Regularized spectral methods for clustering signed networks

We study the problem of $k$-way clustering in signed graphs. Considerable attention in recent years has been devoted to analyzing and modeling signed graphs, where the affinity measure between nodes takes either positive or negative values. Recently, Cucuringu et al. [CDGT 2019] proposed a spectral method, namely SPONGE (Signed Positive over Negative Generalized Eigenproblem), which casts the clustering task as a generalized eigenvalue problem optimizing a suitably defined objective function. This approach is motivated by social balance theory, where the clustering task aims to decompose a given network into disjoint groups, such that individuals within the same group are connected by as many positive edges as possible, while individuals from different groups are mainly connected by negative edges. Through extensive numerical simulations, SPONGE was shown to achieve state-of-the-art empirical performance. On the theoretical front, [CDGT 2019] analyzed SPONGE and the popular Signed Laplacian method under the setting of a Signed Stochastic Block Model (SSBM), for $k=2$ equal-sized clusters, in the regime where the graph is moderately dense. In this work, we build on the results in [CDGT 2019] on two fronts for the normalized versions of SPONGE and the Signed Laplacian. Firstly, for both algorithms, we extend the theoretical analysis in [CDGT 2019] to the general setting of $k \geq 2$ unequal-sized clusters in the moderately dense regime. Secondly, we introduce regularized versions of both methods to handle sparse graphs -- a regime where standard spectral methods underperform -- and provide theoretical guarantees under the same SSBM model. To the best of our knowledge, regularized spectral methods have so far not been considered in the setting of clustering signed graphs. We complement our theoretical results with an extensive set of numerical experiments on synthetic data.Comment: 55 pages, 5 figure

Code Coverage Analysis of Object-Oriented Programming

Code coverage analysis is a vital activity in any software testing process. It provides developers with a measure of how well their source code is being exercised by the test runs.It estimates the e_ectiveness of the test by detecting errors/bugs in the code. In order to perform e_cient software testing and coverage analysis we must adopt a systematic way and a sound theoretical basis for testing the programs. In our project, we are describing the implementation of a testing tool, Java Bytecode Understanding and Testing(JaBUTi) tool for testing Java programs. JaBUTi works with Java Bytecode so no source code is required for the code coverage analysis. It shows the De_nition-Use Graph(DUG) for every method of a class which helps in the structural testing approach, both control ow testing and data ow testing. It consists of a code coverage tool, slicing tool and static metrics tool. In our project, we are using JaBUTi as a code coverage tool for coverage analysis of Java programs.We have proposed an algorithm for coverage analysis of code to desired percentage. In our algorithm we are taking Java Bytecode as an input

Basal Cell Ameloblastoma of Mandible: A Rare Case Report with Review

Ameloblastoma is a slow-growing benign neoplasm that has a strong tendency to local invasion and that can grow to be quite large without metastasizing. Rare examples of distant metastasis of an ameloblastoma in lungs or regional lymph nodes do exist. It has an aggressive and recurrent course and is rarely metastatic. Radiographically it shares common features with other lesions such as the giant cell tumor, aneurysmal bone cyst, and renal cell carcinoma metastasis; a definitive diagnosis can only be made with histopathology. Basal cell ameloblastoma is believed to be the rarest histologic subtype in which the tumor is composed of more primitive cells and has even fewer features of peripheral palisading. Till date, only few cases of basal cell ameloblastoma have been reported in the literature. Considering the rarity of the lesion, we report here an interesting and unique case of basal cell ameloblastoma of the mandible occurring in a very old patient

Regularized spectral methods for clustering signed networks

International audienceWe study the problem of k-way clustering in signed graphs. Considerable attention in recent years has been devoted to analyzing and modeling signed graphs, where the affinity measure betweennodes takes either positive or negative values. Recently, [CDGT19] proposed a spectral method,namely SPONGE (Signed Positive over Negative Generalized Eigenproblem), which casts the clustering task as a generalized eigenvalue problem optimizing a suitably defined objective function.This approach is motivated by social balance theory, where the clustering task aims to decomposea given network into disjoint groups, such that individuals within the same group are connected byas many positive edges as possible, while individuals from different groups are mainly connected bynegative edges. Through extensive numerical simulations, SPONGE was shown to achieve state-of-the-art empirical performance. On the theoretical front, [CDGT19] analyzed SPONGE, as well asthe popular Signed Laplacian based spectral method under the setting of a Signed Stochastic BlockModel, for k=2 equal-sized clusters, in the regime where the graph is moderately dense. In this work, we build on the results in [CDGT19] on two fronts for the normalized versions of SPONGE and the Signed Laplacian. Firstly, for both algorithms, we extend the theoretical analysisin [CDGT19] to the general setting of k>2 unequal-sized clusters in the moderately dense regime. Secondly, we introduce regularized versions of both methods to handle sparse graphs – a regime where standard spectral methods are known to underperform – and provide theoretical guaranteesunder the same setting of a Signed Stochastic Block Model. To the best of our knowledge, regularized spectral methods have so far not been considered in the setting of clustering signed graphs. Wecomplement our theoretical results with an extensive set of numerical experiments on synthetic data

