Analysis of the hierarchical structure of the B. subtilis transcriptional regulatory network

The transcriptional regulation of gene expression is orchestrated by complex networks of interacting genes. Increasing evidence indicates that these `transcriptional regulatory networks' (TRNs) in bacteria have an inherently hierarchical architecture, although the design principles and the specific advantages offered by this type of organization have not yet been fully elucidated. In this study, we focussed on the hierarchical structure of the TRN of the gram-positive bacterium Bacillus subtilis and performed a comparative analysis with the TRN of the gram-negative bacterium Escherichia coli. Using a graph-theoretic approach, we organized the transcription factors (TFs) and sigma-factors in the TRNs of B. subtilis and E. coli into three hierarchical levels (Top, Middle and Bottom) and studied several structural and functional properties across them. In addition to many similarities, we found also specific differences, explaining the majority of them with variations in the distribution of s-factors across the hierarchical levels in the two organisms. We then investigated the control of target metabolic genes by transcriptional regulators to characterize the differential regulation of three distinct metabolic subsystems (catabolism, anabolism and central energy metabolism). These results suggest that the hierarchical architecture that we observed in B. subtilis represents an effective organization of its TRN to achieve flexibility in response to a wide range of diverse stimuli.

A Distributed TDMA Slot Scheduling Algorithm for Spatially Correlated Contention in WSNs

In WSNs the communication traffic is often time and space correlated, where multiple nodes in a proximity start transmitting simultaneously. Such a situation is known as spatially correlated contention. The random access method to resolve such contention suffers from high collision rate, whereas the traditional distributed TDMA scheduling techniques primarily try to improve the network capacity by reducing the schedule length. Usually, the situation of spatially correlated contention persists only for a short duration, and therefore generating an optimal or suboptimal schedule is not very useful. Additionally, if an algorithm takes very long time to schedule, it will not only introduce additional delay in the data transfer but also consume more energy. In this paper, we present a distributed TDMA slot scheduling (DTSS) algorithm, which considerably reduces the time required to perform scheduling, while restricting the schedule length to the maximum degree of interference graph. The DTSS algorithm supports unicast, multicast, and broadcast scheduling, simultaneously without any modification in the protocol. We have analyzed the protocol for average case performance and also simulated it using Castalia simulator to evaluate its runtime performance. Both analytical and simulation results show that our protocol is able to considerably reduce the time required for scheduling.

Rainbow matchings in strongly edge-colored graphs

A rainbow matching of an edge-colored graph G is a matching in which no two edges have the same color. There have been several studies regarding the maximum size of a rainbow matching in a properly edge-colored graph G in terms of its minimum degree 3(G). Wang (2011) asked whether there exists a function f such that a properly edge-colored graph G with at least f (delta(G)) vertices is guaranteed to contain a rainbow matching of size delta(G). This was answered in the affirmative later: the best currently known function Lo and Tan (2014) is f(k) = 4k - 4, for k >= 4 and f (k) = 4k - 3, for k <= 3. Afterwards, the research was focused on finding lower bounds for the size of maximum rainbow matchings in properly edge-colored graphs with fewer than 4 delta(G) - 4 vertices. Strong edge-coloring of a graph G is a restriction of proper edge-coloring where every color class is required to be an induced matching, instead of just being a matching. In this paper, we give lower bounds for the size of a maximum rainbow matching in a strongly edge-colored graph Gin terms of delta(G). We show that for a strongly edge-colored graph G, if |V(G)| >= 2 |3 delta(G)/4|, then G has a rainbow matching of size |3 delta(G)/4|, and if |V(G)| < 2 |3 delta(G)/4|, then G has a rainbow matching of size |V(G)|/2] In addition, we prove that if G is a strongly edge-colored graph that is triangle-free, then it contains a rainbow matching of size at least delta(G). (C) 2015 Elsevier B.V. All rights reserved.

