1,731,436 research outputs found
Approximating Sparsest Cut in Low Rank Graphs via Embeddings from Approximately Low Dimensional Spaces
No full textWe consider the problem of embedding a finite set of points x_1, ... , x_n in R^d that satisfy l_2^2 triangle inequalities into l_1, when the points are approximately low-dimensional. Goemans (unpublished, appears in a work of Magen and Moharammi (2008) ) showed that such points residing in exactly d dimensions can be embedded into l_1 with distortion at most sqrt{d}. We prove the following robust analogue of this statement: if there exists a r-dimensional subspace Pi such that the projections onto this subspace satisfy sum_{i,j in [n]} norm{Pi x_i - Pi x_j}_2^2 >= Omega(1) * sum_{i,j \in [n]} norm{x_i - x_j}_2^2, then there is an embedding of the points into l_1 with O(sqrt{r}) average distortion. A consequence of this result is that the integrality gap of the well-known Goemans-Linial SDP relaxation for the Uniform Sparsest Cut problem is O(sqrt{r}) on graphs G whose r-th smallest normalized eigenvalue of the Laplacian satisfies lambda_r(G)/n >= Omega(1)*Phi_{SDP}(G). Our result improves upon the previously known bound of O(r) on the average distortion, and the integrality gap of the Goemans-Linial SDP under the same preconditions, proven in [Deshpande and Venkat, 2014], and [Deshpande, Harsha and Venkat 2016]
Murali, Venkat (Prof Emeritus)
No full textDepartment of Mathematics Venkat Murali Top 30 Rhodes Researchers 2012</a
Embedding Approximately Low-Dimensional l_2^2 Metrics into l_1
No full textGoemans showed that any n points x_1,..., x_n in d-dimensions satisfying l_2^2 triangle inequalities can be embedded into l_{1}, with worst-case distortion at most sqrt{d}. We consider an extension of this theorem to the case when the points are approximately low-dimensional as opposed to exactly low-dimensional, and prove the following analogous theorem, albeit with average distortion guarantees: There exists an l_{2}^{2}-to-l_{1} embedding with average distortion at most the stable rank, sr(M), of the matrix M consisting of columns {x_i-x_j}_{i<j}. Average distortion embedding suffices for applications such as the SPARSEST CUT problem. Our embedding gives an approximation algorithm for the SPARSEST CUT problem on low threshold-rank graphs, where earlier work was inspired by Lasserre SDP hierarchy, and improves on a previous result of the first and third author [Deshpande and Venkat, in Proc. 17th APPROX, 2014]. Our ideas give a new perspective on l_{2}^{2} metric, an alternate proof of Goemans' theorem, and a simpler proof for average distortion sqrt{d}
B. Venkat Mani
No full textMember of the steering committee B. Venkat Mani is Professor of German, and Director of the Center for South Asia at the University of Wisconsin-Madison. He received his B.A. (Honors) and M.A. in German Studies from the Jawaharlal Nehru University, New Delhi, and a M.A. and Ph.D. in German Studies from Stanford University. His research and teaching focus on 19th to 21st Century German literature and culture, migrants and refugees in the German and European context, book and digital cultu..
DEA 4580 Course Syllabus - Spring 11
No full textDEA 4580, Introduction to REVIT and Building Information Modeling (BIM), Course Syllabus by Instructor Ramnath Venkat, Spring 201
Numerical modeling of microfluidic two-phase electrohydrodynamic instability:
No full textOrganic-aqueous liquid (phenol) extraction is one of many standard techniques to efficiently purify DNA directly from cells. Effective dispersion of one fluid phase in the other increases the surface area over which biological component partitioning may occur, and hence enhances DNA extraction efficiency. Electrohydrodynamic (EHD) instability can be harnessed to achieve this goal and has been experimentally demonstrated by Zahn and Reddy (2006). In this work, analysis and simulation are combined to study two-phase EHD instability. In the
problem configuration, the organic (phenol) phase flows into the microchannel in parallel with and sandwiched between two aqueous streams, creating a three-layer planar geometry; the two liquid phases are immiscible. An electric field is applied to induce instability and to break the organic stream into droplets. The Taylor-Melcher leaky-dielectric model is employed to investigate this phenomenon. A linear analysis is carried out with a Chebyshev pseudo-spectral method, whereas a fully nonlinear numerical simulation is implemented using a finite volume, immersed boundary method (IBM). The results from both models compare favorably with each other. The linear analysis reveals basic instability characteristics such as kink and sausage modes. On the other hand, the nonlinear simulation predicts surface deformation in the strongly nonlinear regime pertinent to droplet formation. These numerical tools will be used to investigate the effects of the applied electric field, geometry, and convective flow rate on mixing and dispersion. The eventual objective is to maximize surface area of the organic phase under given experimental conditions for optimized DNA extraction.M.S.Includes bibliographical references (p. 101-104)by Venkat raman Thenkarai Narayana
Unprecedented Move
No full textIn this issue, Dr. Venkat Pulla, Coordinator, Social Work Discipline & Senior Lecturer, Australian Catholic University, Australia (Brisbane Campus), writes the editorial on denominations by Modi Government to deal the pervasive corruption in India
DEA 4580 Course Syllabus - Spring 10
No full textDEA 4580, Intro to REVIT and Building Information Modeling (BIM), Course Syllabus by Instructor Ramnath Venkat, Spring 201
Secularism vs. Sectarianism: The Turbulent Relationship Between Politics and Religion in Post-Colonial Indian Communities
No full textTharun Venkat explores the root causes of modern-day conflicts in India over political-religious questions and the role of the consititutional principle of secularism
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