# Glossary of Technical Terms and API ElementsΒΆ

- additivity
- The property which states that a given response can be explained by a linear sum of the inputs.
- condition number
- A measure of the sensitivity of a function. In terms of linear equations, the condition number gives a bound on the inaccuracy of the solution and is a property of the matrix of the linear coefficients, not of the input.
- conditioning
- The process of decreasing the condition number of a function.
- connection density
- The connection strength between two regions divided by the size of the target region.
- connection strength
- The sum of the connection weights from all voxels in a source :term`region` to all voxels in a target region.
- coarse structures
- major brain divisions
The set of 12 major brain divisions from the 3D Allen Mouse Brain Reference Atlas. These include:

- Isocortex
- Olfactory Areas
- Hippocampus
- Cortical Subplate
- Striatum
- Pallidum
- Thalamus
- Hypothalamus
- Midbrain
- Pons
- Medulla
- Cerebellum

- cross validation
A model validation technique used in estimating the predictive accuracy of a model. Typically, the data are partitioned into two sets:

- a training set with which the model is fit
- a testing set with which the prediction error of the fitted model is determined.

Often, this partitioning is repeated K times (typically 5 or 10) using unique samples for the testing set accross each of the K folds.

See https://en.wikipedia.org/wiki/Cross-validation_(statistics) for more information.

- edge density
- The total number of edges in a graph over the total possible number of edges in a graph.
- elastic-net
- A regularization that combines the lasso with ridge regression
- frobenius norm
- The 2-norm of a matrix viewed as a vector.
- homogeneous
- homogeneity
- Generally: of the same kind.
- homogeneous model
- The connectivity model at the level of regions that assumes that intra-regional connectivity is homogeneous and that inter-regional connectivity satisfies an additivity property. This model is based on non-negative linear least squares.
- ill-conditioned
- A function with a high condition number.
- kernel
- In nonparametric statistics, a kernel is a window function that describes the weighting method with which to combine sample information.
- lasso
- A regrularization technique that utilizes the L1 norm to promote sparsity in terms of the model parameters. See https://en.wikipedia.org/wiki/Lasso_(statistics)
- linear least squares
- Method of approximately solving a system of linear equations by minimizing the sum of squared difference between the prediction and the data.
- mesoscale
- A coarser scale than that of single neurons or cortical columns, but finer than the set of coarse structures. Can refer to the level of regions (especially summary structures) or to the level of voxels.
- nonparametric regression
- regression which does not assume the form of the estimator.
- normalized connection density
- The connection strength between two regions divided by the product of their sizes.
- normalized connection strength
- The connection strength between two regions divided by the size of the source region.
- quadratic program
- quadratic programming
- qp
- See https://en.wikipedia.org/wiki/Quadratic_programming
- radial basis function
- A real-valued function whose value only depends on the distance from the origin.
- region
- regions
- regional
- A structure in the brain, usually refering to a fine scale structure.
- regionalized model
- The connectivity model at the level of regions constructed by integrating the voxel model.
- regressor
- regressors
- regression
- Predictive modeling technique that attempts to determine the strength of relation between inputs and responses.
- ridge regression
- tikhonov regularization
- A regularization technique that shrinks the model parameter coefficients by utilizing an L2 penalty. See https://en.wikipedia.org/wiki/Tikhonov_regularization
- singular value decomposition
- See https://en.wikipedia.org/wiki/Singular-value_decomposition
- structure
- structures
- See region
- summary structures
- The set of 293 brain structures representing a summary level ontology for the mouse brain.
- voxel model
- The connectivity model based on nonparametric regression at the resolution at the voxel scale.
- voxel
- voxels
- A 3-D cubic volume element; the generalization of a pixel.
- well-conditioned
- A function with a low condition number.
- white matter
- fiber tracts
- Tissue that surrounds and insulates neurons.
- wildtype
- C57BL/6J
- Mice of strain C57BL/6J which have not been genetically altered.