SEPARATION DIMENSION OF BOUNDED DEGREE GRAPHS

The separation dimension of a graph G is the smallest natural number k for which the vertices of G can be embedded in R-k such that any pair of disjoint edges in G can be separated by a hyperplane normal to one of the axes. Equivalently, it is the smallest possible cardinality of a family F of total orders of the vertices of G such that for any two disjoint edges of G, there exists at least one total order in F in which all the vertices in one edge precede those in the other. In general, the maximum separation dimension of a graph on n vertices is Theta(log n). In this article, we focus on bounded degree graphs and show that the separation dimension of a graph with maximum degree d is at most 2(9) (log*d)d. We also demonstrate that the above bound is nearly tight by showing that, for every d, almost all d-regular graphs have separation dimension at least d/2]

Boxicity and cubicity of product graphs

The boxicity (cubicity) of a graph G is the minimum natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes (axis-parallel unit cubes) in R-k. In this article, we give estimates on the boxicity and the cubicity of Cartesian, strong and direct products of graphs in terms of invariants of the component graphs. In particular, we study the growth, as a function of d, of the boxicity and the cubicity of the dth power of a graph with respect to the three products. Among others, we show a surprising result that the boxicity and the cubicity of the dth Cartesian power of any given finite graph is, respectively, in O(log d/ log log d) and circle dot(d/ log d). On the other hand, we show that there cannot exist any sublinear bound on the growth of the boxicity of powers of a general graph with respect to strong and direct products. (C) 2015 Elsevier Ltd. All rights reserved.

Heterochromatic paths in edge colored graphs without small cycles and heterochromatic-triangle-free graphs

Conditions for the existence of heterochromatic Hamiltonian paths and cycles in edge colored graphs are well investigated in literature. A related problem in this domain is to obtain good lower bounds for the length of a maximum heterochromatic path in an edge colored graph G. This problem is also well explored by now and the lower bounds are often specified as functions of the minimum color degree of G - the minimum number of distinct colors occurring at edges incident to any vertex of G - denoted by v(G). Initially, it was conjectured that the lower bound for the length of a maximum heterochromatic path for an edge colored graph G would be 2v(G)/3]. Chen and Li (2005) showed that the length of a maximum heterochromatic path in an edge colored graph G is at least v(G) - 1, if 1 <= v(G) <= 7, and at least 3v(G)/5] + 1 if v(G) >= 8. They conjectured that the tight lower bound would be v(G) - 1 and demonstrated some examples which achieve this bound. An unpublished manuscript from the same authors (Chen, Li) reported to show that if v(G) >= 8, then G contains a heterochromatic path of length at least 120 + 1. In this paper, we give lower bounds for the length of a maximum heterochromatic path in edge colored graphs without small cycles. We show that if G has no four cycles, then it contains a heterochromatic path of length at least v(G) - o(v(G)) and if the girth of G is at least 4 log(2)(v(G)) + 2, then it contains a heterochromatic path of length at least v(G) - 2, which is only one less than the bound conjectured by Chen and Li (2005). Other special cases considered include lower bounds for the length of a maximum heterochromatic path in edge colored bipartite graphs and triangle-free graphs: for triangle-free graphs we obtain a lower bound of 5v(G)/6] and for bipartite graphs we obtain a lower bound of 6v(G)-3/7]. In this paper, it is also shown that if the coloring is such that G has no heterochromatic triangles, then G contains a heterochromatic path of length at least 13v(G)/17)]. This improves the previously known 3v(G)/4] bound obtained by Chen and Li (2011). We also give a relatively shorter and simpler proof showing that any edge colored graph G contains a heterochromatic path of length at least (C) 2015 Elsevier Ltd. All rights reserved.

On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan in Discrete Math. 55:221-232, 1985), while for example the problems of finding a minimum s-t separator that induces a connected graph or forms an independent set are fixed-parameter tractable when parameterized by the size of the separator (Marx et al. in ACM Trans. Algorithms 9(4): 30, 2013). Motivated by these results, we study properties that generalize cliques, independent sets, and connected graphs, and determine the complexity of finding separators satisfying these properties. We investigate these problems also on bounded-degree graphs. Our results are as follows: Finding a minimum c-connected s-t separator is FPT for c=2 and W1]-hard for any ca parts per thousand yen3. Finding a minimum s-t separator with diameter at most d is W1]-hard for any da parts per thousand yen2. Finding a minimum r-regular s-t separator is W1]-hard for any ra parts per thousand yen1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. Finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless .

