Galactic Dark Matter and Bertrand Space-times

Bertrand space-times (BSTs) are static, spherically symmetric solutions of Einstein's equations, that admit stable, closed orbits. Starting from the fact that to a good approximation, stars in the disc or halo regions of typical galaxies move in such orbits, we propose that, under certain physical assumptions, the dark matter distribution of some low surface brightness (LSB) galaxies can seed a particular class of BSTs. In the Newtonian limit, it is shown that for flat rotation curves, our proposal leads to an analytic prediction of the NFW dark matter profile. We further show that the dark matter distribution that seeds the BST, is described by a two-fluid anisotropic model, and present its analytic solution. A new solution of the Einstein's equations, with an internal BST and an external Schwarzschild metric, is also constructed.Comment: 1+21 Pages, LaTeX, 9 .eps figures. Minor changes. Version published in PR

Astrophysics of Bertrand Space-times

We construct a model for galactic dark matter that arises as a solution of Einstein gravity, and is a Bertrand space-time matched with an external Schwarzschild metric. This model can explain galactic rotation curves. Further, we study gravitational lensing in these space-times, and in particular we consider Einstein rings, using the strong lensing formalism of Virbhadra and Ellis. Our results are in good agreement with observational data, and indicate that under certain conditions, gravitational lensing effects from galactic dark matter may be similar to that from Schwarzschild backgrounds.Comment: 1 + 21 Pages, 8 .eps figure

Galactic space-times in modified theories of gravity

We study Bertrand space-times (BSTs), which have been proposed as viable models of space-times seeded by galactic dark matter, in modified theories of gravity. We first critically examine the issue of galactic rotation curves in General Relativity, and establish the usefulness of BSTs to fit experimental data in this context. We then study BSTs in metric $f(R)$ gravity and in Brans-Dicke theories. For the former, the nature of the Newtonian potential is established, and we also compute the effective equation of state and show that it can provide good fits to some recent experimental results. For the latter, we calculate the Brans-Dicke scalar analytically in some limits and numerically in general, and find interesting constraints on the parameters of the theory. Our results provide evidence for the physical nature of Bertrand space-times in modified theories of gravity.Comment: 1 + 29 Pages, LaTeX, 12 .eps figures. Some discussions improved. Published versio

Literature Survey on Interplay of Topics, Information Diffusion and Connections on Social Networks

Researchers have attempted to model information diffusion and topic trends and lifecycle on online social networks. They have investigated the role of content, social connections and communities, familiarity and behavioral similarity in this context. The current article presents a survey of representative models that perform topic analysis, capture information diffusion, and explore the properties of social connections in the context of online social networks. The article concludes with a set of outlines of open problems and possible directions of future research interest. This article is intended for researchers to identify the current literature, and explore possibilities to improve the art

Assessment of Effectiveness of Content Models for Approximating Twitter Social Connection Structures

This paper explores the social quality (goodness) of community structures formed across Twitter users, where social links within the structures are estimated based upon semantic properties of user-generated content (corpus). We examined the overlap of the community structures of the constructed graphs, and followership-based social communities, to find the social goodness of the links constructed. Unigram, bigram and LDA content models were empirically investigated for evaluation of effectiveness, as approximators of underlying social graphs, such that they maintain the {\it community} social property. Impact of content at varying granularities, for the purpose of predicting links while retaining the social community structures, was investigated. 100 discussion topics, spanning over 10 Twitter events, were used for experiments. The unigram language model performed the best, indicating strong similarity of word usage within deeply connected social communities. This observation agrees with the phenomenon of evolution of word usage behavior, that transform individuals belonging to the same community tending to choose the same words, made by Danescu et al. (2013), and raises a question on the literature that use, without validation, LDA for content-based social link prediction over other content models. Also, semantically finer-grained content was observed to be more effective compared to coarser-grained content

Topic Lifecycle on Social Networks: Analyzing the Effects of Semantic Continuity and Social Communities

