The harmonic consistency index for the analytic hierarchy process

A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9, as is often recommended. Using simulation, the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret. In addition, new properties of the column sums of reciprocal matrices are obtained.     

Circadian synchrony in networks of protein rhythm driven neurons

The interaction between gene activation and cellular activity has recently emerged as a critical aspect of brain behavior, but the dynamics of networks incorporating these interactions are poorly understood. An interesting phenomena arises when the genetic activation oscillates endogenously and a network of such cells synchronize to a coherent rhythm, such as is the case with the suprachiasmatic nucleus. To explain this synchronization, we propose a model in which a mRNA/protein expression cycle drives neurons electrical activity, and synaptic activation shifts the phase of the protein rhythm. Using lattice networks, we demonstrate that these interactions are sufficient to generate coherent oscillation. © 2006 Wiley Periodicals, Inc. Complexity 12: 67–72, 2006     

Automatic labeling and characterization of objects using artificial neural networks

Existing NASA supported scientific databases are usually developed and managed by a team of database administrators whose main concern is the efficiency of the databases in terms of normalization and data search constructs. The populating of the database is usually done in a manual fashion by row and column as the data become available, and the data dictionary is usually defined by the same team (at times with little input from the end science user). This process is tedious, error prone and self-limiting in terms of what can be described in a relational Data Base Management System (DBMS). The next generation Earth remote sensing platforms [i.e., Earth Observing System (EOS)] will be capable of generating data at a rate of over 300 Megabits per second from a suite of instruments designed for different applications. What is needed is an innovative approach that creates object-oriented data-bases that segment, characterize, and catalog, and are manageable in a domain-specific context, and whose contents are available interactively and in near-real-time to the user community. This paper describes work in progress that utilizes an artificial neural net approach to characterize satellite imagery of undefined objects into high-level data objects. The characterized data is then dynamically allocated to an object-oriented database where it can be reviewed and accessed by a user. The definition, development, and evolution of the overall data system model are steps in the creation of an application-driven knowledge-based scientific information system.     

Linear matrix inequality representation of sets

This article concerns the question, Which subsets of ?^m can be represented with linear matrix inequalities (LMIs)? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also, before having much hope of representing engineering problems as LMIs by automatic methods, one needs a good idea of which problems can and cannot be represented by LMIs. Little is currently known about such problems. In this article we give a necessary condition that we call “rigid convexity,” which must hold for a set ?? ? ?^m in order for ?? to have an LMI representation. Rigid convexity is proved to be necessary and sufficient when m = 2. This settles a question formally stated by Pablo Parrilo and Berndt Sturmfels in [15]. As shown by Lewis, Parillo, and Ramana [11], our main result also establishes (in the case of three variables) a 1958 conjecture by Peter Lax on hyperbolic polynomials. © 2006 Wiley Periodicals, Inc.     

Adjugates in Banach algebras

A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

     

Fabrication of quantum dots on the InSb (110) surface

Using a scanning tunneling microscope, quantum dots with diameters of order 25 Å have been fabricated on the cleaved InSb (110) surface in UHV. Both In and Sb atoms were clearly resolved on the cleaved surface.