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Search Results: 1 - 10 of 1903 matches for " Deepayan Sarkar "
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Limiting spectral distribution for Wigner matrices with dependent entries
Arijit Chakrabarty,Rajat Subhra Hazra,Deepayan Sarkar
Mathematics , 2013,
Abstract: In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit description of the moments of the limiting measure. We also show that in some special cases the Gaussian assumption can be relaxed. The description of the limiting measure can also be made via its Stieltjes transform which is characterized as the solution of a functional equation. In two special cases, we get a description of the limiting measure - one as a free product convolution of two distributions, and the other one as a dilation of the Wigner semicircular law.
From random matrices to long range dependence
Arijit Chakrabarty,Rajat Subhra Hazra,Deepayan Sarkar
Mathematics , 2014,
Abstract: Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the limiting spectral distribution is determined by the absolutely continuous component of the spectral measure of the stationary process, a phenomenon resembling that in the situation where the entries of the matrix are i.i.d. On the other hand, the discrete component contributes to the limiting behavior of the eigenvalues in a completely different way. Therefore, this helps to define a boundary between short and long range dependence of a stationary Gaussian process in the context of random matrices.
Nonparametric Link Prediction in Large Scale Dynamic Networks
Purnamrita Sarkar,Deepayan Chakrabarti,Michael Jordan
Computer Science , 2011,
Abstract: We propose a nonparametric approach to link prediction in large-scale dynamic networks. Our model uses graph-based features of pairs of nodes as well as those of their local neighborhoods to predict whether those nodes will be linked at each time step. The model allows for different types of evolution in different parts of the graph (e.g, growing or shrinking communities). We focus on large-scale graphs and present an implementation of our model that makes use of locality-sensitive hashing to allow it to be scaled to large problems. Experiments with simulated data as well as five real-world dynamic graphs show that we outperform the state of the art, especially when sharp fluctuations or nonlinearities are present. We also establish theoretical properties of our estimator, in particular consistency and weak convergence, the latter making use of an elaboration of Stein's method for dependency graphs.
Nonparametric Link Prediction in Dynamic Networks
Purnamrita Sarkar,Deepayan Chakrabarti,Michael Jordan
Computer Science , 2012,
Abstract: We propose a non-parametric link prediction algorithm for a sequence of graph snapshots over time. The model predicts links based on the features of its endpoints, as well as those of the local neighborhood around the endpoints. This allows for different types of neighborhoods in a graph, each with its own dynamics (e.g, growing or shrinking communities). We prove the consistency of our estimator, and give a fast implementation based on locality-sensitive hashing. Experiments with simulated as well as five real-world dynamic graphs show that we outperform the state of the art, especially when sharp fluctuations or non-linearities are present.
iFlow: A Graphical User Interface for Flow Cytometry Tools in Bioconductor
Kyongryun Lee,Florian Hahne,Deepayan Sarkar,Robert Gentleman
Advances in Bioinformatics , 2009, DOI: 10.1155/2009/103839
Abstract: Flow cytometry (FCM) has become an important analysis technology in health care and medical research, but the large volume of data produced by modern high-throughput experiments has presented significant new challenges for computational analysis tools. The development of an FCM software suite in Bioconductor represents one approach to overcome these challenges. In the spirit of the R programming language (Tree Star Inc., “FlowJo”), these tools are predominantly console-driven, allowing for programmatic access and rapid development of novel algorithms. Using this software requires a solid understanding of programming concepts and of the R language. However, some of these tools|in particular the statistical graphics and novel analytical methods|are also useful for nonprogrammers. To this end, we have developed an open source, extensible graphical user interface (GUI) iFlow, which sits on top of the Bioconductor backbone, enabling basic analyses by means of convenient graphical menus and wizards. We envision iFlow to be easily extensible in order to quickly integrate novel methodological developments.
