lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their corresponding unit spheres). We also assume mixture weights for the different components. We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces. We study the recovery of the most significant subspace by minimizing the lp-averaged distances of data points from d-dimensional subspaces, where p>0. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 0<p<=1, then for any fraction of outliers the most significant subspace can be recovered by lp minimization with overwhelming probability (which depends on the generating distribution and its parameters). We show that when adding small noise around the underlying subspaces the most significant subspace can be nearly recovered by lp minimization for any 0<p<=1 with an error proportional to the noise level. On the other hand, if p>1 and there is more than one underlying subspace, then with overwhelming probability the most significant subspace cannot be recovered or nearly recovered. This last result does not require spherically symmetric outliers.Comment: This is a revised version of the part of 1002.1994 that deals with single subspace recovery. V3: Improved estimates (in particular for Lemma 3.1 and for estimates relying on it), asymptotic dependence of probabilities and constants on D and d and further clarifications; for simplicity it assumes uniform distributions on spheres. V4: minor revision for the published versio

Advanced backcross QTL mapping of resistance to Fusarium head blight and plant morphological traits in a Triticum macha × T. aestivum population

While many reports on genetic analysis of Fusarium head blight (FHB) resistance in bread wheat have been published during the past decade, only limited information is available on FHB resistance derived from wheat relatives. In this contribution, we report on the genetic analysis of FHB resistance derived from Triticum macha (Georgian spelt wheat). As the origin of T. macha is in the Caucasian region, it is supposed that its FHB resistance differs from other well-investigated resistance sources. To introduce valuable alleles from the landrace T. macha into a modern genetic background, we adopted an advanced backcross QTL mapping scheme. A backcross-derived recombinant-inbred line population of 321 BC2F3 lines was developed from a cross of T. macha with the Austrian winter wheat cultivar Furore. The population was evaluated for Fusarium resistance in seven field experiments during four seasons using artificial inoculations. A total of 300 lines of the population were genetically fingerprinted using SSR and AFLP markers. The resulting linkage map covered 33 linkage groups with 560 markers. Five novel FHB-resistance QTL, all descending from T. macha, were found on four chromosomes (2A, 2B, 5A, 5B). Several QTL for morphological and developmental traits were mapped in the same population, which partly overlapped with FHB-resistance QTL. Only the 2BL FHB-resistance QTL co-located with a plant height QTL. The largest-effect FHB-resistance QTL in this population mapped at the spelt-type locus on chromosome 5A and was associated with the wild-type allele q, but it is unclear whether q has a pleiotropic effect on FHB resistance or is closely linked to a nearby resistance QTL

Rodent scope: A user-configurable digital wireless telemetry system for freely behaving animals

This paper describes the design and implementation of a wireless neural telemetry system that enables new experimental paradigms, such as neural recordings during rodent navigation in large outdoor environments. RoSco, short for Rodent Scope, is a small lightweight user-configurable module suitable for digital wireless recording from freely behaving small animals. Due to the digital transmission technology, RoSco has advantages over most other wireless modules of noise immunity and online user-configurable settings. RoSco digitally transmits entire neural waveforms for 14 of 16 channels at 20 kHz with 8-bit encoding which are streamed to the PC as standard USB audio packets. Up to 31 RoSco wireless modules can coexist in the same environment on non-overlapping independent channels. The design has spatial diversity reception via two antennas, which makes wireless communication resilient to fading and obstacles. In comparison with most existing wireless systems, this system has online user-selectable independent gain control of each channel in 8 factors from 500 to 32,000 times, two selectable ground references from a subset of channels, selectable channel grounding to disable noisy electrodes, and selectable bandwidth suitable for action potentials (300 Hz–3 kHz) and low frequency field potentials (4 Hz–3 kHz). Indoor and outdoor recordings taken from freely behaving rodents are shown to be comparable to a commercial wired system in sorting for neural populations. The module has low input referred noise, battery life of 1.5 hours and transmission losses of 0.1% up to a range of 10 m

Genetic parameter and correlation estimates of processing traits in half-sib progenies of tropical-adapted carrot germplasm Parâmetros genéticos e correlações entre características para processamento em progênies de meios-irmãos de germoplasma de cenoura tropical

The estimate of the genetic parameters associated with processing (fresh-cut) traits, including root length (RL), is crucial for carrot breeding programs in tropical areas. The cultivar Alvorada is an important germplasm due to its resistance to nematodes, leaf blight, heat-tolerance, and high carotenoid content. Seventy-four 'Alvorada' half-sib progenies were evaluated during the summer of 2005 in the Federal District, Brazil, in a randomized complete block design with three replications. Thirteen competitive plants in each block were randomly selected and evaluated and/or classified for RL and for number of leaves (NL), leaf length (LL), root tip type (RT), root mass (RW), crown shape (CS), root diameter (RD), and xylem diameter (XD). The Pearson's correlation coefficients and the heritability values were estimated for all traits. The path analysis was also used considering the RL trait as dependent variable. The heritability for RL ranged from 12 to 44%. For the other traits, the values ranged from 3% (RD) to 79% (LL). Phenotypic and genotypic correlations among all traits were low to intermediate. Path analysis indicated positive direct relationship between RL and RW, whereas RD and XD displayed negative direct effect on RL. Longer roots had narrow diameter and narrow XD. Recurrent selection based upon either half-sib or S1 families would be more effective than mass phenotypic recurrent selection in increasing RL and to develop populations expressing multiple desirable processing traits in tropical-adapted carrot germplasm.<br>A estimativa de parâmetros genéticos associados com caracteres de processamento industrial, incluindo comprimento de raiz (RL), é crucial para programas de melhoramento de cenoura para áreas tropicais. A cultivar Alvorada é um importante germoplasma devido à sua resistência a nematóides e queima-das-folhas, tolerância ao calor e alto conteúdo de carotenóides. Setenta e quatro progênies meio-irmãs derivadas de 'Alvorada' foram avaliadas durante o verão de 2005 no Distrito Federal (DF), em blocos casualizados com três repetições. Treze plantas competitivas em cada bloco foram selecionadas ao acaso e avaliadas ou classificadas para RL, número de folhas (NL), comprimento de folhas (LL), tipo de ponta de raiz (RT), massa de raiz (RW), formato do ombro da raiz (CS), diâmetro da raiz (RD) e diâmetro do xilema (XD). Foi estimada a correlação de Pearson entre os caracteres, realizada a análise de trilha considerando RL como a variável dependente; o coeficiente de herdabilidade e outros parâmetros genéticos. Os valores de herdabilidade para RL variaram entre 12 e 44%. Para os outros caracteres, os valores variaram de 3% (RD) a 79% (LL). Os valores observados para as correlações fenotípicas e genotípicas entre todos os caracteres variaram de baixos a intermediários. A análise de trilha indicou efeito positivo para a relação entre RL e RW, muito embora RD e XD tivessem efeitos diretos negativos em RL. Maiores raizes apresentaram menores diâmetros e menores XD. Métodos de seleção recorrente baseados em meio-irmãos ou famílias S1 podem ser mais efetivos que seleção recorrente fenotípica massal no aumento de RL e no desenvolvimento de populações com caracteres desejáveis para o processamento em germoplasma de cenoura tropical