On the cubicity of bipartite graphs

A unit cube in k-dimension (or a k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k, where each R-i is a closed interval on the real line of the form [a(j), a(i), + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. Many NP-complete graph problems can be solved efficiently or have good approximation ratios in graphs of low cubicity. In most of these cases the first step is to get a low dimensional cube representation of the given graph. It is known that for graph G, cub(G) <= left perpendicular2n/3right perpendicular. Recently it has been shown that for a graph G, cub(G) >= 4(Delta + 1) In n, where n and Delta are the number of vertices and maximum degree of G, respectively. In this paper, we show that for a bipartite graph G = (A boolean OR B, E) with |A| = n(1), |B| = n2, n(1) <= n(2), and Delta' = min {Delta(A),Delta(B)}, where Delta(A) = max(a is an element of A)d(a) and Delta(B) = max(b is an element of B) d(b), d(a) and d(b) being the degree of a and b in G, respectively , cub(G) <= 2(Delta' + 2) bar left rightln n(2)bar left arrow. We also give an efficient randomized algorithm to construct the cube representation of G in 3 (Delta' + 2) bar right arrowIn n(2)bar left arrow dimension. The reader may note that in general Delta' can be much smaller than Delta.

An account of chronological developments in control of distributed parameter systems

Control systems arising in many engineering fields are often of distributed parameter type, which are modeled by partial differential equations. Decades of research have lead to a great deal of literature on distributed parameter systems scattered in a wide spectrum.Extensions of popular finite-dimensional techniques to infinite-dimensional systems as well as innovative infinite-dimensional specific control design approaches have been proposed. A comprehensive account of all the developments would probably require several volumes and is perhaps a very difficult task. In this paper, however, an attempt has been made to give a brief yet reasonably representative account of many of these developments in a chronological order. To make it accessible to a wide audience, mathematical descriptions have been completely avoided with the assumption that an interested reader can always find the mathematical details in the relevant references.

Computational systems approach for drug target discovery

Importance of the field: The shift in focus from ligand based design approaches to target based discovery over the last two to three decades has been a major milestone in drug discovery research. Currently, it is witnessing another major paradigm shift by leaning towards the holistic systems based approaches rather the reductionist single molecule based methods. The effect of this new trend is likely to be felt strongly in terms of new strategies for therapeutic intervention, new targets individually and in combinations, and design of specific and safer drugs. Computational modeling and simulation form important constituents of new-age biology because they are essential to comprehend the large-scale data generated by high-throughput experiments and to generate hypotheses, which are typically iterated with experimental validation. Areas covered in this review: This review focuses on the repertoire of systems-level computational approaches currently available for target identification. The review starts with a discussion on levels of abstraction of biological systems and describes different modeling methodologies that are available for this purpose. The review then focuses on how such modeling and simulations can be applied for drug target discovery. Finally, it discusses methods for studying other important issues such as understanding targetability, identifying target combinations and predicting drug resistance, and considering them during the target identification stage itself. What the reader will gain: The reader will get an account of the various approaches for target discovery and the need for systems approaches, followed by an overview of the different modeling and simulation approaches that have been developed. An idea of the promise and limitations of the various approaches and perspectives for future development will also be obtained. Take home message: Systems thinking has now come of age enabling a `bird's eye view' of the biological systems under study, at the same time allowing us to `zoom in', where necessary, for a detailed description of individual components. A number of different methods available for computational modeling and simulation of biological systems can be used effectively for drug target discovery.

How to write a passable technical paper

In my job I see many students who have not learned to write a technical paper. When they do competent work, I want them to be able to write passable reports. This article is for them. There are well established principles for citing the relevant work of others; for not copying things without giving credit; for not stealing. If a reader feels you have copied anything, a figure, even a phrase, from elsewhere without citing its source, then you are guilty of plagiarism in the eyes of that reader. Committing plagiarism is so bad that I cannot do justice to it here. So I merely say: never do it. On, then, to writing your own honest and original material. Art requires talent. In contrast, through discipline and persistence alone, you can learn how to differentiate functions and ride bicycles. Similarly, you can write a passable technical paper. You just have to realize that your job does not end with research. Writing a passable paper involves extra work.

Continuity Metric for Unit Selection based Text-to-Speech Synthesis

A new method based on unit continuity metric (UCM) is proposed for optimal unit selection in text-to-speech (TTS) synthesis. UCM employs two features, namely, pitch continuity metric and spectral continuity metric. The methods have been implemented and tested on our test bed called MILE-TTS and it is available as web demo. After verification by a self selection test, the algorithms are evaluated on 8 paragraphs each for Kannada and Tamil by native users of the languages. Mean-opinion-score (MOS) shows that naturalness and comprehension are better with UCM based algorithm than the non-UCM based ones. The naturalness of the TTS output is further enhanced by a new rule based algorithm for pause prediction for Tamil language. The pauses between the words are predicted based on parts-of-speech information obtained from the input text.

Dynamic scheduling in manufacturing systems using brownian approximations

Recently, Brownian networks have emerged as an effective stochastic model to approximate multiclass queueing networks with dynamic scheduling capability, under conditions of balanced heavy loading. This paper is a tutorial introduction to dynamic scheduling in manufacturing systems using Brownian networks. The article starts with motivational examples. It then provides a review of relevant weak convergence concepts, followed by a description of the limiting behaviour of queueing systems under heavy traffic. The Brownian approximation procedure is discussed in detail and generic case studies are provided to illustrate the procedure and demonstrate its effectiveness. This paper places emphasis only on the results and aspires to provide the reader with an up-to-date understanding of dynamic scheduling based on Brownian approximations.