Efficient Computation of Invariant Tori in Volume-Preserving Maps

In this paper we implement a numerical algorithm to compute codimension-one tori in three-dimensional, volume-preserving maps. A torus is defined by its conjugacy to rigid rotation, which is in turn given by its Fourier series. The algorithm employs a quasi-Newton scheme to find the Fourier coefficients of a truncation of the series. This technique is based upon the theory developed in the accompanying article by Blass and de la Llave. It is guaranteed to converge assuming the torus exists, the initial estimate is suitably close, and the map satisfies certain nondegeneracy conditions. We demonstrate that the growth of the largest singular value of the derivative of the conjugacy predicts the threshold for the destruction of the torus. We use these singular values to examine the mechanics of the breakup of the tori, making comparisons to Aubry-Mather and anti-integrability theory when possible

Barriers to Transport and Mixing in Volume-Preserving Maps with Nonzero Flux

In this paper we identify the geometric structures that restrict transport and mixing in perturbations of integrable volume-preserving systems with nonzero net flux. Unlike KAM tori, these objects cannot be continued to the tori present in the integrable system but are generated by resonance and have a contractible direction. We introduce a remarkably simple algorithm to analyze the behavior of these maps and obtain quantitative properties of the tori. In particular, we present assertions regarding the distribution of the escape times of the unbounded orbits, the abundance of tori, and the size of the resonant regions

When does the concavity index constrain stream power parameters?

By defining the attributes of river networks, we can quantitatively extract records of climatic and tectonic changes from them. The stream power incision model (SPIM) provides a framework within which this can be achieved, as it facilitates the calculation of the relative rock uplift from river characteristics. One parameter that has been widely employed in tectonic and fluvial geomorphology is the channel steepness index, a metric that can represent the normalized rock uplift rate experienced by a river. However, to accurately infer the channel steepness index, we must accurately estimate m/n, the ratio between the two positive exponents of the SPIM. Present methodologies to constrain m/n rely on an assumption that rock uplift and erodibility are spatially invariant. These conditions are rarely present on Earth. In this study, we use a synthetic example and examples from the Siwalik Hills and Olympic Mountains to demonstrate how existing methodologies to constrain m/n produce systematic errors when there is spatial variation, and particularly spatial gradients, in the processes driving landscape evolution. To solve this problem, we present a methodology to estimate m/n based on a large river network inversion that accounts for spatial variation in landscapes. After demonstrating that the methodology can accurately recover m/n in our synthetic landscape, we show that our methodology can reconcile contrasting observations in the Siwaliks, and is critical to inferring accurate values of channel steepness index in the Olympic Mountains. This highlights the utility of large topographic inversions for investigating landscape dynamics

Functional MRI To Evaluate “Sense of Self” following Perforator Flap Breast Reconstruction

Background: Breast reconstruction is associated with high levels of patient satisfaction. Previous patient satisfaction studies have been subjective. This study utilizes functional magnetic resonance imaging (fMRI) to objectively evaluate “sense of self” following deep inferior epigastric perforator (DIEP) flap breast reconstruction in an attempt to better understand patient perception. Methods: Prospective fMRI analysis was performed on four patients before and after delayed unilateral DIEP flap breast reconstruction, and on four patients after immediate unilateral DIEP flap breast reconstruction. Patients were randomly cued to palpate their natural breast, mastectomy site or breast reconstruction, and external silicone models. Three regions of interest (ROIs) associated with self-recognition were examined using a general linear model, and compared using a fixed effects and random effects ANOVA, respectively. Results: In the delayed reconstruction group, activation of the ROIs was significantly lower at the mastectomy site compared to the natural breast (p<0.01). Ten months following reconstruction, activation of the ROIs in the reconstructed breast was not significantly different from that observed with natural breast palpation. In the immediate reconstruction group, palpation of the reconstructed breast was also similar to the natural breast. This activity was greater than that observed during palpation of external artificial models (p<0.01). Conclusions: Similar activation patterns were observed during palpation of the reconstructed and natural breasts as compared to the non-reconstructed mastectomy site and artificial models. The cognitive process represented by this pattern may be a mechanism by which breast reconstruction improves self-perception, and thus patient satisfaction following mastectomy

Boost the Lead Conversion Efficiency for the Synthesis of Colloidal 2D PbS Nanosheets

In the synthesis of colloidal PbS nanosheets, the supernatant of the reaction solution is reused to boost the lead conversion efficiency. It doubles the conversion efficiency of the lead precursors to the PbS nanosheets. The nanosheets synthesized by reusing the supernatant have similar morphology, nearly identical thickness, and optical properties as the original ones, confirmed by transmission electron microscopy, X-ray diffraction, and photoluminescence spectroscopy. This method reduces the toxic Pb-containing waste during the synthesis, a step toward the green and scalable synthesis of colloidal 2D PbS nanosheets

An Upper Mass Limit on a Red Supergiant Progenitor for the Type II-Plateau Supernova SN 2006my

