On Three Generalizations of Contraction

We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic properties, like convergence to an attractor or entrainment to a periodic excitation, and allowing initial transients does not affect this asymptotic behavior. We provide sufficient conditions for GC, and demonstrate their usefulness using examples of systems that are not contractive, with respect to any norm, yet are GC

Universality of Electron Mobility in LaAlO3_3/SrTiO3_3 and bulk SrTiO3_3

Metallic LaAlO$_3$/SrTiO$_3$ (LAO/STO) interfaces attract enormous attention, but the relationship between the electron mobility and the sheet electron density, $n_s$, is poorly understood. Here we derive a simple expression for the three-dimensional electron density near the interface, $n_{3D}$, as a function of $n_s$ and find that the mobility for LAO/STO-based interfaces depends on $n_{3D}$ in the same way as it does for bulk doped STO. It is known that undoped bulk STO is strongly compensated with $N \simeq 5 \times 10^{18}~\rm{cm^{-3}}$ background donors and acceptors. In intentionally doped bulk STO with a concentration of electrons $n_{3D} < N$ background impurities determine the electron scattering. Thus, when $n_{3D} < N$ it is natural to see in LAO/STO the same mobility as in the bulk. On the other hand, in the bulk samples with $n_{3D} > N$ the mobility collapses because scattering happens on $n_{3D}$ intentionally introduced donors. For LAO/STO the polar catastrophe which provides electrons is not supposed to provide equal number of random donors and thus the mobility should be larger. The fact that the mobility is still the same implies that for the LAO/STO the polar catastrophe model should be revisited.Comment: 4 pages and 1 figur

Food Insecurity as a Barrier to Sustained Antiretroviral Therapy Adherence in Uganda

Background: Food insecurity is emerging as an important barrier to antiretroviral (ARV) adherence in sub-Saharan Africa and elsewhere, but little is known about the mechanisms through which food insecurity leads to ARV non-adherence and treatment interruptions. Methodology: We conducted in-depth, open-ended interviews with 47 individuals (30 women, 17 men) living with HIV/AIDS recruited from AIDS treatment programs in Mbarara and Kampala, Uganda to understand how food insecurity interferes with ARV therapy regimens. Interviews were transcribed, coded for key themes, and analyzed using grounded theory. Findings: Food insecurity was common and an important barrier to accessing medical care and ARV adherence. Five mechanisms emerged for how food insecurity can contribute to ARV non-adherence and treatment interruptions or to postponing ARV initiation: 1) ARVs increased appetite and led to intolerable hunger in the absence of food; 2) Side effects of ARVs were exacerbated in the absence of food; 3) Participants believed they should skip doses or not start on ARVs at all if they could not afford the added nutritional burden; 4) Competing demands between costs of food and medical expenses led people either to default from treatment, or to give up food and wages to get medications; 5) While working for food for long days in the fields, participants sometimes forgot medication doses. Despite these obstacles, many participants still reported high ARV adherence and exceptional motivation to continue therapy. Conclusions: While reports from sub-Saharan Africa show excellent adherence to ARVs, concerns remain that these successes are not sustainable in the presence of widespread poverty and food insecurity. We provide further evidence on how food insecurity can compromise sustained ARV therapy in a resource-limited setting. Addressing food insecurity as part of emerging ARV treatment programs is critical for their long-term success

Transportation Costs Impede Sustained Adherence and Access to HAART in a Clinic Population in Southwestern Uganda: A Qualitative Study

The cost of transportation for monthly clinic visits has been identified as a potential barrier to antiretroviral (ARV) adherence in sub-Saharan Africa and elsewhere, although there is limited data on this issue. We conducted open-ended interviews with 41 individuals living with HIV/AIDS and attending a clinic in Mbarara, Uganda, to understand structural barriers to ARV adherence and clinical care. Almost all respondents cited the need to locate funds for the monthly clinic visit as a constant source of stress and anxiety, and lack of money for transportation was a key factor in cases of missed doses and missed medical appointments. Participants struggled with competing demands between transport costs and other necessities such as food, housing and school fees. Our findings suggest that transportation costs can compromise both ARV adherence and access to care. Interventions that address this barrier will be important to ensure the success of ARV programs in sub-Saharan Africa