Coverage and error models of protein-protein interaction data by directed graph analysis
Tony Chiang, Denise Scholtens, Deepayan Sarkar, Robert Gentleman, Wolfgang Huber
Genome Biology , 2007, DOI: 10.1186/gb-2007-8-9-r186
Abstract: Within the past decade a large amount of data on protein-protein interactions in cellular systems has been obtained by the high-throughput scaling of technologies, such as the yeast two-hybrid (Y2H) system and affinity purification-mass spectrometry (AP-MS) [1-15]. This opens the possibility for molecular and computational biologists to obtain a comprehensive understanding of cellular systems and their modules [16]. There are many references in the literature, however, to the apparent noisiness and low quality of high-throughput protein interaction data. Evaluation studies have reported discrepancies between the datasets, large error rates, lack of overlap, and contradictions between experiments [17-30]. The interpretation and integration of these large sets of protein interaction data represents a grand challenge for computational biology.In essence, inference on the existence of an interaction between two proteins is made based on the measured data, and such inference can either be right or wrong. Most publicly available data are stored as positive measured results, and therefore most analyses have employed the most obvious method to infer interactions; a positive observation indicates an interaction, whereas a negative observation or no observation does not. This method, although useful and sometimes unavoidable, does not make use of other indicators for the presence or absence of interactions.The most useful and yet seldom used indicator is the information about which set of interactions were tested. As mentioned, most studies report positively measured interactions but few report the negative measurements. It is quite often the case that untested protein pairs and negative measurements are not distinguished. A second indicator of the presence of an interaction is reciprocity. Bait to prey systems allow for the testing of an interaction between a pair of proteins in two directions. If bi-directionally tested, we anticipate the result as both positive or both neg
flowCore: a Bioconductor package for high throughput flow cytometry
Florian Hahne, Nolwenn LeMeur, Ryan R Brinkman, Byron Ellis, Perry Haaland, Deepayan Sarkar, Josef Spidlen, Errol Strain, Robert Gentleman
BMC Bioinformatics , 2009, DOI: 10.1186/1471-2105-10-106
Abstract: We developed a set of flexible open source computational tools in the R package flowCore to facilitate the analysis of these complex data. A key component of which is having suitable data structures that support the application of similar operations to a collection of samples or a clinical cohort. In addition, our software constitutes a shared and extensible research platform that enables collaboration between bioinformaticians, computer scientists, statisticians, biologists and clinicians. This platform will foster the development of novel analytic methods for flow cytometry.The software has been applied in the analysis of various data sets and its data structures have proven to be highly efficient in capturing and organizing the analytic work flow. Finally, a number of additional Bioconductor packages successfully build on the infrastructure provided by flowCore, open new avenues for flow data analysis.Automation technologies developed during the last several years have enabled the use of flow cytometry (FCM) to generate large, complex data sets in both basic and clinical research applications [1]. A serious bottleneck in the interpretation of existing studies and the application of high throughput FCM to even larger, more complex problems is that data management and data analysis methods have not advanced sufficiently far from the methods developed for applications of FCM to small-scale, tube-based studies [2]. In particular, the data often need to be organized into groups of samples based on combinations of additional covariates and similar operations need to be applied to these groups in a transparent and reproducible manner. Furthermore, the growing depth of knowledge in the field of immunology, for instance the characterization of distinct human T-cell sub-population [3], clearly argues for more systematic approaches.Some of the consequences of the lag of efficient software solutions are difficulties in maintaining the integrity and documentation of large dat
2D+t Wavelet Domain Video Watermarking
Deepayan Bhowmik,Charith Abhayaratne
Advances in Multimedia , 2012, DOI: 10.1155/2012/973418
Abstract: A novel watermarking framework for scalable coded video that improves the robustness against quality scalable compression is presented in this paper. Unlike the conventional spatial-domain (t?+?2D) water-marking scheme where the motion compensated temporal filtering (MCTF) is performed on the spatial frame-wise video data to decompose the video, the proposed framework applies the MCTF in the wavelet domain (2D?+?t) to generate the coefficients to embed the watermark. Robustness performances against scalable content adaptation, such as Motion JPEG 2000, MC-EZBC, or H.264-SVC, are reviewed for various combinations of motion compensated 2D?+?t?+?2D using the proposed framework. The MCTF is improved by modifying the update step to follow the motion trajectory in the hierarchical temporal decomposition by using direct motion vector fields in the update step and implied motion vectors in the prediction step. The results show smaller embedding distortion in terms of both peak signal to noise ratio and flickering metrics compared to frame-by-frame video watermarking while the robustness against scalable compression is improved by using 2D?+?t over the conventional t?+?2D domain video watermarking, particularly for blind watermarking schemes where the motion is estimated from the watermarked video. 1. Introduction Several attempts have been made to extend the image watermarking algorithms into video watermarking by using them either on frame-by-frame basis or on 3D decomposed video. The initial attempts on video watermarking were made by frame-by-frame embedding [1–4], due to its simplicity in implementation using image watermarking algorithms. Such watermarking algorithms consider embedding on selected frames located at fixed intervals to make them robust against frame dropping-based temporal adaptations of video. In this case, each frame is treated separately as an individual image; hence, any image-watermarking algorithm can be adopted to achieve the intended robustness. But frame-by-frame watermarking schemes often perform poorly in terms of flickering artefacts and robustness against various video processing attacks including temporal desynchronization, video collusion, video compression attacks, and so forth. In order to address some of these issues, the video temporal dimension is exploited using different transforms, such as discrete Fourier transform (DFT), discrete cosine transform (DCT), or discrete wavelet transform (DWT). These algorithms decompose the video by performing spatial 2D transform on individual frames followed by 1D transform in the
Perfect Entanglement Transport in Quantum Spin Chain Systems  [PDF]
Sujit Sarkar
Journal of Quantum Information Science (JQIS) , 2011, DOI: 10.4236/jqis.2011.13014
Abstract: We propose a mechanism for perfect entanglement transport in anti-ferromagnetic (AFM) quantum spin chain systems with modulated exchange coupling and also for the modulation of on-site magnetic field. We use the principle of adiabatic quantum pumping process for entanglement transfer in the spin chain systems. We achieve the perfect entanglement transfer over an arbitrarily long distance and a better entanglement transport for longer AFM spin chain system than for the ferromagnetic one. We explain analytically and physically—why the entanglement hops in alternate sites. We find the condition for blocking of entanglement transport even in the perfect pumping situation. Our analytical solution interconnects quantum many body physics and quantum information science.
Kronecker Graphs: An Approach to Modeling Networks
Jure Leskovec,Deepayan Chakrabarti,Jon Kleinberg,Christos Faloutsos,Zoubin Ghahramani
Physics , 2008,
Abstract: How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization.
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