Densest Subgraph in Dynamic Graph Streams

In this paper, we consider the problem of approximating the densest subgraph in the dynamic graph stream model. In this model of computation, the input graph is defined by an arbitrary sequence of edge insertions and deletions and the goal is to analyze properties of the resulting graph given memory that is sub-linear in the size of the stream. We present a single-pass algorithm that returns a $(1+\epsilon)$ approximation of the maximum density with high probability; the algorithm uses O(\epsilon^{-2} n \polylog n) space, processes each stream update in \polylog (n) time, and uses \poly(n) post-processing time where $n$ is the number of nodes. The space used by our algorithm matches the lower bound of Bahmani et al.~(PVLDB 2012) up to a poly-logarithmic factor for constant $\epsilon$. The best existing results for this problem were established recently by Bhattacharya et al.~(STOC 2015). They presented a $(2+\epsilon)$ approximation algorithm using similar space and another algorithm that both processed each update and maintained a $(4+\epsilon)$ approximation of the current maximum density in \polylog (n) time per-update.Comment: To appear in MFCS 201

A tight lower bound instance for k-means++ in constant dimension

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial $k$ centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from the given points. For $i > 1$, pick a point to be the $i^{th}$ center with probability proportional to the square of the Euclidean distance of this point to the closest previously $(i-1)$ chosen centers. The k-means++ seeding algorithm is not only simple and fast but also gives an $O(\log{k})$ approximation in expectation as shown by Arthur and Vassilvitskii. There are datasets on which this seeding algorithm gives an approximation factor of $\Omega(\log{k})$ in expectation. However, it is not clear from these results if the algorithm achieves good approximation factor with reasonably high probability (say $1/poly(k)$). Brunsch and R\"{o}glin gave a dataset where the k-means++ seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability that is exponentially small in $k$. However, this and all other known lower-bound examples are high dimensional. So, an open problem was to understand the behavior of the algorithm on low dimensional datasets. In this work, we give a simple two dimensional dataset on which the seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability exponentially small in $k$. This solves open problems posed by Mahajan et al. and by Brunsch and R\"{o}glin.Comment: To appear in TAMC 2014. arXiv admin note: text overlap with arXiv:1306.420

Parametric t-Distributed Stochastic Exemplar-centered Embedding

Parametric embedding methods such as parametric t-SNE (pt-SNE) have been widely adopted for data visualization and out-of-sample data embedding without further computationally expensive optimization or approximation. However, the performance of pt-SNE is highly sensitive to the hyper-parameter batch size due to conflicting optimization goals, and often produces dramatically different embeddings with different choices of user-defined perplexities. To effectively solve these issues, we present parametric t-distributed stochastic exemplar-centered embedding methods. Our strategy learns embedding parameters by comparing given data only with precomputed exemplars, resulting in a cost function with linear computational and memory complexity, which is further reduced by noise contrastive samples. Moreover, we propose a shallow embedding network with high-order feature interactions for data visualization, which is much easier to tune but produces comparable performance in contrast to a deep neural network employed by pt-SNE. We empirically demonstrate, using several benchmark datasets, that our proposed methods significantly outperform pt-SNE in terms of robustness, visual effects, and quantitative evaluations.Comment: fixed typo

Bidirectional PageRank Estimation: From Average-Case to Worst-Case

We present a new algorithm for estimating the Personalized PageRank (PPR) between a source and target node on undirected graphs, with sublinear running-time guarantees over the worst-case choice of source and target nodes. Our work builds on a recent line of work on bidirectional estimators for PPR, which obtained sublinear running-time guarantees but in an average-case sense, for a uniformly random choice of target node. Crucially, we show how the reversibility of random walks on undirected networks can be exploited to convert average-case to worst-case guarantees. While past bidirectional methods combine forward random walks with reverse local pushes, our algorithm combines forward local pushes with reverse random walks. We also discuss how to modify our methods to estimate random-walk probabilities for any length distribution, thereby obtaining fast algorithms for estimating general graph diffusions, including the heat kernel, on undirected networks.Comment: Workshop on Algorithms and Models for the Web-Graph (WAW) 201

The effects of dietary supplementation of astaxanthin and Β-carotene on the reproductive performance and egg quality of female goldfish (Carassius auratus)

