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 .

Stability of Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous layer

We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.

Identification of dominant modes in random dynamical and aeroelastic systems

Identification of dominant modes is an important step in studying linearly vibrating systems, including flow-induced vibrations. In the presence of uncertainty, when some of the system parameters and the external excitation are modeled as random quantities, this step becomes more difficult. This work is aimed at giving a systematic treatment to this end. The ability to capture the time averaged kinetic energy is chosen as the primary criterion for selection of modes. Accordingly, a methodology is proposed based on the overlap of probability density functions (pdf) of the natural and excitation frequencies, proximity of the natural frequencies of the mean or baseline system, modal participation factor, and stochastic variation of mode shapes in terms of the modes of the baseline system - termed here as statistical modal overlapping. The probabilistic descriptors of the natural frequencies and mode shapes are found by solving a random eigenvalue problem. Three distinct vibration scenarios are considered: (i) undamped arid damped free vibrations of a bladed disk assembly, (ii) forced vibration of a building, and (iii) flutter of a bridge model. Through numerical studies, it is observed that the proposed methodology gives an accurate selection of modes. (C) 2015 Elsevier Ltd. All rights reserved.

A hybrid method for stochastic response analysis of a vibrating structure

Response analysis of a linear structure with uncertainties in both structural parameters and external excitation is considered here. When such an analysis is carried out using the spectral stochastic finite element method (SSFEM), often the computational cost tends to be prohibitive due to the rapid growth of the number of spectral bases with the number of random variables and the order of expansion. For instance, if the excitation contains a random frequency, or if it is a general random process, then a good approximation of these excitations using polynomial chaos expansion (PCE) involves a large number of terms, which leads to very high cost. To address this issue of high computational cost, a hybrid method is proposed in this work. In this method, first the random eigenvalue problem is solved using the weak formulation of SSFEM, which involves solving a system of deterministic nonlinear algebraic equations to estimate the PCE coefficients of the random eigenvalues and eigenvectors. Then the response is estimated using a Monte Carlo (MC) simulation, where the modal bases are sampled from the PCE of the random eigenvectors estimated in the previous step, followed by a numerical time integration. It is observed through numerical studies that this proposed method successfully reduces the computational burden compared with either a pure SSFEM of a pure MC simulation and more accurate than a perturbation method. The computational gain improves as the problem size in terms of degrees of freedom grows. It also improves as the timespan of interest reduces.

Divide and Conquer: Efficient Large-Scale Structure from Motion Using Graph Partitioning

Despite significant advances in recent years, structure-from-motion (SfM) pipelines suffer from two important drawbacks. Apart from requiring significant computational power to solve the large-scale computations involved, such pipelines sometimes fail to correctly reconstruct when the accumulated error in incremental reconstruction is large or when the number of 3D to 2D correspondences are insufficient. In this paper we present a novel approach to mitigate the above-mentioned drawbacks. Using an image match graph based on matching features we partition the image data set into smaller sets or components which are reconstructed independently. Following such reconstructions we utilise the available epipolar relationships that connect images across components to correctly align the individual reconstructions in a global frame of reference. This results in both a significant speed up of at least one order of magnitude and also mitigates the problems of reconstruction failures with a marginal loss in accuracy. The effectiveness of our approach is demonstrated on some large-scale real world data sets.

Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory

This paper presents the stability analysis of functionally graded plate integrated with piezoelectric actuator and sensor at the top and bottom face, subjected to electrical and mechanical loading. The finite element formulation is based on first order and higher order shear deformation theory, degenerated shell element, von-Karman hypothesis and piezoelectric effect. The equation for static analysis is derived by using the minimum energy principle and solutions for critical buckling load is obtained by solving eigenvalue problem. The material properties of the functionally graded plate are assumed to be graded along the thickness direction according to simple power law function. Two types of boundary conditions are used, such as SSSS (simply supported) and CSCS (simply supported along two opposite side perpendicular to the direction of compression and clamped along the other two sides). Sensor voltage is calculated using present analysis for various power law indices and FG (functionally graded) material gradations. The stability analysis of piezoelectric FG plate is carried out to present the effects of power law index, material variations, applied mechanical pressure and piezo effect on buckling and stability characteristics of FG plate.

