Online Tensor Methods for Learning Latent Variable Models

We introduce an online tensor decomposition based approach for two latent variable modeling problems namely, (1) community detection, in which we learn the latent communities that the social actors in social networks belong to, and (2) topic modeling, in which we infer hidden topics of text articles. We consider decomposition of moment tensors using stochastic gradient descent. We conduct optimization of multilinear operations in SGD and avoid directly forming the tensors, to save computational and storage costs. We present optimized algorithm in two platforms. Our GPU-based implementation exploits the parallelism of SIMD architectures to allow for maximum speed-up by a careful optimization of storage and data transfer, whereas our CPU-based implementation uses efficient sparse matrix computations and is suitable for large sparse datasets. For the community detection problem, we demonstrate accuracy and computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic modeling problem, we also demonstrate good performance on the New York Times dataset. We compare our results to the state-of-the-art algorithms such as the variational method, and report a gain of accuracy and a gain of several orders of magnitude in the execution time.Comment: JMLR 201

A review on efficacy of Kayaseka in Pakshaghata

Man has always feared two things death and disease. Stroke is a disease which appears suddenly with strong pathophysiology. It is responsible for more dependency than any other disease since it hampers the functional ability of person sometimes it may even lead to death. As birds need both wings to maintain posture, co-ordination of movements, execution of different movements similarly humans need both halves. If a bird loses its one wing it is unable to fly and even live due to depraved morbidity. In the same way when person suffers from stroke he is a like bird with clipped wings. Pakshaghata is a Vatavyadhi. Acharyas have established it under Astamahagada. In all types of Vatavyadhi, Snehana and Swedana are mentioned as a line of treatment. Acharya Charaka advocates the use of Ushnaveerya Parisheka in the mitigation of Vata Dosha. Induction of Swedana by unique procedure of pouring liquid by warm medicated oil on body is known as Parisheka Sweda. When it is performed on whole body along with the Abhyanga, is known as Kayaseka

Theoretical and experimental investigation of Raman modes, ferroelectric and dielectric properties of relaxor Na0.5Bi0.5TiO3

We use a combination of first-principles density functional theoretical analysis and experimental characterization to understand the lattice dynamics, dielectric and ferroelectric properties of lead-free relaxor ferroelectric Na0.5Bi0.5TiO3 (NBT) system. Vibrational spectrum determined through our calculations agrees well with the observed Raman spectrum, and allows assignment of symmetry labels to modes. The calculated Born effective charges reveal (a) two distinct types of Ti ions at the B-site with anomalous dynamical charges differing by up 1.6e, and (b) Na and Bi ions at the A-site exhibit disparate dynamical charges of about 1 and 5.5e, respectively. Thus, there exist hetero-polar activity at both A and B-sites in NBT, and disorder associated with these hetero-polar ions is responsible for its relaxor behaviour. Large dielectric response of NBT arises primarily from phonons, and specifically the modes involving Bi-O (109 cm-1) and Ti-O (246, 276 cm-1) vibrations, respectively

Comparative study of adenosine deaminase activity, insulin resistance and lipoprotein(a) among smokers and healthy non-smokers

Background: Adenosine deaminase also known as adenosine aminohydrolase involved in purine metabolism. Its primary function is development and maintenance of immune system. The main objective of the study was to estimate adenosine deaminase (ADA) enzyme and find its correlation with lipoprotein(a) and insulin resistance among smokers and healthy non-smokers.Methods: Fifty smokers and fifty healthy non-smokers were selected based on WHO definition. ADA, lipid profile and glucose was estimated on a fully automated analyser by IFCC approved methods and lipoprotein(a) was done by latex enhanced immune-turbidimetric assay method respectively.Results: After appropriate screening ADA activity and insulin was significantly elevated among smokers when compared with healthy non-smokers. A positive correlation was found between pack size of cigarette and ADA activity and also with Lp(a) respectively. In addition, there was no correlation between serum lipid profile and ADA activity.Conclusions: Adenosine deaminase activity was increased in patients in response to nicotine which is the key component of cigarette smoke. These findings indicate that nicotine and carbon monoxide can alter lipoprotein synthesis and also modify LDL to oxidized form which can lead to ischemic heart disease

Quasiparticle spectra from a non-empirical optimally-tuned range-separated hybrid density functional

