Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions

In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of semi-inner-products, we can obtain the explicit representations of the dual (normalized-duality-mapping) elements of support vector machine solutions. In addition, we can introduce the reproduction property in a generalized native space by Fourier transform techniques such that it becomes a reproducing kernel Banach space, which can be even embedded into Sobolev spaces, and its reproducing kernel is set up by the related positive definite function. The representations of the optimal solutions of support vector machines (regularized empirical risks) in these reproducing kernel Banach spaces are formulated explicitly in terms of positive definite functions, and their finite numbers of coefficients can be computed by fixed point iteration. We also give some typical examples of reproducing kernel Banach spaces induced by Mat\'ern functions (Sobolev splines) so that their support vector machine solutions are well computable as the classical algorithms. Moreover, each of their reproducing bases includes information from multiple training data points. The concept of reproducing kernel Banach spaces offers us a new numerical tool for solving support vector machines.Comment: 26 page

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Essential Role for endogenous siRNAs during meiosis in mouse oocytes.

The RNase III enzyme DICER generates both microRNAs (miRNAs) and endogenous short interfering RNAs (endo-siRNAs). Both small RNA species silence gene expression post-transcriptionally in association with the ARGONAUTE (AGO) family of proteins. In mammals, there are four AGO proteins (AGO1-4), of which only AGO2 possesses endonucleolytic activity. siRNAs trigger endonucleolytic cleavage of target mRNAs, mediated by AGO2, whereas miRNAs cause translational repression and mRNA decay through association with any of the four AGO proteins. Dicer deletion in mouse oocytes leads to female infertility due to defects during meiosis I. Because mouse oocytes express both miRNAs and endo-siRNAs, this phenotype could be due to the absence of either class of small RNA, or both. However, we and others demonstrated that miRNA function is suppressed in mouse oocytes, which suggested that endo-siRNAs, not miRNAs, are essential for female meiosis. To determine if this was the case we generated mice that express a catalytically inactive knock-in allele of Ago2 (Ago2ADH) exclusively in oocytes and thereby disrupted the function of siRNAs. Oogenesis and hormonal response are normal in Ago2ADH oocytes, but meiotic maturation is impaired, with severe defects in spindle formation and chromosome alignment that lead to meiotic catastrophe. The transcriptome of these oocytes is widely perturbed and shows a highly significant correlation with the transcriptome of Dicer null and Ago2 null oocytes. Expression of the mouse transcript (MT), the most abundant transposable element in mouse oocytes, is increased. This study reveals that endo-siRNAs are essential during meiosis I in mouse females, demonstrating a role for endo-siRNAs in mammals.This research was supported by the National Institutes of Health Grants HD022681 (to RMS), and R37 GM062534-14 (to GJH), National Human Genome Research Institute 5T32HG000046-13 (to FL) and by a kind gift from Kathryn W. Davis. GJH is an investigator of the Howard Hughes Medical Institute. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.This is the final version of the article. It first appeared from PLoS via http://dx.doi.org/10.1371/journal.pgen.100501

Localness of energy cascade in hydrodynamic turbulence, II. Sharp spectral filter

We investigate the scale-locality of subgrid-scale (SGS) energy flux and inter-band energy transfers defined by the sharp spectral filter. We show by rigorous bounds, physical arguments and numerical simulations that the spectral SGS flux is dominated by local triadic interactions in an extended turbulent inertial-range. Inter-band energy transfers are also shown to be dominated by local triads if the spectral bands have constant width on a logarithmic scale. We disprove in particular an alternative picture of ``local transfer by nonlocal triads,'' with the advecting wavenumber mode at the energy peak. Although such triads have the largest transfer rates of all {\it individual} wavenumber triads, we show rigorously that, due to their restricted number, they make an asymptotically negligible contribution to energy flux and log-banded energy transfers at high wavenumbers in the inertial-range. We show that it is only the aggregate effect of a geometrically increasing number of local wavenumber triads which can sustain an energy cascade to small scales. Furthermore, non-local triads are argued to contribute even less to the space-average energy flux than is implied by our rigorous bounds, because of additional cancellations from scale-decorrelation effects. We can thus recover the -4/3 scaling of nonlocal contributions to spectral energy flux predicted by Kraichnan's ALHDIA and TFM closures. We support our results with numerical data from a $512^3$ pseudospectral simulation of isotropic turbulence with phase-shift dealiasing. We conclude that the sharp spectral filter has a firm theoretical basis for use in large-eddy simulation (LES) modeling of turbulent flows.Comment: 42 pages, 9 figure

