Fixed Point vs. First-Order Logic on Finite Ordered Structures with Unary Relations

We prove that first order logic is strictly weaker than fixed point logic over every infinite classes of finite ordered structures with unary relations: Over these classes there is always an inductive unary relation which cannot be defined by a first-order formula, even when every inductive sentence (i.e., closed formula) can be expressed in first-order over this particular class. Our proof first establishes a property valid for every unary relation definable by first-order logic over these classes which is peculiar to classes of ordered structures with unary relations. In a second step we show that this property itself can be expressed in fixed point logic and can be used to construct a non-elementary unary relation.

A Characterization of First-Order Definable Subsets on Classes of Finite Total Orders

We give an explicit and easy-to-verify characterization for subsets in finite total orders (infinitely many of them in general) to be uniformly definable by a first-order formula. From this characterization we derive immediately that Beth's definability theorem does not hold in any class of finite total orders, as well as that McColm's first conjecture is true for all classes of finite total orders. Another consequence is a natural 0-1 law for definable subsets on finite total orders expressed as a statement about the possible densities of first-order definable subsets.

Generating Representative ISP Technologies From First-Principles

Understanding and modeling the factors that underlie the growth and evolution of network topologies are basic questions that impact capacity planning, forecasting, and protocol research. Early topology generation work focused on generating network-wide connectivity maps, either at the AS-level or the router-level, typically with an eye towards reproducing abstract properties of observed topologies. But recently, advocates of an alternative "first-principles" approach question the feasibility of realizing representative topologies with simple generative models that do not explicitly incorporate real-world constraints, such as the relative costs of router configurations, into the model. Our work synthesizes these two lines by designing a topology generation mechanism that incorporates first-principles constraints. Our goal is more modest than that of constructing an Internet-wide topology: we aim to generate representative topologies for single ISPs. However, our methods also go well beyond previous work, as we annotate these topologies with representative capacity and latency information. Taking only demand for network services over a given region as input, we propose a natural cost model for building and interconnecting PoPs and formulate the resulting optimization problem faced by an ISP. We devise hill-climbing heuristics for this problem and demonstrate that the solutions we obtain are quantitatively similar to those in measured router-level ISP topologies, with respect to both topological properties and fault-tolerance.

Statistical properties of first-order bang-bang Pll with nonzero loop delay

A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state How diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for some cases. After obtaining the state probability, statistical characteristics such as mean gain of the binary phase detector and timing error variance are calculated and demonstrated.

Investigation of numerical atomic orbitals for first-principles calculations of the electronic and transport properties of silicon nanowire structures

This thesis is focused on the application of numerical atomic basis sets in studies of the structural, electronic and transport properties of silicon nanowire structures from first-principles within the framework of Density Functional Theory. First we critically examine the applied methodology and then offer predictions regarding the transport properties and realisation of silicon nanowire devices. The performance of numerical atomic orbitals is benchmarked against calculations performed with plane waves basis sets. After establishing the convergence of total energy and electronic structure calculations with increasing basis size we have shown that their quality greatly improves with the optimisation of the contraction for a fixed basis size. The double zeta polarised basis offers a reasonable approximation to study structural and electronic properties and transferability exists between various nanowire structures. This is most important to reduce the computational cost. The impact of basis sets on transport properties in silicon nanowires with oxygen and dopant impurities have also been studied. It is found that whilst transmission features quantitatively converge with increasing contraction there is a weaker dependence on basis set for the mean free path; the double zeta polarised basis offers a good compromise whereas the single zeta basis set yields qualitatively reasonable results. Studying the transport properties of nanowire-based transistor setups with p+-n-p+ and p+-i-p+ doping profiles it is shown that charge self-consistency affects the I-V characteristics more significantly than the basis set choice. It is predicted that such ultrascaled (3 nm length) transistors would show degraded performance due to relatively high source-drain tunnelling currents. Finally, it is shown the hole mobility of Si nanowires nominally doped with boron decreases monotonically with decreasing width at fixed doping density and increasing dopant concentration. Significant mobility variations are identified which can explain experimental observations.

