FocusedILS is the ParamILS variant that adapts the number of evaluation runs assigned to different configurations. Its pairwise comparisons use common benchmark instances and random seeds, extending the evidence when necessary instead of comparing arbitrary means from different run lists.^[ref]

An original example shows why unequal evidence needs care. Suppose configuration $A$ has completed two runs with costs $(2,2)$ seconds, while $B$ has four costs $(3,3,30,30)$ seconds. Their available means, $2$ and $16.5$, mix different instance coverage. On the two shared runs the comparison is $2$ against $3$. If extending $A$ to the same four runs gives $(2,2,40,40)$, its mean becomes $21$, reversing the ranking against $B$'s $16.5$. Matching the evidence does not prevent a ranking from changing when more evidence arrives.

The run allocation and the configuration search are different layers. Iterated local search proposes which settings to compare; the FocusedILS comparison procedure determines how much measured evidence supports the decision. BasicILS instead uses a fixed evaluation count $N$. Both still depend on a declared cost statistic and a representative workload.

The example is a finite-data illustration, not a confidence interval or proof about unseen inputs. A setting selected after adaptive evaluation should be assessed on unused instances, with the full tuning budget recorded. The cost of finding the configuration and the subsequent cost of running it answer different questions.

A paleomagnetic pole is a reconstructed geomagnetic-pole position inferred from remanent magnetic directions in rocks of a specified age, under a stated field model. In a geocentric axial dipole model, inclination $I$ gives paleolatitude $\lambda$ through $\tan I=2\tan \lambda$.

Oriented samples, age control and corrections for later deformation are essential. Stepwise thermal or alternating-field demagnetization helps separate older magnetization from later overprints. Comparing poles of different ages produces an apparent polar-wander path, which records motion relative to a continental block as well as possible field changes. An axial-dipole direction alone does not fix paleolongitude.^[ref]

A P-element vector is an engineered DNA carrier that uses P element recognition sequences to introduce cargo into chromosomes when the required P-element transposase is available. The mobile carrier and the enzyme source can be separate. Retaining the needed element ends does a different job from encoding the enzyme that acts on them.^[ref]

In the 1982 transformation study, a P-element vector carrying a wild-type Drosophila melanogaster rosy sequence produced germline transformants with inherited chromosomal copies and restored eye colour. The visible phenotype tested function of the transferred gene, while integration and transmission to descendants provided different evidence about its physical and hereditary fate.^[ref]

For an invented inheritance calculation, assume one autosomal insertion, a heterozygote crossed to an insertion-free animal, and ordinary segregation without viability or transmission distortion. Half the offspring are expected to inherit the insertion. This fraction is conditional on the genetic model; it is not the percentage of injected embryos that will be transformed. A fluorescent or visible signal alone also does not establish a stable single-copy insertion, and an inserted cargo need not express identically at every genomic location.

P-body assembly is the formation of a P-body from interacting RNA and proteins in the cytoplasm. It involves both the availability of participating molecules and their organization into a detectable structure. RNA processing activity, molecular association and the appearance of a fluorescent focus are related but distinct observations.

A 2005 study tested RNA's contribution by treating enriched P-body material with ribonuclease A, then examining the material recovered after centrifugation. RNA digestion disrupted the enriched foci. In cells, blocking translation initiation increased P-bodies, whereas blocking elongation retained messages in polysomes and promoted dissociation of the bodies.^[ref] These comparisons link assembly to RNA integrity and availability rather than simply to the presence of a decay-related protein.

The assay requires controls. Digestion of an enriched preparation tests its integrity under those conditions, not every molecular event in a living cell. A fluorescence change can reflect altered label abundance, redistribution or visibility. Comparing the recovered material and its fluorescent components helps separate disappearance of a visible focus from loss of the marked protein itself.

An original P-body detection threshold example makes the visibility issue quantitative. Suppose a fixed image contains candidate foci with measured intensities $(2,5,9)$. Counting only intensities at least 6 reports one focus; lowering the threshold to 4 reports two, without any change to the biological sample. Thus an imaging count is a measurement rule applied to the assembly, not the assembly process itself. This example is not a physical nucleation threshold.

