A DNA microarray is a microarray whose spatially indexed sites carry known DNA sequences. A labelled sample binds through DNA hybridization, and signal at each site reports complementary material retained there. In a gene expression assay, material derived from messenger RNA is compared across many genes in parallel; the readout depends on transcript abundance and the chemistry of binding and labelling.^[ref]

The 1995 experiment used robotic printing of Complementary DNA onto glass, allowing many tests in a small hybridization volume.^[ref]

For a synthetic calculation, suppose the two sample signals are 1,000 and 600 units, with background 200 units in each. Background-corrected signals are 800 and 400, giving a ratio of $2$ and a base-two logarithm of $1$. The raw ratio $1000/600$ would give a different answer. Further correction for sample-wide effects may still be required. A transcript ratio supports an interpretation about gene expression; deriving a protein abundance ratio requires additional evidence about biological translation and turnover.

A nanometre is $10^{-9}$ metres. The prefix nano denotes the exact decimal factor $10^{-9}$. A length of $500\mathrm{nm}$ is $5\times 10^{-7}\mathrm{m}$, a typical visible-light wavelength.^[ref]

The unit is convenient for comparing molecules, thin films and optical wavelengths. A smaller number of nanometres does not by itself identify a different physical regime: the relevant comparison may be with an atomic spacing, a mean free path or a wavelength, depending on the experiment.

A millimetre, symbol $\mathrm{mm}$, is exactly one thousandth of a metre: $1\mathrm{mm}=10^{-3}\mathrm{m}$. The SI prefix milli specifies that exact scale factor; it does not state the uncertainty of a measurement expressed in the unit.^[ref]

For example, a thickness of $0.25\mathrm{mm}$ is $250\mu \mathrm{m}$ or $2.5\times 10^{-4}\mathrm{m}$. Powers of a unit require powers of the conversion factor: $1{\mathrm{mm}}^2=10^{-6}{\mathrm{m}}^2$ and $1{\mathrm{mm}}^3=10^{-9}{\mathrm{m}}^3$. Thus a cube with 10 millimetre edges has volume $1000{\mathrm{mm}}^3=1{\mathrm{cm}}^3$, not $1000{\mathrm{cm}}^3$. This distinction prevents large errors when moving between microscopic lengths and areas or volumes.

A decimetre, symbol $\mathrm{dm}$, is exactly one tenth of a metre:The SI prefix deci fixes the factor $10^{-1}$. This exact relation concerns units; the uncertainty of a measured length still depends on the measurement.^[ref]

The decimetre connects familiar lengths to volume particularly neatly. A cube with edges $1\mathrm{dm}$ has volumeThus a litre is exactly a cubic decimetre, while a cubic metre contains 1,000 litres. The exponent acts on the conversion factor as well as the unit: a cubic decimetre is not one tenth of a cubic metre.^[ref]

For example, a rectangular container measuring $2\mathrm{dm}$ by $3\mathrm{dm}$ by $0.5\mathrm{dm}$ has volume $3\mathrm{d}{\mathrm{m}}^3=3\mathrm{L}$, assuming the stated dimensions describe its interior. A length conversion becomes a cubic conversion when used to compute volume.

A micrometre, symbol $\mu \mathrm{m}$, is a unit of measurement for length equal to one millionth of a metre:The SI prefix micro supplies the exact factor $10^{-6}$.^[ref]

For an invented measurement example, a metal foil of thickness $25\mu \mathrm{m}$ has thickness $0.025\mathrm{mm}$. Forty such layers have combined thickness $1000\mu \mathrm{m}=1\mathrm{mm}$ if they lie flat without gaps. The calculation makes a small length tangible without assuming a particular measuring instrument.

Unit conversion does not remove measurement uncertainty. A reported thickness of $(25\pm 1)\mu \mathrm{m}$ becomes $(0.025\pm 0.001)\mathrm{mm}$: both the value and its uncertainty receive the same exact scale factor.

HMAC constructs a message authentication code from a cryptographic hash function and a shared secret key. For a hash $H$ with input block size $B$ bytes, normalize the key to a $B$-byte string $K_0$: first hash it if it is longer than $B$, then pad with zero bytes. The construction isHere $\oplus$ is bytewise exclusive or, $\Vert$ is concatenation of strings, ipad repeats byte 0x36, and opad repeats byte 0x5c. The inner and outer keyed hashing stages are part of the construction, rather than interchangeable placements of a key beside a message.^[ref]

A concrete interoperability example uses SHA-256, a member of SHA-2. Its block size is64 bytes while its full digest is32 bytes. With a key of20 0x0b bytes and the ASCII message Hi There, the hexadecimal tag is b0344c61d8db38535ca8afceaf0bf12b881dc200c9833da726e9376c2e32cff7.^[ref]

The receiver recomputes the tag using the shared key and checks the received tag. HMAC authenticates the message without concealing its contents; encryption is a separate operation. Because both parties know the key, both can make valid tags. A valid tag also remains valid when the same authenticated message is sent again, so replay handling belongs to the surrounding cryptographic protocol.

HMAC's original analysis and design are due to Mihir Bellare, Ran Canetti and Hugo Krawczyk.^[ref]

A movable memory object is a live allocation that its memory-management system may relocate while preserving its identity and valid references. Moving the stored bytes is only part of the operation: references must be updated, or an indirection mechanism must continue to locate the object. This capability permits memory compaction. Microsoft's primary runtime documentation describes separate marking, reference-relocation and object-compaction phases of garbage collection.^[ref]

For an illustrative16-byte object initially starting at offset24, compaction may place its bytes at offset0. A reference to its beginning then changes from24 to0; a reference five bytes inside it changes from29 to5. In general, moving the base from $a$ to $a^{\prime }$ maps a tracked interior reference $a+k$ to $a^{\prime }+k$. An unrelated integer with value29 must not be rewritten merely because it resembles the old address.

The memory manager therefore needs reliable knowledge of roots and references, including those held in other live objects. A garbage collection root can keep an object reachable while its address changes. If an external consumer requires the address to stay fixed, a pinned memory object imposes a relocation constraint instead. Movability is a property of the reference-management arrangement, not simply of whether the object contains bytes that can be copied.

A raw C programming language pointer returned by an ordinary allocator generally prevents arbitrary hidden movement, because the allocator does not control all copies of that address.^[ref] Physical-page movement under virtual memory is another layer: an operating system may preserve virtual addresses while changing the underlying physical mapping. It need not make the application-level object movable in its own address space.