Coccosphere geometry measurements from culture experiments on the coccolithophore species Calcidiscus leptoporus, Calcidiscus quadriperforatus and Helicosphaera carteri

Coccolithophores are a key phytoplankton group that exhibit remarkable diversity in their biology, ecology, and calcitic exoskeletons (coccospheres). An understanding of the physiological processes that underpin coccosphere architecture is essential for maximizing the information that can be retrieved from their extensive fossil record. Using culturing experiments on four modern species from three long-lived families, we investigate how coccosphere architecture responds to population shifts from rapid (exponential) to slowed (stationary) growth phases as nutrients become depleted. These experiments reveal statistical differences in cell size and the number of coccoliths per cell between these two growth phases, specifically that cells in exponential-phase growth are typically smaller with fewer coccoliths, whereas cells experiencing growth-limiting nutrient depletion have larger coccosphere sizes and greater numbers of coccoliths per cell. Although the exact numbers are species-specific, these growth-phase shifts in coccosphere geometry are common to four different coccolithophore families (Calcidiscaceae, Coccolithaceae, Isochrysidaceae, Helicosphaeraceae), demonstrating that this is a core physiological response to nutrient depletion across a representative diversity of this phytoplankton group. Polarised light microscopy was used for all coccosphere geometry measurements.

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

Exploring the joint compositional variability of major components and trace elements in the Tellus soil geochemistry survey (Northern Ireland)

The complexity of modern geochemical data sets is increasing in several aspects (number of available samples, number of elements measured, number of matrices analysed, geological-environmental variability covered, etc), hence it is becoming increasingly necessary to apply statistical methods to elucidate their structure. This paper presents an exploratory analysis of one such complex data set, the Tellus geochemical soil survey of Northern Ireland (NI). This exploratory analysis is based on one of the most fundamental exploratory tools, principal component analysis (PCA) and its graphical representation as a biplot, albeit in several variations: the set of elements included (only major oxides vs. all observed elements), the prior transformation applied to the data (none, a standardization or a logratio transformation) and the way the covariance matrix between components is estimated (classical estimation vs. robust estimation). Results show that a log-ratio PCA (robust or classical) of all available elements is the most powerful exploratory setting, providing the following insights: the first two processes controlling the whole geochemical variation in NI soils are peat coverage and a contrast between “mafic” and “felsic” background lithologies; peat covered areas are detected as outliers by a robust analysis, and can be then filtered out if required for further modelling; and peat coverage intensity can be quantified with the %Br in the subcomposition (Br, Rb, Ni).

Prior knowledge transfer across transcriptional data sets and technologies using compositional statistics yields new mislabelled ovarian cell line

Here, we describe gene expression compositional assignment (GECA), a powerful, yet simple method based on compositional statistics that can validate the transfer of prior knowledge, such as gene lists, into independent data sets, platforms and technologies. Transcriptional profiling has been used to derive gene lists that stratify patients into prognostic molecular subgroups and assess biomarker performance in the pre-clinical setting. Archived public data sets are an invaluable resource for subsequent in silico validation, though their use can lead to data integration issues. We show that GECA can be used without the need for normalising expression levels between data sets and can outperform rank-based correlation methods. To validate GECA, we demonstrate its success in the cross-platform transfer of gene lists in different domains including: bladder cancer staging, tumour site of origin and mislabelled cell lines. We also show its effectiveness in transferring an epithelial ovarian cancer prognostic gene signature across technologies, from a microarray to a next-generation sequencing setting. In a final case study, we predict the tumour site of origin and histopathology of epithelial ovarian cancer cell lines. In particular, we identify and validate the commonly-used cell line OVCAR-5 as non-ovarian, being gastrointestinal in origin. GECA is available as an open-source R package.

Mechanical properties and cellular response of novel electrospun nanofibers for ligament tissue engineering: Effects of orientation and geometry

Electrospun nanofibers are a promising material for ligamentous tissue engineering, however weak mechanical properties of fibers to date have limited their clinical usage. The goal of this work was to modify electrospun nanofibers to create a robust structure that mimics the complex hierarchy of native tendons and ligaments. The scaffolds that were fabricated in this study consisted of either random or aligned nanofibers in flat sheets or rolled nanofiber bundles that mimic the size scale of fascicle units in primarily tensile load bearing soft musculoskeletal tissues. Altering nanofiber orientation and geometry significantly affected mechanical properties; most notably aligned nanofiber sheets had the greatest modulus; 125% higher than that of random nanofiber sheets; and 45% higher than aligned nanofiber bundles. Modifying aligned nanofiber sheets to form aligned nanofiber bundles also resulted in approximately 107% higher yield stresses and 140% higher yield strains. The mechanical properties of aligned nanofiber bundles were in the range of the mechanical properties of the native ACL: modulus=158±32MPa, yield stress=57±23MPa and yield strain=0.38±0.08. Adipose derived stem cells cultured on all surfaces remained viable and proliferated extensively over a 7 day culture period and cells elongated on nanofiber bundles. The results of the study suggest that aligned nanofiber bundles may be useful for ligament and tendon tissue engineering based on their mechanical properties and ability to support cell adhesion, proliferation, and elongation.

