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This thesis is dedicated to analysing the general structure of two- and three-point correlation functions of conserved currents of arbitrary integer or half-integer spins in three- and four-dimensional (super)conformal field theory., Comment: PhD Thesis, 207 pages. Based on arXiv:2102.04827, arXiv:2108.01865, arXiv:2204.04899, arXiv:2210.13135, arXiv:2302.00593, arXiv:2305.02233 and arXiv:2307.11435

We analyse the general structure of the three-point functions involving conserved higher-spin ``vector-like" supercurrents $J_{s}(z) := J_{\alpha(s) \dot{\alpha}(s)}(z)$ in four-dimensional $\mathcal{N}=1$ superconformal field theory. Using the constraints of superconformal symmetry and superfield conservation equations, we utilise a computational approach to analyse the general structure of the three-point function $\langle J^{}_{s_{1}}(z_{1}) \, J'_{s_{2}}(z_{2}) \, J''_{s_{3}}(z_{3}) \rangle$ and provide a general classification of the results. We demonstrate that the three-point function is fixed up to $2 \min (s_{i}) + 2$ independent conserved structures, which we propose to hold for arbitrary superspins. In addition, we show that the conserved structures can be classified as parity-even or parity-odd in superspace based on their transformation properties under superinversion., Comment: 65 pages; v2: moved some content to Appendix A, accepted for publication in Physical Review D

Self-centred regular graphs which are Ollivier-Ricci Bonnet-Myers sharp have been completely classified. When the conditions of self-centeredness and regularity are removed it is an open problem on what the classification is. We present a complete classification of Bonnet-Myers sharp graphs with a diameter 2 and show that there exists Bonnet-Myers sharp graphs of diameter 3, 4 and 6 that belong to a family of graphs called symmetrical antitees.

We analyse the general structure of the three-point functions involving conserved higher-spin currents $J_{s} := J_{\alpha(i) \dot{\alpha}(j)}$ belonging to any Lorentz representation in four-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we computationally analyse the general structure of three-point functions $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$ for arbitrary spins and propose a classification of the results. For bosonic vector-like currents with $i=j$, it is known that the number of independent conserved structures is $2 \min (s_{i}) + 1$. For the three-point functions of conserved currents with arbitrarily many dotted and undotted indices, we show that in many cases the number of structures deviates from $2 \min (s_{i}) + 1$., Comment: 40 pages. arXiv admin note: text overlap with arXiv:2210.13135

We consider the analytic construction of three-point functions of conserved higher-spin supercurrents in three-dimensional $\mathcal{N}=1$ superconformal field theory which are Grassmann-odd in superspace. In particular, these include the three-point functions of the supercurrent and flavour currents, which contain the three-point functions of the energy-momentum tensor and conserved vector currents at the component level. We present an analytic proof for arbitrary superspins that these correlators do not possess a parity-violating contribution. We also prove that the parity-even contribution is unique, and exists (under an assumption that is well supported by the computational approach of arXiv:2302.00593) for arbitrary superspins. The construction of the parity-even sector is shown to reduce to solving a system of linear homogeneous equations with a tri-diagonal matrix of co-rank one, which we solve explicitly for arbitrary superspins., Comment: 33 pages

We analyse the general structure of the three-point functions of conserved higher-spin supercurrents in 3D, $\mathcal{N}=1$ superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation functions of conserved higher-spin currents. We develop a manifestly supersymmetric formalism to compute the three-point function $\langle \mathbf{J}^{}_{s_{1}} \mathbf{J}'_{s_{2}} \mathbf{J}''_{s_{3}} \rangle$, where $\mathbf{J}^{}_{s_{1}}$, $\mathbf{J}'_{s_{2}}$ and $\mathbf{J}''_{s_{3}}$ are conserved higher-spin supercurrents with superspins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). Using a computational approach limited only by computer power, we analytically impose the constraints arising from the superfield conservation equations and symmetries under permutations of superspace points. Explicit solutions for three-point functions are presented and we provide a complete classification of the results for $s_{i} \leq 20 $; the pattern is very clear, and we propose that our classification holds for arbitrary superspins. We demonstrate that Grassmann-even three-point functions are fixed up to one parity-even structure and one parity-odd structure, while Grassmann-odd three-point functions are fixed up to a single parity-even structure. The existence of the parity-odd structure in the Grassmann-even correlation functions is subject to a set of triangle inequalities in the superspins. For completeness, we also analyse the structure of three-point functions involving conserved higher-spin supercurrents and scalar superfields., Comment: 54 pages; v2: minor corrections, references added. arXiv admin note: substantial text overlap with arXiv:2210.13135

We analyse the general structure of the three-point functions involving conserved bosonic and fermionic higher-spin currents in three-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we use a computational formalism to analyse the general structure of $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$, where $J^{}_{s_{1}}$, $J'_{s_{2}}$ and $J''_{s_{3}}$ are conserved currents with spins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). The calculations are completely automated for any chosen spins and are limited only by computer power. We find that the correlation function is in general fixed up to two independent even structures, and one odd structure, subject to a set of triangle inequalities. We also analyse the structure of three-point functions involving higher-spin currents and fundamental scalars and spinors., Comment: 56 pages; v2: minor edits, references added