First principles modelling of nucleation and growth during atomic layer deposition onto III-V substrates

Atomic layer deposition (ALD) is now used in semiconductor fabrication lines to deposit nanometre-thin oxide films, and has thus enabled the introduction of high-permittivity dielectrics into the CMOS gate stack. With interest increasing in transistors based on high mobility substrates, such as GaAs, we are investigating the surface treatments that may improve the interface characteristics. We focus on incubation periods of ALD processes on III-V substrates. We have applied first principles Density Functional Theory (DFT) to investigate detailed chemistry of these early stages of growth, specifically substrate and ALD precursor interaction. We have modelled the ‘clean-up’ effect by which organometallic precursors: trimethylaluminium (TMA) or hafnium and titanium amides clean arsenic oxides off the GaAs surface before ALD growth of dielectric commences and similar effect on Si3N4 substrate. Our simulations show that ‘clean-up’ of an oxide film strongly depends on precursor ligand, its affinity to the oxide and the redox character of the oxide. The predominant pathway for a metalloid oxide such as arsenic oxide is reduction, producing volatile molecules or gettering oxygen from less reducible oxides. An alternative pathway is non-redox ligand exchange, which allows non-reducible oxides (e.g. SiO2) to be cleaned-up. First principles study shows also that alkylamides are more susceptible to decomposition rather than migration on the oxide surface. This improved understanding of the chemical principles underlying ‘clean-up’ allows us to rationalize and predict which precursors will perform the reaction. The comparison is made between selection of metal chlorides, methyls and alkylamides precursors.

First principles simulation of amorphous silicon bulk, interfaces, and nanowires for photovoltaics

Amorphous silicon has become the material of choice for many technologies, with major applications in large area electronics: displays, image sensing and thin film photovoltaic cells. This technology development has occurred because amorphous silicon is a thin film semiconductor that can be deposited on large, low cost substrates using low temperature. In this thesis, classical molecular dynamics and first principles DFT calculations have been performed to generate structural models of amorphous and hydrogenated amorphous silicon and interfaces of amorphous and crystalline silicon, with the ultimate aim of understanding the photovoltaic properties of core-shell crystalline amorphous Si nanowire structures. We have shown, unexpectedly, from the simulations, that our understanding of hydrogenated bulk a-Si needs to be revisited, with our robust finding that when fully saturated with hydrogen, bulk a-Si exhibits a constant optical energy gap, irrespective of the hydrogen concentration in the sample. Unsaturated a-Si:H, with a lower than optimum hydrogen content, shows a smaller optical gap, that increases with hydrogen content until saturation is reached. The mobility gaps obtained from an analysis of the electronic states show similar behavior. We also obtained that the optical and mobility gaps show a volcano curve as the H content is varied from 7% (undersaturation) to 18% (mild oversaturation). In the case of mild over saturation, the mid-gap states arise exclusively from an increase in the density of strained Si-Si bonds. Analysis of our structures shows the extra H atoms in this case form a bridge between neighboring silicon atoms which increases the corresponding Si-Si distance and promotes bond length disorder in the sample. That has the potential to enhance the Staebler-Wronski effect. Planar interface models of amorphous-crystalline silicon have been generated in Si (100), (110) and (111) surfaces. The interface models are characterized by structure, RDF, electronic density of states and optical absorption spectrum. We find that the least stable (100) surface will result in the formation of the thickest amorphous silicon layer, while the most stable (110) surface forms the smallest amorphous region. We calculated for the first time band offsets of a-Si:H/c-Si heterojunctions from first principles and examined the influence of different surface orientations and amorphous layer thickness on the offsets and implications for device performance. The band offsets depend on the amorphous layer thickness and increase with thickness. By controlling the amorphous layer thickness we can potentially optimise the solar cell parameters. Finally, we have successfully generated different amorphous layer thickness of the a-Si/c-Si and a-Si:H/c-Si 5 nm nanowires from heat and quench. We perform structural analysis of the a-Si-/c-Si nanowires. The RDF, Si-Si bond length distributions, and the coordination number distributions of amorphous regions of the nanowires reproduce similar behaviour compared to bulk amorphous silicon. In the final part of this thesis we examine different surface terminating chemical groups, -H, - OH and –NH2 in (001) GeNW. Our work shows that the diameter of Ge nanowires and the nature of surface terminating groups both play a significant role in both the magnitude and the nature of the nanowire band gaps, allowing tuning of the band gap by up to 1.1 eV. We also show for the first time how the nanowire diameter and surface termination shifts the absorption edge in the Ge nanowires to longer wavelengths. Thus, the combination of nanowire diameter and surface chemistry can be effectively utilised to tune the band gaps and thus light absorption properties of small diameter Ge nanowires.

