Matroid and Knapsack Center Problems

In the classic $k$-center problem, we are given a metric graph, and the objective is to open $k$ nodes as centers such that the maximum distance from any vertex to its closest center is minimized. In this paper, we consider two important generalizations of $k$-center, the matroid center problem and the knapsack center problem. Both problems are motivated by recent content distribution network applications. Our contributions can be summarized as follows: 1. We consider the matroid center problem in which the centers are required to form an independent set of a given matroid. We show this problem is NP-hard even on a line. We present a 3-approximation algorithm for the problem on general metrics. We also consider the outlier version of the problem where a given number of vertices can be excluded as the outliers from the solution. We present a 7-approximation for the outlier version. 2. We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s). It is known that the knapsack center problem with a single knapsack constraint admits a 3-approximation. However, when there are at least two knapsack constraints, we show this problem is not approximable at all. To complement the hardness result, we present a polynomial time algorithm that gives a 3-approximate solution such that one knapsack constraint is satisfied and the others may be violated by at most a factor of $1+\epsilon$. We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by $1+\epsilon$.Comment: A preliminary version of this paper is accepted to IPCO 201

Selection from read-only memory with limited workspace

Given an unordered array of $N$ elements drawn from a totally ordered set and an integer $k$ in the range from $1$ to $N$, in the classic selection problem the task is to find the $k$-th smallest element in the array. We study the complexity of this problem in the space-restricted random-access model: The input array is stored on read-only memory, and the algorithm has access to a limited amount of workspace. We prove that the linear-time prune-and-search algorithm---presented in most textbooks on algorithms---can be modified to use $\Theta(N)$ bits instead of $\Theta(N)$ words of extra space. Prior to our work, the best known algorithm by Frederickson could perform the task with $\Theta(N)$ bits of extra space in $O(N \lg^{*} N)$ time. Our result separates the space-restricted random-access model and the multi-pass streaming model, since we can surpass the $\Omega(N \lg^{*} N)$ lower bound known for the latter model. We also generalize our algorithm for the case when the size of the workspace is $\Theta(S)$ bits, where $\lg^3{N} \leq S \leq N$. The running time of our generalized algorithm is $O(N \lg^{*}(N/S) + N (\lg N) / \lg{} S)$, slightly improving over the $O(N \lg^{*}(N (\lg N)/S) + N (\lg N) / \lg{} S)$ bound of Frederickson's algorithm. To obtain the improvements mentioned above, we developed a new data structure, called the wavelet stack, that we use for repeated pruning. We expect the wavelet stack to be a useful tool in other applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201

Ergot: A New Disease Threat to Sorghum in the Americas and Australia

Sorghum, Sorghum bicolor (L.) Moench, is the world’s fifth most important cereal crop, cultivated on about 45 million hectares for food, feed, beverage, and fodder. The most significant technological change since the 1960s has been the development and use of F1 hybrid seed (14), which has lead to a dramatic improvement in the crop’s productivity. Sorghum cultivation in intensive, commercialized systems where yields average 3 to 5 t ha-1 relies almost totally on hybrid seed. In contrast, yields vary widely and average less than 1 t ha-1 in low-input production systems

Susceptibility to ergot in Zimbabwe of sorghums tbat remained uninfected in their native climates in Ethiopia and Rwanda

Forty-four local Ethiopian and Rwandan sorghums (Sorghum bicolor) were observed to remain free of ergot, or had only low incidence, in their natural equatorial latitudes and were potentially of interest, in the design of male-sterile lines for F| hybrid breeding, if they possessed a physiologically based resistance mechanism. These sorghums were therefore also investigated under natural and artificial disease pressures in Zimbabwe where unadapted development and inappropriate long daylengtb prevented flowering in 18 accessions. Of the remaining 16 Ethiopian and 10 Rwandan accessions which flowered, only one from each country remained free of ergot. The susceptibility expressed was ascribed to observed asynchrony of stigma exsertion with anthesis. In the Rwandan accession that persistently remained free of ergot in Zimbabwe, histology of ovules showed pollination before floret gaping, so that a general principle of disease escape due to efficient pollination is proposed for the Ethiopian and Rwandan sorghums in their native climates. The findings emphasize that cleistogamy is a desirable character for avoiding ergot infection in self-fertile sorghums and suggest that the Ethiopian and Rwandan sorghutns may not generally be useful for breeding ergot-resistant male-sterile female lines. However, a few accessions deserve more detailed study as a potential genetic resource, before a firm conclusion that all apparent resistance is disease escape owing to efficient pollination

