An octonion algebra originating in combinatorics

C.H. Yang discovered a polynomial version of the classical Lagrange identity expressing the product of two sums of four squares as another sum of four squares. He used it to give short proofs of some important theorems on composition of delta-codes (now known as T-sequences). We investigate the possible new versions of his polynomial Lagrange identity. Our main result shows that all such identities are equivalent to each other.Comment: 11 pages, A simpler proof of the main theorem, due to Alberto Elduque, is inserted. The paper will appear in the Proc. Amer. Math. So

Extracting Functional Modules from Biological Pathways

It has been proposed that functional modules are the fundamental units of cellular function. Methods to identify these modules have thus far relied on gene expression data or protein-protein interaction (PPI) data, but have a few limitations. We propose a new method, using biological pathway data to identify functional modules, that can potentially overcome these limitations. We also construct a network of these modules using functionally relevant PPI data. This network displays the flow and integration of information between modules and can be used to map cellular function

General response theory of topologically stable Fermi points and its implications for disordered cases

We develop a general response theory of gapless Fermi points with nontrivial topological charges for gauge and nonlinear sigma fields, which asserts that the topological character of the Fermi points is embodied as the terms with discrete coefficients proportional to the corresponding topological charges. Applying the theory to the effective non-linear sigma models for topological Fermi points with disorders in the framework of replica approach, we derive rigorously the Wess-Zumino terms with the topological charges being their levels in the two complex symmetry classes of A and AIII. Intriguingly, two nontrivial examples of quadratic Fermi points with the topological charge `2' are respectively illustrated for the classes A and AIII. We also address a qualitative connection of topological charges of Fermi points in the real symmetry classes to the topological terms in the non-linear sigma models, based on the one-to-one classification correspondence.Comment: 8 pages and 2 figures, revised version with appendi

Genetic algorithm and neural network hybrid approach for job-shop scheduling

Copyright @ 1998 ACTA PressThis paper proposes a genetic algorithm (GA) and constraint satisfaction adaptive neural network (CSANN) hybrid approach for job-shop scheduling problems. In the hybrid approach, GA is used to iterate for searching optimal solutions, CSANN is used to obtain feasible solutions during the iteration of genetic algorithm. Simulations have shown the valid performance of the proposed hybrid approach for job-shop scheduling with respect to the quality of solutions and the speed of calculation.This research is supported by the National Nature Science Foundation and National High -Tech Program of P. R. China

A cellular automata modelling of dendritic crystal growth based on Moore and von Neumann neighbourhood

An important step in understanding crystal growth patterns involves simulation of the growth processes using mathematical models. In this paper some commonly used models in this area are reviewed, and a new simulation model of dendritic crystal growth based on the Moore and von Neumann neighbourhoods in cellular automata models are introduced. Simulation examples are employed to find ap- propriate parameter configurations to generate dendritic crystal growth patterns. Based on these new modelling results the relationship between tip growth speed and the parameters of the model are investigated

Angular momentum I ground state probabilities of boson systems interacting by random interactions

In this paper we report our systematic calculations of angular momentum $I$ ground state probabilities ($P(I)$) of boson systems with spin $l$ in the presence of random two-body interactions. It is found that the P(0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P(0) dominance is partly connected to the even number of identical particles. It is also noticed that the $P(I_{max})$'s of bosons with spin $l$ do not follow the 1/N ($N=l+1$, referring to the number of independent two-body matrix elements) relation. The properties of the $P(I)$'s obtained in boson systems with spin $l$ are discussed.Comment: 8 pages and 3 figure

Topological Classification and Stability of Fermi Surfaces

In the framework of the Cartan classification of Hamiltonians, a kind of topological classification of Fermi surfaces is established in terms of topological charges. The topological charge of a Fermi surface depends on its codimension and the class to which its Hamiltonian belongs. It is revealed that six types of topological charges exist, and they form two groups with respect to the chiral symmetry, with each group consisting of one original charge and two descendants. It is these nontrivial topological charges which lead to the robust topological protection of the corresponding Fermi surfaces against perturbations that preserve discrete symmetries.Comment: 5 pages, published version in PR