Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of 2 pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles t so that, from any initial configuration of t pebbles on its vertices, one can place a pebble on any given target vertex via such pebbling steps. It is known that deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter 2 graphs, and that deciding whether the pebbling number has a prescribed upper bound is Π[P over 2]-complete. On the other hand, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and many authors have studied which graphs are Class 0 and what graph properties guarantee it, with no characterization in sight. In this paper we investigate an important family of diameter 3 chordal graphs called split graphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide a formula for the pebbling number of a split graph, along with an algorithm for calculating it that runs in O(n[superscript β]) time, where β = 2ω/(ω + 1) [= over ∼] 1.41 and ω [= over ∼] 2.376 is the exponent of matrix multiplication. Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0.

We constructed an 11-arm, walk-through, human radial-arm maze (HRAM) as a translational instrument to compare existing methodology in the areas of rodent and human learning and memory research. The HRAM, utilized here, serves as an intermediary test between the classic rat radial-arm maze (RAM) and standard human neuropsychological and cognitive tests. We show that the HRAM is a useful instrument to examine working memory ability, explore the relationships between rodent and human memory and cognition models, and evaluate factors that contribute to human navigational ability. One-hundred-and-fifty-seven participants were tested on the HRAM, and scores were compared to performance on a standard cognitive battery focused on episodic memory, working memory capacity, and visuospatial ability. We found that errors on the HRAM increased as working memory demand became elevated, similar to the pattern typically seen in rodents, and that for this task, performance appears similar to Miller's classic description of a processing-inclusive human working memory capacity of 7 ± 2 items. Regression analysis revealed that measures of working memory capacity and visuospatial ability accounted for a large proportion of variance in HRAM scores, while measures of episodic memory and general intelligence did not serve as significant predictors of HRAM performance. We present the HRAM as a novel instrument for measuring navigational behavior in humans, as is traditionally done in basic science studies evaluating rodent learning and memory, thus providing a useful tool to help connect and translate between human and rodent models of cognitive functioning.

Food and water shortages are two of the greatest challenges facing humans in the coming century. While our theoretical understanding of how humans become vulnerable to and cope with hunger is relatively well developed, anthropological research on parallel problems in the water domain is limited. By carefully considering well-established propositions derived from the food literature against what is known about water, our goal in this essay is to advance identifying, theorizing, and testing a broader anthropology of resource insecurity. Our analysis focuses on (1) the causes of resource insecurity at the community level, (2) “coping” responses to resource insecurity at the household level, and (3) the effect of insecurity on emotional well-being and mental health at the individual level. Based on our findings, we argue that human experiences of food and water insecurity are sufficiently similar to facilitate a broader theory of resource insecurity, including in how households and individuals cope. There are also important differences between food and water insecurity, including the role of structural factors (such as markets) in creating community-level vulnerabilities. These suggest food and water insecurity may also produce household struggles and individual suffering along independent pathways.

Chemical composition affects virtually all aspects of astrobiology, from stellar astrophysics to molecular biology. We present a synopsis of the research results presented at the “Stellar Stoichiometry” Workshop Without Walls hosted at Arizona State University April 11–12, 2013, under the auspices of the NASA Astrobiology Institute. The results focus on the measurement of chemical abundances and the effects of composition on processes from stellar to planetary scales. Of particular interest were the scientific connections between processes in these normally disparate fields. Measuring the abundances of elements in stars and giant and terrestrial planets poses substantial difficulties in technique and interpretation. One of the motivations for this conference was the fact that determinations of the abundance of a given element in a single star by different groups can differ by more than their quoted errors.

The problems affecting the reliability of abundance estimations and their inherent limitations are discussed. When these problems are taken into consideration, self-consistent surveys of stellar abundances show that there is still substantial variation (factors of ∼2) in the ratios of common elements (e.g., C, O, Na, Al, Mg, Si, Ca) important in rock-forming minerals, atmospheres, and biology. We consider how abundance variations arise through injection of supernova nucleosynthesis products into star-forming material and through photoevaporation of protoplanetary disks. The effects of composition on stellar evolution are substantial, and coupled with planetary atmosphere models can result in predicted habitable zone extents that vary by many tens of percent. Variations in the bulk composition of planets can affect rates of radiogenic heating and substantially change the mineralogy of planetary interiors, affecting properties such as convection and energy transport.