The chemical activity of an RNA-processing complex can also differ from the organization of many complexes into one visible focus. To explain P-body assembly, ask separately which molecules associate, what promotes larger-scale organization and what the microscope can detect. Greater focus number or size alone does not specify a faster rate of RNA decay.

Autoxidation is oxidation of a substance by molecular oxygen, commonly proceeding through a self-propagating free radical chain in organic materials. The name does not mean that initiation is unnecessary. Light, existing peroxides or other radical sources can start a chain, and changes in initiation can alter the observed rate.

A basic hydrocarbon propagation scheme writes the substrate as $\mathrm{RH}$:A peroxyl radical is converted into a hydroperoxide while generating a new carbon-centered radical. The two-step cycle consumes substrate and oxygen but regenerates a chain carrier. Radical–radical reactions can terminate chains; hydroperoxide decomposition can create further initiating species.

An original limiting kinetic model assumes abundant oxygen, approximately constant substrate concentration and termination dominated by pairs of peroxyl radicals. If initiation supplies radicals at rate $R_i$ and termination removes them at $2k_t{P}^2$, the steady radical concentration isQuadrupling $R_i$ then doubles the propagation rate rather than quadrupling it. This scaling follows from the stated balance; it need not hold when oxygen delivery, changing substrate or other termination pathways control the experiment.

A motivating modern apparatus is the inhibited autoxidation assay. A primary method co-oxidizes a hydrocarbon substrate with a BODIPY-based signal carrier and monitors progress with a visible-light spectrophotometer. Comparing inhibited and uninhibited traces tests radical trapping while distinguishing reaction rate from trapping capacity.^[ref]

A reduced signal slope can reflect chemical inhibition or inadequate oxygen supply, so controls for oxygen-limited autoxidation, probe response and matched initiation matter. The chain mechanism helps explain why excluding oxygen, intercepting radicals and changing peroxide decomposition can affect oxidation differently. An arbitrary antioxidant-assay signal alone does not establish product identity or a biological benefit.

Font hinting guides the adjustment of a scaled outline font to the target pixel grid before rasterization. In TrueType, instructions can control how outline points move at a particular size and resolution. Grid fitting can preserve important strokes when faithful geometric scaling would leave them awkwardly positioned between pixels.^[ref]

For an idealized example, two equal-width vertical strokes can overlap different fractions of neighboring pixels after scaling. Their rasterized darkness can then differ despite equal geometric widths. Coordinating the adjusted stroke positions and widths can make their displayed weights more consistent. The target depends on the requested size: a correction suitable for a small glyph need not be appropriate when many more pixels resolve its outline.

Font hinting changes the geometry used for rendering, rather than the underlying Unicode text or its grapheme clusters. Glyph substitution, glyph positioning and font hinting solve different parts of the path from encoded text to a visible image.

Hydrogenphosphate, $\mathrm{HP}{\mathrm{O}}_4^{2-}$, is the doubly charged anion produced by removing a proton from dihydrogenphosphate. It is therefore the conjugate base of dihydrogenphosphate, and it is also the conjugate acid of fully deprotonated orthophosphate, $\mathrm{P}{\mathrm{O}}_4^{3-}$. These species share the same single-phosphorus, four-oxygen framework.^[ref]

The remaining proton allows hydrogenphosphate to participate on either side of an acid-base reaction:In the first reaction, hydrogenphosphate accepts a proton; in the second, it donates one. For a simple accounting example, one mole of $\mathrm{N}{\mathrm{a}}_2\mathrm{HP}{\mathrm{O}}_4$ supplies one mole of phosphate units and two moles of sodium counterions when dissolved. Subsequent proton transfers can change how those phosphate units are distributed between chemical species without changing the total amount of phosphorus. A stated concentration of total inorganic phosphate must therefore be distinguished from the concentration of hydrogenphosphate itself.

