Right orthogonal class of pure projective modules over pure hereditary rings

Let $\mathcal{W}$ be the class of all pure projective modules. In this article, $\mathcal{W}$-injective modules is defined via the vanishing of cohomology of pure projective modules. First we show that every module has a $\mathcal{W}$-injective coresolution over an arbitrary ring and the class of all $\mathcal{W}$-injective modules is coresolving over a pure-hereditary ring. Further, we analyze the dimension of $\mathcal{W}$-injective coresolution over a pure-hereditary ring. It is shown that \Fcor_{\mathcal{W}^{\bot}}(R) = \sup\{\pd(G) \colon G is a pure projective $R$-module\} = \sup\{\cores_{\mathcal{W}^{\bot}}(M) \colon M is an $R$-module$\}.$ Finally, we give some equivalent conditions of $\mathcal{W}$-injective envelope with the unique mapping property. The dimension has desirable properties when the ring is semisimple artinian.Comment: 17 pages, 9 figure

Toddlers Acquire Verb Transitivity in Non-Social Overhearing Contexts

Acquiring word meanings is typically described as a social process involving live interaction and joint attention to the referent. However, the ability to learn meanings in non- social contexts could be useful in many overhearing situations, in which speech may not be child-directed, and learners may lack discourse and/or situational context. Is social context required to trigger toddlers’ abilities to map verbs to meaning? We address this question in the following experiment. Our results indicate that 2-year-olds can acquire a novel verb’s meaning even in socially impoverished contexts. This finding has implications for treatment of children with Autism Spectrum Disorders.American Philosophical Society (Franklin Research Grant

Data Mining for Simple Sequence Repeats in Oil Palm Expressed Sequence Tags

Expressed Sequence Tags or ESTs are small pieces of DNA sequence that are generated by sequencing either one or both ends of an expressed gene. ESTs provide researchers with a quick and inexpensive route for discovering new genes, for obtaining data on gene expression and regulation, and for constructing genome maps. Oil palm EST sequences as available in public domain are downloaded. They were grouped and made contigs using CAP3 and Phrap. Microsatellite repeats are located using 5 softwares (MISA, TRA, TROLL, SSRIT, SSR primer). Among the 5 methods MISA is found to be the best. It can elucidate the compound repeat also. Frequency and total number (202) of SSR were detected. Mononucleotide repeat is more abundant especially ‘A/T’ repeats in Oil palm. Flanking primers were designed using primer3, SSR primers. The results of the study are given as an online database ‘MEMCO’ to help Oil palm researchers

Solidarity across generations in New Zealand: Factors influencing parental support for children within a three-generational context

Interest in ascertaining the nature and extent of intergenerational exchanges between those in mid-life, and members of their kinship network has arisen because demographic, social and policy changes have brought into question the ability of individuals in this stage of the family and individual life course to respond to what may be the conflicting support needs of older and younger generations. Trends of delayed childbearing for example, suggest that at mid-life, individuals are increasingly likely to be involved in parenting roles. At the same time, as they contemplate their own pre-retirement needs, they may also be more involved with the caring needs of ageing parents who are living longer. It has thus been argued that the mid-life period carries the potential for complex, and perhaps competing intergenerational requirements for support and care, compromising the ability of those in this life stage to show their solidarity towards both younger and older kin. Research on intergenerational relations has focused mainly on the adult child and elderly parent dyad in the context of population ageing and much less work has been done to understand the nature of intergenerational exchanges in the context of more complex structures extending beyond dyads to include triads of three co-surviving generations. This paper addresses this lacuna by establishing whether, in the context of a kinship structure of three co-surviving generations, the likelihood of a child receiving assistance from their mid-life parent is influenced by the characteristics of an ascending generation, the mid-life respondent’s own ageing parent. Empirical investigation draws on the theoretical framework of micro-level, inter-generational solidarity developed by Bengtson and others, in which exchanges of assistance are conceptualised as bonds of functional solidarity. Underlying the analysis is therefore an investigation of the premise that mid-life individuals are at the centre of competing inter-generational requirements. Data are from the 1997 New Zealand survey ‘Transactions in the Mid-Life Family’, a sample of 750 males and females aged between 40 and 54. Analysis is based on a sub-population of 310 respondents with at least one surviving ageing parent or in-law and one child aged over 15, none of whom live together. Multivariate logistic regression techniques are used and the dependant variable of functional solidarity is represented as a three-category variable of emotional, in-kind and financial support. Findings indicate that when an ageing parent’s bond with the mid-life respondent is characterised by emotional support, this also enhances the child’s chances of benefiting from all dimensions of parental support. Likewise, children are more likely to benefit from in-kind help if their own grandparents also receive it. Results do not clearly suggest that a greater number of elderly members in a kin network necessarily represent a drain on the mid-life respondent’s resources, at least not those of an emotional nature. Life-course specific support requirements of younger and older generations may mean that mid-life individuals in fact respond to complementary rather than competing needs

