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 non-zero 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

Relational practices and reflexivity: Exploring the responses of women entrepreneurs to changing household dynamics

This qualitative study explores how and why women, positioned as mothers, wives, or carers, navigate changing household dynamics, related to care and reproductive resources, and become entrepreneurial. Drawing on relational reflexivity, we show how women’s embodied, intimate relations with important others in the household form the focal point for entrepreneurial activities and offer evidence of their entrepreneurial agency. Our analysis reveals the emergence of three relational practices that result in a new venture as the entrepreneurial response of women. We critically evaluate normative analyses on gender, entrepreneurship, and household

High Degree of Heterogeneity in Alzheimer's Disease Progression Patterns

There have been several reports on the varying rates of progression among Alzheimer's Disease (AD) patients; however, there has been no quantitative study of the amount of heterogeneity in AD. Obtaining a reliable quantitative measure of AD progression rates and their variances among the patients for each stage of AD is essential for evaluating results of any clinical study. The Global Deterioration Scale (GDS) and Functional Assessment Staging procedure (FAST) characterize seven stages in the course of AD from normal aging to severe dementia. Each GDS/FAST stage has a published mean duration, but the variance is unknown. We use statistical analysis to reconstruct GDS/FAST stage durations in a cohort of 648 AD patients with an average follow-up time of 4.78 years. Calculations for GDS/FAST stages 4–6 reveal that the standard deviations for stage durations are comparable with their mean values, indicating the presence of large variations in the AD progression among patients. Such amount of heterogeneity in the course of progression of AD is consistent with the existence of several sub-groups of AD patients, which differ by their patterns of decline

In Silico Elucidation of the Recognition Dynamics of Ubiquitin

Elucidation of the mechanism of biomacromolecular recognition events has been a topic of intense interest over the past century. The inherent dynamic nature of both protein and ligand molecules along with the continuous reshaping of the energy landscape during the binding process renders it difficult to characterize this process at atomic detail. Here, we investigate the recognition dynamics of ubiquitin via microsecond all-atom molecular dynamics simulation providing both thermodynamic and kinetic information. The high-level of consistency found with respect to experimental NMR data lends support to the accuracy of the in silico representation of the conformational substates and their interconversions of free ubiquitin. Using an energy-based reweighting approach, the statistical distribution of conformational states of ubiquitin is monitored as a function of the distance between ubiquitin and its binding partner Hrs-UIM. It is found that extensive and dense sampling of conformational space afforded by the µs MD trajectory is essential for the elucidation of the binding mechanism as is Boltzmann sampling, overcoming inherent limitations of sparsely sampled empirical ensembles. The results reveal a population redistribution mechanism that takes effect when the ligand is at intermediate range of 1–2 nm from ubiquitin. This mechanism, which may be depicted as a superposition of the conformational selection and induced fit mechanisms, also applies to other binding partners of ubiquitin, such as the GGA3 GAT domain

Modelling imperfect adherence to HIV induction therapy

Abstract Background Induction-maintenance therapy is a treatment regime where patients are prescribed an intense course of treatment for a short period of time (the induction phase), followed by a simplified long-term regimen (maintenance). Since induction therapy has a significantly higher chance of pill fatigue than maintenance therapy, patients might take drug holidays during this period. Without guidance, patients who choose to stop therapy will each be making individual decisions, with no scientific basis. Methods We use mathematical modelling to investigate the effect of imperfect adherence during the inductive phase. We address the following research questions: 1. Can we theoretically determine the maximal length of a possible drug holiday and the minimal number of doses that must subsequently be taken while still avoiding resistance? 2. How many drug holidays can be taken during the induction phase? Results For a 180 day therapeutic program, a patient can take several drug holidays, but then has to follow each drug holiday with a strict, but fairly straightforward, drug-taking regimen. Since the results are dependent upon the drug regimen, we calculated the length and number of drug holidays for all fifteen protease-sparing triple-drug cocktails that have been approved by the US Food and Drug Administration. Conclusions Induction therapy with partial adherence is tolerable, but the outcome depends on the drug cocktail. Our theoretical predictions are in line with recent results from pilot studies of short-cycle treatment interruption strategies and may be useful in guiding the design of future clinical trials

AtriplaR/anti-TB combination in TB/HIV patients. Drug in focus

Co-administration of anti-tuberculosis and antiretroviral therapy is often inevitable in high-burden countries where tuberculosis is the most common opportunistic infection associated with HIV/AIDS. Concurrent use of rifampicin and several antiretroviral drugs is complicated by pharmacokinetic drug-drug interaction. Pubmed and Google search following the key words tuberculosis, HIV, emtricitabine, tenofovir efavirenz, interaction were used to find relevant information on each drug of the fixed dose combination AtriplaR RESULTS: Information on generic name, trade name, pharmacokinetic parameter, metabolism and the pharmacokinetic interaction with Anti-TB drugs of emtricitabine, tenofovir, and efavirenz was obtained. Fixed dose combination of emtricitabine/tenofovir/efavirenz (ATRIPLAR) which has been approved by Food and Drug Administration shows promising results as far as safety and efficacy is concerned in TB/HIV co-infection patients, hence can be considered effective and safe antiretroviral drug in TB/HIV management for adult and children above 3 years of age