On Locally Gabriel Geometric Graphs

Let be a set of points in the plane. A geometric graph on is said to be locally Gabriel if for every edge in , the Euclidean disk with the segment joining and as diameter does not contain any points of that are neighbors of or in . A locally Gabriel graph(LGG) is a generalization of Gabriel graph and is motivated by applications in wireless networks. Unlike a Gabriel graph, there is no unique LGG on a given point set since no edge in a LGG is necessarily included or excluded. Thus the edge set of the graph can be customized to optimize certain network parameters depending on the application. The unit distance graph(UDG), introduced by Erdos, is also a LGG. In this paper, we show the following combinatorial bounds on edge complexity and independent sets of LGG: (i) For any , there exists LGG with edges. This improves upon the previous best bound of . (ii) For various subclasses of convex point sets, we show tight linear bounds on the maximum edge complexity of LGG. (iii) For any LGG on any point set, there exists an independent set of size .

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

PolyMage: Automatic Optimization for Image Processing Pipelines

This paper presents the design and implementation of PolyMage, a domain-specific language and compiler for image processing pipelines. An image processing pipeline can be viewed as a graph of interconnected stages which process images successively. Each stage typically performs one of point-wise, stencil, reduction or data-dependent operations on image pixels. Individual stages in a pipeline typically exhibit abundant data parallelism that can be exploited with relative ease. However, the stages also require high memory bandwidth preventing effective utilization of parallelism available on modern architectures. For applications that demand high performance, the traditional options are to use optimized libraries like OpenCV or to optimize manually. While using libraries precludes optimization across library routines, manual optimization accounting for both parallelism and locality is very tedious. The focus of our system, PolyMage, is on automatically generating high-performance implementations of image processing pipelines expressed in a high-level declarative language. Our optimization approach primarily relies on the transformation and code generation capabilities of the polyhedral compiler framework. To the best of our knowledge, this is the first model-driven compiler for image processing pipelines that performs complex fusion, tiling, and storage optimization automatically. Experimental results on a modern multicore system show that the performance achieved by our automatic approach is up to 1.81x better than that achieved through manual tuning in Halide, a state-of-the-art language and compiler for image processing pipelines. For a camera raw image processing pipeline, our performance is comparable to that of a hand-tuned implementation.

Framework for morphometric classification of cells in imaging flow cytometry

Imaging flow cytometry is an emerging technology that combines the statistical power of flow cytometry with spatial and quantitative morphology of digital microscopy. It allows high-throughput imaging of cells with good spatial resolution, while they are in flow. This paper proposes a general framework for the processing/classification of cells imaged using imaging flow cytometer. Each cell is localized by finding an accurate cell contour. Then, features reflecting cell size, circularity and complexity are extracted for the classification using SVM. Unlike the conventional iterative, semi-automatic segmentation algorithms such as active contour, we propose a noniterative, fully automatic graph-based cell localization. In order to evaluate the performance of the proposed framework, we have successfully classified unstained label-free leukaemia cell-lines MOLT, K562 and HL60 from video streams captured using custom fabricated cost-effective microfluidics-based imaging flow cytometer. The proposed system is a significant development in the direction of building a cost-effective cell analysis platform that would facilitate affordable mass screening camps looking cellular morphology for disease diagnosis. Lay description In this article, we propose a novel framework for processing the raw data generated using microfluidics based imaging flow cytometers. Microfluidics microscopy or microfluidics based imaging flow cytometry (mIFC) is a recent microscopy paradigm, that combines the statistical power of flow cytometry with spatial and quantitative morphology of digital microscopy, which allows us imaging cells while they are in flow. In comparison to the conventional slide-based imaging systems, mIFC is a nascent technology enabling high throughput imaging of cells and is yet to take the form of a clinical diagnostic tool. The proposed framework process the raw data generated by the mIFC systems. The framework incorporates several steps: beginning from pre-processing of the raw video frames to enhance the contents of the cell, localising the cell by a novel, fully automatic, non-iterative graph based algorithm, extraction of different quantitative morphological parameters and subsequent classification of cells. In order to evaluate the performance of the proposed framework, we have successfully classified unstained label-free leukaemia cell-lines MOLT, K562 and HL60 from video streams captured using cost-effective microfluidics based imaging flow cytometer. The cell lines of HL60, K562 and MOLT were obtained from ATCC (American Type Culture Collection) and are separately cultured in the lab. Thus, each culture contains cells from its own category alone and thereby provides the ground truth. Each cell is localised by finding a closed cell contour by defining a directed, weighted graph from the Canny edge images of the cell such that the closed contour lies along the shortest weighted path surrounding the centroid of the cell from a starting point on a good curve segment to an immediate endpoint. Once the cell is localised, morphological features reflecting size, shape and complexity of the cells are extracted and used to develop a support vector machine based classification system. We could classify the cell-lines with good accuracy and the results were quite consistent across different cross validation experiments. We hope that imaging flow cytometers equipped with the proposed framework for image processing would enable cost-effective, automated and reliable disease screening in over-loaded facilities, which cannot afford to hire skilled personnel in large numbers. Such platforms would potentially facilitate screening camps in low income group countries; thereby transforming the current health care paradigms by enabling rapid, automated diagnosis for diseases like cancer.