Dihydrogenphosphate, ${\mathrm{H}}_2\mathrm{P}{\mathrm{O}}_4^{-}$, is the singly charged anion obtained when phosphoric acid loses one proton. It is one protonation state of orthophosphate: one phosphorus atom remains connected to four oxygen atoms. Dihydrogenphosphate is the conjugate base of phosphoric acid and the conjugate acid of hydrogenphosphate.^[ref]

For example, reaction with hydroxide can transfer a proton from dihydrogenphosphate to the added base:The total electric charge is $-2$ on either side, and the number of phosphorus atoms is unchanged. This is an acid-base reaction, rather than the breaking of a pyrophosphate bridge. Together, dihydrogenphosphate and hydrogenphosphate can form a buffer solution, accepting added base or acid through interconversion. Their relative amounts at chemical equilibrium depend on pH and the relevant dissociation constant; a total phosphate measurement alone does not determine the amount of dihydrogenphosphate.

Pyrimidine is the aromatic organic compound ${\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}_2$ with a six-membered ring containing nitrogen at positions $1$ and $3$. It is therefore a diazine, specifically 1,3-diazine.^[ref]

Changing the nitrogen positions gives different molecules: pyridazine has the $1,2$ arrangement, while pyrazine has the $1,4$ arrangement. The same elemental formula therefore does not uniquely specify ring connectivity. In the $1,3$ arrangement, the two nitrogen atoms have one ring carbon between them along the shorter path; in the $1,2$ arrangement they are adjacent.^[ref]

Cytosine, thymine and uracil contain a pyrimidine-derived ring framework, but their added groups and bonding make them chemically distinct from unsubstituted pyrimidine. This distinguishes a parent ring structure from the biological nucleobases named by association with that structure.

A diazine is an aromatic six-membered heterocyclic compound whose parent ring contains four carbon atoms and two nitrogen atoms. The three unsubstituted parent arrangements share formula ${\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}_2$ but differ in connectivity: pyridazine is the $1,2$ arrangement, pyrimidine the $1,3$ arrangement, and pyrazine the $1,4$ arrangement.^[ref]

Why only three? Fix one nitrogen at position $1$ on a six-membered ring. The other can be adjacent, separated by one intervening ring atom, or opposite. Reflection identifies the remaining apparent alternatives: positions $6$ and $2$ describe the same adjacent arrangement, while $5$ and $3$ describe the same next-nearest arrangement. Thus the distinct shortest ring separations are one, two and three bonds.

The three diazines are constitutional isomers, not different orientations of one molecule. Rotating a drawing changes its appearance without changing its atom-to-atom connections. Moving a ring nitrogen to another connectivity position instead changes which chemical compound the drawing represents. This makes the diazine family a compact example of why a molecular formula alone does not specify chemical identity.

A cone point of an oriented two-dimensional orbifold is a point with a chart modeled on a disk modulo a nontrivial finite cyclic rotation group. For a group of order $m$, its local quotient metric has total angle $2\pi /m$, and its stabilizer is cyclic of order $m$.

For example, identifying the edges of a planar sector of angle $2\pi /3$ gives the local order-three model. The underlying quotient neighborhood is homeomorphic to a disk, so the cone order is not detectable from topology alone. A point with order one is an ordinary nonsingular point.

A cone point is distinct from a mirror boundary point, whose local group acts by a reflection. It also differs from a general metric cone singularity: an orbifold cone angle must be of the form $2\pi /m$ with positive integer $m$. A teardrop orbifold has exactly one such exceptional point on an underlying sphere.

A teardrop orbifold is an orbifold whose underlying topological space is a two-sphere and which has exactly one cone point of an orbifold of order $m>1$. A neighborhood of that point is modeled on a disk modulo rotations by multiples of $2\pi /m$; every other point has trivial local group.

Topologically, a disk modulo this finite rotation group is still a disk. The local stabilizer is therefore extra orbifold information invisible in the underlying sphere. The singularity order distinguishes teardrops that have the same underlying topological space.

The teardrop is a standard example of a bad orbifold: it has no manifold orbifold covering. Cutting it into an ordinary disk and a disk with one order-$m$ cone point exposes incompatible nontrivial covering behavior along their common boundary. Thus being locally a finite quotient does not imply being globally covered by a manifold.^[ref]