Shifted distinct-part partition identities in arithmetic progressions

The partition function $p(n)$, which counts the number of partitions of a positive integer $n$, is widely studied. Here, we study partition functions $p_S(n)$ that count partitions of $n$ into distinct parts satisfying certain congruence conditions. A shifted partition identity is an identity of the form $p_{S_1}(n-H) = p_{S_2}(n)$ for all $n$ in some arithmetic progression. Several identities of this type have been discovered, including two infinite families found by Alladi. In this paper, we use the theory of modular functions to determine the necessary and sufficient conditions for such an identity to exist. In addition, for two specific cases, we extend Alladi's theorem to other arithmetic progressions

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Breaking Down Prepaid Cards: Heartland Alliance Webinar

Prepaid cards are everywhere, but unlike debit cards linked to a checking account there are no formal federal regulations to protect consumers' funds. Consumers and organizations have difficulty accurately evaluating their real-world costs because many prepaid cards have hidden fees with confusing disclosure forms. This webinar will provide clarity on prepaid cards, the regulations which govern them, and the direction of the industry

Lovecraft, decadence, and aestheticism

H. P. Lovecraft (1890–1937) has an enduring influence on Gothic culture across media, and his vision is regarded usually as one of deep pessimism. In his fiction, he reveals the horrifying truth of the insignificance of humanity in the context of an indifferent cosmos. However, Lovecraft was also a committed aesthete, and found profound solace in the appreciation of art, architecture, and literature. This essay explores the relationship of his philosophy and writing to this aestheticism, and especially the influence of Walter Pater on the consolations of art, and its role in creating meaning in the face of a meaningless universe

Direct-coupled micro-magnetometer with Y-Ba-Cu-O nano-slit SQUID fabricated with a focused helium ion beam.

Direct write patterning of high-transition temperature (high-T C) superconducting oxide thin films with a focused helium ion beam is a formidable approach for the scaling of high-T C circuit feature sizes down to the nanoscale. In this letter, we report using this technique to create a sensitive micro superconducting quantum interference device (SQUID) magnetometer with a sensing area of about 100 × 100 μm2. The device is fabricated from a single 35-nm thick YBa2Cu3O7- δ film. A flux concentrating pick-up loop is directly coupled to a 10 nm × 20 μm nano-slit SQUID. The SQUID is defined entirely by helium ion irradiation from a gas field ion source. The irradiation converts the superconductor to an insulator, and no material is milled away or etched. In this manner, a very narrow non-superconducting nano-slit is created entirely within the plane of the film. The narrow slit dimension allows for maximization of the coupling to the field concentrator. Electrical measurements reveal a large 0.35 mV modulation with a magnetic field. We measure a white noise level of 2 μΦ0/Hz1∕2. The field noise of the magnetometer is 4 pT/Hz1∕2 at 4.2 K