Discovery of relict subglacial lakes and their geometry and mechanism of drainage

Recent proxy measurements reveal that subglacial lakes beneath modern ice sheets periodically store and release large volumes of water, providing an important but poorly understood influence on contemporary ice dynamics and mass balance. This is because direct observations of how lake drainage initiates and proceeds are lacking. Here we present physical evidence of the mechanism and geometry of lake drainage from the discovery of relict subglacial lakes formed during the last glaciation in Canada. These palaeo-subglacial lakes comprised shallow (<10 m) lenses of water perched behind ridges orientated transverse to ice flow. We show that lakes periodically drained through channels incised into bed substrate (canals). Canals sometimes trend into eskers that represent the depositional imprint of the last high-magnitude lake outburst. The subglacial lakes and channels are preserved on top of glacial lineations, indicating long-term re-organization of the subglacial drainage system and coupling to ice flow.

Some Inverse Problems in Analysis and Geometry

Thesis (Ph.D.)--University of Washington, 2016-08

Influence of the cutting edge micro-geometry of PCBN tools on the flank wear in orthogonal quenched and tempered turning M2 steel

Quenched and tempered high-speed steels obtained by powder metallurgy are commonly used in automotive components, such as valve seats of combustion engines. In order to machine these components, tools with high wear resistance and appropriate cutting edge geometry are required. This work aims to investigate the influence of the edge preparation of polycrystalline cubic boron nitride (PCBN) tools on the wear behavior in the orthogonal longitudinal turning of quenched and tempered M2 high-speed steels obtained by powder metallurgy. For this research, PCBN tools with high and low-CBN content have been used. Two different cutting edge geometries with a honed radius were tested: with a ground land (S shape) and without it (E shape). Also, the cutting speed was varied from 100 to 220 m/min. A rigid CNC lathe was used. The results showed that the high-CBN, E-shaped tool presented the longest life for a cutting speed of 100 m/min. High-CBN tools with a ground land and honed edge radius (S shaped) showed edge damage and lower values of the tool’s life. Low-CBN, S-shaped tools showed similar results, but with an inferior performance when compared with tools with high CBN content in both forms of edge preparation.

Optical properties of semiconductor quantum wires

This thesis presents theoretical investigations of the sub band structure and optical properties of semiconductor quantum wires. For the subband structure, we employ multiband effective-mass theory and the effective bond-orbital model both of which fully account for the band mixing and material anisotropy. We also treat the structure geometry in detail taking account of such effects as the compositional grading across material interfaces. Based on the subband structure, we calculate optical properties of quantum-wire structures. A recuring theme is the cross-over from one- to ~wo-dimensional behavior in these structures. This complicated behavior procludes the application of simple theoretical models to obtain the electronic structure. In particular, we calculate laser properties of quantum wires grown in V-grooves and find enhanced performance compared with quantum-well lasers. We also investigate optical anisotropy in quantum-wire arrays and propose an electro-optic device based on such structures.

Geometry and topography in James Joyce's Ulysses and Finnegans Wake

Following the development of non-Euclidean geometries from the mid-nineteenth century onwards, Euclid’s system had come to be re-conceived as a language for describing reality rather than a set of transcendental laws. As Henri Poincaré famously put it, ‘[i]f several geometries are possible, is it certain that our geometry [...] is true?’. By examining Joyce’s linguistic play and conceptual engagement with ground-breaking geometric constructs in Ulysses and Finnegans Wake, this thesis explores how his topographical writing of place encapsulates a common crisis between geometric and linguistic modes of representation within the context of modernity. More specifically, it investigates how Joyce presents Euclidean geometry and its topographical applications as languages, rather than ideally objective systems, for describing visual reality; and how, conversely, he employs language figuratively to emulate the systems by which the world is commonly visualised. With reference to his early readings of Giordano Bruno, Henri Poincaré and other critics of the Euclidean tradition, it investigates how Joyce’s obsession with measuring and mapping space throughout his works enters into his more developed reflections on the codification of visual signs in Finnegans Wake. In particular, this thesis sheds new light on Joyce’s developing fascination with the ‘geometry of language’ practised by Bruno, whose massive influence on Joyce is often assumed to exist in Joyce studies yet is rarely explored in any great detail.

Magnetoresistance in a High Mobility Two-Dimensional Electron System as a Function of Sample Geometry

In a high mobility two-dimensional electron gas (2DEG) realized in a GaAs/Al0.3Ga0.7As quantum well we observe changes in the Shubnikov-de Haas oscillations (SdHO) and in the Hall resistance for different sample geometries. We observe for each sample geometry a strong negative magnetoresistance around zero magnetic field which consists of a peak around zero magnetic field and of a huge magnetoresistance at larger fields. The peak around zero magnetic field is left unchanged for different geometries.

