The group-7 transition metal with atomic number 75.

Measurement of gene expression together with positions within a tissue. Its spatial units can be individual molecules, segmented cells or capture regions; these units should not be conflated.

An error in assigning a complete molecular form. Controlling peptide-level identification error does not automatically control errors in intact-form identity or modification linkage.

The extracellular matrix is the material outside cells that supplies structural and biochemical context to a tissue. Its composition and geometry affect adhesion, mechanics and signaling. The distinction between cell behavior and its environment is therefore interactive rather than a separation between active cells and inert filler.

A connective tissue with specialised extracellular matrix, providing support in structures including much of the developing vertebrate skeleton.

Bone is living mineralized connective tissue forming major parts of the vertebrate endoskeleton. Its extracellular matrix combines organic material with mineral, supporting both toughness and stiffness. Cells continually remodel it, so a bone is a regulated tissue rather than an inert stone.

A tissue forming a lining or covering. Its normal organization and differentiation state matter when comparing epithelial tumors with adjacent tissue.

fibrosis is persistent accumulation and remodeling of extracellular material in tissue. In mechanobiology, altered matrix architecture and resistance can change the forces experienced by resident cells.

Muscle is tissue specialized for force generation through contractile machinery. Skeletal muscle, smooth muscle and cardiac muscle differ in cellular organization and control. Shortening is one possible outcome: a muscle can also generate force while its overall length remains nearly constant.^[ref]

Connective tissue supports, connects or separates other tissues through cells embedded in extracellular matrix. Its forms include loose supporting tissue, tendons, cartilage and bone. Variation in matrix composition and organization explains their very different mechanical behavior.

$\mathrm{S}{\mathrm{n}}_5^{2-}$, a five-vertex trigonal-bipyramidal Zintl cluster. Removing five mainly s-rich lone pairs from its 22 valence electrons leaves 12 skeletal electrons.

The metallic tetragonal form of tin stable near ordinary room temperature at ambient pressure.

The diamond-cubic form of tin favoured below about $13{}^{\circ }\mathrm{C}$ at ambient pressure. Its lower density than white tin contributes to the damage associated with tin pest.

Degradation associated with the slow transformation of white tin to lower-density grey tin. Nucleation, impurities and thermal history strongly affect its kinetics.

Perturbation theory for an isolated eigenvalue with a one-dimensional eigenspace. First-order nondegenerate perturbation theory gives the diagonal perturbation expectation, while second-order nondegenerate perturbation theory accounts for coupling to other unperturbed eigenstates through energy denominators. Symmetry can permit its use within one block even if another, uncoupled symmetry block has the same unperturbed eigenvalue.

For perturbation $V_0{e}^{-{\beta }^2{x}^2}$ and oscillator inverse length $\alpha =\sqrt{m\omega /\hslash }$, direct Gaussian expectation values give $\Delta E_0=V_0\alpha /({\alpha }^2+{\beta }^2{)}^{1/2}$ and $\Delta E_1=V_0{\alpha }^3/({\alpha }^2+{\beta }^2{)}^{3/2}$. A narrow perturbation samples the odd state's node and suppresses its shift by two extra powers of $\alpha /\beta$. A broad perturbation approaches a constant energy offset for both states.

A constant-amplitude drive lasting $T$ gives the Fourier transform in the title, where $\mathrm{sinc}x=\sin x/x$ and its value at zero is one. The transition probability in weak driving has a finite resonant maximum, first zeros at $\delta =\pm 2\pi /T$, and decreasing side lobes. Longer duration increases the peak as $T^2$ and narrows its width as $1/T$. The rotating-wave approximation discards a rapidly oscillating counterrotating term; it can have a small absolute error but a large relative error at the resonant term's zeros.

A uniform field $E(t)=E_0{e}^{-t/\tau }\Theta (t)$ couples through $V=-qEx$. Its first-order transition amplitude is $-q⟨f|x|i⟩\tilde{E}({\omega }_{fi})/(i\hslash )$, so the leading probability is $q^2|x_{fi}{|}^2{E}_0^2{\tau }^2/[{\hslash }^2(1+{\omega }_{fi}^2{\tau }^2)]$. A real pulse has equal spectral intensity at opposite frequencies; populations and dipole elements determine which upward or downward transitions are possible. Small peak amplitude does not remove the need to check total transition probability.