Regularized Halfspace Depth for Functional Data

Data depth is a powerful nonparametric tool originally proposed to rank multivariate data from center outward. In this context, one of the most archetypical depth notions is Tukey's halfspace depth. In the last few decades notions of depth have also been proposed for functional data. However, Tukey's depth cannot be extended to handle functional data because of its degeneracy. Here, we propose a new halfspace depth for functional data which avoids degeneracy by regularization. The halfspace projection directions are constrained to have a small reproducing kernel Hilbert space norm. Desirable theoretical properties of the proposed depth, such as isometry invariance, maximality at center, monotonicity relative to a deepest point, upper semi-continuity, and consistency are established. Moreover, the regularized halfspace depth can rank functional data with varying emphasis in shape or magnitude, depending on the regularization. A new outlier detection approach is also proposed, which is capable of detecting both shape and magnitude outliers. It is applicable to trajectories in L2, a very general space of functions that include non-smooth trajectories. Based on extensive numerical studies, our methods are shown to perform well in terms of detecting outliers of different types. Three real data examples showcase the proposed depth notion

Bootstrap inference in functional linear regression models with scalar response under heteroscedasticity

Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue, conditional mean (projection of the slope function) estimates have complicated sampling distributions due to the infinite dimensional regressors, which create truncation bias and scaling problems that are compounded by non-constant variance under heteroscedasticity. As a foundation for distributional inference, we establish a central limit theorem for the estimated projection under general dependent errors, and subsequently we develop a paired bootstrap method to approximate sampling distributions. The proposed paired bootstrap does not follow the standard bootstrap algorithm for finite dimensional regressors, as this version fails outside of a narrow window for implementation with functional regressors. The reason owes to a bias with functional regressors in a naive bootstrap construction. Our bootstrap proposal incorporates debiasing and thereby attains much broader validity and flexibility with truncation parameters for inference under heteroscedasticity; even when the naive approach may be valid, the proposed bootstrap method performs better numerically. The bootstrap is applied to construct confidence intervals for projections and for conducting hypothesis tests for the slope function. Our theoretical results on bootstrap consistency are demonstrated through simulation studies and also illustrated with real data examples

Chemoenzymatic Synthesis of Glycosylated Macrolactam Analogues of the Macrolide Antibiotic YC‐17

YC‐17 is a 12‐membered ring macrolide antibiotic produced from Streptomyces venezuelae ATCC 15439 and is composed of the polyketide macrolactone 10‐deoxymethynolide appended with D‐desosamine. In order to develop structurally diverse macrolactam analogues of YC‐17 with improved therapeutic potential, a combined approach involving chemical synthesis and engineered cell‐based biotransformation was employed. Eight new antibacterial macrolactam analogues of YC‐17 were generated by supplying a novel chemically synthesized macrolactam aglycone to S. venezuelae mutants harboring plasmids capable of synthesizing several unnatural sugars for subsequent glycosylation. Some YC‐17 macrolactam analogues were active against erythromycin‐resistant bacterial pathogens and displayed improved metabolic stability in vitro. The enhanced therapeutic potential demonstrated by these glycosylated macrolactam analogues reveals the unique potential of chemoenzymatic synthesis in antibiotic drug discovery and development.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/113147/1/adsc_201500250_sm_miscellaneous_information.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/113147/2/2697_ftp.pd

Pilot KaVA monitoring on the M87 jet: confirming the inner jet structure and superluminal motions at sub-pc scales

We report the initial results of our high-cadence monitoring program on the radio jet in the active galaxy M87, obtained by the KVN and VERA Array (KaVA) at 22 GHz. This is a pilot study that preceded a larger KaVA-M87 monitoring program, which is currently ongoing. The pilot monitoring was mostly performed every two to three weeks from December 2013 to June 2014, at a recording rate of 1 Gbps, obtaining the data for a total of 10 epochs. We successfully obtained a sequence of good quality radio maps that revealed the rich structure of this jet from <~1 mas to 20 mas, corresponding to physical scales (projected) of ~0.1-2 pc (or ~140-2800 Schwarzschild radii). We detected superluminal motions at these scales, together with a trend of gradual acceleration. The first evidence for such fast motions and acceleration near the jet base were obtained from recent VLBA studies at 43 GHz, and the fact that very similar kinematics are seen at a different frequency and time with a different instrument suggests these properties are fundamental characteristics of this jet. This pilot program demonstrates that KaVA is a powerful VLBI array for studying the detailed structural evolution of the M87 jet and also other relativistic jets.Comment: 10 pages, 9 figures, accepted for publication in PAS

Tristetraprolin inhibits the growth of human glioma cells through downregulation of urokinase plasminogen activator/urokinase plasminogen activator receptor mRNAs