Small-molecule inhibitors of phosphatidylcholine transfer protein/StarD2 identified by high-throughput screening

Phosphatidylcholine transfer protein (PC–TP, also referred to as StarD2) is a highly specific intracellular lipid-binding protein that catalyzes the transfer of phosphatidylcholines between membranes in vitro. Recent studies have suggested that PC–TP in vivo functions to regulate fatty acid and glucose metabolism, possibly via interactions with selected other proteins. To begin to address the relationship between activity in vitro and biological function, we undertook a high-throughput screen to identify small-molecule inhibitors of the phosphatidylcholine transfer activity of PC–TP. After adapting a fluorescence quench assay to measure phosphatidylcholine transfer activity, we screened 114,752 compounds of a small-molecule library. The high-throughput screen identified 14 potential PC–TP inhibitors. Of these, 6 compounds exhibited characteristics consistent with specific inhibition of PC–TP activity, with IC50 values that ranged from 4.1 to 95.0 ?M under conditions of the in vitro assay. These compounds should serve as valuable reagents to elucidate the biological function of PC–TP. Because mice with homozygous disruption of the PC–TP gene (Pctp) are sensitized to insulin action and relatively resistant to the development of atherosclerosis, these inhibitors may also prove to be of value in the management of diabetes and atherosclerotic cardiovascular diseases

Electrophysiological Signatures of Spatial Boundaries in the Human Subiculum.

Environmental boundaries play a crucial role in spatial navigation and memory across a wide range of distantly related species. In rodents, boundary representations have been identified at the single-cell level in the subiculum and entorhinal cortex of the hippocampal formation. Although studies of hippocampal function and spatial behavior suggest that similar representations might exist in humans, boundary-related neural activity has not been identified electrophysiologically in humans until now. To address this gap in the literature, we analyzed intracranial recordings from the hippocampal formation of surgical epilepsy patients (of both sexes) while they performed a virtual spatial navigation task and compared the power in three frequency bands (1-4, 4-10, and 30-90 Hz) for target locations near and far from the environmental boundaries. Our results suggest that encoding locations near boundaries elicited stronger theta oscillations than for target locations near the center of the environment and that this difference cannot be explained by variables such as trial length, speed, movement, or performance. These findings provide direct evidence of boundary-dependent neural activity localized in humans to the subiculum, the homolog of the hippocampal subregion in which most boundary cells are found in rodents, and indicate that this system can represent attended locations that rather than the position of one\u27s own body

Electrical Stimulation Modulates High γ Activity and Human Memory Performance.

Direct electrical stimulation of the brain has emerged as a powerful treatment for multiple neurological diseases, and as a potential technique to enhance human cognition. Despite its application in a range of brain disorders, it remains unclear how stimulation of discrete brain areas affects memory performance and the underlying electrophysiological activities. Here, we investigated the effect of direct electrical stimulation in four brain regions known to support declarative memory: hippocampus (HP), parahippocampal region (PH) neocortex, prefrontal cortex (PF), and lateral temporal cortex (TC). Intracranial EEG recordings with stimulation were collected from 22 patients during performance of verbal memory tasks. We found that high γ (62-118 Hz) activity induced by word presentation was modulated by electrical stimulation. This modulatory effect was greatest for trials with poor memory encoding. The high γ modulation correlated with the behavioral effect of stimulation in a given brain region: it was negative, i.e., the induced high γ activity was decreased, in the regions where stimulation decreased memory performance, and positive in the lateral TC where memory enhancement was observed. Our results suggest that the effect of electrical stimulation on high γ activity induced by word presentation may be a useful biomarker for mapping memory networks and guiding therapeutic brain stimulation

Young women's use of a microbicide surrogate: The complex influence of relationship characteristics and perceived male partners' evaluations

This is the post-print version of the article. The official published version can be found at the link below.Currently in clinical trials, vaginal microbicides are proposed as a female-initiated method of sexually transmitted infection prevention. Much of microbicide acceptability research has been conducted outside of the United States and frequently without consideration of the social interaction between sex partners, ignoring the complex gender and power structures often inherent in young women’s (heterosexual) relationships. Accordingly, the purpose of this study was to build on existing microbicide research by exploring the role of male partners and relationship characteristics on young women’s use of a microbicide surrogate, an inert vaginal moisturizer (VM), in a large city in the United States. Individual semi-structured interviews were conducted with 40 young women (18–23 years old; 85% African American; 47.5% mothers) following use of the VM during coital events for a 4 week period. Overall, the results indicated that relationship dynamics and perceptions of male partners influenced VM evaluation. These two factors suggest that relationship context will need to be considered in the promotion of vaginal microbicides. The findings offer insights into how future acceptability and use of microbicides will be influenced by gendered power dynamics. The results also underscore the importance of incorporating men into microbicide promotion efforts while encouraging a dialogue that focuses attention on power inequities that can exist in heterosexual relationships. Detailed understanding of these issues is essential for successful microbicide acceptability, social marketing, education, and use.This study was funded by a grant from National Institutes of Health (NIHU19AI 31494) as well as research awards to the first author: Friends of the Kinsey Institute Research Grant Award, Indiana University’s School of HPER Graduate Student Grant-in-Aid of Research Award, William L. Yarber Sexual Health Fellowship, and the Indiana University Graduate and Professional Student Organization Research Grant