The present research was aimed to study the effects of different sources of carotenoids and their varying concentrations on the reproductive functions of goldfish. The study was carried out in seven treatments with three replicates at the Bony Fish Hatchery Complex (Rasht, Iran) from December 2011 to May 2012.Experimental diets containing 50, 100, and 150 mg kg-1 astaxanthin and 50, 100, and 150 mg kg-1 β-carotene along with a carotenoid free basic carp feed as control were utilized. The goldfish broodstock were fed with the formulated diets for a period of four months. In May, eggs obtained from the female goldfish were fertilized with the semen of identical male goldfish fed with control diet and the absolute, working and relative fecundities and egg fertilization along with egg survival rate were estimated for different treatments during incubation period. The results showed that there was no significant difference in the fecundity rates among different diet treatments. Nevertheless, the diameter and the number of egg per gram of the fertilized eggs in fish in the A150 (astaxanthin 150 mg kg-1) treatment were greater than those in the other treatments (P ≤ 0.05) and this treatment showed higher egg survival rates in the incubation period (P ≤ 0.05). Correlation of egg astaxanthin with fertilization rate and survival rate was significant. Moreover, there was significant correlation between β-carotene and survival rate (P ≤ 0.05)

Association of PON1-L55M genetic variation and breast cancer risk: A case-control trial

Background: Paraoxonase 1 (PON1), a multifactorial antioxidant enzyme, has a defensive role against oxidative stress, which is believed to contribute to cancer development. This study aimed to investigate the association of PON1-L55M functional polymorphism with breast cancer risk. Material and methods: In the experimental study, blood samples were collected from 150 healthy women controls and 150 breast cancer subjects. The L55M genotyping was performed by polymerase chain reaction-restriction fragment length polymorphism. Results: Our analysis showed that the genotypes distribution is in Hardy-Weinberg equilibrium for both case and control groups. Our data revealed that there are significant associations between PON1-L55M polymorphism and breast cancer risk in homozygote (OR= 2.13, 95CI= 1.14-4.00, p= 0.018), dominant (OR= 1.72, 95CI= 1.07-2.76, p= 0.024), and allelic (OR= 1.55, 95CI= 1.12-2.15, p= 0.008) models. Conclusions: Our results suggest that the PON1-L55M genetic variation could be a genetic risk factor for breast cancer risk and it could be considered as a molecular biomarker for screening of susceptible women. © 2020 Asian Pacific Organization for Cancer Prevention

On Conceptually Simple Algorithms for Variants of Online Bipartite Matching

We present a series of results regarding conceptually simple algorithms for bipartite matching in various online and related models. We first consider a deterministic adversarial model. The best approximation ratio possible for a one-pass deterministic online algorithm is $1/2$, which is achieved by any greedy algorithm. D\"urr et al. recently presented a $2$-pass algorithm called Category-Advice that achieves approximation ratio $3/5$. We extend their algorithm to multiple passes. We prove the exact approximation ratio for the $k$-pass Category-Advice algorithm for all $k \ge 1$, and show that the approximation ratio converges to the inverse of the golden ratio $2/(1+\sqrt{5}) \approx 0.618$ as $k$ goes to infinity. The convergence is extremely fast --- the $5$-pass Category-Advice algorithm is already within $0.01\%$ of the inverse of the golden ratio. We then consider a natural greedy algorithm in the online stochastic IID model---MinDegree. This algorithm is an online version of a well-known and extensively studied offline algorithm MinGreedy. We show that MinDegree cannot achieve an approximation ratio better than $1-1/e$, which is guaranteed by any consistent greedy algorithm in the known IID model. Finally, following the work in Besser and Poloczek, we depart from an adversarial or stochastic ordering and investigate a natural randomized algorithm (MinRanking) in the priority model. Although the priority model allows the algorithm to choose the input ordering in a general but well defined way, this natural algorithm cannot obtain the approximation of the Ranking algorithm in the ROM model

An ethnobotanical study of medicinal plants administered for the treatment of hypertension