We analyze two pre-supernova (SN) and three post-SN high-resolution images of the site of the Type II-Plateau supernova SN 2006my in an effort to either detect the progenitor star or to constrain its properties. Following image registration, we find that an isolated stellar object is not detected at the location of SN 2006my in either of the two pre-SN images. In the first, an I-band image obtained with the Wide-Field and Planetary Camera 2 on board the Hubble Space Telescope, the offset between the SN 2006my location and a detected source ("Source 1") is too large: > 0.08", which corresponds to a confidence level of non-association of 96% from our most liberal estimates of the transformation and measurement uncertainties. In the second, a similarly obtained V-band image, a source is detected ("Source 2") that has overlap with the SN 2006my location but is definitively an extended object. Through artificial star tests carried out on the precise location of SN 2006my in the images, we derive a 3-sigma upper bound on the luminosity of a red supergiant that could have remained undetected in our pre-SN images of log L/L_Sun = 5.10, which translates to an upper bound on such a star's initial mass of 15 M_Sun from the STARS stellar evolutionary models. Although considered unlikely, we can not rule out the possibility that part of the light comprising Source 1, which exhibits a slight extension relative to other point sources in the image, or part of the light contributing to the extended Source 2, may be due to the progenitor of SN 2006my. Only additional, high-resolution observations of the site taken after SN 2006my has faded beyond detection can confirm or reject these possibilities.Comment: Minor text changes from Version 1. Appendix added detailing the determination of confidence level of non-association of point sources in two registered astronomical image

Integrated Spacecraft Autonomous Attitude Control (ISAAC)

The purpose of this project is to give undergraduate students an opportunity to design, manufacture, and maintain a mock spacecraft to be used as a testbed for autonomous control systems. The spacecraft is based on two previous models: the JX-01, an undergraduate built testbed, and the Asteroid Free Flyer led by NASA engineer and ERAU doctoral student, Michael Dupuis. This model includes cable improvements, Inertial Measurement Units (IMU), Light Detection and Ranging (LIDAR), and object-based state estimation to improve control stabilization. When completed, the hardware built for this project will provide undergraduates and researchers a platform with which they can test control algorithms and spacecraft component design. The results gathered from the project thus far is the building and design and controls experience between the team. After completion we will be able to obtain a properly modeled control algorithm and test it against multiple conditions. The final goal of the spacecraft is to provide the capabilities and perform experiments to test multiple methods to mitigate the effects of internal and external forces such as fuel sloshing, solar radiation, debris collision, and CG change

Factors affecting consistency and accuracy in identifying modern macroperforate planktonic foraminifera

Planktonic foraminifera are widely used in biostratigraphic, palaeoceanographic and evolutionary studies, but the strength of many study conclusions could be weakened if taxonomic identifications are not reproducible by different workers. In this study, to assess the relative importance of a range of possible reasons for among-worker disagreement in identification, 100 specimens of 26 species of macroperforate planktonic foraminifera were selected from a core-top site in the subtropical Pacific Ocean. Twenty-three scientists at different career stages – including some with only a few days experience of planktonic foraminifera – were asked to identify each specimen to species level, and to indicate their confidence in each identification. The participants were provided with a species list and had access to additional reference materials. We use generalised linear mixed-effects models to test the relevance of three sets of factors in identification accuracy: participant-level characteristics (including experience), species-level characteristics (including a participant’s knowledge of the species) and specimen-level characteristics (size, confidence in identification). The 19 less experienced scientists achieve a median accuracy of 57 %, which rises to 75 % for specimens they are confident in. For the 4 most experienced participants, overall accuracy is 79 %, rising to 93 % when they are confident. To obtain maximum comparability and ease of analysis, everyone used a standard microscope with only 35× magnification, and each specimen was studied in isolation. Consequently, these data provide a lower limit for an estimate of consistency. Importantly, participants could largely predict whether their identifications were correct or incorrect: their own assessments of specimen-level confidence and of their previous knowledge of species concepts were the strongest predictors of accuracy

Development of Preclinical Ultrasound Imaging Techniques to Identify and Image Sentinel Lymph Nodes in a Cancerous Animal Model

Lymph nodes (LNs) are believed to be the first organs targeted by colorectal cancer cells detached from a primary solid tumor because of their role in draining interstitial fluids. Better detection and assessment of these organs have the potential to help clinicians in stratification and designing optimal design of oncological treatments for each patient. Whilst highly valuable for the detection of primary tumors, CT and MRI remain limited for the characterization of LNs. B-mode ultrasound (US) and contrast-enhanced ultrasound (CEUS) can improve the detection of LNs and could provide critical complementary information to MRI and CT scans; however, the European Federation of Societies for Ultrasound in Medicine and Biology (EFSUMB) guidelines advise that further evidence is required before US or CEUS can be recommended for clinical use. Moreover, knowledge of the lymphatic system and LNs is relatively limited, especially in preclinical models. In this pilot study, we have created a mouse model of metastatic cancer and utilized 3D high-frequency ultrasound to assess the volume, shape, and absence of hilum, along with CEUS to assess the flow dynamics of tumor-free and tumor-bearing LNs in vivo. The aforementioned parameters were used to create a scoring system to predict the likelihood of a disease-involved LN before establishing post-mortem diagnosis with histopathology. Preliminary results suggest that a sum score of parameters may provide a more accurate diagnosis than the LN size, the single parameter currently used to predict the involvement of an LN in disease