BAC library resources for map-based cloning and physical map construction in barley (Hordeum vulgare L.)

Background: Although second generation sequencing (2GS) technologies allow re-sequencing of previously gold-standard-sequenced genomes, whole genome shotgun sequencing and de novo assembly of large and complex eukaryotic genomes is still difficult. Availability of a genome-wide physical map is therefore still a prerequisite for whole genome sequencing for genomes like barley. To start such an endeavor, large insert genomic libraries, i.e. Bacterial Artificial Chromosome (BAC) libraries, which are unbiased and representing deep haploid genome coverage, need to be ready in place. Result: Five new BAC libraries were constructed for barley (Hordeum vulgare L.) cultivar Morex. These libraries were constructed in different cloning sites (HindIII, EcoRI, MboI and BstXI) of the respective vectors. In order to enhance unbiased genome representation and to minimize the number of gaps between BAC contigs, which are often due to uneven distribution of restriction sites, a mechanically sheared library was also generated. The new BAC libraries were fully characterized in depth by scrutinizing the major quality parameters such as average insert size, degree of contamination (plate wide, neighboring, and chloroplast), empty wells and off-scale clones (clones with 250 fragments). Additionally a set of gene-based probes were hybridized to high density BAC filters and showed that genome coverage of each library is between 2.4 and 6.6 X. Conclusion: BAC libraries representing >20 haploid genomes are available as a new resource to the barley research community. Systematic utilization of these libraries in high-throughput BAC fingerprinting should allow developing a genome-wide physical map for the barley genome, which will be instrumental for map-based gene isolation and genome sequencing.Daniela Schulte, Ruvini Ariyadasa, Bujun Shi, Delphine Fleury, Chris Saski, Michael Atkins, Pieter deJong, Cheng-Cang Wu, Andreas Graner, Peter Langridge and Nils Stei

MEMS Deformable Mirrors for Space-Based High-Contrast Imaging

Micro-Electro-Mechanical Systems (MEMS) Deformable Mirrors (DMs) enable precise wavefront control for optical systems. This technology can be used to meet the extreme wavefront control requirements for high contrast imaging of exoplanets with coronagraph instruments. MEMS DM technology is being demonstrated and developed in preparation for future exoplanet high contrast imaging space telescopes, including the Wide Field Infrared Survey Telescope (WFIRST) mission which supported the development of a 2040 actuator MEMS DM. In this paper, we discuss ground testing results and several projects which demonstrate the operation of MEMS DMs in the space environment. The missions include the Planet Imaging Concept Testbed Using a Recoverable Experiment (PICTURE) sounding rocket (launched 2011), the Planet Imaging Coronagraphic Technology Using a Reconfigurable Experimental Base (PICTURE-B) sounding rocket (launched 2015), the Planetary Imaging Concept Testbed Using a Recoverable Experiment - Coronagraph (PICTURE-C) high altitude balloon (expected launch 2019), the High Contrast Imaging Balloon System (HiCIBaS) high altitude balloon (launched 2018), and the Deformable Mirror Demonstration Mission (DeMi) CubeSat mission (expected launch late 2019). We summarize results from the previously flown missions and objectives for the missions that are next on the pad. PICTURE had technical difficulties with the sounding rocket telemetry system. PICTURE-B demonstrated functionality at >100 km altitude after the payload experienced 12-g RMS (Vehicle Level 2) test and sounding rocket launch loads. The PICTURE-C balloon aims to demonstrate 10(-7) contrast using a vector vortex coronagraph, image plane wavefront sensor, and a 952 actuator MEMS DM. The HiClBaS flight experienced a DM cabling issue, but the 37-segment hexagonal piston-tip-tilt DM is operational post-flight. The DeMi mission aims to demonstrate wavefront control to a precision of less than 100 nm RMS in space with a 140 actuator MEMS DM.DARPA; NASA Space Technology Research FellowshipOpen Access JournalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]