Numerical algebraic geometry approach to polynomial optimization, The

2017 Summer.Includes bibliographical references.Numerical algebraic geometry (NAG) consists of a collection of numerical algorithms, based on homotopy continuation, to approximate the solution sets of systems of polynomial equations arising from applications in science and engineering. This research focused on finding global solutions to constrained polynomial optimization problems of moderate size using NAG methods. The benefit of employing a NAG approach to nonlinear optimization problems is that every critical point of the objective function is obtained with probability-one. The NAG approach to global optimization aims to reduce computational complexity during path tracking by exploiting structure that arises from the corresponding polynomial systems. This thesis will consider applications to systems biology and life sciences where polynomials solve problems in model compatibility, model selection, and parameter estimation. Furthermore, these techniques produce mathematical models of large data sets on non-euclidean manifolds such as a disjoint union of Grassmannians. These methods will also play a role in analyzing the performance of existing local methods for solving polynomial optimization problems

The Sloan Digital Sky Survey peculiar velocity catalogue

We present a new catalogue of distances and peculiar velocities (PVs) of 34 059 early-type galaxies derived from fundamental plane (FP) measurements using data from the Sloan Digital Sky Survey (SDSS). This 7016deg2 homogeneous sample comprises the largest set of PVs produced to date and extends the reach of PV surveys up to a redshift limit of z = 0.1. Our SDSS-based FP distance measurements have a mean uncertainty of 23 per cent. Alongside the data, we produce an ensemble of 2048 mock galaxy catalogues that reproduce the data selection function, and are used to validate our fitting pipelines and check for systematic errors. We uncover a significant trend between group richness and mean surface brightness within the sample, which may hint at an environmental dependence within the FP or the presence of unresolved systematics, and can result in biased PVs. This is removed by using multiple FP fits as function of group richness, a procedure made tractable through a new analytic derivation for the integral of a three-dimensional (3D) Gaussian over non-trivial limits. Our catalogue is calibrated to the zero-point of the CosmicFlows-III sample with an uncertainty of 0.004 dex (not including cosmic variance or the error within CosmicFlows-III itself), which is validated using independent cross-checks with the predicted zero-point from the 2M++ reconstruction of our local velocity field. Finally, as an example of what is possible with our new catalogue, we obtain preliminary bulk flow measurements up to a depth of 135h−1Mpc⁠. We find a slightly larger-than-expected bulk flow at high redshift, although this could be caused by the presence of the Shapley supercluster, which lies outside the SDSS PV footprint

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

Human Verbal Memory Encoding Is Hierarchically Distributed in a Continuous Processing Stream.

Processing of memory is supported by coordinated activity in a network of sensory, association, and motor brain regions. It remains a major challenge to determine where memory is encoded for later retrieval. Here, we used direct intracranial brain recordings from epilepsy patients performing free recall tasks to determine the temporal pattern and anatomical distribution of verbal memory encoding across the entire human cortex. High γ frequency activity (65-115 Hz) showed consistent power responses during encoding of subsequently recalled and forgotten words on a subset of electrodes localized in 16 distinct cortical areas activated in the tasks. More of the high γ power during word encoding, and less power before and after the word presentation, was characteristic of successful recall and observed across multiple brain regions. Latencies of the induced power changes and this subsequent memory effect (SME) between the recalled and forgotten words followed an anatomical sequence from visual to prefrontal cortical areas. Finally, the magnitude of the memory effect was unexpectedly found to be the largest in selected brain regions both at the top and at the bottom of the processing stream. These included the language processing areas of the prefrontal cortex and the early visual areas at the junction of the occipital and temporal lobes. Our results provide evidence for distributed encoding of verbal memory organized along a hierarchical posterior-to-anterior processing stream

Circadian rhythms are associated with variation in photosystem II function and photoprotective mechanisms