We present a method for obtaining outer valence quasiparticle excitation energies from a DFT-based calculation, with accuracy that is comparable to that of many-body perturbation theory within the GW approximation. The approach uses a range-separated hybrid density functional, with asymptotically exact and short-range fractional Fock exchange. The functional contains two parameters - the range separation and the short-range Fock fraction. Both are determined non-empirically, per system, based on satisfaction of exact physical constraints for the ionization potential and many-electron self-interaction, respectively. The accuracy of the method is demonstrated on four important benchmark organic molecules: perylene, pentacene, 3,4,9,10-perylene-tetracarboxylic-dianydride (PTCDA) and 1,4,5,8-naphthalene-tetracarboxylic dianhydride (NTCDA). We envision that for finite systems the approach could provide an inexpensive alternative to GW, opening the door to the study of presently out of reach large-scale systems

Aliovalent cation ordering, coexisting ferroelectric structures, and electric field induced phase transformation in lead-free ferroelectric Na0.5Bi0.5TiO3

Using first-principles calculations, we show that a specific chemical ordering of Na and Bi in Na0.5Bi0.5TiO3 is responsible for the co-existence of its ferroelectric phases with rhombohedral R3c and monoclinic Cc structures, which are relevant to its morphotropic phase boundary and large piezoelectric response. We identify the signatures of chemical ordering in the calculated phonon spectra and establish the prevalence of A-type ordering through comparison with experiment. We uncover a mechanism of the observed electric field induced Cc to lower energy R3c structural transformation promoted by a hybrid soft mode involving a combination of TiO6 rotations and a polar component

Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the residual. We prove convergence to the globally optimal solution under natural incoherence conditions on the low rank component, and bounded level of sparse perturbations. We compare our method with natural baselines which apply robust matrix PCA either to the {\em flattened} tensor, or to the matrix slices of the tensor. Our method can provably handle a far greater level of perturbation when the sparse tensor is block-structured. This naturally occurs in many applications such as the activity detection task in videos. Our experiments validate these findings. Thus, we establish that tensor methods can tolerate a higher level of gross corruptions compared to matrix methods

Tensor Contractions with Extended BLAS Kernels on CPU and GPU

Tensor contractions constitute a key computational ingredient of numerical multi-linear algebra. However, as the order and dimension of tensors grow, the time and space complexities of tensor-based computations grow quickly. In this paper, we propose and evaluate new BLAS-like primitives that are capable of performing a wide range of tensor contractions on CPU and GPU efficiently. We begin by focusing on single-index contractions involving all the possible configurations of second-order and third-order tensors. Then, we discuss extensions to more general cases. Existing approaches for tensor contractions spend large amounts of time restructuring the data which typically involves explicit copy and transpose operations. In this work, we summarize existing approaches and present library-based approaches that avoid memory movement. Through systematic benchmarking, we demonstrate that our approach can achieve 10x speedup on a K40c GPU and 2x speedup on dual-socket Haswell-EP CPUs, using MKL and CUBLAS respectively, for small and moderate tensor sizes. This is relevant in many machine learning applications such as deep learning, where tensor sizes tend to be small, but require numerous tensor contraction operations to be performed successively. Concretely, we implement a Tucker decomposition and show that using our kernels yields atleast an order of magnitude speedup as compared to state-of-the-art libraries

Evaluation of antibacterial and antifungal activity of root and root callus extracts of Trianthema decandra L.

Trianthema decandra L. root and root callus extracts of different solvents viz.,petroleum ether, chloroform, ethyl acetate and ethanol were tested against both Gram positive and Gram negative bacteria and also against Fusarium spp. Root callus extract of chloroform and ethanol showed significant activity against Bacillus subtilis, B. cereus. Staphylococcus aureus, Staph. epidermis and also against the other spp. of Gram negative bacteria viz., Pseudomonas aeruginosa, Klebseilla pneumonia, Alcaligens faecalis, Proteus vulgaris Enterobacter aerogenes,Salmonella typhi, Salmonella tyhimurium, Salmonella paratyphi A and Salmonella enterica subsp. enterica with a MIC of 3.12 to 12.50 μg/ml when compared to root extract of chloroform, ethyl acetate and ethanol of Trianthema decandra. Root callus extract of chloroform, ethyl acetate and ethanol showed activity against Fusarium verticilliodes, F. anthophilum, F. oxysporum and F. proliferatum with a lowest MIC of 3.12 μg/ml when compared to root extract of Trianthema decandra. The result showsthat antibacterial and antifungal activity was more in root callus extract than root extract