On the Gabor frame set for compactly supported continuous functions

We identify a class of continuous compactly supported functions for which the known part of the Gabor frame set can be extended. At least for functions with support on an interval of length two, the curve determining the set touches the known obstructions. Easy verifiable sufficient conditions for a function to belong to the class are derived, and it is shown that the B-splines (Formula presented.) , (Formula presented.) , and certain ???continuous and truncated??? versions of several classical functions (e.g., the Gaussian and the two-sided exponential function) belong to the class. The sufficient conditions for the frame property guarantees the existence of a dual window with a prescribed size of the support.ope

Molecular Identification of Rickettsial Endosymbionts in the Non-Phagotrophic Volvocalean Green Algae

Background: The order Rickettsiales comprises Gram-negative obligate intracellular bacteria (also called rickettsias) that are mainly associated with arthropod hosts. This group is medically important because it contains human-pathogenic species that cause dangerous diseases. Until now, there has been no report of non-phagotrophic photosynthetic eukaryotes, such as green plants, harboring rickettsias. Methodology/Principal Findings: We examined the bacterial endosymbionts of two freshwater volvocalean green algae: unicellular Carteria cerasiformis and colonial Pleodorina japonica. Epifluorescence microscopy using 49-6-deamidino-2phenylindole staining revealed the presence of endosymbionts in all C. cerasiformis NIES-425 cells, and demonstrated a positive correlation between host cell size and the number of endosymbionts. Strains both containing and lacking endosymbionts of C. cerasiformis (NIES-425 and NIES-424) showed a.10-fold increase in cell number and typical sigmoid growth curves over 192 h. A phylogenetic analysis of 16 S ribosomal (r)RNA gene sequences from the endosymbionts of C. cerasiformis and P. japonica demonstrated that they formed a robust clade (hydra group) with endosymbionts of various non-arthropod hosts within the family Rickettsiaceae. There were significantly fewer differences in the 16 S rRNA sequences of the rickettsiacean endosymbionts between C. cerasiformis and P. japonica than in the chloroplast 16 S rRNA or 18 S rRNA of the host volvocalean cells. Fluorescence in situ hybridization demonstrated the existence of the rickettsiacea

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

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

On Partition of Unities Generated by Entire Functions and Gabor Frames in L2(Rd) and 2(Zd)

We characterize the entire functions P of d variables, d???2, for which the Zd-translates of P??[0,N]d satisfy the partition of unity for some N???N. In contrast to the one-dimensional case, these entire functions are not necessarily periodic. In the case where P is a trigonometric polynomial, we characterize the maximal smoothness of P??[0,N]d, as well as the function that achieves it. A number of especially attractive constructions are achieved, e.g., of trigonometric polynomials leading to any desired (finite) regularity for a fixed support size. As an application we obtain easy constructions of matrix-generated Gabor frames in L2(Rd), with small support and high smoothness. By sampling this yields dual pairs of finite Gabor frames in ???2(Zd).clos