The circadian clock regulates many aspects of leaf gas supply and biochemical demand for CO2 20 , and is hypothesized to improve plant performance. Yet the extent to which the clock may regulate the efficiency of photosystem II (PSII) and photoprotective mechanisms such as heat dissipation remains largely unexplored. Based on measurements of chlorophyll a fluorescence, we estimated the maximum efficiency of photosystem II in light (Fv'/Fm') and heat dissipation by non-photochemical quenching (NPQ). We further dissected total NPQ into its main components, qE (pH-dependent quenching), qT (state-transition quenching) and qI (quenching related to photoinhibition), in clock mutant genotypes of Arabidopsis thaliana, the cognate wild-type genotypes, and a panel of recombinant inbred lines (RILs) expressing quantitative variation in clock period. Compared to mutants with altered clock function, we observed that wild-type genotypes with clock period lengths of approximately 24 hr had both higher levels of Fv'/Fm ', indicative of improved PSII function, and reduced NPQ, suggestive of lower stress on PSII light harvesting complexes. In the RILs, genetic variances were significant for Fv'/Fm' and all three components of NPQ, with qE explaining the greatest proportion of NPQ. Bivariate tests of association and structural equation models of hierarchical trait relationships showed that quantitative clock variation was empirically associated with Fv'/Fm' and NPQ, with qE mediating the relationship with gas exchange. The results demonstrate significant segregating variation for all photoprotective components, and suggest the adaptive significance of the clock may partly derive from its regulation of the light reactions of photosynthesis and of photoprotective mechanisms. Key words: Arabidopsis thaliana, circadian rhythms, chlorophyll a fluorescence, maximum efficiency of PSII, non-photochemical quenchin

The Hubble constant and dark energy from cosmological distance measures

We study how the determination of the Hubble constant from cosmological distance measures is affected by models of dark energy and vice versa. For this purpose, constraints on the Hubble constant and dark energy are investigated using the cosmological observations of cosmic microwave background, baryon acoustic oscillations and type Ia suprenovae. When one investigates dark energy, the Hubble constant is often a nuisance parameter, thus it is usually marginalized over. On the other hand, when one focuses on the Hubble constant, simple dark energy models such as a cosmological constant and a constant equation of state are usually assumed. Since we do not know the nature of dark energy yet, it is interesting to investigate the Hubble constant assuming some types of dark energy and see to what extent the constraint on the Hubble constant is affected by the assumption concerning dark energy. We show that the constraint on the Hubble constant is not affected much by the assumption for dark energy. We furthermore show that this holds true even if we remove the assumption that the universe is flat. We also discuss how the prior on the Hubble constant affects the constraints on dark energy and/or the curvature of the universe.Comment: 45 pages, 15 figure

Space Shuttle Orbiter Structures and Mechanisms

The Space Shuttle Orbiter has performed exceptionally well over its 30 years of flight experience. Among the many factors behind this success were robust, yet carefully monitored, structural and mechanical systems. From highlighting key aspects of the design to illustrating lessons learned from the operation of this complex system, this paper will attempt to educate the reader on why some subsystems operated flawlessly and why specific vulnerabilities were exposed in others. Specific areas to be covered will be the following: high level configuration overview, primary and secondary structure, mechanical systems ranging from landing gear to the docking system, and windows

Conditioning Intensity, Pre-Transplant Flow Cytometric Measurable Residual Disease, and Outcome in Adults with Acute Myeloid Leukemia Undergoing Allogeneic Hematopoietic Cell Transplantation

How conditioning intensity is related to outcomes of AML patients undergoing allografting in morphologic remission is an area of great ongoing interest. We studied 743 patients in morphologic remission and known pre-transplant measurable residual disease (MRD) status determined by multiparameter flow cytometry (MFC) who received a first allograft after myeloablative, reduced intensity, or nonmyeloablative conditioning (MAC, RIC, and NMA). Overall, relapse-free survival (RFS) and overall survival (OS) were longer after MAC than RIC or NMA conditioning, whereas relapse risks were not different. Among MRD(pos)patients, 3-year estimates of relapse risks and survival were similar across conditioning intensities. In contrast, among MRD(neg)patients, 3-year RFS and OS were longer for MAC (69% and 71%) than RIC (47% and 55%) and NMA conditioning (47% and 52%). Three-year relapse risks were lowest after MAC (18%) and highest after NMA conditioning (30%). Our data indicate an interaction between conditioning intensity, MFC-based pre-transplant MRD status, and outcome, with benefit of intensive conditioning primarily for patients transplanted in MRD(neg)remission. Differing from recent findings from other studies that indicated MAC is primarily beneficial for some or all patients with MRD(pos)pre-HCT status, our data suggest MAC should still be considered for MRD(neg)AML patients if tolerated