Precursor adsorption on copper surfaces as the first step during the deposition of copper: a density functional study with van der Waals correction

Copper dimethylamino-2-propoxide [Cu(dmap)2] is used as a precursor for low-temperature atomic layer deposition (ALD) of copper thin films. Chemisorption of the precursor is the necessary first step of ALD, but it is not known in this case whether there is selectivity for adsorption sites, defects, or islands on the substrate. Therefore, we study the adsorption of the Cu(dmap)2 molecule on the different sites on flat and rough Cu surfaces using PBE, PBE-D3, optB88-vdW, and vdW-DF2 methods. We found the relative order of adsorption energies for Cu(dmap)2 on Cu surfaces is Eads (PBE-D3) > Eads (optB88-vdW) > Eads (vdW-DF2) > Eads (PBE). The PBE and vdW-DF2 methods predict one chemisorption structure, while optB88-vdW predicts three chemisorption structures for Cu(dmap)2 adsorption among four possible adsorption configurations, whereas PBE-D3 predicts a chemisorbed structure for all the adsorption sites on Cu(111). All the methods with and without van der Waals corrections yield a chemisorbed molecule on the Cu(332) step and Cu(643) kink because of less steric hindrance on the vicinal surfaces. Strong distortion of the molecule and significant elongation of Cu–N bonds are predicted in the chemisorbed structures, indicating that the ligand–Cu bonds break during the ALD of Cu from Cu(dmap)2. The molecule loses its initial square-planar structure and gains linear O–Cu–O bonding as these atoms attach to the surface. As a result, the ligands become unstable and the precursor becomes more reactive to the coreagent. Charge redistribution mainly occurs between the adsorbate O–Cu–O bond and the surface. Bader charge analysis shows that electrons are donated from the surface to the molecule in the chemisorbed structures, so that the Cu center in the molecule is partially reduced.

A microscopic study of structural and electronic properties of functionalized silicon surfaces based on first-principles