Prevalence and risk factors associated with sexually transmitted diseases (STDs) in Sikkim

The population of Sikkim is a unique blend of multi-tribal and metropolitan culture. However, till date, no data regarding prevalence of sexually transmitted diseases (henceforth abbreviated as STDs) among this population is available and hence requires attention. Hence the objective is to determine the prevalence of STDs in Sikkim and to describe associated risk factors. A cross-sectional study involving 'Questionnaire-based anonymous feedback system' was followed to collect data from 2,000 individuals across the society. The four most common STDs, gonorrhea, syphilis, chlamydia and HIV, were considered for the study. Total 69 (3.6 %) cases of STDs were found in 1,918 individuals was affected by at least one of the STDs, out of which 43 were males and 26 were females. Cases of gonorrhea, syphilis, chlamydiasis and HIV were 25, 22, 4 and 18 respectively. Out of total 69 cases of STDs, 20 individuals were also suffering from some kind of hepatitis. Addictions like alcoholism, smoking and drugs were also found in significant number, with 1,019 (>50 %) individuals with at least one of these addictions. Relative risk analysis indicates that gender-wise females are more vulnerable to STDs than males. The number of partners, addictions, especially alcohol and drug abuse, also contribute to STD cases. STDs act as a significant risk factor in transmitting some of the types of hepatitis. In such cases, females are more vulnerable than males. The results suggest that new community health programs are essential for both, HIV and non-HIV STDs in Sikkim

Effect of illumination intensity and temperature on open circuit voltage in organic solar cells

The effect of illumination intensity and temperature on open circuit voltage (Voc) in organic photovoltaic devices has been investigated. Voc is observed to saturate at high illumination intensities. The illuminated J-V characteristics at different intensities intersect the dark characteristic at a single point. This intersection point is shown to be equal to the built-in voltage (Vbi) in the sample. A reduction in temperature shows increment in saturated Voc. This increment in saturated Voc is attributed to the variation of Vbi with temperature. A model has been presented that explains the observed behavior of Vbi at different temperatures

Prevalence and risk factors associated with gastro-intestinal tract infections in Sikkim

The present study explored the association between dietary, drinking water, drinking (alcohol) and sedentary lifestyle habits with gastroenteritis in population of Sikkim. Data were collected with help of a detailed questionnaire from 2000 urban and rural people, aged more than 15 years. Our study found that gastroenteritis is wide spread in Sikkim, with the most common disorders being amoebiasis, food-poisoning, gastric ulcer and cholera. The results show that drinking water and alcohol are major risk factors for gastroenteritis than food habits like vegetarian or nonvegetarian diet and working habits. Study also indicates the role of ethnic fermented foods in gastroenteritis, which needs further experimental validation

Basal Cell Ameloblastoma of Mandible: A Rare Case Report with Review

Ameloblastoma is a slow-growing benign neoplasm that has a strong tendency to local invasion and that can grow to be quite large without metastasizing. Rare examples of distant metastasis of an ameloblastoma in lungs or regional lymph nodes do exist. It has an aggressive and recurrent course and is rarely metastatic. Radiographically it shares common features with other lesions such as the giant cell tumor, aneurysmal bone cyst, and renal cell carcinoma metastasis; a definitive diagnosis can only be made with histopathology. Basal cell ameloblastoma is believed to be the rarest histologic subtype in which the tumor is composed of more primitive cells and has even fewer features of peripheral palisading. Till date, only few cases of basal cell ameloblastoma have been reported in the literature. Considering the rarity of the lesion, we report here an interesting and unique case of basal cell ameloblastoma of the mandible occurring in a very old patient