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.

In this article, we suggest that graduate programs in predominantly white institutions can and should be sites of self-education and tribal nation building. In arguing this, we examine how a particular graduate program and the participants of that program engaged tribal nation building, and then we suggest that graduate education writ large must also adopt an institutional orientation of nation building. We connect Guinier’s notion of democratic merit to our discussion of nation building as a way to suggest a rethinking of “success” and “merit” in graduate education. We argue that higher education should be centrally concerned with capacity building and graduates who aim to serve their communities.

Background: Meiotic recombination has traditionally been explained based on the structural requirement to stabilize homologous chromosome pairs to ensure their proper meiotic segregation. Competing hypotheses seek to explain the emerging findings of significant heterogeneity in recombination rates within and between genomes, but intraspecific comparisons of genome-wide recombination patterns are rare. The honey bee (Apis mellifera) exhibits the highest rate of genomic recombination among multicellular animals with about five cross-over events per chromatid.

Results: Here, we present a comparative analysis of recombination rates across eight genetic linkage maps of the honey bee genome to investigate which genomic sequence features are correlated with recombination rate and with its variation across the eight data sets, ranging in average marker spacing ranging from 1 Mbp to 120 kbp. Overall, we found that GC content explained best the variation in local recombination rate along chromosomes at the analyzed 100 kbp scale. In contrast, variation among the different maps was correlated to the abundance of microsatellites and several specific tri- and tetra-nucleotides.

Conclusions: The combined evidence from eight medium-scale recombination maps of the honey bee genome suggests that recombination rate variation in this highly recombining genome might be due to the DNA configuration instead of distinct sequence motifs. However, more fine-scale analyses are needed. The empirical basis of eight differing genetic maps allowed for robust conclusions about the correlates of the local recombination rates and enabled the study of the relation between DNA features and variability in local recombination rates, which is particularly relevant in the honey bee genome with its exceptionally high recombination rate.

The inverse problem associated with electrochemical impedance spectroscopy requiring the solution of a Fredholm integral equation of the first kind is considered. If the underlying physical model is not clearly determined, the inverse problem needs to be solved using a regularized linear least squares problem that is obtained from the discretization of the integral equation. For this system, it is shown that the model error can be made negligible by a change of variables and by extending the effective range of quadrature. This change of variables serves as a right preconditioner that significantly improves the condition of the system. Still, to obtain feasible solutions the additional constraint of non-negativity is required. Simulations with artificial, but realistic, data demonstrate that the use of non-negatively constrained least squares with a smoothing norm provides higher quality solutions than those obtained without the non-negative constraint. Using higher-order smoothing norms also reduces the error in the solutions. The L-curve and residual periodogram parameter choice criteria, which are used for parameter choice with regularized linear least squares, are successfully adapted to be used for the non-negatively constrained Tikhonov least squares problem. Although these results have been verified within the context of the analysis of electrochemical impedance spectroscopy, there is no reason to suppose that they would not be relevant within the broader framework of solving Fredholm integral equations for other applications.

Data from the New Immigrant Survey were used to describe the home environments of 638 children ages birth to three whose parents legally immigrated to the United States. Thirty-two indicators of home conditions were clustered into 4 domains: discipline and socioemotional support, learning materials, enriching experiences, and family activities. Results revealed variation in how frequently infants from every country (Mexico, El Salvador, India, Philippines) and region (East Asia, Europe, Caribbean, Africa) studied experienced each home environmental condition. There were differences between countries and regions on many indicators as well as differences based on parents’ level of education. The experiences documented for children of recent legal immigrants were similar to those documented for children of native-born families in other studies.