Surface modification of silicon with organic monolayers tethered to the surface by different linkers is an important process in realizing future (opto-)electronic devices. Understanding the role played by the nature of the linking group and the chain length on the adsorption structures and electronic properties of these assemblies is vital to advance this technology. This Thesis is a study of such properties and contributes in particular to a microscopic understanding of induced changes in the work function of experimentally studied functionalized silicon surfaces. Using first-principles density functional theory (DFT), at the first step, we provide predictions for chemical trends in the work function of hydrogenated silicon (111) surfaces modified with various terminations. For nonpolar terminating atomic species such as F, Cl, Br, and I, the change in the work function is directly proportional to the amount of charge transferred from the surface, thus relating to the difference in electronegativity of the adsorbate and silicon atoms. The change is a monotonic function of coverage in this case, and the work function increases with increasing electronegativity. Polar species such as −TeH, −SeH, −SH, −OH, −NH2, −CH3, and −BH2 do not follow this trend due to the interaction of their dipole with the induced electric field at the surface. In this case, the magnitude and sign of the surface dipole moment need to be considered in addition to the bond dipole to generally describe the change in work function. Compared to hydrogenated surfaces, there is slight increase in the work function of H:Si(111)-XH, where X = Te, Se, and S, whereas reduction is observed for surfaces covered with −OH, −CH3, and −NH2. Next, we study the hydrogen passivated Si(111) surface modified with alkyl chains of the general formula H:Si–(CH2)n–CH2 and H:Si–X–(CH2)n–CH3, where X = NH, O, S and n = (0, 1, 3, 5, 7, 9, 11), at half coverage. For (X)–Hexyl and (X)–Dodecyl functionalization, we also examined various coverages up to full monolayer grafting in order to validate the result of half covered surface and the linker effect on the coverage. We find that it is necessary to take into account the van der Waals interaction between the alkyl chains. The strongest binding is for the oxygen linker, followed by S, N, and C, irrespective of chain length. The result revealed that the sequence of the stability is independent of coverage; however, linkers other than carbon can shift the optimum coverage considerably and allow further packing density. For all linkers apart from sulfur, structural properties, in particular, surface-linker-chain angles, saturate to a single value once n > 3. For sulfur, we identify three regimes, namely, n = 0–3, n = 5–7, and n = 9–11, each with its own characteristic adsorption structures. Where possible, our computational results are shown to be consistent with the available experimental data and show how the fundamental structural properties of modified Si surfaces can be controlled by the choice of linking group and chain length. Later we continue by examining the work function tuning of H:Si(111) over a range of 1.73 eV through adsorption of alkyl monolayers with general formula -[Xhead-group]-(CnH2n)-[Xtail-group], X = O(H), S(H), NH(2). The work function is practically converged at 4 carbons (8 for oxygen), for head-group functionalization. For tail-group functionalization and with both head- and tail-groups, there is an odd-even effect in the behavior of the work function, with peak-to-peak amplitudes of up to 1.7 eV in the oscillations. This behavior is explained through the orientation of the terminal-group's dipole. The shift in the work function is largest for NH2-linked and smallest for SH-linked chains and is rationalized in terms of interface dipoles. Our study reveals that the choice of the head- and/or tail-groups effectively changes the impact of the alkyl chain length on the work function tuning using self-assembled monolayers and this is an important advance in utilizing hybrid functionalized Si surfaces. Bringing together the understanding gained from studying single type functionalization of H:Si(111) with different alkyl chains and bearing in mind how to utilize head-group, tail-group or both as well as monolayer coverage, in the final part of this Thesis we study functionalized H:Si(111) with binary SAMs. Aiming at enhancing work function adjustment together with SAM stability and coverage we choose a range of terminations and linker-chains denoted as –X–(Alkyl) with X = CH3, O(H), S(H), NH(2) and investigate the stability and work function of various binary components grafted onto H:Si(111) surface. Using binary functionalization with -[NH(2)/O(H)/S(H)]-[Hexyl/Dodecyl] we show that work function can be tuned within the interval of 3.65-4.94 eV and furthermore, enhance the SAM’s stability. Although direct Si-C grafted SAMs are less favourable compared to their counterparts with O, N or S linkage, regardless of the ratio, binary functionalized alkyl monolayers with X-alkyl (X = NH, O) is always more stable than single type alkyl functionalization with the same coverage. Our results indicate that it is possible to go beyond the optimum coverage of pure alkyl functionalized SAMs (50%) by adding a linker with the correct choice of the linker. This is very important since dense packed monolayers have fewer defects and deliver higher efficiency. Our results indicate that binary anchoring can modify the charge injection and therefore bond stability while preserving the interface electronic structure.

