Exclusion of arriving material from a region by an intervening feature. A broad incident angular distribution can reduce shadowing but does not guarantee conformality.

A DNA hairpin is a stem-loop formed within one DNA strand. Complementary arms can pair while intervening bases form a loop; bases outside the paired arms remain overhangs.

Ablation of engineered receptor-expressing cells using diphtheria toxin. Receptor-negative toxin controls, time-course verification and survival of untargeted compartments are essential.

The classical parallax-calibration problem combines measurement errors with the greater volume available at larger distances. A locally uniform spatial population has $p(r)\propto r^2$, which transforms under $r=1/\varpi$ to $p(\varpi )\propto {\varpi }^{-4}$ on the valid distance interval. Parallax cuts and the nonlinear conversion to luminosity can bias calibration samples. A correction is not universal: the population model, selection information and inferential target must be specified. Distinguish the repeated-sampling bias of a selected sample from inference for a particular star using a justified prior.^[ref]

For a measured stellar parallax $\hat{\varpi }$ with known standard deviation ${\sigma }_{\varpi }>0$, a simple astrometric model is $\hat{\varpi }\mid r\sim N(1/r,{\sigma }_{\varpi }^2)$, using compatible angular and distance units. ThusThis likelihood approaches a positive constant as $r\to \infty$. An unbounded constant-volume-density prior proportional to $r^2$ therefore gives an improper posterior. One proper alternative iswhich combines spherical volume growth with an exponentially decreasing spatial number density. The normalization follows from ${\int }_0^{\infty }{r}^2{e}^{-r/L}dr=2L^3$. Multiplying by the bounded likelihood gives a normalizable posterior even for non-positive measured parallaxes.^[ref]

A negative measured stellar parallax is compatible with a positive true distance under this noisy model; it should not be inverted into a negative distance. When the likelihood becomes nearly flat over the relevant distances, the posterior approaches the chosen prior, whose mode is $2L$. The scale $L$ represents population and survey knowledge, not an additional distance measurement. Testing sensitivity to that choice is part of honest low-signal Bayesian inference.

An RR Lyrae star is a short-period pulsating evolved star used as a distance tracer in old populations. Its calibrated luminosity depends on composition and photometric band; infrared period-luminosity-metallicity relations are especially useful. extinction, crowding, mode identification and calibration remain important.

A plot of stellar magnitude against a colour index. It is an observational counterpart of the Hertzsprung-Russell diagram, but converting colour to effective temperature and magnitude to luminosity requires calibration, extinction and distance information. A coeval population's main-sequence turnoff helps estimate its stellar age.

For $dX/dt=P-kX$ with locally fixed coefficients, $X(t)=P/k+(X_0-P/k)e^{-kt}$. Setting $dX/dt\simeq 0$ requires $1/k$ to be short compared with changes in production, loss and transport. A major reservoir can fail this test even when nearby radicals rapidly adjust.

A statistical model combining fixed effects with random effects. The grouping structure determines the correlations represented by the model.

quantum statistical mechanics describes equilibrium and fluctuations with density matrices and traces over a quantum Hilbert space. The canonical equilibrium state is $e^{-\beta H}/Z$, while particle exchange introduces $H-\mu N$ in the grand canonical ensemble. Noncommutativity and particle exchange distinguish it from a classical phase-space distribution.

classical statistical mechanics assigns probability distributions to classical states. For a Hamiltonian particle system the canonical weight is $e^{-\beta H}$ on phase space. The weak-exchange, high-temperature limit of a quantum gas supplies the measure $d^{d}x{d}^{d}p/(2\pi \hslash {)}^d$ per particle and the indistinguishable-particle factor $1/N!$.

Boundaries or inclusions change the available thermal or quantum fluctuations and thereby the free energy. Their force follows from $F=-\partial \mathcal{F}/\partial d$ under specified control conditions. Electromagnetic dispersion, depletion and critical fluctuations are distinct realizations, with signs and ranges set by their physical modes and boundary conditions.

Overestimation of effect magnitude when noisy discoveries are selected for unusually strong apparent effects. Independent replication and explicit modeling of the selection process help correct the bias.

A pseudolikelihood multiplies conditional probabilities rather than the full joint likelihood function. It can be useful for fitting a Markov random field, but using the product itself as a probability density defines a different model unless an additional equivalence is established.

An analysis in which data capable of revealing the sought result are hidden while selection and inference procedures are chosen. It reduces result-dependent tuning. calibration samples and predefined validation samples remain necessary; blinding does not itself correct a defective background model.

A copolymer with an ideal sequence in which the probability of a monomeric unit is independent of neighbouring units. A real copolymer made by concurrent radical reactions can have sequence correlations; a feed ratio does not by itself establish incorporated composition or independent-unit statistics.

A copolymer containing $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CHCl}-$ and $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}(\mathrm{OAc})-$ units. Hydrolysis changes the acetate side groups without requiring cleavage of the carbon backbone, provided competing degradation is controlled.

A copolymer containing $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CHCl}-$ and $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}(\mathrm{OH})-$ units. It describes the intended chemical composition, not a guarantee that unselective alkaline treatment yields an undegraded polymer.