Introduction: The incidence of cardiovascular diseases (CVDs) is very high in human societies and their prevention and treatment are the most important priority in many countries. Hypertension makes an important contribution to the development of CVDs. Objectives: This study aimed to collect the ethno-medicinal knowledge of the traditional healers of Shiraz on medicinal plants used in the treatment of hypertension. Materials and Methods: Ethno-medicinal data were collected from September 2012 to July 2013 through direct interview. Twenty-five healers were interviewed using semi-structured questionnaires and their traditional ethno-medicinal knowledge was recorded. Questionnaires were included apothecary personal information, plant local name, plant parts used, method of preparation, season of harvest and traditional use. Data collected from surveys and interviews were transferred to Microsoft Excel 2007 and analyzed. Results: Analysis of data showed that, 27 medicinal plants from 22 families are used for the treatment of hypertension. The families with most antihypertensive species were Apiaceae (8), Rosaceae (8) and Papaveraceae (8). The most frequently used plant parts were leaves (36) followed by fruits (30), aerial part (17) and branches (7). The most frequently used preparation method was decoction (95). Borago officinalis (51.85), Berberis vulgaris (51.58) had the highest frequency of mention. Conclusion: The ethno-medicinal survey of medicinal plants recommended by traditional healers for the treatment of hypertension provides new areas of research on the antihypertensive effect of medicinal plants. In the case of safety and effectiveness, they can be refined and processed to produce natural drugs

PHYTOTHERAPY IN FUNGI AND FUNGAL DISEASE: A REVIEW OF EFFECTIVE MEDICINAL PLANTS ON IMPORTANT FUNGAL STRAINS AND DISEASES

Infectious diseases are among the most important common diseases worldwide that bring stupendous costs for human community. Medicinal plants are considered a rich source of antimicrobial agents and therefore can be used as antimicrobial remedies because of producing secondary metabolites. This article was designed to review the effective medicinal plants on fungi and fungal disease. In this study, the relevant articles published in Persian and English languages were searched for in the databases Magiran, Iranmedex, Irandoc, PubMed, Scopus, SID, Web of Science, and Science Direct using the search engine Google Scholar. To maximize the comprehensiveness of the search, the general terms antimicrobial, dermatophyte, mycotic, Iran, and anti-Candida as well as their Persian equivalents were used. AND and OR were used for combining searches. Medicinal herbs such as Zataria multiflora, Thymus vulgaris, Thymus kotschyanus, Punicagranatum L., Rosmarinus officinalis L., Matricaria chamomilla L., Urtica dioica L., Mentha piperita L. and Salvia officinalis L., Thymus vulgaris, Salvia officinalis, Eucalyptus globulus, Myentha piperita, Oliveria decumbens, Echinophora Platyloba, Thymus eriocalyx and Thymus X-porlock, Achillea millefolium, Artemisia sieberi, Cuminum cyminum, Nigella sativa, Heracleum persicum, Hyssopus officinalis, Matricaria recutital, Menta spicata, Foeniculum vulgare, Pimpinella anisum, Plargonium graveolens, Rosmarinus officinalis, Saturia hortensis, Zataria multiflora, Thymus kotschyanus, Zataria multiflora, Ziziphora clinopodioides, Mentha piperita L., Physalis alkekengi L., Hymenocrater longiflorus Benth and are the most important Medicinal herbs effective on fungal diseases. Medicinal herbs mentioned in this study due to phenolic compounds and antioxidant activities have antifungal effects

A review on most important herbal and synthetic antihelmintic drugs

Parasites and parasitic diseases are widely spread in the world. Their adverse effects on health and social economic society cause tremendous public health problems. Parasitic infections in different ways (water, soil, food and vegetables) can affect humans and induce other complications such as gastrointestinal disorders, malnutrition, anemia and allergies and sometimes even life threatening. Medicinal plants are being widely used, either as a single drug or in combination with synthetic drugs. These medicinal plants are considered as a valuable source of unique natural products and drugs for development of medicines against various disorders and diseases. In this article the recently published papers about medicinal plants and parasites were reviewed, using scientific sites such as Medline, PubMed and Google Scholar. The used terms included: herbal medicine, medicinal plants, and antihelmintic drugs, antinematoda, anticestoda, antitrematoda. From the above collected literature it might be concluded that these plants are promising potential sources for preparation of new drugs or for pharmacological and therapeutic applications