Revised notation for partial derivatives

A Revised Textual Tree Trace Notation for Prolog

Decomposition of Multiport Elements in a Revised Multibond Graph Notation

Decomposition rules are derived for multiport-transformers, -resistors, -storage elements and -gyrators into land 2-port elements, junctions and bonds. It appears that it is useful to extend the vectorbond, or rather multibond, notation recently proposed by the author with a “multibond array”. Canonical forms are introduced on the basis of minimal realization, because decompositions of multipor...

Derivatives and Partial Derivatives for Regular Shuffle Expressions

There is a rich variety of shuffling operations ranging from asynchronous interleaving to various forms of synchronizations. We introduce a general shuffling operation which subsumes earlier forms of shuffling. We further extend the notion of a Brzozowski derivative and a Antimirov partial derivative to the general shuffling operation and thus to many earlier forms of shuffling. This extension ...

Combinatorics of Partial Derivatives

The natural forms of the Leibniz rule for the kth derivative of a product and of Faà di Bruno’s formula for the kth derivative of a composition involve the differential operator ∂/∂x1 · · · ∂xk rather than dk/dxk, with no assumptions about whether the variables x1, . . . , xk are all distinct, or all identical, or partitioned into several distinguishable classes of indistinguishable variables. ...

Efficient Hessian computation using sparse matrix derivatives in RAM notation.

This article proposes a new, more efficient method to compute the minus two log likelihood, its gradient, and the Hessian for structural equation models (SEMs) in reticular action model (RAM) notation. The method exploits the beneficial aspect of RAM notation that the matrix derivatives used in RAM are sparse. For an SEM with K variables, P parameters, and P' entries in the symmetrical or asymm...