The impact of first pregnancy and delivery on pelvic floor dysfunction

Background: The first childbirth has the greatest impact on a woman’s pelvic floor when major changes occur. The aim of this study was to comprehensively describe pelvic floor dysfunction (PFD) in young nulliparous women, and its correlation with postnatal pathology. Methods: A prospective study was performed at Cork University Maternity Hospital, Ireland. Initially 1484 nulliparous women completed the validated Australian Pelvic Floor Questionnaire at 15 weeks’ gestation and repeatedly at one year postnatally (N=872). In the second phase, at least one year postnatally, 202 participants without subsequent pregnancies attended the clinical follow up which included: pelvic organ prolapse quantification, a 3D-Transperineal ultrasound scan and collagen level assessment. Results: A high pre-pregnancy prevalence of various types of PFD was detected, which in the majority of cases persisted postnatally and included multiple types of PFD. The first birth had a negative impact on severity of pre-pregnancy symptoms in <15% of cases. Apart from prolapse, vaginal delivery, including instrumental delivery did not increase the risk of PFD symptoms, where as Caesarean section was protective for all types of PFD. The first birth had a bigger impact on pre-existing symptoms of overactive bladder compared to stress urinary incontinence. Pelvic organ prolapse is extremely prevalent in young primiparous women, however usually it is low grade and asymptomatic. Congenital factors and high collagen type III levels play an important role in the aetiology of pelvic organs prolapse. Levator ani trauma is present in one in three women after the first pregnancy and delivery. Conclusion: The main damage to the pelvic floor most likely occurs due to an undiagnosed congenital intrinsic weakness of the pelvic floor structures. PFD is highly associated with first childbirth, however it seems that pregnancy and delivery are contributing factors only which unmask the congenital intrinsic weakness of the pelvic floor support.

At the Vanguard of Design Science: First Impressions and Early Findings from Ongoing Research

Published Version

The ‘Celtic’ dimension of pre-first World War religious discourse in Britain: Wellesley Tudor Pole and the Glastonbury phenomenon

This article will explore the contribution made to the construction of discourse around religion outside of mainstream Christianity, at the turn of the twentieth century in Britain, by a Celticist movement as represented by Wellesley Tudor Pole (d.1968) and his connection to the Glastonbury phenomenon. I will detail the interconnectedness of individuals and movements occupying this discursive space and their interest in efforts to verify the authenticity of an artefact which Tudor Pole claimed was once in the possession of Jesus. Engagement with Tudor Pole’s quest to prove the provenance of the artefact, and his contention that a pre-Christian culture had existed in Ireland which had extended itself to Glastonbury and Iona creating the foundation for an authentic Western mystical tradition, is presented as one facet of a broader, contemporary discourse on alternative ideas and philosophies. In conclusion, I will juxtapose Tudor Pole’s fascination with Celtic origins and the approach of leading figures in the ‘Celtic Revival’ in Ireland, suggesting intersections and alterity in the construction of their worldview. The paper forms part of a chapter in a thesis under-preparation which examines the construction of discourse on religion outside of mainstream Christianity at the turn of the twentieth century, and in particular the role played by visiting religious reformers from Asia. The aim is to recover the (mostly forgotten) history of these engagements.

Paclitaxel versus doxorubicin as first-line single-agent chemotherapy for metastatic breast cancer: a European Organization for Research and Treatment of Cancer Randomized Study with cross-over.

PURPOSE: To compare the efficacy of paclitaxel versus doxorubicin given as single agents in first-line therapy of advanced breast cancer (primary end point, progression-free survival ¿PFS) and to explore the degree of cross-resistance between the two agents. PATIENTS AND METHODS: Three hundred thirty-one patients were randomized to receive either paclitaxel 200 mg/m(2), 3-hour infusion every 3 weeks, or doxorubicin 75 mg/m(2), intravenous bolus every 3 weeks. Seven courses were planned unless progression or unacceptable toxicity occurred before the seven courses were finished. Patients who progressed within the seven courses underwent early cross-over to the alternative drug, while a delayed cross-over was optional for the remainder of patients at the time of disease progression. RESULTS: Objective response in first-line therapy was significantly better (P =.003) for doxorubicin (response rate ¿RR, 41%) than for paclitaxel (RR, 25%), with doxorubicin achieving a longer median PFS (7.5 months for doxorubicin v 3.9 months for paclitaxel, P <.001). In second-line therapy, cross-over to doxorubicin (91 patients) and to paclitaxel (77 patients) gave response rates of 30% and 16%, respectively. The median survival durations of 18.3 months for doxorubicin and 15.6 months for paclitaxel were not significantly different (P =.38). The doxorubicin arm had greater toxicity, but this was counterbalanced by better symptom control. CONCLUSION: At the dosages and schedules used in the present study, doxorubicin achieves better disease and symptom control than paclitaxel in first-line treatment. Doxorubicin and paclitaxel are not totally cross-resistant, which supports further investigation of these drugs in combination or in sequence, both in advanced disease and in the adjuvant setting.