Urokinase plasminogen activator (uPA) and urokinase plasminogen activator receptor (uPAR) play a major role in the infiltrative growth of glioblastoma. Downregulatoion of the uPA and uPAR has been reported to inhibit the growth glioblastoma. Here, we demonstrate that tristetraprolin (TTP) inhibits the growth of U87MG human glioma cells through downregulation of uPA and uPAR. Our results show that expression level of TTP is inversely correlated with those of uPA and uPAR in human glioma cells and tissues. TTP binds to the AU-rich elements within the 3&apos; untranslated regions of uPA and uPAR and overexpression of TTP decreased the expression of uPA and uPAR through enhancing the degradation of their mRNAs. In addition, overexpression of TTP inhibited the growth and invasion of U87MG cells. Our findings implicate that TTP can be used as a promising therapeutic target to treat human glioma

NGL-1/LRRC4C Deletion Moderately Suppresses Hippocampal Excitatory Synapse Development and Function in an Input-Independent Manner

Netrin-G ligand-1 (NGL-1), also known as LRRC4C, is a postsynaptic densities (PSDs)-95-interacting postsynaptic adhesion molecule that interacts trans-synaptically with presynaptic netrin-G1. NGL-1 and its family member protein NGL-2 are thought to promote excitatory synapse development through largely non-overlapping neuronal pathways. While NGL-2 is critical for excitatory synapse development in specific dendritic segments of neurons in an input-specific manner, whether NGL-1 has similar functions is unclear. Here, we show that Lrrc4c deletion in male mice moderately suppresses excitatory synapse development and function, but surprisingly, does so in an input-independent manner. While NGL-1 is mainly detected in the stratum lacunosum moleculare (SLM) layer of the hippocampus relative to the stratum radiatum (SR) layer, NGL-1 deletion leads to decreases in the number of PSDs in both SLM and SR layers in the ventral hippocampus. In addition, both SLM and SR excitatory synapses display suppressed short-term synaptic plasticity in the ventral hippocampus. These morphological and functional changes are either absent or modest in the dorsal hippocampus. The input-independent synaptic changes induced by Lrrc4c deletion involve abnormal translocation of NGL-2 from the SR to SLM layer. These results suggest that Lrrc4c deletion moderately suppresses hippocampal excitatory synapse development and function in an input-independent manner

Identifying novel genetic variants for brain amyloid deposition: a genome-wide association study in the Korean population

Background: Genome-wide association studies (GWAS) have identified a number of genetic variants for Alzheimer's disease (AD). However, most GWAS were conducted in individuals of European ancestry, and non-European populations are still underrepresented in genetic discovery efforts. Here, we performed GWAS to identify single nucleotide polymorphisms (SNPs) associated with amyloid β (Aβ) positivity using a large sample of Korean population. Methods: One thousand four hundred seventy-four participants of Korean ancestry were recruited from multicenters in South Korea. Discovery dataset consisted of 1190 participants (383 with cognitively unimpaired [CU], 330 with amnestic mild cognitive impairment [aMCI], and 477 with AD dementia [ADD]) and replication dataset consisted of 284 participants (46 with CU, 167 with aMCI, and 71 with ADD). GWAS was conducted to identify SNPs associated with Aβ positivity (measured by amyloid positron emission tomography). Aβ prediction models were developed using the identified SNPs. Furthermore, bioinformatics analysis was conducted for the identified SNPs. Results: In addition to APOE, we identified nine SNPs on chromosome 7, which were associated with a decreased risk of Aβ positivity at a genome-wide suggestive level. Of these nine SNPs, four novel SNPs (rs73375428, rs2903923, rs3828947, and rs11983537) were associated with a decreased risk of Aβ positivity (p < 0.05) in the replication dataset. In a meta-analysis, two SNPs (rs7337542 and rs2903923) reached a genome-wide significant level (p < 5.0 × 10-8). Prediction performance for Aβ positivity increased when rs73375428 were incorporated (area under curve = 0.75; 95% CI = 0.74-0.76) in addition to clinical factors and APOE genotype. Cis-eQTL analysis demonstrated that the rs73375428 was associated with decreased expression levels of FGL2 in the brain. Conclusion: The novel genetic variants associated with FGL2 decreased risk of Aβ positivity in the Korean population. This finding may provide a candidate therapeutic target for AD, highlighting the importance of genetic studies in diverse populations

Bootstrap inference in functional linear regression models

We consider functional linear regression models (FLRMs) with functional regressor and scalar response, where the inference of the slope function is an important problem. However, even though asymptotic inference methods exist in FLRMs, these methods are limited in applicability because a wrong scaling factor is used; truncation bias in the limit is neglected; or only homoscedastic errors are assumed, which may not happen in practice. Consequently, it is necessary to develop alternative inference methods, such as bootstrap, that use the correct scaling, accommodate possible bias, and are valid even under heteroscedasticity. In this thesis, we introduce three bootstrap methods in FLRMs, namely the residual bootstrap, paired bootstrap, and wild bootstrap. Their theoretical validities are established, and their performances are numerically demonstrated. Central limit theorems for the projection are studied as well, which are fundamental results themselves and are basis to verify bootstrap validity