On a Special Co-cycle Basis of Graphs

In this paper we consider the problems of computing a minimum co-cycle basis and a minimum weakly fundamental co-cycle basis of a directed graph G. A co-cycle in G corresponds to a vertex partition (S,V ∖ S) and a { − 1,0,1} edge incidence vector is associated with each co-cycle. The vector space over ℚ generated by these vectors is the co-cycle space of G. Alternately, the co-cycle space is the orthogonal complement of the cycle space of G. The minimum co-cycle basis problem asks for a set of co-cycles that span the co-cycle space of G and whose sum of weights is minimum. Weakly fundamental co-cycle bases are a special class of co-cycle bases, these form a natural superclass of strictly fundamental co-cycle bases and it is known that computing a minimum weight strictly fundamental co-cycle basis is NP-hard. We show that the co-cycle basis corresponding to the cuts of a Gomory-Hu tree of the underlying undirected graph of G is a minimum co-cycle basis of G and it is also weakly fundamental.

New approximation algorithms for minimum cycle bases of graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time 0(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time 0(n(3+2/k)), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega)) bound. We also present a 2-approximation algorithm with O(m(omega) root n log n) expected running time, a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

Understanding Membranes through the Molecular Design of Lipids

Lipids are amphiphilic molecules that are composed of hydrophilic and hydrophobic regions. A typical membranous aggregate (vesicles, water-filled lipid nanospheres) is formed upon the self-organization of lipids in water from a diverse collection of amphiphiles producing a dynamic supramolecular structure that shows phase behavior and ordering as required for specific biological functions. The determination of various physical properties of lipid aggregates is the key to determining structure-function relationships. Over the years, we have designed and synthesized a wide variety of lipid molecular systems for the investigation of their membrane-forming properties and have used them for purposes such as gene delivery and enzyme activation. In this feature article, we focus on our work on various types of lipids including ion-paired amphiphiles, cholesterol-based lipids, aromatic lipids, macrocyclic lipids containing disulfide tethers; cationic dimeric lipids, and so forth. The emphasis is oil experimental design and bottom-line conclusions.

BER analysis of space-time block codes from generalized complex orthogonal designs for M-PSK

In this paper, we present an analysis for the bit error rate (BER) performance of space-time block codes (STBC) from generalized complex orthogonal designs for M-PSK modulation. In STBCs from complex orthogonal designs (COD), the norms of the column vectors are the same (e.g., Alamouti code). However, in generalized COD (GCOD), the norms of the column vectors may not necessarily be the same (e.g., the rate-3/5 and rate-7/11 codes by Su and Xia in [1]). STBCs from GCOD are of interest because of the high rates that they can achieve (in [2], it has been shown that the maximum achievable rate for STBCs from GCOD is bounded by 4/5). While the BER performance of STBCs: from COD (e.g., Alamouti code) can be simply obtained from existing analytical expressions for receive diversity with the same diversity order by appropriately scaling the SNR, this can not be done for STBCs from GCOD (because of the unequal norms of the column vectors). Our contribution in this paper is that we derive analytical expressions for the BER performance of any STBC from GCOD. Our BER analysis for the GCOD captures the performance of STBCs from COD as special cases. We validate our results with two STBCs from GCOD reported by Su and Xia in [1], for 5 and 6 transmit antennas (G(5) and G(6) in [1]) with rates 7/11 and 3/5, respectively.

Investigation of true remnant polarization response in heterostructured artificial biferroics

Epitaxial bilayered thin films composed of ferromagnetic La0.6Sr0.4MnO3 and ferroelectric 0.7Pb (Mg1/3Nb2/3)O3-0.3(PbTiO3) were fabricated on LaAlO3 (100) substrates by pulsed laser ablation. Ferroelectric, ferromagnetic and magneto-dielectric characterizations performed earlier indicated the possible existence of strain-mediated magneto-electric coupling in these biferroic heterostructures. In order to investigate their true remnant polarization characteristics, usable in devices, room-temperature polarization versus electric field, positive-up negative-down (PUND) pulse polarization studies and remnant hysteresis measurements were carried out. The PUND and remnant hysteresis measurements revealed the significant contribution of the non-remnant component in the observed polarization hysteresis response of these heterostructures. (C) 2010 Published by Elsevier Ltd

Supervisory Control for Real-Time Systems Based on Conflict-Tolerant Controllers

This paper addresses the problem of detecting and resolving conflicts due to timing constraints imposed by features in real-time and hybrid systems. We consider systems composed of a base system with multiple features or controllers, each of which independently advise the system on how to react to input events so as to conform to their individual specifications. We propose a methodology for developing such systems in a modular manner based on the notion of conflict-tolerant features that are designed to continue offering advice even when their advice has been overridden in the past. We give a simple priority-based scheme forcomposing such features. This guarantees the maximal use of each feature. We provide a formal framework for specifying such features, and a compositional technique for verifying systems developed in this framework.