Recovery of a US Endangered Fish

BACKGROUND: More fish have been afforded US Endangered Species Act protection than any other vertebrate taxonomic group, and none has been designated as recovered. Shortnose sturgeon (Acipenser brevirostrum) occupy large rivers and estuaries along the Atlantic coast of North America, and the species has been protected by the US Endangered Species Act since its enactment. METHODOLOGY/PRINCIPAL FINDINGS: Data on the shortnose sturgeon in the Hudson River (New York to Albany, NY, USA) were obtained from a 1970s population study, a population and fish distribution study we conducted in the late 1990s, and a fish monitoring program during the 1980s and 1990s. Population estimates indicate a late 1990s abundance of about 60,000 fish, dominated by adults. The Hudson River population has increased by more than 400% since the 1970s, appears healthy, and has attributes typical for a long-lived species. Our population estimates exceed the government and scientific population recovery criteria by more than 500%, we found a positive trend in population abundance, and key habitats have remained intact despite heavy human river use. CONCLUSIONS/SIGNIFICANCE: Scientists and legislators have called for changes in the US Endangered Species Act, the Act is being debated in the US Congress, and the Act has been characterized as failing to recover species. Recovery of the Hudson River population of shortnose sturgeon suggests the combination of species and habitat protection with patience can yield successful species recovery, even near one of the world's largest human population centers

Dynamism in the solar core

Recent results of a mixed shell model heated asymmetrically by transient increases in nuclear burning indicate the transient generation of small hot spots inside the Sun somewhere between 0.1 and 0.2 solar radii. These hot bubbles are followed by a nonlinear differential equation system with finite amplitude non-homologous perturbations which is solved in a solar model. Our results show the possibility of a direct connection between the dynamic phenomena of the solar core and the atmospheric activity. Namely, an initial heating about DQ_0 ~ 10^{31}-10^{37} ergs can be enough for a bubble to reach the outer convective zone. Our calculations show that a hot bubble can arrive into subphotospheric regions with DQ_final ~ 10^{28} - 10^{34} ergs with a high speed, up to 10 km s-1, approaching the local sound speed. We point out that the developing sonic boom transforms the shock front into accelerated particle beam injected upwards into the top of loop carried out by the hot bubble above its forefront traveling from the solar interior. As a result, a new perspective arises to explain flare energetics. We show that the particle beams generated by energetic deep-origin hot bubbles in the subphotospheric layers have masses, energies, and chemical compositions in the observed range of solar chromospheric and coronal flares. It is shown how the emergence of a hot bubble into subphotospheric regions offers a natural mechanism that can generate both the eruption leading to the flare and the observed coronal magnetic topology for reconnection. We show a list of long-standing problems of solar physics that our model explains. We present some predictions for observations, some of which are planned to be realized in the near future.Comment: 44 pages, 20 figure

Calculating Stage Duration Statistics in Multistage Diseases

Many human diseases are characterized by multiple stages of progression. While the typical sequence of disease progression can be identified, there may be large individual variations among patients. Identifying mean stage durations and their variations is critical for statistical hypothesis testing needed to determine if treatment is having a significant effect on the progression, or if a new therapy is showing a delay of progression through a multistage disease. In this paper we focus on two methods for extracting stage duration statistics from longitudinal datasets: an extension of the linear regression technique, and a counting algorithm. Both are non-iterative, non-parametric and computationally cheap methods, which makes them invaluable tools for studying the epidemiology of diseases, with a goal of identifying different patterns of progression by using bioinformatics methodologies. Here we show that the regression method performs well for calculating the mean stage durations under a wide variety of assumptions, however, its generalization to variance calculations fails under realistic assumptions about the data collection procedure. On the other hand, the counting method yields reliable estimations for both means and variances of stage durations. Applications to Alzheimer disease progression are discussed

A Structure-Based Approach for Mapping Adverse Drug Reactions to the Perturbation of Underlying Biological Pathways

Adverse drug reactions (ADR), also known as side-effects, are complex undesired physiologic phenomena observed secondary to the administration of pharmaceuticals. Several phenomena underlie the emergence of each ADR; however, a dominant factor is the drug's ability to modulate one or more biological pathways. Understanding the biological processes behind the occurrence of ADRs would lead to the development of safer and more effective drugs. At present, no method exists to discover these ADR-pathway associations. In this paper we introduce a computational framework for identifying a subset of these associations based on the assumption that drugs capable of modulating the same pathway may induce similar ADRs. Our model exploits multiple information resources. First, we utilize a publicly available dataset pairing drugs with their observed ADRs. Second, we identify putative protein targets for each drug using the protein structure database and in-silico virtual docking. Third, we label each protein target with its known involvement in one or more biological pathways. Finally, the relationships among these information sources are mined using multiple stages of logistic-regression while controlling for over-fitting and multiple-hypothesis testing. As proof-of-concept, we examined a dataset of 506 ADRs, 730 drugs, and 830 human protein targets. Our method yielded 185 ADR-pathway associations of which 45 were selected to undergo a manual literature review. We found 32 associations to be supported by the scientific literature