Geometric Network Creation Games

Network Creation Games are a well-known approach for explaining and analyzing the structure, quality and dynamics of real-world networks like the Internet and other infrastructure networks which evolved via the interaction of selfish agents without a central authority. In these games selfish agents which correspond to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games has only considered the creation of networks with unit-weight edges. In practice, e.g. when constructing a fiber-optic network, the choice of which nodes to connect and also the induced price for a link crucially depends on the distance between the involved nodes and such settings can be modeled via edge-weighted graphs. We incorporate arbitrary edge weights by generalizing the well-known model by Fabrikant et al.[PODC'03] to edge-weighted host graphs and focus on the geometric setting where the weights are induced by the distances in some metric space. In stark contrast to the state-of-the-art for the unit-weight version, where the Price of Anarchy is conjectured to be constant and where resolving this is a major open problem, we prove a tight non-constant bound on the Price of Anarchy for the metric version and a slightly weaker upper bound for the non-metric case. Moreover, we analyze the existence of equilibria, the computational hardness and the game dynamics for several natural metrics. The model we propose can be seen as the game-theoretic analogue of a variant of the classical Network Design Problem. Thus, low-cost equilibria of our game correspond to decentralized and stable approximations of the optimum network design.Comment: Accepted at 31st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '19). 33 pages, 11 figure

SAAGs: Biased stochastic variance reduction methods for large-scale learning

Stochastic approximation is one of the effective approach to deal with the large-scale machine learning problems and the recent research has focused on reduction of variance, caused by the noisy approximations of the gradients. In this paper, we have proposed novel variants of SAAG-I and II (Stochastic Average Adjusted Gradient) (Chauhan et al. 2017), called SAAG-III and IV, respectively. Unlike SAAG-I, starting point is set to average of previous epoch in SAAG-III, and unlike SAAG-II, the snap point and starting point are set to average and last iterate of previous epoch in SAAG-IV, respectively. To determine the step size, we have used Stochastic Backtracking-Armijo line Search (SBAS) which performs line search only on selected mini-batch of data points. Since backtracking line search is not suitable for large-scale problems and the constants used to find the step size, like Lipschitz constant, are not always available so SBAS could be very effective in such cases. We have extended SAAGs (I, II, III and IV) to solve non-smooth problems and designed two update rules for smooth and non-smooth problems. Moreover, our theoretical results have proved linear convergence of SAAG-IV for all the four combinations of smoothness and strong-convexity, in expectation. Finally, our experimental studies have proved the efficacy of proposed methods against the state-of-art techniques

Faster learning by reduction of data access time

Nowadays, the major challenge in machine learning is the Big Data challenge. The big data problems due to large number of data points or large number of features in each data point, or both, the training of models have become very slow. The training time has two major components: Time to access the data and time to process (learn from) the data. So far, the research has focused only on the second part, i.e., learning from the data. In this paper, we have proposed one possible solution to handle the big data problems in machine learning. The idea is to reduce the training time through reducing data access time by proposing systematic sampling and cyclic/sequential sampling to select mini-batches from the dataset. To prove the effectiveness of proposed sampling techniques, we have used Empirical Risk Minimization, which is commonly used machine learning problem, for strongly convex and smooth case. The problem has been solved using SAG, SAGA, SVRG, SAAG-II and MBSGD (Mini-batched SGD), each using two step determination techniques, namely, constant step size and backtracking line search method. Theoretical results prove the same convergence for systematic sampling, cyclic sampling and the widely used random sampling technique, in expectation. Experimental results with bench marked datasets prove the efficacy of the proposed sampling techniques and show up to six times faster training

Young stellar population and ongoing star formation in the HII complex Sh2-252

In this paper an extensive survey of the star forming complex Sh2-252 has been undertaken with an aim to explore its hidden young stellar population as well as to understand the structure and star formation history. This complex is composed of five embedded clusters associated with the sub-regions A, C, E, NGC 2175s and Teu 136. Using 2MASS-NIR and Spitzer-IRAC, MIPS photometry we identified 577 young stellar objects (YSOs), of which, 163 are Class I, 400 are Class II and 14 are transition disk YSOs. Spatial distribution of the candidate YSOs shows that they are mostly clustered around the sub-regions in the western half of the complex, suggesting enhanced star formation activity towards its west. Using the spectral energy distribution and optical colour-magnitude diagram based age analyses, we derived probable evolutionary status of the sub-regions of Sh2-252. Our analysis shows that the region A is the youngest (~ 0.5 Myr), the regions B, C and E are of similar evolutionary stage (~ 1-2 Myr) and the clusters NGC 2175s and Teu 136 are slightly evolved (~ 2-3 Myr). Morphology of the region in the 1.1 mm map shows a semi-circular shaped molecular shell composed of several clumps and YSOs bordering the western ionization front of Sh2-252. Our analyses suggest that next generation star formation is currently under way along this border and that possibly fragmentation of the matter collected during the expansion of the HII region as one of the major processes responsible for such stars. We observed the densest concentration of YSOs (mostly Class I, ~ 0.5 Myr) at the western outskirts of the complex, within a molecular clump associated with water and methanol masers and we suggest that it is indeed a site of cluster formation at a very early evolutionary stage, sandwiched between the two relatively evolved CHII regions A and B.Comment: 19 pages, 13 figures, Accepted for publication in MNRA

