Basis Expansions for Functional Snippets

Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed approach allows one to consistently estimate an infinite-rank covariance function from functional snippets. We establish the convergence rates for the proposed estimators and illustrate their finite-sample performance via simulation studies and two data applications.Comment: 51 pages, 10 figure

VI-Band Follow-Up Observations of Ultra-Long-Period Cepheid Candidates in M31

The ultra-long period Cepheids (ULPCs) are classical Cepheids with pulsation periods exceeding $\approx 80$ days. The intrinsic brightness of ULPCs are ~1 to ~3 mag brighter than their shorter period counterparts. This makes them attractive in future distance scale work to derive distances beyond the limit set by the shorter period Cepheids. We have initiated a program to search for ULPCs in M31, using the single-band data taken from the Palomar Transient Factory, and identified eight possible candidates. In this work, we presented the VI-band follow-up observations of these eight candidates. Based on our VI-band light curves of these candidates and their locations in the color-magnitude diagram and the Period-Wesenheit diagram, we verify two candidates as being truly ULPCs. The six other candidates are most likely other kinds of long-period variables. With the two confirmed M31 ULPCs, we tested the applicability of ULPCs in distance scale work by deriving the distance modulus of M31. It was found to be $\mu_{M31,ULPC}=24.30\pm0.76$ mag. The large error in the derived distance modulus, together with the large intrinsic dispersion of the Period-Wesenheit (PW) relation and the small number of ULPCs in a given host galaxy, means that the question of the suitability of ULPCs as standard candles is still open. Further work is needed to enlarge the sample of calibrating ULPCs and reduce the intrinsic dispersion of the PW relation before re-considering ULPCs as suitable distance indicators.Comment: 13 pages, with 14 Figures and 4 Tables (one online table). AJ accepte

Alternative Splicing and Expression Profile Analysis of Expressed Sequence Tags in Domestic Pig

Domestic pig (Sus scrofa domestica) is one of the most important mammals to humans. Alternative splicing is a cellular mechanism in eukaryotes that greatly increases the diversity of gene products. Expression sequence tags (ESTs) have been widely used for gene discovery, expression profile analysis, and alternative splicing detection. In this study, a total of 712,905 ESTs extracted from 101 different non-normalized EST libraries of the domestic pig were analyzed. These EST libraries cover the nervous system, digestive system, immune system, and meat production related tissues from embryo, newborn, and adult pigs, making contributions to the analysis of alternative splicing variants as well as expression profiles in various stages of tissues. A modified approach was designed to cluster and assemble large EST datasets, aiming to detect alternative splicing together with EST abundance of each splicing variant. Much efforts were made to classify alternative splicing into different types and apply different filters to each type to get more reliable results. Finally, a total of 1,223 genes with average 2.8 splicing variants were detected among 16,540 unique genes. The overview of expression profiles would change when we take alternative splicing into account

Genomic Insights into Speciation History and Local Adaptation of an Alpine Aspen in the Qinghai–Tibet Plateau and Adjacent Highlands

Natural selection serves as an important agent to drive and maintain interspecific divergence. Populus rotundifolia Griff. is an alpine aspen species that mainly occurs in the Qinghai–Tibet Plateau (QTP) and adjacent highlands, whereas its sister species, P. davidiana Dode, is distributed across southwest and central to northeast China in much lower altitude regions. In this study, we collected genome resequencing data of 53 P. rotundifolia and 42 P. davidiana individuals across their natural distribution regions. Our population genomic data suggest that the two species are well delimitated in the allopatric regions, but with hybrid zones in their adjacent region in the eastern QTP. Coalescent simulations suggest that P. rotundifolia diverged from P. davidiana in the middle Pleistocene with following continuous gene flow since divergence. In addition, we found numerous highly diverged genes with outlier signatures that are likely associated with high‐altitude adaptation of these alpine aspens. Our finding indicate that Quaternary climatic changes and natural selection have greatly contributed to the origin and distinction maintenance of P. rotundifolia in the QTP

Tetra­aqua­bis(2-methyl­benzimidazolium-1,3-diacetato-κO)zinc(II) tetra­hydrate

The asymmetric unit of the title compound, [Zn(C12H11N2O4)2(H2O)4]·4H2O, contains one-half of the complex mol­ecule and two uncoordin­ated water mol­ecules. The four water O atoms in the equatorial plane around the ZnII centre ( symmetry) form a distorted square-planar arrangement, while the distorted octa­hedral coordination geometry is completed by the O atoms of the zwitterionic 2-methyl­benzimidazolium-1,3-diacetate ligands in the axial positions. The benzimidazole ring system is planar, with a maximum deviation of 0.041 (3) Å. Intra­molecular O—H⋯O hydrogen bonding results in the formation of a non-planar six-membered ring. In the crystal structure, strong intra- and inter­molecular O—H⋯O hydrogen bonds link the mol­ecules into a three-dimensional network. π–π contacts between benzimidazole rings [centroid–centroid distance = 3.899 (1) Å] may further stabilize the structure

Humanin Rescues Cultured Rat Cortical Neurons from NMDA-Induced Toxicity Not by NMDA Receptor

Excitatory neurotoxicity has been implicated in many pathological situations and there is no effective treatment available. Humanin is a 24-aa peptide cloned from the brain of patients with Alzheimer’s disease (AD). In the present study, excitatory toxicity was induced by N-methyl-D-aspartate (NMDA) in primarily cultured rat cortical neurons. MTT assessment, lactate dehydrogenase (LDH) release, and calcein staining were employed to evaluate the protective activity of humanin on NMDA induced toxicity. The results suggested that NMDA (100 μmol/L, 2.5 hr) triggered neuronal morphological changes, lactate dehydrogenase (LDH) release (166% of the control), reduction of cell viability (about 50% of the control), and the decrease of living cell density (about 50% of the control). When pretreated with humanin, the toxicity was suppressed. The living cells’ density of humanin treated group was similar to that of control. The cell viability was attenuated dose-dependently (IC50 = 0.132 nmol/L). The LDH release was also neutralized in a dose-dependent manner. In addition, the intracellular Ca2+ overloading triggered by NMDA reverted quickly and humanin could not inhibit it. These findings indicate that humanin can rescue cortical neurons from NMDA-induced toxicity in rat but not through interfering with NMDA receptor directly

The Improved Algorithm of Fast Panorama Stitching for Image Sequence and Reducing the Distortion Errors

The traditional image stitching result based on the SIFT feature points extraction, to a certain extent, has distortion errors. The panorama, especially, would get more seriously distorted when compositing a panoramic result using a long image sequence. To achieve the goal of creating a high-quality panorama, the improved algorithm is proposed in this paper, including altering the way of selecting the reference image and putting forward a method that can compute the transformation matrix for any image of the sequence to align with the reference image in the same coordinate space. Additionally, the improved stitching method dynamically selects the next input image based on the number of SIFT matching points. Compared with the traditional stitching process, the improved method increases the number of matching feature points and reduces SIFT feature detection area of the reference image. The experimental results show that the improved method can not only accelerate the efficiency of image stitching processing, but also reduce the panoramic distortion errors, and finally we can obtain a pleasing panoramic result