Cross-intersecting families and primitivity of symmetric systems

Let $X$ be a finite set and $\mathfrak p\subseteq 2^X$, the power set of $X$, satisfying three conditions: (a) $\mathfrak p$ is an ideal in $2^X$, that is, if $A\in \mathfrak p$ and $B\subset A$, then $B\in \mathfrak p$; (b) For $A\in 2^X$ with $|A|\geq 2$, $A\in \mathfrak p$ if $\{x,y\}\in \mathfrak p$ for any $x,y\in A$ with $x\neq y$; (c) $\{x\}\in \mathfrak p$ for every $x\in X$. The pair $(X,\mathfrak p)$ is called a symmetric system if there is a group $\Gamma$ transitively acting on $X$ and preserving the ideal $\mathfrak p$. A family $\{A_1,A_2,\ldots,A_m\}\subseteq 2^X$ is said to be a cross-$\mathfrak{p}$-family of $X$ if $\{a, b\}\in \mathfrak{p}$ for any $a\in A_i$ and $b\in A_j$ with $i\neq j$. We prove that if $(X,\mathfrak p)$ is a symmetric system and $\{A_1,A_2,\ldots,A_m\}\subseteq 2^X$ is a cross-$\mathfrak{p}$-family of $X$, then $$\sum_{i=1}^m|{A}_i|\leq\left\{ \begin{array}{cl} |X| & \hbox{if $m\leq \frac{|X|}{\alpha(X,\, \mathfrak p)}$,} \\ m\, \alpha(X,\, \mathfrak p) & \hbox{if $m\geq \frac{|X|}{\alpha{(X,\, \mathfrak p)}}$,} \end{array}\right.$$ where $\alpha(X,\, \mathfrak p)=\max\{|A|:A\in\mathfrak p\}$. This generalizes Hilton's theorem on cross-intersecting families of finite sets, and provides analogs for cross-$t$-intersecting families of finite sets, finite vector spaces and permutations, etc. Moreover, the primitivity of symmetric systems is introduced to characterize the optimal families.Comment: 15 page

AB-QTL analysis for two populations of winter barley sharing the donor of <i>Hordeum vulgare </i>ssp<i>. spontaneum</i>