Multiwavelength Study of NGC 281 Region

We present a multiwavelength study of the NGC 281 complex which contains the young cluster IC 1590 at the center, using deep wide-field optical UBVI_c photometry, slitless spectroscopy along with archival data sets in the near-infrared (NIR) and X-ray. The extent of IC 1590 is estimated to be ~6.5 pc. The cluster region shows a relatively small amount of differential reddening. The majority of the identified young stellar objects (YSOs) are low mass PMS stars having age <1-2 Myr and mass 0.5-3.5 M_\odot. The slope (\Gamma) of the mass function for IC 1590, in the mass range 2 < M/M_\odot \le 54, is found to be -1.11+-0.15. The slope of the K-band luminosity function (0.37+-0.07) is similar to the average value (~0.4) reported for young clusters. The distribution of gas and dust obtained from the IRAS, CO and radio maps indicates clumpy structures around the central cluster. The radial distribution of the young stellar objects, their ages, \Delta(H-K) NIR-excess, and the fraction of classical T Tauri stars suggest triggered star formation at the periphery of the cluster region. However, deeper optical, NIR and MIR observations are needed to have a conclusive view of star formation scenario in the region. The properties of the Class 0/I and Class II sources detected by using the Spitzer mid-infrared observations indicate that a majority of the Class II sources are X-ray emitting stars, whereas X-ray emission is absent from the Class 0/I sources. The spatial distribution of Class 0/I and Class II sources reveals the presence of three sub-clusters in the NGC 281 West region.Comment: 29 pages, 21 figures and 11 tables, Accepted for the publication in PAS

Seaweeds A Potential Source for Functional Foods

Seaweeds are microalgae growing in coastal regions and resistant to salinity. Seaweeds are rich resources of natural nutrients some of which cannot be obtained from terrestrial plants. Bioactive compounds of seaweeds such as sulphated polysaccharides, peptides, minerals, phlorotannins, carotenoids and sulfolipids have proven health benefits against various diseases. Traditionally, seaweeds are used as folk medicine for treating diseases like goiter, wounds, burns, rashes, inflammation, diabetes and also gaining attention of pharmaceutical industries due to their anti-cancer, anti-aging, anti-angiogenesis, anti-bacterial, anti-viral and antioxidant properties. Seaweeds polysaccharides have wide applications in foods as well as in pharmaceutical industry due to their bio-chemical properties such as stabilizer, emulsifier and gelling property. In food industry, seaweed polysaccharides are used as a functional ingredient in many products such as frozen foods, ice-cream, jam, jelly, beverages etc. Several commercial food preparations from seaweeds are also available in the market such as sea salt, nori snack wasabi, pink rock salt, seaweed thins toasted coconuts, crunchy seaweed chips, raw unroasted seaweed under different brand names. The present review is a compilation of nutritional, pharmacological and food properties of seaweeds along with its potential towards development of functional foods

Complexes of Organotin(IV) Halides with Neutral Schiff Bases of Salicylaldehyde & 2-Hydroxy-l-naphthaldehyde with 2-Aminopyridine

1023-102

Optical and Near-infrared survey of the stellar contents associated with the star-forming Complex Sh2-252

We present the analyses of the stellar contents associated with the HII region Sh2-252 using UBVRI photometry, slit and slitless spectroscopy along with the NIR data from 2MASS for an area ~1 degree x 1 degree. We studied the sub-regions of Sh2-252 which includes four compact-HII (CHII) regions, namely A, B, C and E and two clusters NGC 2175s and Teutsch 136 (Teu 136). Of the fifteen spectroscopically observed bright stars, eight have been identified as massive members of spectral class earlier than B3. From the spectro-photometric analyses, we derived the average distance of the region as 2.4+/-0.2 kpc and the reddening of the massive members is found to vary between 0.35 to 2.1 mag. We found that NGC 2175s and Teu 136, located towards the eastern edge of the complex are the sub-clusters of Sh2-252. The stellar surface density distribution in K-band shows clustering associated with the regions A, C, E, NGC 2175s and Teu 136. We have also identified the candidate ionizing sources of the CHII regions. 61 H_alpha emission sources are identified using slitless spectroscopy. The distribution of the H_alpha emission sources and candidate YSOs with IR excess on the V/(V-I) CMD shows that a majority of them have approximate ages between 0.1 - 5 Myr and masses in the range of 0.3 - 2.5 M_sun. The CMDs of the candidate YSOs in the individual regions also show an age spread of 0.1 - 5 Myr for each of them. We calculated the KLFs for the sub-regions A, C, E, NGC 2175s and Teu 136. Within errors, the KLFs for all the sub-regions are found to be similar and comparable to that of young clusters of age < 5 Myr. We also estimated the mass functions (MFs) of the PMS sample of the individual regions in the mass range of 0.3 - 2.5 M_sun. In general, the slopes of the MFs of all the sub-regions are found comparable to the Salpeter value.Comment: published in MNRA

A survey of some new approaches in maximum age limit and accuracy of luminescence application to archaeological chronometry

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