We present the discovery of a giant tidal tail of stars associated with F8D1, the closest known example of an ultra-diffuse galaxy (UDG). F8D1 sits in a region of the sky heavily contaminated by Galactic cirrus and has been poorly studied since its discovery two decades ago. The tidal feature was revealed in a deep map of resolved red giant branch stars constructed using data from our Subaru Hyper Suprime-Cam survey of the M81 Group. It has an average surface brightness of $\mu_g \sim 32$ mag arcsec$^{-2}$ and can be traced for over a degree on the sky (60 kpc at the distance of F8D1) with our current imagery. We revisit the main body properties of F8D1 using deep multiband imagery acquired with MegaCam on CFHT and measure effective radii of $1.7-1.9$ kpc, central surface brightnesses of $24.7-25.7$ mag and a stellar mass of $\sim7 \times 10^7 M_{\odot}$. Assuming a symmetric feature on the other side of the galaxy, we calculate that $30-36$% of F8D1's present-day luminosity is contained in the tail. We argue that the most likely origin of F8D1's disruption is a recent close passage to M81, which would have stripped its gas and quenched its star formation. As the only UDG that has so far been studied to such faint surface brightness depths, the unveiling of F8D1's tidal disruption is important. It leaves open the possibility that many other UDGs could be the result of similar processes, with the most telling signatures of this lurking below current detection limits., Comment: Accepted for publication in MNRAS. 16 pages, 12 figures, 3 tables

A novel y-y'-y" dual-superlattice superalloy, with promising mechanical properties up to elevated temperatures was recently reported. The present work employs state of the art chemical and spatial characterization techniques to study the effect systematic additions of Mo, W and Fe and variations in Nb and Al contents have on the phase fraction, thermal stability, elemental partitioning and mechanical properties. Alloys were produced through arc melting followed by heat treatment. Multi-scale characterization techniques and hardness testing were employed to characterize their microstructure, thermal stability and mechanical properties. Alterations in such properties or in elemental partitioning behaviour were then explained through thermodynamic modelling. A modest addition of 1.8 at.% Mo had a strong effect on the microstructure and thermal stability: it minimized microstructural coarsening during heat treatments while not significantly decreasing the y' solvus temperature. A reduction of Nb by 0.6 at.%, strongly reduced the y" volume fraction, without affecting the y' volume fraction. The reduced precipitate fraction led to a significant reduction in alloy hardness. Fe, added to achieve better processability and reduced material cost, decreased the y' solvus temperature and caused rapid microstructural coarsening during heat treatments, without affecting alloy hardness. A reduction of Al by 0.4 at.%, reduced the y' volume fraction and the y' solvus temperature, also without affecting alloy hardness. The addition of 0.9 at.% W decreased the y' solvus temperature but increased both precipitate volume fractions. These data will be invaluable to optimize current alloy design and to inform future alloy design efforts.

We investigate the properties of a four-dimensional conformal field theory possessing a fermionic higher-spin current $Q_{\alpha(2k) \dot{\alpha}}$. Using a computational approach, we examine the number of independent tensor structures contained in the three-point correlation functions of two fermionic higher-spin currents with the conserved vector current $V_{m}$, and with the energy-momentum tensor $T_{m n}$. In particular, the $k = 1$ case corresponds to a "supersymmetry-like" current, that is, a fermionic conserved current with identical properties to the supersymmetry current which appears in $\mathcal{N} = 1$ superconformal field theories. However, we show that in general, the three-point correlation functions $\langle Q Q T\rangle $, $\langle \bar{Q} Q V\rangle $ and $\langle \bar{Q} Q T\rangle $ are not consistent with $\mathcal{N}=1$ supersymmetry, Comment: 44 pages; v2: minor corrections

Streamlined qBOLD acquisitions enable experimentally straightforward observations of brain oxygen metabolism. $R_2^\prime$ maps are easily inferred; however, the Oxygen extraction fraction (OEF) and deoxygenated blood volume (DBV) are more ambiguously determined from the data. As such, existing inference methods tend to yield very noisy and underestimated OEF maps, while overestimating DBV. This work describes a novel probabilistic machine learning approach that can infer plausible distributions of OEF and DBV. Initially, we create a model that produces informative voxelwise prior distribution based on synthetic training data. Contrary to prior work, we model the joint distribution of OEF and DBV through a scaled multivariate logit-Normal distribution, which enables the values to be constrained within a plausible range. The prior distribution model is used to train an efficient amortized variational Bayesian inference model. This model learns to infer OEF and DBV by predicting real image data, with few training data required, using the signal equations as a forward model. We demonstrate that our approach enables the inference of smooth OEF and DBV maps, with a physiologically plausible distribution that can be adapted through specification of an informative prior distribution. Other benefits include model comparison (via the evidence lower bound) and uncertainty quantification for identifying image artefacts. Results are demonstrated on a small study comparing subjects undergoing hyperventilation and at rest. We illustrate that the proposed approach allows measurement of gray matter differences in OEF and DBV and enables voxelwise comparison between conditions, where we observe significant increases in OEF and $R_2^\prime$ during hyperventilation.