The objective of the present study was to detect favourable exotic QTL alleles for the improvement of agronomic traits, pathogen resistance and non-parasitic browning in two BC2DH populations derived from the crosses of two German winter barley varieties, Carola and Theresa (Hordeum vulgare ssp. vulgare, in the following abbreviated Hv), with the wild barley accession ISR101-23 (Hordeum vulgare ssp. vulgare, in the following abbreviated Hsp) from Israel. The two BC2DH populations (termed C101 and T101) were genotyped with 82 and 78 SSR markers, respectively. C101 and T101 consisted of 282 and 104 BC2DH lines, respectively. Sixteen agronomic traits, four pathogen resistances and the non-parasitic browning were evaluated at up to six different locations and in two consecutive years. QTL analysis was carried out with a three-factorial ANOVA including the marker as fixed effect and the environment and lines nested in the marker genotype as well as the respective interactions as random effects. In addition, cold damage (COD) and neighbouring plots of the seriously cold-damaged plots (N) were used as co-variables for those traits which were significantly affected by COD and N. In C101, 35 favorable exotic QTL effects out of 183 putative QTLs were detected for ten agronomic traits, four pathogen resistances and non-parasitic browning. Among these putative QTLs, 22 (19.1 %) of 115 QTLs detected for agronomic traits exhibited favorable effects and 13 (19.1 %) of 68 QTLs identified for disease resistances and non-parasitic browning were associated with improvements. A crossover interaction QTL effect of the Hsp allele on yield, detected on chromosome 6H in C101, was associated with a yield increase of 8.2 % averaged across three environments. However, in the remaining two environments the Hsp effect was associated with a yield reduction of 4.6 %. In addition, favourable effects of exotic alleles were detected for all pathogen resistances and non-parasitic browning in this study. For instance, the symptoms of leaf rust, net blotch, powdery mildew, scald and non-parasitic browning symptoms at QlrC101-3H, QnbC101-6Hd, QpmC101-2H, QrhC101-7Ha und QnpbC101-5Ha were reduced by 26.2 %, 20.8 %, 17.8 %, 4.9 % and 14.9 % in C101, respectively (Table 17). In T101, 85 putative QTLs were discovered for eleven agronomic traits, four pathogen resistances and non-parasitic browning. The exotic genotype improved the performance at 13 (19.4 %) of 67 QTLs detected for agronomic traits and no favorable QTL effect was identified for disease resistances and non-parasitic browning in T101 (Table 19). Thirty-nine putative QTLs detected in C101 were confirmed by 40 QTLs detected in T101. Altogether, 65 (24.3 %) QTL effects among 268 putative QTLs localized in both populations and 21 (43.8 %) favorable QTL effects among 48 favorable QTL effects identified in both populations were verified in other barley QTL and linkage analyses. About 56 % favorable exotic QTL alleles identified in this study were so far not detected in other barley QTL studies. These favorable Hsp alleles may be new alleles.AB-QTL-Analyse in zwei Wintergersten-Populationen mit einem gemeinsamen Donor Die Ziel des vorliegenden Projekts war, vorteilhafte exotische QTL-Allele für die Verbesserung der agronomischen Leistung, der Krankheitsresistenz und der unspezifischen Blattflecken in zwei BC2DH-Populationnen zu ermitteln, die aus den Kreuzungen der beiden deutschen Wintergerstesorten Carola und Theresa (Hordeum vulgare ssp. vulgare, im folgenden mit Hv abgekürzt) mit der Wildgersten-Akzession ISR101-23 (Hordeum vulgare ssp. spontaneum, im folgenden mit Hsp abgekürzt) aus Israel abgeleitet wurden. Die zwei BC2DH-Populationen (benannt C101 und T101) wurden mit 82 und 78 SSR-Markern genotypisiert. C101 und T101 bestanden aus 282 und 104 BC2DH-Linien. Insgesamt 16 agronomische Merkmale, vier Krankheitsresistenzen sowie unspezifische Blattflecken wurden an bis zu sechs unterschiedlichen Umwelten und über zwei Jahre ausgewertet. Die QTL-Analyse wurde mit einer 3-faktoriellen ANOVA durchgeführt, mit dem Marker als fixen Effekt, der Linie geschachtelt in Markergenotyp, der Umwelt und den entsprechenden Interaktionen als zufällige Effekte. In C101 wurden 35 vorteilhafte exotische QTL-Effekte aus 183 putativen QTLs für 10 agronomische Merkmale, vier Krankheitsresistenzen und unspezifische Blattflecken ermittelt. Unter den vorteilhaften exotischen QTLs wurden 22 (19,1 %) vorteilhafte QTL-Effekte für agronomische Merkmale, und 13 (19,1 %) für Krankheitsresistenzen und unspezifische Blattflecken identifiziert. Ein crossover QTL-Effekt des Hsp-Alleles auf Ertrag, ermittelt auf Chromosom 6H in C101, war mit einer Ertragszunahme von 8,2 %, gemittelt über drei Umwelten, verbunden (Table 17). Allerdings war der Hsp-Effekt in den restlichen zwei Umwelten mit einer Ertragsabnahme von 4,6 % assoziert. Die Symptome für Zwergrost, Netzflecken, Mehltau, Rynchosporium und unspezifische Blattflecken wurden in C101 durch exotische Allele an den QTLs QlrC101-3H, QnbC101-6Hd, QpmC101-2H, QrhC101-7Ha und QnpbC101-5Ha um 26,2 %, 20,8 %, 17,8 %, 4,9 % beziehungsweise 14,9 % reduziert. In T101 wurden 85 putative QTLs für elf agronomische Merkmale, Krankheitsresistenzen und unspezifische Blattflecken entdeckt. Der exotische Genotyp verbesserte die Leistung bei 13 (18,6 %) von 70 QTLs, die für agronomische Merkmale ermittelt wurden (Table 19). Insgesamt 39 putative QTLs, die in C101 ermittelt wurden, wurden durch 40 QTLs in T101 bestätigt. Von 268 putativen QTLs und 48 vorteilhaften exotischen Effekten, die in beiden Populationen gefunden wurden, konnten 65 (24,3 %) QTLs beziehungsweise 21 (43,6 %) vorteilhafte exotische Effekte in anderen QTL-Analysen der Gerste wiedergefunden werden. Ungefähr 64 % der vorteilhaften exotischen QTL-Allele, die in dieser Studie identifiziert wurden, konnten nicht in anderen Studien der Gerste ermittelt werden. Diese vorteilhaften Hsp-Allele könnten daher neue Allele sein

SED, a normalization free method for DNA microarray data analysis

BACKGROUND: Analysis of DNA microarray data usually begins with a normalization step where intensities of different arrays are adjusted to the same scale so that the intensity levels from different arrays can be compared with one other. Both simple total array intensity-based as well as more complex "local intensity level" dependent normalization methods have been developed, some of which are widely used. Much less developed methods for microarray data analysis include those that bypass the normalization step and therefore yield results that are not confounded by potential normalization errors. RESULTS: Instead of focusing on the raw intensity levels, we developed a new method for microarray data analysis that maps each gene's expression intensity level to a high dimensional space of SEDs (Signs of Expression Difference), the signs of the expression intensity difference between a given gene and every other gene on the array. Since SED are unchanged under any monotonic transformation of intensity levels, the SED based method is normalization free. When tested on a multi-class tumor classification problem, simple Naive Bayes and Nearest Neighbor methods using the SED approach gave results comparable with normalized intensity-based algorithms. Furthermore, a high percentage of classifiers based on a single gene's SED gave good classification results, suggesting that SED does capture essential information from the intensity levels. CONCLUSION: The results of testing this new method on multi-class tumor classification problems suggests that the SED-based, normalization-free method of microarray data analysis is feasible and promising

