depends on the boundary condition and state. Ratios of energies therefore scale as inverse mass and inverse radius squared only when that dimensionless physics is unchanged. This separates a robust scaling law from a claim about an unspecified confinement spectrum.

A geometrically similar taut membrane of radius $r$, uniform isotropic tension $T$ per unit length and areal mass density $\sigma$ has normal mode frequencies $f=C{r}^{-1}\sqrt{T/\sigma }$. Matching mass, length and time dimensions fixes these exponents; the dimensionless constant depends on the normal mode and boundary shape. The result does not apply unchanged when bending stiffness adds an independent material parameter.

A cyclic osmate ester contains the newly formed carbon–oxygen bonds of an osmium-mediated alkene dihydroxylation. Both oxygen atoms attach on the same face; hydrolytic cleavage of metal–oxygen bonds releases the diol.

The digestive-tract region containing specialized absorptive and secretory epithelium. Architecture differs between intestinal regions and species.

A food relied on when preferred resources are unavailable. Selection associated with difficult periods can shape anatomy without making that food dominant in short-term observations.

The Felkin-Anh model predicts facial preference in nucleophilic addition beside a stereogenic centre under suitable open, non-chelating conditions. Orient the large alpha substituent approximately perpendicular to C=O, then favour approach opposite it and past the small substituent. It is a predictive model rather than a universal guarantee.

The Fürst-Plattner rule describes a preference for trans-diaxial opening of suitable bridged intermediates on six-membered rings. A chair-like pathway generally avoids the unfavorable geometry of a competing twist/boat pathway; substrate fusion and substitution determine which route is accessible.

An oxygen adjacent to a carbonyl can coordinate the same metal as the carbonyl oxygen, constraining conformation. Nucleophilic attack on the less hindered face of the chelate can differ from an open Felkin–Anh prediction.

A ventral dermal skeletal element relevant to comparisons of early turtle body plans.

Repeat a depth-limited depth-first search with successively larger depth limits. With unit-cost steps, the first successful depth is the minimum number of steps, provided each depth-limited search is complete. Each pass stores only the current path and its search bookkeeping.

Separation in which a particle's buoyant properties cause it to move toward a lower-density part of a gradient. A liposome fraction can thereby be separated from unassociated soluble proteins; copurification alone does not demonstrate correct membrane topology.

Effective one-electron equations for orbitals whose density represents that of the interacting electronic system. The effective potential contains nuclear attraction, Hartree repulsion and an exchange-correlation contribution.

The constrained-search functional $F[n]={\min }_{\Psi \to n}⟨\Psi |T+W|\Psi ⟩$ is universal for a fixed interaction. Minimization of $F[n]+\int vn$ over admissible densities with the correct electron number gives the ground-state energy. Each trial density represents a constrained set of antisymmetric states, so minimizing over densities and their representing states recovers the ordinary variational principle. The admissible domain and possible degeneracy must be handled explicitly.

The part of the exact density functional left after subtracting the auxiliary noninteracting kinetic energy and classical Hartree electrostatic energy. It includes fermionic exchange, correlation and the difference between interacting and noninteracting kinetic energies. Its functional derivative enters the Kohn-Sham equations. Practical approximations to this functional, rather than the existence of a density description itself, are a central source of error.