We consider $\mathcal{N=1}$ superconformal field theories in three-dimensions possessing a conserved current multiplet $\mathcal{F}_{ (\alpha_{1} \alpha_{2} \alpha_{3} \alpha_{4}) }$ which we refer to as the superspin-2 current multiplet. At the component level it contains a conserved spin-2 current different from the energy-momentum tensor and a conserved fermionic higher spin current of spin 5/2. Using a superspace formulation, we calculate correlation functions involving $\mathcal{F}$, focusing particularly on the three-point function $ \langle \mathcal{F} \mathcal{F} \mathcal{F} \rangle $. After imposing the constraints arising from conservation equations and invariance under permutation of superspace points, we find that the parity-even and parity-odd sectors of this three-point function are each fixed up to a single coefficient. The presence of the parity-odd contribution is rather non-trivial, as there is an apparent tension between supersymmetry and the existence of parity-odd structures., Comment: 49 pages; v2: minor corrections, v3: minor corrections, published version

Purpose. Elevations in initially obtained serum lactate levels are strong predictors of mortality in critically ill patients. Identifying patients whose serum lactate levels are more likely to increase can alert physicians to intensify care and guide them in the frequency of tending the blood test. We investigate whether machine learning models can predict subsequent serum lactate changes. Methods. We investigated serum lactate change prediction using the MIMIC-III and eICU-CRD datasets in internal as well as external validation of the eICU cohort on the MIMIC-III cohort. Three subgroups were defined based on the initial lactate levels: i) normal group (<2 mmol/L), ii) mild group (2-4 mmol/L), and iii) severe group (>4 mmol/L). Outcomes were defined based on increase or decrease of serum lactate levels between the groups. We also performed sensitivity analysis by defining the outcome as lactate change of >10% and furthermore investigated the influence of the time interval between subsequent lactate measurements on predictive performance. Results. The LSTM models were able to predict deterioration of serum lactate values of MIMIC-III patients with an AUC of 0.77 (95% CI 0.762-0.771) for the normal group, 0.77 (95% CI 0.768-0.772) for the mild group, and 0.85 (95% CI 0.840-0.851) for the severe group, with a slightly lower performance in the external validation. Conclusion. The LSTM demonstrated good discrimination of patients who had deterioration in serum lactate levels. Clinical studies are needed to evaluate whether utilization of a clinical decision support tool based on these results could positively impact decision-making and patient outcomes., Comment: 15 pages, 6 Appendices

We consider mixed three-point correlation functions of the supercurrent and flavour current in three-dimensional $1 \leq \mathcal{N} \leq 4$ superconformal field theories. Our method is based on the decomposition of the relevant tensors into irreducible components to guarantee that all possible tensor structures are systematically taken into account. We show that only parity even structures appear in the correlation functions. In addition to the previous results obtained in arXiv:1503.04961, it follows that supersymmetry forbids parity odd structures in three-point functions involving the supercurrent and flavour current multiplets., Comment: 54 pages, v2: minor typos corrected, references added, v3: section 7 added, published version

The service lives of nickel superalloys are often limited by environmental degradation. The present study compares oxidation, sulfidation and hot corrosion at 750C of three variants of a polycrystalline superalloy: a baseline alloy, a variant containing 1wt% Mn and one containing 0.5wt% Si. Mn reduced the oxidation rate without changing the scale morphology. The MnCr2O4 scale formed proved more protective against sulfidation and hot corrosion, but internal sulfides extended the damage depth. Si modified the oxide morphology to a continuous Cr2O3-Al2O3 dual layer. This provided improved protection, reducing the sulfidation depth by 2/3 and the hot corrosion depth by 1/2., Comment: 21 pages

This paper introduces a method for unsupervised tokenization of Controller Area Network (CAN) data payloads using bit level transition analysis and a greedy grouping strategy. The primary goal of this proposal is to extract individual time series which have been concatenated together before transmission onto a vehicle's CAN bus. This process is necessary because the documentation for how to properly extract data from a network may not always be available; passenger vehicle CAN configurations are protected as trade secrets. At least one major manufacturer has also been found to deliberately misconfigure their documented extraction methods. Thus, this proposal serves as a critical enabler for robust third-party security auditing and intrusion detection systems which do not rely on manufacturers sharing confidential information., Comment: 2018 IEEE 88th Vehicular Technology Conference (VTC2018-Fall)

While natural language processing (NLP) of unstructured clinical narratives holds the potential for patient care and clinical research, portability of NLP approaches across multiple sites remains a major challenge. This study investigated the portability of an NLP system developed initially at the Department of Veterans Affairs (VA) to extract 27 key cardiac concepts from free-text or semi-structured echocardiograms from three academic medical centers: Weill Cornell Medicine, Mayo Clinic and Northwestern Medicine. While the NLP system showed high precision and recall measurements for four target concepts (aortic valve regurgitation, left atrium size at end systole, mitral valve regurgitation, tricuspid valve regurgitation) across all sites, we found moderate or poor results for the remaining concepts and the NLP system performance varied between individual sites., Comment: Under review with AMIA 2019