Efficient algorithms for reconstructing gene content by co-evolution

<p>Abstract</p> <p>Background</p> <p>In a previous study we demonstrated that co-evolutionary information can be utilized for improving the accuracy of ancestral gene content reconstruction. To this end, we defined a new computational problem, the Ancestral Co-Evolutionary (ACE) problem, and developed algorithms for solving it.</p> <p>Results</p> <p>In the current paper we generalize our previous study in various ways. First, we describe new efficient computational approaches for solving the ACE problem. The new approaches are based on reductions to classical methods such as linear programming relaxation, quadratic programming, and min-cut. Second, we report new computational hardness results related to the ACE, including practical cases where it can be solved in polynomial time.</p> <p>Third, we generalize the ACE problem and demonstrate how our approach can be used for inferring parts of the genomes of <it>non-ancestral</it> organisms. To this end, we describe a heuristic for finding the portion of the genome ('dominant set’) that can be used to reconstruct the rest of the genome with the lowest error rate. This heuristic utilizes both evolutionary information and co-evolutionary information.</p> <p>We implemented these algorithms on a large input of the ACE problem (95 unicellular organisms, 4,873 protein families, and 10, 576 of co-evolutionary relations), demonstrating that some of these algorithms can outperform the algorithm used in our previous study. In addition, we show that based on our approach a ’dominant set’ cab be used reconstruct a major fraction of a genome (up to 79%) with relatively low error-rate (<it>e.g.</it> 0.11). We find that the ’dominant set’ tends to include metabolic and regulatory genes, with high evolutionary rate, and low protein abundance and number of protein-protein interactions.</p> <p>Conclusions</p> <p>The <it>ACE</it> problem can be efficiently extended for inferring the genomes of organisms that exist today. In addition, it may be solved in polynomial time in many practical cases. Metabolic and regulatory genes were found to be the most important groups of genes necessary for reconstructing gene content of an organism based on other related genomes.</p

Discovering local patterns of co - evolution: computational aspects and biological examples

<p>Abstract</p> <p>Background</p> <p>Co-evolution is the process in which two (or more) sets of orthologs exhibit a similar or correlative pattern of evolution. Co-evolution is a powerful way to learn about the functional interdependencies between sets of genes and cellular functions and to predict physical interactions. More generally, it can be used for answering fundamental questions about the evolution of biological systems.</p> <p>Orthologs that exhibit a strong signal of co-evolution in a certain part of the evolutionary tree may show a mild signal of co-evolution in other branches of the tree. The major reasons for this phenomenon are noise in the biological input, genes that gain or lose functions, and the fact that some measures of co-evolution relate to rare events such as positive selection. Previous publications in the field dealt with the problem of finding sets of genes that co-evolved along an entire underlying phylogenetic tree, without considering the fact that often co-evolution is local.</p> <p>Results</p> <p>In this work, we describe a new set of biological problems that are related to finding patterns of <it>local </it>co-evolution. We discuss their computational complexity and design algorithms for solving them. These algorithms outperform other bi-clustering methods as they are designed specifically for solving the set of problems mentioned above.</p> <p>We use our approach to trace the co-evolution of fungal, eukaryotic, and mammalian genes at high resolution across the different parts of the corresponding phylogenetic trees. Specifically, we discover regions in the fungi tree that are enriched with positive evolution. We show that metabolic genes exhibit a remarkable level of co-evolution and different patterns of co-evolution in various biological datasets.</p> <p>In addition, we find that protein complexes that are related to gene expression exhibit non-homogenous levels of co-evolution across different parts of the <it>fungi </it>evolutionary line. In the case of mammalian evolution, signaling pathways that are related to <it>neurotransmission </it>exhibit a relatively higher level of co-evolution along the <it>primate </it>subtree.</p> <p>Conclusions</p> <p>We show that finding local patterns of co-evolution is a computationally challenging task and we offer novel algorithms that allow us to solve this problem, thus opening a new approach for analyzing the evolution of biological systems.</p

CodonLogo: a sequence logo-based viewer for codon patterns

Motivation: Conserved patterns across a multiple sequence alignment can be visualized by generating sequence logos. Sequence logos show each column in the alignment as stacks of symbol(s) where the height of a stack is proportional to its informational content, whereas the height of each symbol within the stack is proportional to its frequency in the column. Sequence logos use symbols of either nucleotide or amino acid alphabets. However, certain regulatory signals in messenger RNA (mRNA) act as combinations of codons. Yet no tool is available for visualization of conserved codon patterns