A posterior methylation profile gives the posterior probability of DNA methylation at each modeled site. It differs from one sampled binary pattern and from a maximum-probability joint pattern.

A genomic interval with a statistically supported difference in DNA methylation between the compared samples.

A DNA methyltransferase transfers a methyl group to DNA, commonly using S-adenosylmethionine as donor. Different enzymes modify different bases or sequence contexts. Some preserve an existing pattern after DNA replication, whereas others establish new marks. Consequently, unchanged sequence can coexist with altered DNA methylation and gene regulation; the modification changes chemical information on the inherited template rather than necessarily changing its base order. ^[ref]

Loss of methylated cytosines through active enzymatic replacement or through failed maintenance during replication.

Re-establishment of a pre-existing methylation pattern following DNA replication.

A daughter duplex can initially contain a modified parental strand paired with an unmodified new strand. A maintenance system restores the matching mark, whereas de novo methylation establishes marks at previously unmodified positions. These are different ways to preserve or alter an epigenetic pattern. ^[ref]

Establishment of methylation at a site that lacks the previous methylation pattern; sequence-directed and chromatin-directed recruitment provide specificity.

Methylation in the symmetric CG sequence context.

The symmetry matters after DNA replication: each daughter duplex can retain a methylated parental strand and an initially unmodified new strand. Maintenance DNA methylation can use that relationship to help restore the previous pattern, without changing the underlying base sequence. ^[ref]

Methylation in the CHG sequence context, where H is A, C or T; its restoration is strongly coupled to H3K9 methylation.

Methylation in an asymmetric CHH sequence context, where H is A, C or T; maintenance of the pattern requires repeated targeting rather than direct copying from a symmetric dyad.

The fraction or distribution of intended variants actually constructed or sampled, with those two meanings distinguished. Unequal variant frequencies and repeated clones reduce effective exploration.

Unlabelled DNA containing recognition sites for the protein being tested. Competition can draw that protein away from labelled DNA without necessarily removing other proteins from the labelled assembly.

DNA that lacks the selected recognition sequence but can accept nonspecific interactions or transferred histones. Its effect must be interpreted against controls for all components.

For a symmetric monovalent reservoir with number density $n$ of each species, linearizing Poisson-Boltzmann theory gives the displayed inverse screening length. A planar potential decays exponentially; a spherical far field also has a geometrical inverse-distance factor. Increasing salt reduces the range of repulsion. Fixed surface potential, fixed charge and charge regulation need not give identical interaction amplitudes.

A deep short-distance minimum can bind contacting particles, while a more distant shallow minimum can permit loose reversible aggregates. A repulsive barrier between them controls kinetic access to contact. Salt can lower that barrier through screening. Molecular-scale steric or hydration forces lie outside the simplest continuum dispersion-plus-double-layer model.

Division of integers that returns an integer quotient rather than an exact fraction. A rounding convention is required for negative operands. For $n\ge 0$ and $d>0$, the quotient is $q=\lfloor n/d\rfloor$ and the remainder is $r=n-qd$ with $0\le r<d$.

A positive integer $n$ is semidivisible when it lies strictly between the squares of consecutive prime numbers $p<q$,and is divisible by exactly one of $p$ and $q$. The strict inequalities exclude both endpoint squares. For example, $8$ is semidivisible because $2^2<8<3^2$ and only $2$ divides $8$. The integer $6$ lies in the same band but is divisible by both prime numbers, so it is excluded.

Within one band, a divisibility calculation can avoid testing every integer. Add the sums of integer multiples of $p$ and of $q$, then subtract twice the sum of integer multiples of $pq$. Each doubly divisible number was counted twice and should count zero times. Each sum is an arithmetic progression, and the same inclusion-exclusion bookkeeping works for counts instead of sums.

A divisibility rule tests whether one integer divides another by replacing it with a simpler equivalent condition. For a base-$b$ expansion $N={\sum }_i{d}_i{b}^i$, the congruence class of $b$ modulo the candidate divisor determines a rule.

In base ten, $10\equiv 1(\mathrm{mod}9)$, so $N$ and its digit sum have the same residue modulo nine. Also $10\equiv -1(\mathrm{mod}11)$, so divisibility by eleven is equivalent to divisibility of the alternating digit sum. For example, $121$ passes because $1-2+1=0$. These tests follow from modular arithmetic and depend on the numerical base.

At normal incidence, alternating layers with indices $n_H,n_L$ and optical thicknesses $n_H{d}_H=n_L{d}_L={\lambda }_0/4$ give reinforcing reflected waves near design wavelength ${\lambda }_0$. Their periodic transfer matrix has a stop band when its Bloch phase is complex. A finite stack has nonzero transmission and its exterior impedances matter. Introducing a suitably phased central defect can support a transmission resonance within the stop band; a one-dimensional stop band is not a complete three-dimensional photonic gap.

A lattice atom given a recoil by an incident particle. Its subsequent collisions can generate a displacement cascade; its energy distribution depends on the incident radiation and material.

A sequence of atomic recoils and local relaxation following an energetic impact in a solid. It can leave isolated Frenkel pairs, clusters and regions of altered local structure, rather than one permanent defect per initial collision.