Projective, Sparse, and Learnable Latent Position Network Models

When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the number of nodes, which is inappropriate when the graph is thought to be sparse. We propose an alternative assumption---that the latent positions are generated according to a Poisson point process---and show that it is compatible with various levels of sparsity. Unlike other notions of sparse latent position models in the literature, our framework also defines a projective sequence of probability models, thus ensuring consistency of statistical inference across networks of different sizes. We establish conditions for consistent estimation of the latent positions, and compare our results to existing frameworks for modeling sparse networks.Comment: 51 pages, 2 figure

Design of a Modified Braking System Mechanism for Two Wheeler Vehicles to Increase Safety of the Rider

The present disclosure relates generally to a braking system for a two-wheeler vehicle that enables linkage between the front and rear brakes to help attain a safe braking ratio under all circumstances. In an aspect, the present disclosure provides a mechanical linkage between front and the rear brakes of a two-wheeler vehicle, wherein the linkage can be installed without removing any component of existing braking systems/architectures, and wherein the linkage can enable automatic application of brake on a second brake when brake is applied on a first brake. For instance, when front brake (for the front wheel, for instance) is applied, automatic and ideal proportional brake can be automatically applied to the rear brake (for the rear wheel, for instance), and vise versa

Genetic diversity analysis of the medicinal herb Plantago ovata (Forsk.)

Plantago ovata (Forsk.) (2n = 8) used as laxative, emollient and demulcent, has great commercial and medicinal importance. With India being the largest producer in the world there is still a lack of defined varieties of the species and no coordinated breeding efforts are being made. In the present study, we report the phylogenetic analysis of the crop for its utilization in future breeding programs for defining varieties of the crop. A total of 302 clear and reproducible bands were obtained with random amplified polymorphic DNA (RAPD) techniques involving 35 random primers in 18 selected lines, out of which 198 (65.5%) were polymorphic with an average 8.6 bands per primer. Amplified DNA fragments ranged from 300 to 3400 bp. Dissimilarity indices based on Nei and Li equation ranged from 0.07 to 0.29 indicating moderate level of genetic polymorphism. Hierarchical cluster analysis using SPSS method showed genetic variation amongst genotypes dividing them into three major clusters comprising 10, seven and one genotypes, respectively. The result of present study indicates that RAPD analysis has determined the genetic relationships and estimated the genetic diversity among the genotypes of P. ovata. Key words: Plantago ovata (Forsk.), random amplified polymorphic DNA (RAPD) markers, Nei and Li equation, genetic diversity

Hawkes process as a model of social interactions: a view on video dynamics

We study by computer simulation the "Hawkes process" that was proposed in a recent paper by Crane and Sornette (Proc. Nat. Acad. Sci. USA 105, 15649 (2008)) as a plausible model for the dynamics of YouTube video viewing numbers. We test the claims made there that robust identification is possible for classes of dynamic response following activity bursts. Our simulated timeseries for the Hawkes process indeed fall into the different categories predicted by Crane and Sornette. However the Hawkes process gives a much narrower spread of decay exponents than the YouTube data, suggesting limits to the universality of the Hawkes-based analysis.Comment: Added errors to parameter estimates and further description. IOP style, 13 pages, 5 figure

Genetic diversity analysis of the medicinal herb Plantago ovata (Forsk.)

Plantago ovata (Forsk.) (2n = 8) used as laxative, emollient and demulcent, has great commercial and medicinal importance. With India being the largest producer in the world there is still a lack of defined varieties of the species and no coordinated breeding efforts are being made. In the present study, we report the phylogenetic analysis of the crop for its utilization in future breeding programs for defining varieties of the crop. A total of 302 clear and reproducible bands were obtained with random amplified polymorphic DNA (RAPD) techniques involving 35 random primers in 18 selected lines, out of which 198 (65.5%) were polymorphic with an average 8.6 bands per primer. Amplified DNA fragments ranged from 300 to 3400 bp. Dissimilarity indices based on Nei and Li equation ranged from 0.07 to 0.29 indicating moderate level of genetic polymorphism. Hierarchical cluster analysis using SPSS method showed genetic variation amongst genotypes dividing them into three major clusters comprising 10, seven and one genotypes, respectively. The result of present study indicates that RAPD analysis has determined the genetic relationships and estimated the genetic diversity among the genotypes of P. ovata.Key words: Plantago ovata (Forsk.), random amplified polymorphic DNA (RAPD) markers, Nei and Li equation, genetic diversity

Power-law distributions in empirical data

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws

Spreading in Social Systems: Reflections

In this final chapter, we consider the state-of-the-art for spreading in social systems and discuss the future of the field. As part of this reflection, we identify a set of key challenges ahead. The challenges include the following questions: how can we improve the quality, quantity, extent, and accessibility of datasets? How can we extract more information from limited datasets? How can we take individual cognition and decision making processes into account? How can we incorporate other complexity of the real contagion processes? Finally, how can we translate research into positive real-world impact? In the following, we provide more context for each of these open questions.Comment: 7 pages, chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur

Diabetes conversation map - A novel tool for diabetes management self-efficacy among type 2 diabetes patients in Pakistan: A randomized controlled trial

Background: This study aimed to measure the effect of diabetes education using the novel method of "diabetes conversation map (DCM)"as compared to routine counselling (RC) on diabetes management self-efficacy (DMSE) among patients living with type 2 diabetes in Karachi, Pakistan. Methods: A parallel arm randomized controlled trial among patients with type 2 diabetes aged 30-60 years, with HbA1c > 7%, diagnosed for at least 5 yrs., was conducted at the national institute of diabetes and endocrinology in Karachi, Pakistan. A total 123 type 2 diabetes patients were randomized into DCM (n = 62) or RC (n = 61). Four weekly diabetes control sessions of 40 min each using the DCM or RC was provided. DMSE was measured using a validated Urdu language DMSE tool at baseline and after three months of the randomization. Change in DMSE and HbA1c levels within groups (pre-post) and between the groups after 3 months of enrollment was compared. Results: Baseline characteristics except HbA1c were similar between the two arms. After 3 months of enrollment, there was no change in the DMSE score in the RC arm however, significant increase in DMSE score was noted in the DCM arm (P = < 0.001). The average difference (95% confidence interval) in DMSE score between the DCM and RC arm was 33.7(27.3, 40.0; p = < 0.001) after 3 months of the enrollment. Difference in HbA1c within groups was not significant. Conclusions: DCM significantly improved DMSE among type 2 diabetes patients in a developing country setting like Pakistan. Healthcare workers caring for type 2 diabetes patients need to be trained on DCM to effectively utilize this novel tool for educating diabetes patients. Trial registration: This trial was prospectively registered. ClinicalTrials.gov Identifier: NCT03747471. Date of registration: Nov 20. 2018

Homophily and Contagion Are Generically Confounded in Observational Social Network Studies

We consider processes on social networks that can potentially involve three factors: homophily, or the formation of social ties due to matching individual traits; social contagion, also known as social influence; and the causal effect of an individual's covariates on their behavior or other measurable responses. We show that, generically, all of these are confounded with each other. Distinguishing them from one another requires strong assumptions on the parametrization of the social process or on the adequacy of the covariates used (or both). In particular we demonstrate, with simple examples, that asymmetries in regression coefficients cannot identify causal effects, and that very simple models of imitation (a form of social contagion) can produce substantial correlations between an individual's enduring traits and their choices, even when there is no intrinsic affinity between them. We also suggest some possible constructive responses to these results.Comment: 27 pages, 9 figures. V2: Revised in response to referees. V3: Ditt