Query Click and Text Similarity Graph for Query Suggestions

Query suggestion is an important feature of the search engine with the explosive and diverse growth of web contents. Different kind of suggestions like query, image, movies, music and book etc. are used every day. Various types of data sources are used for the suggestions. If we model the data into various kinds of graphs then we can build a general method for any suggestions. In this paper, we have proposed a general method for query suggestion by combining two graphs: (1) query click graph which captures the relationship between queries frequently clicked on common URLs and (2) query text similarity graph which finds the similarity between two queries using Jaccard similarity. The proposed method provides literally as well as semantically relevant queries for users' need. Simulation results show that the proposed algorithm outperforms heat diffusion method by providing more number of relevant queries. It can be used for recommendation tasks like query, image, and product suggestion.

Multi-dimensional Goodness-of-Fit Tests for Spectrum Sensing Based on Stochastic Distances

In this paper, we study two multi-dimensional Goodness-of-Fit tests for spectrum sensing in cognitive radios. The multi-dimensional scenario refers to multiple CR nodes, each with multiple antennas, that record multiple observations from multiple primary users for spectrum sensing. These tests, viz., the Interpoint Distance (ID) based test and the h, f distance based tests are constructed based on the properties of stochastic distances. The ID test is studied in detail for a single CR node case, and a possible extension to handle multiple nodes is discussed. On the other hand, the h, f test is applicable in a multi-node setup. A robustness feature of the KL distance based test is discussed, which has connections with Middleton's class A model. Through Monte-Carlo simulations, the proposed tests are shown to outperform the existing techniques such as the eigenvalue ratio based test, John's test, and the sphericity test, in several scenarios.

Falcon: A Graph Manipulation Language for Heterogeneous Systems

Graph algorithms have been shown to possess enough parallelism to keep several computing resources busy-even hundreds of cores on a GPU. Unfortunately, tuning their implementation for efficient execution on a particular hardware configuration of heterogeneous systems consisting of multicore CPUs and GPUs is challenging, time consuming, and error prone. To address these issues, we propose a domain-specific language (DSL), Falcon, for implementing graph algorithms that (i) abstracts the hardware, (ii) provides constructs to write explicitly parallel programs at a higher level, and (iii) can work with general algorithms that may change the graph structure (morph algorithms). We illustrate the usage of our DSL to implement local computation algorithms (that do not change the graph structure) and morph algorithms such as Delaunay mesh refinement, survey propagation, and dynamic SSSP on GPU and multicore CPUs. Using a set of benchmark graphs, we illustrate that the generated code performs close to the state-of-the-art hand-tuned implementations.

Electromagnetic analysis of novel class of multiple core/multiple clad step index single mode optical fiber by analytical means

General propagation properties and universal curves are given for double clad single mode fibers with inner cladding index higher or lower than the outer cladding index, using the parameter: inner cladding/core radii ratio. Mode cut-off conditions are also examined for the cases. It is shown that dispersion properties largely differ from the single clad single mode fiber case, leading to large new possibilities for extension of single mode operation for large wavelength tange. Paper demonstrates that how substantially we can extend the single mode operation range by using the raised inner cladding fiber. Throughout we have applied our own computations technique to find out the eigenvalue for a given modes. Detail derivations with all trivial mathematics for eigenmode equation are derived for each case. Paper also demonstrates that there is not much use of using depressed inner cladding fiber. We have also concluded that using the large inner cladding/inner core radius we can significantly increase the single mode operation range for the large wavelength region. (C) 2015 Elsevier GmbH. All rights reserved.

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.