Language and reading development in children learning English as an additional language in primary school in England

Children learning English as an additional language (EAL) are a growing population of learners in English primary schools. These children begin school with differing levels of English language proficiency and tend to underperform in relation to their non‐EAL peers on measures of English oral language and reading. However, little work has examined the developmental trajectories of these skills in EAL learners in England. EAL learners and 33 non‐EAL peers in Year 4 (age 8–9 years) were assessed at three time points over 18 months on measures of oral language (vocabulary, grammar and listening comprehension), phonological processing (spoonerisms and rapid automatised naming) and reading skills (single‐word decoding and passage reading). At t1, EAL learners scored significantly lower than non‐EAL peers in receptive and expressive vocabulary (breadth but not depth), spoonerisms and passage reading accuracy. Contrary to previous research, no significant group differences were found in listening or reading comprehension skills. With the exception of passage reading accuracy, there was no evidence for convergence or divergence between the groups in rate of progress over time. After three years of English‐medium classroom instruction, EAL learners continue to underperform relative to their non‐EAL peers in breadth of English vocabulary knowledge. This discrepancy in vocabulary knowledge does not appear to narrow as a result of regular classroom instruction in the run up to the final stages of primary school, pinpointing vocabulary as a key target for intervention

Assessing direct contributions of morphological awareness and prosodic sensitivity to children’s word reading and reading comprehension

We examined the independent contributions of prosodic sensitivity and morphological awareness to word reading, text reading accuracy, and reading comprehension. We did so in a longitudinal study of English-speaking children (N = 70). At 5 to 7 years of age, children completed the metalinguistic measures along with control measures of phonological awareness and vocabulary. Children completed the reading measures two years later. Morphological awareness, but not prosodic sensitivity made a significant independent contribution to word reading, text reading accuracy and reading comprehension. The effects of morphological awareness on reading comprehension remained after controls for word reading. These results suggest that morphological awareness needs to be considered seriously in models of reading development and that prosodic sensitivity might have primarily indirect relations to reading outcomes. Keywords: Morphological Awareness; Prosody; Word Reading; Reading Comprehension

Multi-Informant Predictors of Social Inclusion for Students with Autism Spectrum Disorders Attending Mainstream School

This study examined differential profiles of behavioural characteristics predictive of successful inclusion in mainstream education for children with autism spectrum disorders (ASD) and comparison students. Multiple regression analyses using behavioural ratings from parents, teachers and peers found some evidence for differential profiles predicting peer acceptance and rejection. High levels of peer-rated shyness significantly predicted social rejection in comparison students only. Parent-rated prosocial behaviour also differentially predicted social acceptance; high-levels of prosocial behaviour predicted acceptance in comparison students, but low-levels were predictive for students with ASD. These findings suggest that schools may seek to augment traditional social skills programmes with awareness raising about ASD among mainstream pupils to utilise peers’ apparent willingness to discount characteristics such as ‘shyness’

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also succesfully tested against simulations of a hard sphere fluid at relatively low density.Comment: 15 pages, 2 figure

Nested reconfigurable robots: theory, design, and realization

Rather than the conventional classification method, we propose to divide modular and reconfigurable robots into intra-, inter-, and nested reconfigurations. We suggest designing the robot with nested reconfigurability, which utilizes individual robots with intra-reconfigurability capable of combining with other homogeneous/heterogeneous robots (inter-reconfigurability). The objective of this approach is to generate more complex morphologies for performing specific tasks that are far from the capabilities of a single module or to respond to programmable assembly requirements. In this paper, we discuss the theory, concept, and initial mechanical design of Hinged-Tetro, a self-reconfigurable module conceived for the study of nested reconfiguration. Hinged-Tetro is a mobile robot that uses the principle of hinged dissection of polyominoes to transform itself into any of the seven one-sided tetrominoes in a straightforward way. The robot can also combine with other modules for shaping complex structures or giving rise to a robot with new capabilities. Finally, the validation experiments verify the nested reconfigurability of Hinged-Tetro. Extensive tests and analyses of intra-reconfiguration are provided in terms of energy and time consumptions. Experiments using two robots validate the inter-reconfigurability of the proposed module