Optimal Quantum Sample Complexity of Learning Algorithms

$\newcommand{\eps}{\varepsilon}$In learning theory, the VC dimension of a concept class $C$ is the most common way to measure its "richness." In the PAC model \Theta\Big(\frac{d}{\eps} + \frac{\log(1/\delta)}{\eps}\Big) examples are necessary and sufficient for a learner to output, with probability $1-\delta$, a hypothesis $h$ that is \eps-close to the target concept $c$. In the related agnostic model, where the samples need not come from a $c\in C$, we know that \Theta\Big(\frac{d}{\eps^2} + \frac{\log(1/\delta)}{\eps^2}\Big) examples are necessary and sufficient to output an hypothesis $h\in C$ whose error is at most \eps worse than the best concept in $C$. Here we analyze quantum sample complexity, where each example is a coherent quantum state. This model was introduced by Bshouty and Jackson, who showed that quantum examples are more powerful than classical examples in some fixed-distribution settings. However, Atici and Servedio, improved by Zhang, showed that in the PAC setting, quantum examples cannot be much more powerful: the required number of quantum examples is \Omega\Big(\frac{d^{1-\eta}}{\eps} + d + \frac{\log(1/\delta)}{\eps}\Big)\mbox{ for all }\eta> 0. Our main result is that quantum and classical sample complexity are in fact equal up to constant factors in both the PAC and agnostic models. We give two approaches. The first is a fairly simple information-theoretic argument that yields the above two classical bounds and yields the same bounds for quantum sample complexity up to a \log(d/\eps) factor. We then give a second approach that avoids the log-factor loss, based on analyzing the behavior of the "Pretty Good Measurement" on the quantum state identification problems that correspond to learning. This shows classical and quantum sample complexity are equal up to constant factors.Comment: 31 pages LaTeX. Arxiv abstract shortened to fit in their 1920-character limit. Version 3: many small changes, no change in result

The effects of linguistic context on visual attention while learning novel verbs

The research reported here was supported by a Franklin Research Grant from the American Philosophical Society and by NIH award number K01DC013306.http://www.cascadilla.com/bucld41toc.htmlPublished versio

Optimizing the Number of Gates in Quantum Search

$$In its usual form, Grover's quantum search algorithm uses $O(\sqrt{N})$ queries and $O(\sqrt{N} \log N)$ other elementary gates to find a solution in an $N$-bit database. Grover in 2002 showed how to reduce the number of other gates to $O(\sqrt{N}\log\log N)$ for the special case where the database has a unique solution, without significantly increasing the number of queries. We show how to reduce this further to $O(\sqrt{N}\log^{(r)} N)$ gates for any constant $r$, and sufficiently large $N$. This means that, on average, the gates between two queries barely touch more than a constant number of the $\log N$ qubits on which the algorithm acts. For a very large $N$ that is a power of 2, we can choose $r$ such that the algorithm uses essentially the minimal number $\frac{\pi}{4}\sqrt{N}$ of queries, and only $O(\sqrt{N}\log(\log^{\star} N))$ other gates.Comment: 11 pages LaTeX. Version 2: small improvements in the proof

A Survey of Quantum Learning Theory

This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably Approximately Correct (PAC) and agnostic learning from classical or quantum examples.Comment: 26 pages LaTeX. v2: many small changes to improve the presentation. This version will appear as Complexity Theory Column in SIGACT News in June 2017. v3: fixed a small ambiguity in the definition of gamma(C) and updated a referenc