Storing information that is also derivable from other stored information. A hard link count summarizes directory entries, while a block allocation bitmap summarizes block ownership in a file system. Such summaries accelerate common operations and permit consistency comparisons; replicated data can additionally assist recovery. Every update must maintain the redundant relationship, or establish a protocol for detecting and repairing divergence.

Unicode assigns code points and character properties for representing written text across languages and technical notation. A code point such as U+0041 identifies the character A; an encoding such as UTF-8 determines the bytes storing it. Code points, bytes and displayed user-perceived characters are different units: a displayed accented letter may use a base character plus a combining mark. Consequently byte counts do not generally give character counts. Normalization specifies relationships between canonically equivalent sequences; glyph appearance also depends on fonts and shaping.^[ref]

Computer architecture studies the organization and behaviour of computers, connecting the operations visible to software with the hardware that executes them. An instruction set architecture specifies the machine-level contract, including instructions, accessible processor registers and addressing behaviour. A microarchitecture is a particular implementation of that contract, including execution units, instruction pipelining and memory caches.^[ref]

Two CPUs can implement the same instruction set architecture while taking different times to run the same computer program. One might overlap independent instructions or use a larger memory cache; neither choice changes what an addition instruction is required to compute. A useful performance model writes execution time as instruction count times average cycles per instruction divided by clock frequency. The factors interact: a design that raises clock frequency can also change cycles per instruction. This separates a program's required behaviour from the engineering choices that determine its cost.

A database is an organized collection of data maintained for queries and updates. A database management system manages that collection, enforcing access rules and database integrity constraints. A relational database represents it through database relations, rather than exposing only an arbitrary collection of bytes in files.

For example, a laboratory can store biological sample identifiers, measurement values and scientific instrument identifiers as database tuples. A database query can select measurements above a threshold and join them to scientific instrument records. A foreign key can require every recorded scientific instrument identifier to name an existing scientific instrument. This makes the connection a maintained rule rather than a convention that every application must remember.

The logical relational schema and actual storage are distinct. A database query plan may use an index or scan database pages while returning the same specified result. Database transactions coordinate related updates, and database integrity constraints restrict the permitted states. PostgreSQL's documentation gives a concrete implementation in which named tables contain rows with named, typed columns and databases group tables.^[ref]

A collection of assertions and rules interpreted together. A logical knowledge base can be studied through its models, its consequences, or a specified nonclassical semantics.

Logic programming represents knowledge and queries through logical clauses, letting an inference procedure search for substitutions making a query true. A fact such as parent(ada, ben) and a rule saying that a parent of a parent is a grandparent can answer a grandparent query without listing every answer explicitly. Prolog commonly combines unification with ordered goal search and backtracking. Declarative meaning and execution strategy must be distinguished: two logically equivalent rule orders can have different termination behaviour. The method connects mathematical logic to executable symbolic inference.

The account of matter in terms of chemical atoms. Whole-number combinations of chemical atoms explain the law of definite proportions and law of multiple proportions for suitable pure chemical compounds.

A reducing substance supplies electrons to another species in a redox reaction and is itself oxidized. The role depends on the reacting pair and conditions, rather than being an immutable label on every molecule.

For example, iron(II) can reduce a suitable oxidant while becoming iron(III). Comparing reduction potentials can predict equilibrium preference, but reaction barriers and chemical speciation still affect whether the transfer occurs rapidly.

A chemical mixture contains two or more components with proportions that can vary. It can be homogeneous, such as a fully mixed solution, or heterogeneous, such as solid particles suspended in a liquid.

Mixing does not require forming one new compound with fixed stoichiometry, although components can interact or react. The mixture's properties depend on composition and phase behavior, so a pure-component property cannot automatically be assigned to the whole sample.

Laboratory apparatus comprises equipment for containing, transforming, controlling, and measuring experimental systems. In chemistry, a beaker contains a sample, a burette measures delivered liquid volume, and a thermometer senses temperature; these are different roles.

A useful experimental description specifies the apparatus features that affect the result, such as vessel closure, calibration, mixing, and sensor position. Naming an instrument alone does not establish what quantity it measured or with what uncertainty.

An inorganic compound is a compound conventionally studied within inorganic chemistry, including many salts, oxides, metals' coordination compounds, and minerals. The category is not determined by the complete absence of carbon: carbon dioxide and carbonates are normally classified as inorganic.

The distinction from organic chemistry is useful for organizing characteristic structures and methods, but the boundary overlaps strongly in organometallic chemistry and biological metal chemistry.

 Article slug not found: "undefined"

A rat is a relatively large mouse-like rodent; the common name covers several lineages. In experimental work it often refers to domesticated strains of Rattus norvegicus. Species and strain matter when comparing measured traits.

The rhesus macaque, Macaca mulatta, is an Old World monkey used in research on physiology, animal behaviour and neuroscience. Its importance as a model depends on the particular trait and comparison, not on an assumption of complete equivalence to humans.

For a complex antisymmetric tensor $A\in {\wedge }^2{\mathbb{C}}^4$, the SU(4) action is $A\mapsto UA{U}^T$. The unitary skew-diagonalization of an antisymmetric matrix gives $A=\mathrm{diag}(aϵ,bϵ)$ in suitable coordinates, where $ϵ=\left(\begin{array}{cc}0& 1\\ -1& 0\end{array}\right)$. If $|a|\ne |b|$, preserving $A{A}^{†}$ forces a stabilizing unitary matrix to preserve the two coordinate planes. The identity $VϵV^T=(\det V)ϵ$ then forces both two-by-two blocks to have determinant one, using $\det U=1$ also when one of $a,b$ vanishes. The exact stabilizer is $SU(2)\times SU(2)$. If $|a|=|b|\ne 0$, the stabilizer is the larger compact symplectic group $USp(4)$. If $a=b=0$, it is all of $SU(4)$. The real structure of the SU4 exterior square imposes $b=\bar{a}$ in this form, so a nonzero real six-dimensional field has the larger symplectic stabilizer, whereas unequal paired singular values are generic for a complex six-dimensional field.

For two coherent square pulses of equal duration $\tau$, pulse-start separation $T\ge \tau$, resonant Rabi angular frequency $\Omega$, and Rabi detuning $\delta$, the initially lower-state transition probability has the displayed leading weak-excitation form when $|\Omega |\tau \ll 1$. Integrating the first-order probability amplitude over both windows gives a sum of two equal Fourier transforms, with relative quantum phase $\delta T$. The factor four from coherent addition makes the central value $(\Omega \tau {)}^2$. The rotating-wave approximation additionally requires many carrier cycles per pulse and near-resonant weak driving.

A human in the earliest postnatal period. Research reports should specify chronological age and, where relevant, gestational or corrected age; an infant sample does not establish performance across the whole period.