Topic lifecycle analysis on Twitter, a branch of study that investigates Twitter topics from their birth through lifecycle to death, has gained immense mainstream research popularity. In the literature, topics are often treated as one of (a) hashtags (independent from other hashtags), (b) a burst of keywords in a short time span or (c) a latent concept space captured by advanced text analysis methodologies, such as Latent Dirichlet Allocation (LDA). The first two approaches are not capable of recognizing topics where different users use different hashtags to express the same concept (semantically related), while the third approach misses out the user's explicit intent expressed via hashtags. In our work, we use a word embedding based approach to cluster different hashtags together, and the temporal concurrency of the hashtag usages, thus forming topics (a semantically and temporally related group of hashtags).We present a novel analysis of topic lifecycles with respect to communities. We characterize the participation of social communities in the topic clusters, and analyze the lifecycle of topic clusters with respect to such participation. We derive first-of-its-kind novel insights with respect to the complex evolution of topics over communities and time: temporal morphing of topics over hashtags within communities, how the hashtags die in some communities but morph into some other hashtags in some other communities (that, it is a community-level phenomenon), and how specific communities adopt to specific hashtags. Our work is fundamental in the space of topic lifecycle modeling and understanding in communities: it redefines our understanding of topic lifecycles and shows that the social boundaries of topic lifecycles are deeply ingrained with community behavior.Comment: 12 pages, 5 figures (13 figures if sub-figures are counted separately), To Appear in ECIR 201

New class of naked singularities and their observational signatures

By imposing suitable junction conditions on a space-like hyper-surface, we obtain a two-parameter family of possible static configurations from gravitational collapse. These exemplify a new class of naked singularities. We show that these admit a consistent description via a two-fluid model, one of which might be dust. We then study lensing and accretion disk properties of our solution and point out possible differences with black hole scenarios. The distinctive features of our solution, compared to the existing naked singularity solutions in the literature are discussed.Comment: Substantial modifications in the results. Present version is fully re-written, and the title is also changed. 24 pages, 10 figure

Self-gravitating fluid systems and galactic dark matter

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space-times that are seeded by galactic dark matter. To this end, we identify a class of space-times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space-time is seen to be the Bertrand space-time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two- fluid models, we show that our galactic space-times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered.Comment: 1+ 24 Pages. Discussions improved. Journal versio

EmTaggeR: A Word Embedding Based Novel Method for Hashtag Recommendation on Twitter

The hashtag recommendation problem addresses recommending (suggesting) one or more hashtags to explicitly tag a post made on a given social network platform, based upon the content and context of the post. In this work, we propose a novel methodology for hashtag recommendation for microblog posts, specifically Twitter. The methodology, EmTaggeR, is built upon a training-testing framework that builds on the top of the concept of word embedding. The training phase comprises of learning word vectors associated with each hashtag, and deriving a word embedding for each hashtag. We provide two training procedures, one in which each hashtag is trained with a separate word embedding model applicable in the context of that hashtag, and another in which each hashtag obtains its embedding from a global context. The testing phase constitutes computing the average word embedding of the test post, and finding the similarity of this embedding with the known embeddings of the hashtags. The tweets that contain the most-similar hashtag are extracted, and all the hashtags that appear in these tweets are ranked in terms of embedding similarity scores. The top-K hashtags that appear in this ranked list, are recommended for the given test post. Our system produces F1 score of 50.83%, improving over the LDA baseline by around 6.53 times, outperforming the best-performing system known in the literature that provides a lift of 6.42 times. EmTaggeR is a fast, scalable and lightweight system, which makes it practical to deploy in real-life applications.Comment: Accepted at the IEEE International Conference on Data Mining (ICDM) 2017 ACUMEN Worksho

Topical Stance Detection for Twitter: A Two-Phase LSTM Model Using Attention

The topical stance detection problem addresses detecting the stance of the text content with respect to a given topic: whether the sentiment of the given text content is in FAVOR of (positive), is AGAINST (negative), or is NONE (neutral) towards the given topic. Using the concept of attention, we develop a two-phase solution. In the first phase, we classify subjectivity - whether a given tweet is neutral or subjective with respect to the given topic. In the second phase, we classify sentiment of the subjective tweets (ignoring the neutral tweets) - whether a given subjective tweet has a FAVOR or AGAINST stance towards the topic. We propose a Long Short-Term memory (LSTM) based deep neural network for each phase, and embed attention at each of the phases. On the SemEval 2016 stance detection Twitter task dataset, we obtain a best-case macro F-score of 68.84% and a best-case accuracy of 60.2%, outperforming the existing deep learning based solutions. Our framework, T-PAN, is the first in the topical stance detection literature, that uses deep learning within a two-phase architecture.Comment: Accepted at the 40th European Conference on Information Retrieval (ECIR), 201