A readout of lipid redistribution between membrane biological populations, for example through fluorescence dequenching. It must be distinguished from aqueous content mixing and leakage.

A measurement of exchange between previously separate enclosed aqueous compartments. Leakage into the surrounding medium is a different event and needs a separate control.

Vesicle docking brings a transport vesicle into close, stable association with its target membrane before membrane fusion. Recognition factors and SNARE proteins help organize the contact. Docking and fusion are experimentally distinct: a carrier can remain attached without exchanging its internal contents with the target compartment. Reconstituted liposomes bearing appropriate SNARE proteins allowed such docked intermediates to be distinguished from subsequent fusion. ^[ref]

A binary meldable heap satisfying heap order and the leftist condition: at each node, the shortest path to a missing child is no longer in the right subtree than in the left. Melding recurses down right spines, swaps children when needed, and takes logarithmic time.

A meldable heap satisfying the min-heap ordering: each parent key is no greater than its children's keys. It combines efficient merging with access to the current minimum key.

A component of measurement error fluctuating between repetitions under specified conditions, as distinguished from a shared systematic error. Independent zero-mean fluctuations of variance ${\sigma }^2$ give a sample-mean variance ${\sigma }^2/N$; correlated fluctuations need not follow this averaging law.

For distinct positive real numbers $a,b$, their logarithmic mean isusing the natural logarithm. Set $L(a,a)=a$ by continuity: the difference quotient of the natural logarithm tends to its derivative $1/a$, so the reciprocal tends to $a$. For example, $L(1,4)=3/\log 4\approx 2.164$.

An integral representation explains its name and its relation to multiplicative interpolation:For $a\ne b$, integrate $a\exp (t\log (b/a))$ directly; for $a=b$, the integrand is constant. Every interpolated value lies between $a$ and $b$, so the logarithmic mean does too. It is symmetric in $a,b$ and homogeneous: $L(ca,cb)=cL(a,b)$ for $c>0$.

A generalized McCarthy function replaces the constants or nesting depth in the McCarthy 91 function by parameters. One explicit two-call family isThe classical example has $(a,b,c)=(100,10,11)$. This name covers several parameter conventions, so the recurrence and parameter restrictions must accompany a claim about termination or values. Arbitrary constants do not guarantee termination: with $b=c=0$ and $n\le a$, evaluation immediately depends on the same unresolved call again. The family is useful for separating a recursive definition from an established total function.

For a monochromatic transverse field depending on $x,t$, with vacuum permittivity and permeability and arbitrary induced transverse current, Ampère's law gives $J_y=-{\partial }_x{H}_z-{ϵ}_0{\partial }_t{E}_y$. Multiplying by ${\mu }_0{H}_z$ and averaging Faraday's law gives the displayed gradient. No constitutive assumption $J=\sigma E$ is required. A steady average removes the field-momentum time derivative.

A local extremum of a real-valued function is either a local maximum or a local minimum, with comparisons restricted to a neighbourhood in its domain. A differentiable interior local extremum is a stationary point, but the converse can fail, as $f(x)=x^3$ at zero shows.

Seroprevalence is the proportion of a specified population with a positive result for a specified antibody assay. Its biological interpretation depends on assay diagnostic sensitivity, diagnostic specificity and the persistence and origin of the measured antibodies. It is not itself the incidence rate of new infection.

An irreversible serocatalytic model describes the transition from seronegative to seropositive after infection. If the force of infection is $\lambda (a)$ and detectable antibodies persist, the seronegative fraction satisfies $s^{\prime }(a)=-\lambda (a)s(a)$, hence seroprevalence is $1-\exp [-{\int }_0^a\lambda (u)du]$ when $s(0)=1$. Antibody loss needs a reverse transition, and imperfect testing needs a separate observation model.

Specific strength is strength divided by density, with the strength convention stated explicitly. For a uniform tie carrying tensile force $F$, allowable stress ${\sigma }_f$ requires area $A\ge F/{\sigma }_f$. Its mass $m=\rho AL$ is therefore at least $FL/({\sigma }_f/\rho )$. Maximizing ${\sigma }_f/\rho$ minimizes mass under this simple strength-limited model. A material with higher strength can still be worse if its density increases more. Mechanical fatigue, buckling, joining and temperature limits can impose additional constraints not captured by this single ratio.