Isotropic Heating of Galaxy Cluster Cores via Rapidly Reorienting AGN Jets

AGN jets carry more than sufficient energy to stave off catastrophic cooling of the intracluster medium (ICM) in the cores of cool-core clusters. However, in order to prevent catastrophic cooling, the ICM must be heated in a near-isotropic fashion and narrow bipolar jets with $P_{\rm jet}=10^{44-45}$ ergs/s, typical of radio AGNs at cluster centres, are inefficient at heating the gas in the transverse direction to the jets. We argue that due to existent conditions in cluster cores, the SMBHs will, in addition to accreting gas via radiatively inefficient flows, experience short stochastic episodes of enhanced accretion via thin discs. In general, the orientation of these accretion discs will be misaligned with the spin axis of the black holes and the ensuing torques will cause the black hole's spin axis (and therefore, the jet axis) to slew and rapidly change direction. This model not only explains recent observations showing successive generations of jet-lobes-bubbles in individual cool-core clusters that are offset from each other in the angular direction with respect to the cluster center, but also shows that AGN jets {\it can} heat the cluster core nearly isotropically on the gas cooling timescale. Our model {\it does} require that the SMBHs at the centers of cool-core clusters be spinning relatively slowly. Torques from individual misaligned discs are ineffective at tilting rapidly spinning black holes by more than a few degrees. Additionally, since SMBHs that host thin accretion discs will manifest as quasars, we predict that roughly 1--2 rich clusters within $z<0.5$ should have quasars at their centers.Comment: 10 pages; accepted in ApJ; updated to conform with the accepted Journal versio

Guaranteed Rank Minimization via Singular Value Projection

Minimizing the rank of a matrix subject to affine constraints is a fundamental problem with many important applications in machine learning and statistics. In this paper we propose a simple and fast algorithm SVP (Singular Value Projection) for rank minimization with affine constraints (ARMP) and show that SVP recovers the minimum rank solution for affine constraints that satisfy the "restricted isometry property" and show robustness of our method to noise. Our results improve upon a recent breakthrough by Recht, Fazel and Parillo (RFP07) and Lee and Bresler (LB09) in three significant ways: 1) our method (SVP) is significantly simpler to analyze and easier to implement, 2) we give recovery guarantees under strictly weaker isometry assumptions 3) we give geometric convergence guarantees for SVP even in presense of noise and, as demonstrated empirically, SVP is significantly faster on real-world and synthetic problems. In addition, we address the practically important problem of low-rank matrix completion (MCP), which can be seen as a special case of ARMP. We empirically demonstrate that our algorithm recovers low-rank incoherent matrices from an almost optimal number of uniformly sampled entries. We make partial progress towards proving exact recovery and provide some intuition for the strong performance of SVP applied to matrix completion by showing a more restricted isometry property. Our algorithm outperforms existing methods, such as those of \cite{RFP07,CR08,CT09,CCS08,KOM09,LB09}, for ARMP and the matrix-completion problem by an order of magnitude and is also significantly more robust to noise.Comment: An earlier version of this paper was submitted to NIPS-2009 on June 5, 200

Massive complex Baker’s cyst treatment with open excision and arthroscopic partial meniscectomy: a case report

Baker’s cyst is known to be associated with intra articular pathologies such as meniscus tears, chondral lesions, synovitis, synovial plica and cruciate ligament injuries. Complex Baker’s cyst excision alone is known to have high chance of recurrence. Combined treatment strategies that addresses intra-articular pathologies with excision of the cyst and closure of the valve, are thought to reduce chances of recurrence of such cysts. We present a case of massive complex Baker’s cyst treated with arthroscopic partial medial meniscectomy, synovectomy, open cystectomy and closure of the valve

Large-scale Multi-label Learning with Missing Labels

The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of labels, and (b) the ability to handle data with missing labels. In this paper, we directly address both these problems by studying the multi-label problem in a generic empirical risk minimization (ERM) framework. Our framework, despite being simple, is surprisingly able to encompass several recent label-compression based methods which can be derived as special cases of our method. To optimize the ERM problem, we develop techniques that exploit the structure of specific loss functions - such as the squared loss function - to offer efficient algorithms. We further show that our learning framework admits formal excess risk bounds even in the presence of missing labels. Our risk bounds are tight and demonstrate better generalization performance for low-rank promoting trace-norm regularization when compared to (rank insensitive) Frobenius norm regularization. Finally, we present extensive empirical results on a variety of benchmark datasets and show that our methods perform significantly better than existing label compression based methods and can scale up to very large datasets such as the Wikipedia dataset

Recovery Guarantees for One-hidden-layer Neural Networks

In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to $\mathit{local~strong~convexity}$ in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation functions satisfy the distilled properties, including rectified linear units (ReLUs), leaky ReLUs, squared ReLUs and sigmoids. For activation functions that are also smooth, we show $\mathit{local~linear~convergence}$ guarantees of gradient descent under a resampling rule. For homogeneous activations, we show tensor methods are able to initialize the parameters to fall into the local strong convexity region. As a result, tensor initialization followed by gradient descent is guaranteed to recover the ground truth with sample complexity $d \cdot \log(1/\epsilon) \cdot \mathrm{poly}(k,\lambda )$ and computational complexity $n\cdot d \cdot \mathrm{poly}(k,\lambda)$ for smooth homogeneous activations with high probability, where $d$ is the dimension of the input, $k$ ($k\leq d$) is the number of hidden nodes, $\lambda$ is a conditioning property of the ground-truth parameter matrix between the input layer and the hidden layer, $\epsilon$ is the targeted precision and $n$ is the number of samples. To the best of our knowledge, this is the first work that provides recovery guarantees for 1NNs with both sample complexity and computational complexity $\mathit{linear}$ in the input dimension and $\mathit{logarithmic}$ in the precision.Comment: ICML 201

Exploring the scope of community-based rehabilitation in ensuring the holistic development of differently-abled people

Background: Globally, it has been estimated that almost 15% of world’s population live with some form of disability, of which the majority are from developing nations.Objectives: To explore the role of community-based rehabilitation (CBR) in the health sector, identify the prevalent challenges, and to suggest measures to facilitate its smooth implementation in community.Methods: An extensive search of all materials related to the topic was made using library sources including Pubmed, Medline and World Health Organization. Keywords used in the search included community, community-based rehabilitation, disabled, and public health.Results: The notion of community-based rehabilitation (CBR) emerged in 1978 with an aim to improve the accessibility of disabled people to rehabilitation services, especially in developing countries, by ensuring optimal use of locally available resources. CBR programs support people with disabilities by providing health services at their doorsteps, and thus estalish a strong linkage between people with disabilities and the health-care system.Conclusion: CBR encompasses a set of interventions that are implemented for a diverse and complex group of disabled people, and thus necessitates careful planning and systematic execution for ensuring welfare of these vulnerable people.Keywords: Community-based rehabilitation, Disabled, Public health, Rehabilitatio