Carla P. Concepcion investigated whether the miR-34 family is necessary for p53-dependent responses. Deletion of the family in the studied house mouse models left major p53 responses intact, distinguishing the necessity of an endogenous regulator from the effects of artificially increasing its expression.^[ref]

David S. Hong investigated delivery of a miR-34a mimic in the phase1 MRX34 study in patients with advanced solid tumours. Encapsulation in a liposome linked a proposed microRNA intervention with the separate experimental problem of delivering an RNA molecule in the body.^[ref]

Tina M. Avolio-Hunter coauthored research on DNA replication.^[ref]

DNA replication copies a double-stranded DNA molecule into two daughter double-stranded DNA molecules. In semiconservative replication, each daughter retains one parental strand and receives one newly synthesized complementary strand. DNA polymerases build the new strands from incoming nucleotides; they do not make RNA or proteins in this copying step. See Alberts et al., Molecular Biology of the Cell, 4th edition (2002): DNA replication mechanisms.

Julia Su Zhou Li coauthored research on chromosomal fragile site.^[ref]

A locus prone to abnormal gaps, undercondensation or breakage under specified cellular conditions. A cytological gap is not by itself proof of a DNA double-strand break.

Kathryn R. Ayscough coauthored research on actin filament.^[ref]

A actin filament assembled from actin subunits. actin filament mass and actin filament number are distinct quantities; subunit exchange can continue while the total mass is approximately steady.

Annelise Sahin coauthored research on Saccharomyces cerevisiae.^[ref]

Saccharomyces cerevisiae is a particular species of yeast, used in baking, brewing and laboratory research. During ordinary vegetative growth it reproduces by budding: a smaller daughter grows from the mother before separation. Laboratory strains can be maintained as either haploid or diploid biological cells. This makes it possible to investigate genes in a single eukaryote, then use controlled crosses and meiosis to connect a genotype to a phenotype. See Burgess, Powers and Mell, Budding Yeast Saccharomyces cerevisiae as a Model Genetic Organism (2017), pp. 1–2.

A lipid bilayer nanodisc is a small bilayer patch stabilized at its edge, often by a surrounding scaffold. It permits controlled lipid composition and study of membrane-associated proteins, while lacking the two separately sealed aqueous compartments of a closed lipid vesicle.

spontaneous curvature is the preferred curvature of a membrane or monolayer in a specified elastic description. Headgroup hydration, chain geometry and leaflet composition can change it; the sign depends on the chosen surface-normal convention.

A liquid-ordered phase combines relatively ordered lipid chains with lateral molecular mobility. It is distinct from a solid gel and can coexist with a liquid-disordered phase in suitable mixtures.

A liquid-disordered phase has relatively disordered lipid chains and lateral molecular mobility. Whether it coexists with a liquid-ordered phase depends on mixture composition and temperature.

A lipid assembly containing a bilayer-like region whose edges are stabilized by other components, often short-chain lipids or detergents. Size and composition affect its use as a membrane mimic.

Let the four haplotype frequencies sum to one and define $D=x_{AB}{x}_{ab}-x_{Ab}{x}_{aB}=x_{AB}-p_A{p}_B$. Recombination at rate $r$ removes the excess association: $\Delta x_{AB}=\Delta x_{ab}=-rD$ and $\Delta x_{Ab}=\Delta x_{aB}=rD$. Marginal allele frequencies are unchanged. Hence $D<0$ generates more $AB$, whereas $D>0$ removes it; a claim that recombination always increases this combination is false.

The random phase approximation treats the independent-particle response to the self-consistent total field, including the induced mean Coulomb potential. With a positive static number-response coefficient ${\Pi }_0=-\delta n/\delta U$, a potential $U=-e\varphi$ gives $\delta n=e{\Pi }_0{\varphi }_{\mathrm{tot}}$. Combining induced charge $-e\delta n$ with Poisson equation gives $ϵ=1+e^2{\Pi }_0/({ϵ}_0{q}^2)$. Exchange-correlation vertex corrections beyond this self-consistent response are omitted. It is a response approximation, not a literal assumption that every microscopic electron phase is independently randomized.

The Kitamasa algorithm evaluates a term of an order-$d$ linear recurrence by reducing powers of $x$ modulo its characteristic polynomial of a linear recurrence. If the recurrence relation is $a_{n+d}={\sum }_{j=0}^{d-1}{c}_j{a}_{n+j}$, reduce $x^N$ modulo $x^d-{\sum }_{j=0}^{d-1}{c}_j{x}^j$ by exponentiation by squaring; the resulting coefficients give $a_N$ as a linear combination of $a_0,\dots ,a_{d-1}$. Straightforward polynomial multiplication gives $O(d^2\log N)$ arithmetic operations.

For the constant-coefficient homogeneous linear recurrence relation $u_{n+r}={\sum }_{j=0}^{r-1}{c}_j{u}_{n+j}$, its characteristic polynomial isA nonzero root $\lambda$ gives the solution $u_n={\lambda }^n$. Over a field of characteristic zero, a root of multiplicity $m$ contributes ${\lambda }^n,n{\lambda }^n,\dots ,n^{m-1}{\lambda }^n$ when $\lambda \ne 0$. The Fibonacci sequence has $p(t)=t^2-t-1$, whose roots give its familiar closed formula.

Equivalently, $p$ annihilates the shift on every solution. Reducing $t^N$ modulo $p(t)$ therefore expresses the distant term $u_N$ as a linear combination of $u_0,\dots ,u_{r-1}$. Repeated squaring in the polynomial quotient ring gives this combination using logarithmically many multiplications in $N$.

For fixed parameters $P,Q$, the two Lucas sequences are the solutions of the linear recurrence relation $W_{n+2}=P{W}_{n+1}-Q{W}_n$ with initial values $U_0=0,U_1=1$ and $V_0=2,V_1=P$. They are the Lucas U-sequence and the Lucas V-sequence. The choice $(P,Q)=(1,-1)$ gives the Fibonacci sequence and the ordinary Lucas numbers.

If $\alpha ,\beta$ are distinct roots of $t^2-Pt+Q$, direct substitution gives $U_n=({\alpha }^n-{\beta }^n)/(\alpha -\beta )$ and $V_n={\alpha }^n+{\beta }^n$. The recurrence itself remains meaningful when the roots coincide or division is unavailable, so it is the safest definition over a general ring. Fast doubling for Lucas sequences exploits these two related solutions to compute distant terms.

A linear recurrence matrix advances a vector of quantities by a fixed linear map: $v_{n+1}=M{v}_n$, hence $v_n=M^n{v}_0$. It can encode several simultaneous linear recurrences and need not satisfy the normalization required of a Markov chain transition matrix.

A difference between the two scalar metric potentials in a specified cosmological convention. Nonrelativistic motions probe the potential in the time-time metric component, while weak gravitational lensing probes their sum. Joint tests can constrain modified gravity, but ordinary anisotropic stress can also generate slip and observational bias must be controlled.