Upper bounds for the number of solutions to quartic Thue equations

We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve (x,y) that allows us to use the theory of linear forms in logarithms. This manuscript improves the results of author's earlier work with Okazaki [2] by giving special treatments to forms with respect to their signature

Lower bounds for Mahler measure that depend on the number of monomials

We prove a new lower bound for the Mahler measure of a polynomial in one and in several variables that depends on the complex coefficients, and the number of monomials. In one variable our result generalizes a classical inequality of Mahler. In $M$ variables our result depends on $\mathbb{Z}^M$ as an ordered group, and in general our lower bound depends on the choice of ordering

Independent relative units of low height

We prove inequalities that compare the relative regulator of an extension of number fields with a product of heights of multiplicatively independent relative units

Large-scale magnetic fields from inflation due to a CPTCPT-even Chern-Simons-like term with Kalb-Ramond and scalar fields

We investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the $CPT$-even dimension-six Chern-Simons-like effective interaction with a fermion current by taking account of the dynamical Kalb-Ramond and scalar fields in inflationary cosmology. It is explicitly demonstrated that the magnetic fields on 1Mpc scale with the field strength of $\sim 10^{-9}$G at the present time can be induced.Comment: 18 pages, 6 figures, version accepted for publication in Eur. Phys. J.

Infertility in iranian traditional medicine from Hakim Mohammad Azam Khan point of view

Introduction: Fertility and having healthy child is one of the valuable indexes in people's health. Incidence of infertility in the world has a treatment economic load and also causes significant psychiatric complications for the infertile couples and threats the health of family. Given the importance of the issue, attention to complementary medicine and use of Iranian traditional medicine can be useful and helpful. This study was performed with aim to evaluate the causes of infertility from Iranian traditional Medicine (ITM) point of view according to the valuable Exir book of Hakim Mohammad Azam Khan. Methods: This study was performed as library based on reference availabe and reliable books of traditional medicine such as law in medicine, store of Kharazmshahi, Aghili's Kholasah al-Hekmah and Moalejat with a focus on Azam Exir, and finally, what Hakim Azam Khan explained about the causes of infertility was stated. Results: Iranian medicine Hokama have suggested various reasons as the causes of infertility in men and women, separately, and stated different treatment methods such as single plants, combined drugs and method performed manually including bloodletting, cupping, and massage, and at the end of the treatment method in food section explained the type of food that is useful for disease. They divided causes of infertility into two groups of male and female factors and emphasized on the existence of semen in men and women and the role of each one in fertility. Sufficient production of semen in males and ovum in females depends on the health of body's main and vital members (including the heart, brain and liver). They reported fertility was possible through the health of genital system and production of reproductive semen in both and simultaneous orgasm of man and woman when having sex. Conclusion: According to the careful viewpoint of Hakim Azam Khan in explaining the causes of infertility and accurately classifying them, as well as description of how to diagnose and treatment courses of each of the infertility causes, it seems that today by relying on their views on empirical research, we can achieve more effective treatments for infertility. © 2015 - Journal Management System

Lower bounds for heights in relative Galois extensions

The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem, we obtain an effective bound for the height of an algebraic number $\alpha$ when the base field $\mathbb{K}$ is a number field and $\mathbb{K}(\alpha)/\mathbb{K}$ is Galois. Our second result establishes an explicit height bound for any nonzero element $\alpha$ which is not a root of unity in a Galois extension $\mathbb{F}/\mathbb{K}$, depending on the degree of $\mathbb{K}/\mathbb{Q}$ and the number of conjugates of $\alpha$ which are multiplicatively independent over $\mathbb{K}$. As a consequence, we obtain a height bound for such $\alpha$ that is independent of the multiplicative independence condition

Community assessment to advance computational prediction of cancer drug combinations in a pharmacogenomic screen

The effectiveness of most cancer targeted therapies is short-lived. Tumors often develop resistance that might be overcome with drug combinations. However, the number of possible combinations is vast, necessitating data-driven approaches to find optimal patient-specific treatments. Here we report AstraZeneca's large drug combination dataset, consisting of 11,576 experiments from 910 combinations across 85 molecularly characterized cancer cell lines, and results of a DREAM Challenge to evaluate computational strategies for predicting synergistic drug pairs and biomarkers. 160 teams participated to provide a comprehensive methodological development and benchmarking. Winning methods incorporate prior knowledge of drug-target interactions. Synergy is predicted with an accuracy matching biological replicates for >60% of combinations. However, 20% of drug combinations are poorly predicted by all methods. Genomic rationale for synergy predictions are identified, including ADAM17 inhibitor antagonism when combined with PIK3CB/D inhibition contrasting to synergy when combined with other PI3K-pathway inhibitors in PIK3CA mutant cells