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

Epidural Auditory Event-Related Potentials in the Rat to Frequency and duration Deviants: Evidence of Mismatch Negativity?

The capacity of the human brain to detect deviance in the acoustic environment pre-attentively is reflected in a brain event-related potential (ERP), mismatch negativity (MMN). MMN is observed in response to the presentation of rare oddball sounds that deviate from an otherwise regular pattern of frequent background standard sounds. While the primate and cat auditory cortex (AC) exhibit MMN-like activity, it is unclear whether the rodent AC produces a deviant response that reflects deviance detection in a background of regularities evident in recent auditory stimulus history or differential adaptation of neuronal responses due to rarity of the deviant sound. We examined whether MMN-like activity occurs in epidural AC potentials in awake and anesthetized rats to high and low frequency and long and short duration deviant sounds. ERPs to deviants were compared with ERPs to common standards and also with ERPs to deviants when interspersed with many different standards to control for background regularity effects. High frequency (HF) and long duration deviant ERPs in the awake rat showed evidence of deviance detection, consisting of negative displacements of the deviant ERP relative to ERPs to both common standards and deviants with many standards. The HF deviant MMN-like response was also sensitive to the extent of regularity in recent acoustic stimulation. Anesthesia in contrast resulted in positive displacements of deviant ERPs. Our results suggest that epidural MMN-like potentials to HF sounds in awake rats encode deviance in an analogous manner to the human MMN, laying the foundation for animal models of disorders characterized by disrupted MMN generation, such as schizophrenia

Development of reference transcriptomes for the major field insect pests of cowpea: a toolbox for insect pest management approaches in West Africa

Cowpea is a widely cultivated and major nutritional source of protein for many people that live in West Africa. Annual yields and longevity of grain storage is greatly reduced by feeding damage caused by a complex of insect pests that include the pod sucking bugs, Anoplocnemis curvipes Fabricius (Hemiptera: Coreidae) and Clavigralla tomentosicollis Stål (Hemiptera: Coreidae); as well as phloem-feeding cowpea aphids, Aphis craccivora Koch (Hemiptera: Aphididae) and flower thrips, Megalurothrips sjostedti Trybom (Thysanoptera: Thripidae). Efforts to control these pests remain a challenge and there is a need to understand the structure and movement of these pest populations in order to facilitate the development of integrated pest management strategies (IPM). Molecular tools have the potential to help facilitate a better understanding of pest populations. Towards this goal, we used 454 pyrosequencing technology to generate 319,126, 176,262, 320,722 and 227,882 raw reads from A. curvipes, A. craccivora, C. tomentosicollis and M. sjostedti, respectively. The reads were de novo assembled into 11,687, 7,647,10,652 and 7,348 transcripts for A. curvipes, A. craccivora, C. tomentosicollis and M. sjostedti, respectively.Functional annotation of the resulting transcripts identified genes putatively involved in insecticide resistance, pathogen defense and immunity. Additionally, sequences that matched the primary aphid endosymbiont, Buchneraaphidicola, were identified among A. craccivora transcripts. Furthermore, 742, 97, 607 and 180 single nucleotide polymorphisms (SNPs) were respectively predicted among A. curvipes, A. craccivora, C. tomentosicollis and M.sjostedti transcripts, and will likely be valuable tools for future molecular genetic marker development. These results demonstrate that Roche 454-based transcriptome sequencing could be useful for the development of genomic resources for cowpea pest insects in West Africa

Modeling Evolution of Resistance by Maruca vitrata (Lepidoptera: Crambidae) to Transgenic Insecticidal Cowpea in Africa

We created a detailed model of the Maruca vitrata (F.) and cowpea [Vigna unguiculata (L.) Walp] system to study the possible evolution of resistance by the insect to transgenic insecticidal cowpea, which is under development. We focused on population dynamics and genetics in a region of west Africa. We simulated single-toxin and pyramided (two-toxin) cowpea and emphasized conservative, worst-case scenarios in our analysis. The results indicate that as long as a pyramided, transgenic cowpea can be developed, seed saving by farmers and reliance on natural refuge are not major problems for resistance management. Furthermore, it is possible that one or both toxins in the pyramid may not need to be high dose for evolution to be delayed significantly (>20 yr or 80 generations for resistance to become a concern if transgenic cowpea is deployed in areas where M. vitrata is endemic). If efforts are made to deploy transgenic cowpea only into the regions where M. vitrata is not endemic, then there is little to no concern with resistance emerging in the M. vitrata populatio

Genetic Differentiation among Maruca vitrata F. (Lepidoptera: Crambidae) Populations on Cultivated Cowpea and Wild Host Plants: Implications for Insect Resistance Management and Biological Control Strategies

Maruca vitrata Fabricius (Lepidoptera: Crambidae) is a polyphagous insect pest that feeds on a variety of leguminous plantsin the tropics and subtropics. The contribution of host-associated genetic variation on population structure wasinvestigated using analysis of mitochondrial cytochrome oxidase 1 (cox1) sequence and microsatellite marker data from M.vitrata collected from cultivated cowpea (Vigna unguiculata L. Walp.), and alternative host plants Pueraria phaseoloides(Roxb.) Benth. var. javanica (Benth.) Baker, Loncocarpus sericeus (Poir), and Tephrosia candida (Roxb.). Analyses ofmicrosatellite data revealed a significant global FST estimate of 0.05 (P#0.001). The program STRUCTURE estimated 2genotypic clusters (co-ancestries) on the four host plants across 3 geographic locations, but little geographic variation waspredicted among genotypes from different geographic locations using analysis of molecular variance (AMOVA; amonggroup variation 20.68%) or F-statistics (FSTLoc =20.01; P = 0.62). These results were corroborated by mitochondrialhaplotype data (QSTLoc = 0.05; P = 0.92). In contrast, genotypes obtained from different host plants showed low butsignificant levels of genetic variation (FSTHost = 0.04; P = 0.01), which accounted for 4.08% of the total genetic variation, butwas not congruent with mitochondrial haplotype analyses (QSTHost = 0.06; P = 0.27). Variation among host plants at a locationand host plants among locations showed no consistent evidence for M. vitrata population subdivision. These resultssuggest that host plants do not significantly influence the genetic structure of M. vitrata, and this has implications forbiocontrol agent releases as well as insecticide resistance management (IRM) for M. vitrata in West Africa.C

Locally Recoverable Codes from Algebraic Curves and Surfaces

A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and Vl\u{a}du\c{t}, we present several constructions of locally recoverable codes from algebraic curves and surfaces.Comment: 27 page