The representation of white matter in the central nervous system

The white matter of the central nervous system (CNS) is difficult to represent in anatomy because it is located predominantly “between” other anatomical entities. In a classic presentation, like a cross section of a brain segment, white matter is present and can be labeled adequately. Several appearances of the same entity are feasible on successive cross section views. The problem is the absence of a global view on long tracts, and more generally, the lack of a comprehensive classification of white matter pathways. Following the recent revision of the Terminologia Anatomica (TA, 1998), in particular the chapter on the nervous system, resulting in the Terminologia Neuroanatomica (TNA, 2017), the authors have developed a new schema for the representation of white matter. In this approach, white matter is directly attached to the CNS, and no longer considered as part of the brain segments. Such a move does not affect the content but redistributes the anatomical entities in a more natural fashion. This paper gives an overall description of this new schema of representation and emphasizes its benefits. The new classification of white matter tracts is developed, selecting the origin as the primary criterion and the type of tract as the secondary criterion

The Representation of White Matter in the Central Nervous System

The white matter of the central nervous system (CNS) is difficult to represent in anatomy because it is located predominantly “between” other anatomical entities. In a classic presentation, like a cross section of a brain segment, white matter is present and can be labeled adequately. Several appearances of the same entity are feasible on successive cross section views. The problem is the absence of a global view on long tracts, and more generally, the lack of a comprehensive classification of white matter pathways. Following the recent revision of the Terminologia Anatomica (TA, 1998), in particular the chapter on the nervous system, resulting in the Terminologia Neuroanatomica (TNA, 2017), the authors have developed a new schema for the representation of white matter. In this approach, white matter is directly attached to the CNS, and no longer considered as part of the brain segments. Such a move does not affect the content but redistributes the anatomical entities in a more natural fashion. This paper gives an overall description of this new schema of representation and emphasizes its benefits. The new classification of white matter tracts is developed, selecting the origin as the primary criterion and the type of tract as the secondary criterion

Characterizing Vickrey allocation rule by anonymity

We consider the problem of allocating finitely many units of an indivisible good among a group of agents when each agent receives at most one unit of the good and pays a non-negative price. For example, imagine that a government allocates a fixed number of licenses to private firms, or that it distributes equally divided lands to households. Anonymity in welfare is a condition of impartiality in the sense that it requires allocation rules to treat agents equally in welfare terms from the viewpoint of agents who are ignorant of their own valuations or identities. We show that the Vickrey allocation rule is the unique allocation rule satisfying strategy-proofness, anonymity in welfare, and individual rationality

Capital allocation for portfolios with non-linear risk aggregation

Existing risk capital allocation methods, such as the Euler rule, work under the explicit assumption that portfolios are formed as linear combinations of random loss/profit variables, with the firm being able to choose the portfolio weights. This assumption is unrealistic in an insurance context, where arbitrary scaling of risks is generally not possible. Here, we model risks as being partially generated by Lévy processes, capturing the non-linear aggregation of risk. The model leads to non-homogeneous fuzzy games, for which the Euler rule is not applicable. For such games, we seek capital allocations that are in the core, that is, do not provide incentives for splitting portfolios. We show that the Euler rule of an auxiliary linearised fuzzy game (non-uniquely) satisfies the core property and, thus, provides a plausible and easily implemented capital allocation. In contrast, the Aumann–Shapley allocation does not generally belong to the core. For the non-homogeneous fuzzy games studied, Tasche’s (1999) criterion of suitability for performance measurement is adapted and it is shown that the proposed allocation method gives appropriate signals for improving the portfolio underwriting profit