The recently introduced generalized Hamiltonian–Real (GHR) calculus comprises, for the first time, the product and chain rules that makes it a powerful tool for quaternion-based optimization and adaptive signal processing. In this paper, we introduce novel dual relationships between the GHR calculus and multivariate real calculus, in order to provide a new, simpler proof of the GHR derivative r...

Recent studies have revealed the rules controlling cell size homeostasis in bacteria. However, whether these mechanisms apply to growth-defective backgrounds remains an open question. Herein, we propose a Markov chain model describing bacterial growth in wt or growth-defective backgrounds and test some of our predictions experimentally. Our results suggest that, in mutant backgrounds, bacteria ...

We investigate two examples of node-based cluster summation rules that have been proposed for the quasicontinuum (QC) method: a force-based approach and an energy-based approach which is a generalization of the nonlocal QC method. We show that, even for the case of nearest-neighbor interaction in a one-dimensional periodic chain, both of these approaches create large errors that cannot be remov...

We implemented a syntactic and semantic tagging system for SemEval 2015 Task 15: Corpus Pattern Analysis. For syntactic tagging, we present a Dependency Chain Search Algorithm that is found to be effective at identifying structurally distant subjects and objects. Other syntactic labels are identified using rules defined over dependency parse structures and the output of a verb classification mo...

The need for service rules, or policies, in supply chains arises if not all the parts processed in the chain are considered identical, but are distinguished by certain attributes. We develop and analyze a methodology to model arbitrary service rules in large supply chains based on a kinetic (traffic flow like) theory and a level set approach. The final result is a system of hyperbolic conservat...

In a recent paper, Luck [1] investigated the critical behaviour of one-dimensional Ising quantum chains with couplings constants modulated according to general non-periodic sequences. In this short note, we take a closer look at the case where the sequences are obtained from (two-letter) substitution rules and at the consequences of Luck’s results at criticality. They imply that only for a cert...

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

In their recent paper, Leng and Parlar (L&P) (2009) analyze information-sharing alliances in a three-level supply chain (consisting of a manufacturer, a distributor, and a retailer) that faces a nonstationary end demand. Supply chain members can share demand information, which reduces information distortion and thus decreases their inventory holding and shortage costs. We expand the results fro...

HOL-TestGen/CirTA is a theorem-prover based test generation environment for specifications written in Circus, a process-algebraic specification language in the tradition of CSP. HOL-TestGen/CirTA is based on a formal embedding of its semantics in Isabelle/HOL, allowing to derive rules over specification constructs in a logically safe way. Beyond the derivation of algebraic laws and calculi for ...