Randomized, controlled trial investigating short-term health-related quality of life with doxorubicin and paclitaxel versus doxorubicin and cyclophosphamide as first-line chemotherapy in patients with metastatic breast cancer: European Organization for Research and Treatment of Cancer Breast Cancer Group, Investigational Drug Branch for Breast Cancer and the New Drug Development Group Study.

PURPOSE: To compare health-related quality of life (HRQOL) in patients with metastatic breast cancer receiving the combination of doxorubicin and paclitaxel (AT) or doxorubicin and cyclophosphamide (AC) as first-line chemotherapy treatment. PATIENTS AND METHODS: Eligible patients (n = 275) with anthracycline-naive measurable metastatic breast cancer were randomly assigned to AT (doxorubicin 60 mg/m(2) as an intravenous bolus plus paclitaxel 175 mg/m(2) as a 3-hour infusion) or AC (doxorubicin 60 mg/m(2) plus cyclophosphamide 600 mg/m(2)) every 3 weeks for a maximum of six cycles. Dose escalation of paclitaxel (200 mg/m(2)) and cyclophosphamide (750 mg/m(2)) was planned at cycle 2 to reach equivalent myelosuppression in the two groups. HRQOL was assessed with the European Organization for Research and Treatment of Cancer (EORTC) Quality of Life Questionnaire C30 and the EORTC Breast Module at baseline and the start of cycles 2, 4, and 6, and 3 months after the last cycle. RESULTS: Seventy-nine percent of the patients (n = 219) completed a baseline measure. However, there were no statistically significant differences in HRQOL between the two treatment groups. In both groups, selected aspects of HRQOL were impaired over time, with increased fatigue, although some clinically significant improvements in emotional functioning were seen, as well as a reduction in pain over time. Overall, global quality of life was maintained in both treatment groups. CONCLUSION: This information is important when advising women patients of the expected HRQOL consequences of treatment regimens and should help clinicians and their patients make informed treatment decisions.

Mature results of a randomized phase II multicenter study of exemestane versus tamoxifen as first-line hormone therapy for postmenopausal women with metastatic breast cancer.

BACKGROUND: Women with hormone-responsive metastatic breast cancer (MBC) may respond to or have stable disease with a number of hormone therapies. We explored the efficacy and safety of the steroidal aromatase inactivator exemestane as first-line hormonal therapy in MBC in postmenopausal women. PATIENTS AND METHODS: Patients with measurable disease were eligible if they had received no prior hormone therapy for metastatic disease and had hormone receptor positive disease or hormone receptor unknown disease with a long disease-free interval from adjuvant therapy. They were randomized to tamoxifen 20 mg/day or exemestane 25 mg/day in this open-label study. RESULTS: Blinded independently reviewed response rates for exemestane and tamoxifen were 41% and 17%, respectively. Fifty-seven per cent of exemestane- and 42% of tamoxifen-treated patients experienced clinical benefit, defined as complete or partial response, or disease stabilization lasting at least 6 months. There was a low incidence of severe flushing, sweating, nausea and edema in women who received exemestane. One exemestane-treated patient had a pulmonary embolism with grade 4 dyspnea. CONCLUSIONS: Exemestane is well tolerated and active in the first-line treatment of hormone-responsive MBC. An ongoing EORTC phase III trial is comparing the efficacy, measuring time-to-disease progression, of exemestane and tamoxifen.