Zero forcing number: Results for computation and comparison with other graph parameters

The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter is useful in the minimum rank/maximum nullity problem, as it gives an upper bound to the maximum nullity. Results for determining graphs with extreme zero forcing numbers, for determining the zero forcing number of a graph with a cut-vertex, and for determining the zero forcing number of unicyclic graphs are presented. The zero forcing number is compared to the path cover number and the maximum nullity with equality of zero forcing number and path cover number shown for all cacti and equality of zero forcing number and maximum nullity shown for a subset of cacti

The least eigenvalues of integral circulant graphs

The integral circulant graph $ICG_n (D)$ has the vertex set $Z_n = \{0, 1, 2, \ldots, n - 1\}$, where vertices $a$ and $b$ are adjacent if $\gcd(a-b,n)\in D$, with $D \subseteq \{d : d \mid n,\ 1\leq d<n\}$. In this paper, we establish that the minimal value of the least eigenvalues (minimal least eigenvalue) of integral circulant graphs $ICG_n(D)$, given an order $n$ with its prime factorization $p_1^{\alpha_1}\cdots p_k^{\alpha_k}$, is equal to $-\frac{n}{p_1}$. Moreover, we show that the minimal least eigenvalue of connected integral circulant graphs $ICG_n(D)$ of order $n$ whose complements are also connected is equal to $-\frac{n}{p_1}+p_1^{\alpha_1-1}$. Finally, we determine the second minimal eigenvalue among all least eigenvalues within the class of connected integral circulant graphs of a prescribed order $n$ and show it to be equal to $-\frac{n}{p_1}+p_1-1$ or $-\frac{n}{p_1}+1$, depending on whether $\alpha_1>1$ or not, respectively. In all the aforementioned tasks, we provide a complete characterization of graphs whose spectra contain these determined minimal least eigenvalues

Automating joiners

Pictures taken from different view points cannot be stitched into a geometrically consistent mosaic, unless the structure of the scene is very special. However, geometrical consistency is not the only criterion for success: incorporating multiple view points into the same picture may produce compelling and informative representations. A multi viewpoint form of visual expression that has recently become highly popular is that of joiners (a term coined by artist David Hockney). Joiners are compositions where photographs are layered on a 2D canvas, with some photographs occluding others and boundaries fully visible. Composing joiners is currently a tedious manual process, especially when a great number of photographs is involved. We are thus interested in automating their construction. Our approach is based on optimizing a cost function encouraging image-to-image consistency which is measured on point-features and along picture boundaries. The optimization looks for consistency in the 2D composition rather than 3D geometrical scene consistency and explicitly considers occlusion between pictures. We illustrate our ideas with a number of experiments on collections of images of objects, people, and outdoor scenes

Opuntia ellisiana Griffiths as livestock feed in areas similar to USDA cold hardiness zones 6-7

The present review compiles the studies carried out so far on Opuntia ellisiana Griffiths. This species, of unknown origin, was first described at the beginning of the 20th century in southern Texas, USA, and introduced to Argentina in 1998. This species, like other Opuntia sps., can be cultivated in a wide range of environments and its lower transpiration per unit of carbon gained in relation to C3 and C4, has lead to in an important increase in water-use efficiency. While O. ellisiana has a lower growth and productivity than O. ficus-indica (L.) Mill. it stands out for its resistance to sub-zero temperatures. Fortunately, the intraspecies variation within O. ellisiana, shortens the time for its use after establishment. There is a wide variation in the nutrient content between the different forage species and clones of Opuntia. Due to the inherently low N availability in arid ecosystems, O. ellisiana, like the other species, has low protein content in natural unfertilized conditions. Some efforts, as the use of N-fertilizer, have been carried out to improve its protein level. About 15% protein levels have been obtained with other Opuntias. Other research has been directed to provide a favorable abiotic environment for a cactus to achieve higher biomass productivity and improved protein levels by interacting with nurse plants, such as Prosopis sps. The last alternative resulted in a significant increase in protein content and cladode quantity per plant of O. ellisiana.The present review compiles the studies carried out so far on Opuntia ellisiana Griffiths. This species, of unknown origin, was first described at the beginning of the 20th century in southern Texas, USA, and introduced to Argentina in 1998. This species, like other Opuntia sps., can be cultivated in a wide range of environments and its lower transpiration per unit of carbon gained in relation to C3 and C4, has lead to in an important increase in water-use efficiency. While O. ellisiana has a lower growth and productivity than O. ficus-indica (L.) Mill. it stands out for its resistance to sub-zero temperatures. Fortunately, the intraspecies variation within O. ellisiana, shortens the time for its use after establishment. There is a wide variation in the nutrient content between the different forage species and clones of Opuntia. Due to the inherently low N availability in arid ecosystems, O. ellisiana, like the other species, has low protein content in natural unfertilized conditions. Some efforts, as the use of N-fertilizer, have been carried out to improve its protein level. About 15% protein levels have been obtained with other Opuntias. Other research has been directed to provide a favorable abiotic environment for a cactus to achieve higher biomass productivity and improved protein levels by interacting with nurse plants, such as Prosopis sps. The last alternative resulted in a significant increase in protein content and cladode quantity per plant of O. ellisiana