An evaluation of space time cube representation of spatiotemporal patterns.

Space time cube representation is an information visualization technique where spatiotemporal data points are mapped into a cube. Information visualization researchers have previously argued that space time cube representation is beneficial in revealing complex spatiotemporal patterns in a data set to users. The argument is based on the fact that both time and spatial information are displayed simultaneously to users, an effect difficult to achieve in other representations. However, to our knowledge the actual usefulness of space time cube representation in conveying complex spatiotemporal patterns to users has not been empirically validated. To fill this gap, we report on a between-subjects experiment comparing novice users' error rates and response times when answering a set of questions using either space time cube or a baseline 2D representation. For some simple questions, the error rates were lower when using the baseline representation. For complex questions where the participants needed an overall understanding of the spatiotemporal structure of the data set, the space time cube representation resulted in on average twice as fast response times with no difference in error rates compared to the baseline. These results provide an empirical foundation for the hypothesis that space time cube representation benefits users analyzing complex spatiotemporal patterns.

Streaming covariance selection with applications to adaptive querying in sensor networks

Sensor networks can be naturally represented as graphical models, where the edge set encodes the presence of sparsity in the correlation structure between sensors. Such graphical representations can be valuable for information mining purposes as well as for optimizing bandwidth and battery usage with minimal loss of estimation accuracy. We use a computationally efficient technique for estimating sparse graphical models which fits a sparse linear regression locally at each node of the graph via the Lasso estimator. Using a recently suggested online, temporally adaptive implementation of the Lasso, we propose an algorithm for streaming graphical model selection over sensor networks. With battery consumption minimization applications in mind, we use this algorithm as the basis of an adaptive querying scheme. We discuss implementation issues in the context of environmental monitoring using sensor networks, where the objective is short-term forecasting of local wind direction. The algorithm is tested against real UK weather data and conclusions are drawn about certain tradeoffs inherent in decentralized sensor networks data analysis. © 2010 The Author. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved.

Music-Theoretic Estimation of Chords and Keys from Audio

This paper proposes a new method for local key and chord estimation from audio signals. This method relies primarily on principles from music theory, and does not require any training on a corpus of labelled audio files. A harmonic content of the musical piece is first extracted by computing a set of chroma vectors. A set of chord/key pairs is selected for every frame by correlation with fixed chord and key templates. An acyclic harmonic graph is constructed with these pairs as vertices, using a musical distance to weigh its edges. Finally, the sequences of chords and keys are obtained by finding the best path in the graph using dynamic programming. The proposed method allows a mutual chord and key estimation. It is evaluated on a corpus composed of Beatles songs for both the local key estimation and chord recognition tasks, as well as a larger corpus composed of songs taken from the Billboard dataset.