There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

‡We describe the use of singular value decomposition in transforming genome-wide expression data from genes 3 arrays space to reduced diagonalized ‘‘eigengenes’’ 3 ‘‘eigenarrays’’ space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling

Computational Analysis of Microarray Data

Stability in Aviation. By Prof. G. H. Bryan, F.E.S. Pp. X + 192. 5S. net. 1911. (Macmillan.)

From Introduction: "The subject of this paper is so broad in scope that a large volume might be devoted to it. In a short paper of this kind it is possible simply to sketch in the high lights of aircraft engine design showing the development to date, the possibilities of the future, and the underlying fundamental principles. Summarizing this development and referring to the graph (Fig.1), we that there is now a water-cooled engine in every power from 150 to 800 HP. and an air-cooled engine in the 200 to 400 HP. classes."

/pdf/aircraft-engine-design-3v346pwxhw.pdf

Aircraft Engine Design

With the advent of Unmanned Aerial Vehicles (UAV) and Micro Aerial Vehicles (MAV) in commercial sectors, their application for transporting and manipulating payloads has attracted many research work. A swarm of agents, cooperatively working to transport and manipulate a payload can overcome the physical limitations of a single agent, adding redundancy and tolerance against failures. In this paper, the dynamics of a swarm connected to a payload via flexible cables are modeled, and a decentralized control is designed using Artificial Potential Field (APF). The swarm is able to transport the payload through an unknown environment to a goal position while avoiding obstacles from the local information received from the onboard sensors. The key contributions are (a) the cables are modelled more accurately using lumped mass model instead of geometric constraints, (b) a decentralized swarm control is designed using potential field approach to ensure hover stability of system without payload state information, (c) the manipulation of payload elevation and azimuth angles are controlled by APF, and (d) the trajectory of the payload for transportation is governed by potential fields generated by goal point and obstacles. The efficacy of the method proposed in this work are evaluated through numerical simulations under the influence of external disturbances and failure of agents.

Decentralized Aerial Transportation and Manipulation of a Cable-Slung Payload With Swarm of Agents

Illustrative examples are presented in this paper to show the applications of the continuation-algorithm-based, recently developed extended bifurcation analysis (EBA) methodology to compute optimum flight parameters of an F/A-18 high-angle-of-attack research vehicle aerodynamic model. A complete model describing the six-degree-of-freedom motion of aircraft is used in this analysis to compute trims for the aircraft in constrained flights, for example, straight and level and steady climb flights. Using the results of such computations, one can plot the performance curves for aircraft which are in contrast to the performance curves usually available in the aircraft design text books. Special features of the performance curves computed here are high-lighted and the reasons for the contrasting features between the performance curves obtained here and the corresponding ones presented in the aircraft design text books are discussed. Primary objective of this work is to show the efficiency of the EBA meth...

Optimum flight parameters and stability computations using continuation technique

This paper presents multi sensor fusion architecture to fuse multi target tracks from the Radar and an Infrared Search & Track (IRST) system. The proposed architecture uses global nearest neighborhood (GNN) algorithm for data association between target tracks of Radar and IRST. Further a GNN based central track manager is proposed to maintain the fused tracks from Radar and IRST. The Radar track outputs are modelled in Cartesian coordinates, providing the target position and velocity states with their corresponding covariance, while the radar detections are in polar coordinates. The IRST track output provides angle only information of the targets with their corresponding covariance. Simulations are carried out in single aircraft - multi target scenario and it is observed that the fused track output has improved angle accuracy with lesser variance. 

Nandan K. Sinha

Papers

Decentralized Aerial Transportation and Manipulation of a Cable-Slung Payload With Swarm of Agents

Optimum flight parameters and stability computations using continuation technique

Airborne Multi Target Track to Track Fusion of Radar and IRST for Advanced Multi Role Combat Aircrafts