Controllability in complex brain networks

Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures. Recently it has been proposed to characterize brain networks in terms of their "controllability", drawing on concepts and methods of control theory. The thesis will review the control theory for networks and its application in neuroscience. In particular, the study will highlight important limitations and some warning and caveats in the brain controllability framework.ope

Macroecological Patterns of Plant Species and Anthropogenic Activities

The study of macroecology not only identifies patterns in the distribution and abundance of species at large spatial and temporal scales, it also gives insight into the processes underlying those patterns. The contribution of this work is not limited to helping develop the field of ecology per se, but also provides important insights into the understanding of large scale processes like climate change, the spread of introduced species, pest control and how increasing pressure from anthropogenic activities threatens biodiversity and ecosystem services. During the first decade following its formal inception, most of the progress in macroecology was made through studies of animal species, and research into plant species continues to lag far behind. This thesis contributes to the study of the macroecology of plant species by examining some selected macroecological patterns that have been studied only for animal species and by including an important issue that might have significant effects on diverse macroecological patterns, namely anthropogenic activities. The second and third chapters of the thesis address the generalised individuals-area relationship (GIAR) and the patch individuals-area relationship (PIAR), two macroecological relationships not previously explored for plant species. I show for the first time the existence of negative GIARs at the intraspecific and interspecific levels in plant species, similar to those documented for animal species. Unlike animal species, I did not find a broadly consistent intraspecific PIAR in plant species; more than half of the tested species showed negative PIARs. The resource concentration hypothesis may help explain those positive PIARs that were observed. The fourth chapter considers the effect of past human activities on current patterns of plant species richness at a landscape scale. Using a detailed database on the historical anthropogenic activities for Cornwall, U.K., I examine the relationship between species richness and the area covered by each historical land-use at two different spatial resolutions (10km x 10km and 2km x 2km). I find that at the 10km x10km scale human activities carried out since the 17th and 19th centuries explain an important proportion of the variation in current plant species richness. In contrast, a model at 2km x 2km scale with upland woods and the total land area of a grid cell explain only 5% of the variation. The fifth and sixth chapters focus on how artificial light at night (ALAN), which has increasingly come to attention as a significant anthropogenic pressure on species, is interacting with the distributions of plant species. In the fourth chapter, I consider the plant family Cactaceae to determine the proportion of the global distribution ranges of species that is being influenced by ALAN, and how this changes with the size of these distribution ranges and over a 21-year period (1992 to 2012). I found that >80% of cacti species are experiencing ALAN somewhere in their distribution range, and that there is a significant upward trend in ALAN in the ranges of the vast majority of species. For the sixth chapter, I consider similar issues for the threatened plant species of Britain, exploiting new remote sensing imagery of nighttime lighting at a very fine spatial resolution (c.340x340m2). Only 8% of Britain is free of artificial light at night and in consequence a high number of threatened plant species have a high proportion of their range under some influence of ALAN.CONACyT (National Council of Science and Technology, Mexico)SEP (Ministry of Education, Mexico