In neural networks, network faults can be exhibited in different forms, such as node fault and weight fault. One kind of weight faults is due to the hardware or software precision. This kind of weight faults can be modelled as multiplicative weight noise. This paper analyzes the capacity of a bidirectional associative memory (BAM) affected by multiplicative weight noise. Assuming that weights a...

This document contains derivations for the method-of-moments algorithms used in the paper. The first section describes the general approach to deriving multiplicative update rules for the components of a non-negative matrix factorization (NMF). The next section discusses the convergence properties of NMF. Then we give the pseudocode of the sequence clustering algorithm for mixture of HMMs. And ...

This paper provides derivations necessary for solving an optimal consumption problem with multiplicative habits and a CRRA ‘outer’ utility function, either for a microeconomic problem with both labor income risk and rate-of-return risk, or for a macroeconomic representative agent model.

The present report is a, somewhat lengthy, addendum to Danos et al.(1997), where the elimination of cuts from derivations in sequent calculus for classical logic was studied`from the point of view of linear logic'. To that purpose a formulation of classical logic was used, that-as in linear logic-distinguishes between multiplicative and additive versions of the binary connectives. The main nove...

Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative 2-dimensional syntax for multiplicative linear logic derivations. The syntax of string diagrams authorizes the definition of a framework where the sequentializabi...