Data-Driven Robust Control of Unknown MIMO Nonlinear System Subject to Input Saturations and Disturbances

This paper presented a new data-driven robust control scheme for unknown nonlinear systems in the presence of input saturation and external disturbances. According to the input and output data of the nonlinear system, a recurrent neural network (RNN) data-driven model is established to reconstruct the dynamics of the nonlinear system. An adaptive output-feedback controller is developed to approximate the unknown disturbances and a novel input saturation compensation method is used to attenuate the effect of the input saturation. Under the proposed adaptive control scheme, the uniformly ultimately bounded convergence of all the signals of the closed-loop nonlinear system is guaranteed via Lyapunov analysis. The simulation results are given to show the effectiveness of the proposed data-driven robust controller

Long-tail Relation Extraction via Knowledge Graph Embeddings and Graph Convolution Networks

We propose a distance supervised relation extraction approach for long-tailed, imbalanced data which is prevalent in real-world settings. Here, the challenge is to learn accurate "few-shot" models for classes existing at the tail of the class distribution, for which little data is available. Inspired by the rich semantic correlations between classes at the long tail and those at the head, we take advantage of the knowledge from data-rich classes at the head of the distribution to boost the performance of the data-poor classes at the tail. First, we propose to leverage implicit relational knowledge among class labels from knowledge graph embeddings and learn explicit relational knowledge using graph convolution networks. Second, we integrate that relational knowledge into relation extraction model by coarse-to-fine knowledge-aware attention mechanism. We demonstrate our results for a large-scale benchmark dataset which show that our approach significantly outperforms other baselines, especially for long-tail relations.Comment: To be published in NAACL 201

Sedimentation of the Lower Cretaceous Xiagou formation and Its Response to Regional Tectonics in the Qingxi Sag, Jiuquan Basin, NW China

Under the constraint of an isochronous sequence stratigraphic framework, sediment infill of the Xiagou Formation reflects the overall control of dynamic tectonic movements and episodic sedimentations in the Qingxi Sag. Structure reactivity during post-depositional processes could cause stratigraphic variations in longitudinal time and lateral space. This study documents sediment infill features and their response to the tectonic evolutions of the Qingxi Sag. The data sets include comparison of cores, well drilling, 3D seismic, inter-well correlation, wave impedance inversion profiles, original strata recovery data, sedimentary fades spatial evolution and their superimposition with paleogeomorphology. The Jiuquan Basin is a Mesozoic-Cenozoic superposition basin comprising an early rifting graben phase and a later compression phase. Since the Early Cretaceous, the basin has undergone four major tectonic episodes: 1) extension during the Early Cretaceous, 2) tectonic inversion caused by northwest-southeast contraction from the Late Cretaceous to the Paleocene, 3) weak extension from the Eocene to the Miocene and 4) contraction from the Miocene to the present. Therefore, the Jiuquan Basin is the product of taphrogenic, collisional and shearing movements. Seismic interpretations of sequence and maximum flooding surface divide the Xiagou Formation into three third order sequences: SQK1g(0), SQK1g(1) and SQK1g(2+3). Five sedimentary facies associations are identified: the shoreland plain, fan delta dominated sedimentary systems, turbidite deposits, shallow lakes and half-deep lake systems. From K1g(0) to K1g(2+3), decreased sandstone percentages in three fan delta areas indicate a continuously transgressive process, which shows the transition from proximal to distal sites in most statistic wells and an obvious decrease of fan delta scales. The northeast-southwest faults control the lakeward distributions of delta fronts and turbidite fans. The correspondence of sedimentary infill and its response to tectonic movements have been demonstrated in the Qingxi Sag. The more active eastern part of the northeastern boundary fault has an important influence on the northeastward migration of depocenters in the Xiagou Formation. The topography developed continuously from K1g(0) to K1g(2+3), but the diminished subsidence indicates the dominant geological process varying from intense fault rifting in an early period to relatively gentle and overall subsidence in a later period during the Early Cretaceous. (C) 2013 Elsevier Ltd. All rights reserved.Key Laboratory of Tectonics and Petroleum Resources, Ministry of Education TPR-2011-09Project of "Double strong effect, driving mechanism and hydrocarbon significance of tectonic activity during depositional period of Dongying Formation in Qikou and Nanpu Sag, Eastern China" 41272122Geological Science