Introduction to geodesics in sub-Riemannian geometry

International audience

Problems in number theory and hyperbolic geometry

In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 (mod ℓ). We use this last result to answer a question of H.C. Chan. In the second part of this thesis [S2] we explore a natural analog of D. Calegari’s result that there are no hyperbolic once-punctured torus bundles over S^1 with trace field having a real place. We prove a contrasting theorem showing the existence of several infinite families of pairs (−χ, p) such that there exist hyperbolic surface bundles over S^1 with trace field of having a real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).

The Effect of Package Geometry on Moisture Driven Degradation of Polymer Aluminum Capacitors

Polymer aluminum electrolytic capacitors were introduced to provide an alternative to liquid electrolytic capacitors. Polymer electrolytic capacitor electric parameters of capacitance and ESR are less temperature dependent than those of liquid aluminum electrolytic capacitors. Furthermore, the electrical conductivity of the polymer used in these capacitors (poly-3,4ethylenedioxithiophene) is orders of magnitude higher than the electrolytes used in liquid aluminum electrolytic capacitors, resulting in capacitors with much lower equivalent series resistance which are suitable for use in high ripple-current applications. The presence of the moisture-sensitive polymer PEDOT introduces concerns on the reliability of polymer aluminum capacitors in high humidity conditions. Highly accelerated stress testing (or HAST) (110ºC, 85% relative humidity) of polymer aluminum capacitors in which the parts were subjected to unbiased HAST conditions for 700 hours was done to understand the design factors that contribute to the susceptibility to degradation of a polymer aluminum electrolytic capacitor exposed to HAST conditions. A large scale study involving capacitors of different electrical ratings (2.5V – 16V, 100µF – 470 µF), mounting types (surface-mount and through-hole) and manufacturers (6 different manufacturers) was done to determine a relationship between package geometry and reliability in high temperature-humidity conditions. A Geometry-Based HAST test in which the part selection limited variations between capacitor samples to geometric differences only was done to analyze the effect of package geometry on humidity-driven degradation more closely. Raman spectroscopy, x-ray imaging, environmental scanning electron microscopy, and destructive analysis of the capacitors after HAST exposure was done to determine the failure mechanisms of polymer aluminum capacitors under high temperature-humidity conditions.

Surface acoustic wave streaming in a PDMS microfluidic system: effect of frequency and fluid geometry & A remote ultrasonic glucose sensor

This thesis describes two separate projects. The first is a theoretical and experimental investigation of surface acoustic wave streaming in microfluidics. The second is the development of a novel acoustic glucose sensor. A separate abstract is given for each here. Optimization of acoustic streaming in microfluidic channels by SAWs Surface Acoustic Waves, (SAWs) actuated on flat piezoelectric substrates constitute a convenient and versatile tool for microfluidic manipulation due to the easy and versatile interfacing with microfluidic droplets and channels. The acoustic streaming effect can be exploited to drive fast streaming and pumping of fluids in microchannels and droplets (Shilton et al. 2014; Schmid et al. 2011), as well as size dependant sorting of particles in centrifugal flows and vortices (Franke et al. 2009; Rogers et al. 2010). Although the theory describing acoustic streaming by SAWs is well understood, very little attention has been paid to the optimisation of SAW streaming by the correct selection of frequency. In this thesis a finite element simulation of the fluid streaming in a microfluidic chamber due to a SAW beam was constructed and verified against micro-PIV measurements of the fluid flow in a fabricated device. It was found that there is an optimum frequency that generates the fastest streaming dependent on the height and width of the chamber. It is hoped this will serve as a design tool for those who want to optimally match SAW frequency with a particular microfluidic design. An acoustic glucose sensor Diabetes mellitus is a disease characterised by an inability to properly regulate blood glucose levels. In order to keep glucose levels under control some diabetics require regular injections of insulin. Continuous monitoring of glucose has been demonstrated to improve the management of diabetes (Zick et al. 2007; Heinemann & DeVries 2014), however there is a low patient uptake of continuous glucose monitoring systems due to the invasive nature of the current technology (Ramchandani et al. 2011). In this thesis a novel way of monitoring glucose levels is proposed which would use ultrasonic waves to ‘read’ a subcutaneous glucose sensitive-implant, which is only minimally invasive. The implant is an acoustic analogy of a Bragg stack with a ‘defect’ layer that acts as the sensing layer. A numerical study was performed on how the physical changes in the sensing layer can be deduced by monitoring the reflection amplitude spectrum of ultrasonic waves reflected from the implant. Coupled modes between the skin and the sensing layer were found to be a potential source of error and drift in the measurement. It was found that by increasing the number of layers in the stack that this could be minimized. A laboratory proof of concept system was developed using a glucose sensitive hydrogel as the sensing layer. It was possible to monitor the changing thickness and speed of sound of the hydrogel due to physiological relevant changes in glucose concentration.