On Binary Matroid Minors and Applications to Data Storage over Small Fields

Locally repairable codes for distributed storage systems have gained a lot of interest recently, and various constructions can be found in the literature. However, most of the constructions result in either large field sizes and hence too high computational complexity for practical implementation, or in low rates translating into waste of the available storage space. In this paper we address this issue by developing theory towards code existence and design over a given field. This is done via exploiting recently established connections between linear locally repairable codes and matroids, and using matroid-theoretic characterisations of linearity over small fields. In particular, nonexistence can be shown by finding certain forbidden uniform minors within the lattice of cyclic flats. It is shown that the lattice of cyclic flats of binary matroids have additional structure that significantly restricts the possible locality properties of $\mathbb{F}_{2}$-linear storage codes. Moreover, a collection of criteria for detecting uniform minors from the lattice of cyclic flats of a given matroid is given, which is interesting in its own right.Comment: 14 pages, 2 figure

On the odd-minor variant of Hadwiger's conjecture

A {\it $K_l$ -expansion} consists of $l$ vertex-disjoint trees, every two of which are joined by an edge. We call such an expansion {\it odd} if its vertices can be two-coloured so that the edges of the trees are bichromatic but the edges between trees are monochromatic. We show that, for every $l$, if a graph contains no odd $K_l$ -expansion then its chromatic number is $O(l \sqrt{\log l})$. In doing so, we obtain a characterization of graphs which contain no odd $K_l$ -expansion which is of independent interest. We also prove that given a graph and a subset $S$ of its vertex set, either there are $k$ vertex-disjoint odd paths with endpoints in $S$, or there is a set X of at most $2k − 2$ vertices such that every odd path with both ends in $S$ contains a vertex in $X$. Finally, we discuss the algorithmic implications of these results

On the odd-minor variant of Hadwiger's conjecture

A {\it $K_l$ -expansion} consists of $l$ vertex-disjoint trees, every two of which are joined by an edge. We call such an expansion {\it odd} if its vertices can be two-coloured so that the edges of the trees are bichromatic but the edges between trees are monochromatic. We show that, for every $l$, if a graph contains no odd $K_l$ -expansion then its chromatic number is $O(l \sqrt{\log l})$. In doing so, we obtain a characterization of graphs which contain no odd $K_l$ -expansion which is of independent interest. We also prove that given a graph and a subset $S$ of its vertex set, either there are $k$ vertex-disjoint odd paths with endpoints in $S$, or there is a set X of at most $2k − 2$ vertices such that every odd path with both ends in $S$ contains a vertex in $X$. Finally, we discuss the algorithmic implications of these results

Increased Concentration of Iodide in Airway Secretions is Associated with Reduced RSV Disease Severity

Recent studies have revealed that the human and nonrodent mammalian airway mucosa contains an oxidative host defense system. This three-component system consists of the hydrogen peroxide (H2O2)-producing enzymes dual oxidase (Duox)1 and Duox2, thiocyanate (SCN−), and secreted lactoperoxidase (LPO). The LPO-catalyzed reaction between H2O2 and SCN− yields the bactericidal hypothiocyanite (OSCN−) in airway surface liquid (ASL). Although SCN− is the physiological substrate of LPO, the Duox/LPO/halide system can generate hypoiodous acid when the iodide (I−) concentration is elevated in ASL. Because hypoiodous acid, but not OSCN−, inactivates respiratory syncytial virus (RSV) in cell culture, we used a lamb model of RSV to test whether potassium iodide (KI) could enhance this system in vivo. Newborn lambs received KI by intragastric gavage or were left untreated before intratracheal inoculation of RSV. KI treatment led to a 10-fold increase in ASL I− concentration, and this I− concentration was approximately 30-fold higher than that measured in the serum. Also, expiratory effort, gross lung lesions, and pulmonary expression of an RSV antigen and IL-8 were reduced in the KI-treated lambs as compared with nontreated control lambs. Inhibition of LPO activity significantly increased lesions, RSV mRNA, and antigen. Similar experiments in 3-week-old lambs demonstrated that KI administration was associated with reduced gross lesions, decreased RSV titers in bronchoalveolar lavage fluid, and reduced RSV antigen expression. Overall, these data indicate that high-dose KI supplementation can be used in vivo to lessen the severity of RSV infections, potentially through the augmentation of mucosal oxidative defenses

Contraction Bidimensionality: the Accurate Picture

We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory -- the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters

A systematic review of methods to assess intake of fruits and vegetables among healthy European adults and children: a DEDIPAC (DEterminants of DIet and Physical Activity) study

Evidence suggests that health benefits are associated with consuming recommended amounts of fruits and vegetables (F&V), yet standardised assessment methods to measure F&V intake are lacking. The current review aims to identify methods to assess F&V intake among children and adults in pan-European studies and inform the development of the DEDIPAC (DEterminants of DIet and Physical Activity) toolbox of methods suitable for use in future European studies. A literature search was conducted using three electronic databases and by hand-searching reference lists. English-language studies of any design which assessed F&V intake were included in the review. Studies involving two or more European countries were included in the review. Healthy, free-living children or adults. The review identified fifty-one pan-European studies which assessed F&V intake. The FFQ was the most commonly used (n 42), followed by 24 h recall (n 11) and diet records/diet history (n 7). Differences existed between the identified methods; for example, the number of F&V items on the FFQ and whether potatoes/legumes were classified as vegetables. In total, eight validated instruments were identified which assessed F&V intake among adults, adolescents or children. The current review indicates that an agreed classification of F&V is needed in order to standardise intake data more effectively between European countries. Validated methods used in pan-European populations encompassing a range of European regions were identified. These methods should be considered for use by future studies focused on evaluating intake of F&V

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Alcoholic Beverage Preference and Dietary Habits in Elderly across Europe: Analyses within the Consortium on Health and Ageing: Network of Cohorts in Europe and the United States (CHANCES) Project

Introduction: The differential associations of beer, wine, and spirit consumption on cardiovascular risk found in observational studies may be confounded by diet. We described and compared dietary intake and diet quality according to alcoholic beverage preference in European elderly. Methods: From the Consortium on Health and Ageing: Network of Cohorts in Europe and the United States (CHANCES), seven European cohorts were included, i.e. four sub-cohorts from EPIC-Elderly, the SENECA Study, the Zutphen Elderly Study, and the Rotterdam Study. Harmonized data of 29,423 elderly participants from 14 European countries were analyzed. Baseline data on consumption of beer, wine, and spirits, and dietary intake were collected with questionnaires. Diet quality was assessed using the Healthy Diet Indicator (HDI). Intakes and scores across categories of alcoholic beverage preference (beer, wine, spirit, no preference, non-consumers) were adjusted for age, sex, socio-economic status, self-reported prevalent diseases, and lifestyle factors. Cohort-specific mean intakes and scores were calculated as well as weighted means combining all cohorts. Results: In 5 of 7 cohorts, persons with a wine preference formed the largest group. After multivariate adjustment, persons with a wine preference tended to have a higher HDI score and intake of healthy foods in most cohorts, but differences were small. The weighted estimates of all cohorts combined revealed that non-consumers had the highest fruit and vegetable intake, followed by wine consumers. Non-consumers and persons with no specific preference had a higher HDI score, spirit consumers the lowest. However, overall diet quality as measured by HDI did not differ greatly across alcoholic beverage preference categories. Discussion: This study using harmonized data from ~30,000 elderly from 14 European countries showed that, after multivariate adjustment, dietary habits and diet quality did not differ greatly according to alcoholic beverage preference