Optimizes ASL-MRF scan design for precise brain hemodynamics quantification.
problem Fixing model parameters in ASL introduces bias, and multiparametric estimation degrades precision.
method Optimizes ASL labeling durations using Cramer-Rao Lower Bound (CRLB) and proposes a neural network regression framework.
result Improved precision in estimating multiple hemodynamic parameters from a single scan.
Automated labeling of intracranial arteries improves accuracy and efficiency.
problem Challenges in accurately labeling intracranial arteries due to variations and limited datasets.
method Graph Neural Network (GNN) combined with hierarchical refinement for improved accuracy.
result Achieved 97.5% node labeling accuracy on a testing set of 105 scans.
DeepCap automates coronary artery segmentation from IVOCT images.
problem Automated segmentation of coronary arteries from IVOCT images is challenging.
method Developed a deep learning method based on capsules for robust, unbiased segmentation.
result DeepCap achieves segmentation quality comparable to state-of-the-art methods.
Consensus NN learns from noisy data only for medical image denoising.
problem Lack of clean training data for medical image denoising.
method Trains neural network using only noisy data by splitting and combining subsets.
result Improved performance on denoising medical images compared to existing methods.
Paper analyzes shapes of brain arterial networks using statistical methods.
problem Quantifying and comparing shapes of brain arterial networks.
method Mathematical representation of BAN shapes as elastic shape graphs, development of Riemannian metrics and geometrical tools.
result Age has a clear, quantifiable effect on BAN shapes, with increased variance in shapes as age increases.
Predicts arterial road incident duration with extreme gradient boosting.
problem Predicting incident duration on arterial roads, especially with limited data.
method Bi-level framework combining classification and regression models.
result Extreme gradient boosting outperformed other models by 53%.
Deep learning improves plaque prediction for coronary artery health.
problem Predicting coronary artery plaque health from CT scans.
method 3D RCNN, 2D multi-view ensemble, 2.5D approach.
result Improved prediction accuracy for revascularization decisions.
Deep learning and radiomics methods assess coronary artery plaque from CT scans.
problem Improving patient management and clinical outcomes by assessing coronary artery plaque.
method Three machine learning approaches: radiomics, deep learning, and fusion of both.
result Methods achieve AUC scores of 0.84-0.88, comparable to FFR measurements.
New framework predicts arterial blood pressure from MRI data using physics-informed neural networks.
problem Clinical applicability of predictive cardiovascular flow models is hindered by computational cost and tedious pre-processing.
method Physics-informed neural networks constrained by conservation of mass and momentum principles.
result Deep neural networks provide physically consistent predictions for arterial blood pressure without conventional simulators.
GSE maps graphs into a space for efficient interaction encoding.
problem Efficiently encoding graph interactions with minimal computations.
method Graph Space Embedding (GSE) maps graphs into a space where interactions are implicitly encoded with minimal computations.
result GSE achieves better performance than traditional algorithms on a real-world clinical dataset.
Machine learning models predict crash rates on narrow lanes.
problem Impact of narrow lanes on arterial road vehicle crashes.
method Applied random forest and least squares boosting machine learning algorithms to crash data.
result Random forest model identified as best for studying narrow lanes' safety impact.
Spin TFTs created by gauging line defects in 3D.
problem Creating spin TFTs from oriented TFTs with framed line defects.
method Constructing a spin TFT from an oriented TFT with framed line defects and a commutative Frobenius algebra.
result Spin TFTs extend earlier classifications and reproduce abelian spin Chern-Simons theories.
From a fresh data science perspective, this thesis discusses the prediction of coronary artery disease based on genetic variations at the DNA base pair level, called Single-Nucleotide Polymorphisms (SNPs), collected from the Ontario Heart Genomics Study (OHGS). First, the thesis explains two commonly used supervised le…
A spin network is a cubic ribbon graph labeled by representations of SU(2). Spin networks are important in various areas of Mathematics (3-dimensional Quantum Topology), Physics (Angular Momentum, Classical and Quantum Gravity) and Chemistry (Atomic Spectroscopy). The evaluation of a spin network is an integ…
We study classical spin networks with group SU(2). In the first part, using gaussian integrals, we compute their generating series in the case where the networks are equipped with holonomies; this generalizes Westbury's formula. In the second part, we use an integral formula for the square of the spin network and perfo…
Study improves CAD diagnosis accuracy by selecting significant features.
problem Improving accuracy of CAD diagnosis through feature selection.
method Integrated machine learning approach using random trees (RTs), C5.0, SVM, and CHAID.
result Random trees model outperforms other models in CAD diagnosis.
Method reconstructs aneurysm growth history from patient parameters using physics-informed autoencoder.
problem Predicting arterial aneurysm rupture due to inaccessible growth time series.
method Physics-informed autoencoder combined with neural network for mapping patient parameters to aneurysm growth time history.
result Incorporating physical model constraints improves time series reconstruction, especially in noisy data.
New metrics found for 6k-dimensional manifolds with positive Ricci curvature.
problem Finding metrics of positive Ricci curvature on simply-connected manifolds.
method Using labeled bipartite graphs to describe certain manifolds and constructing metrics of positive Ricci curvature.
result Many new examples of 6k-dimensional manifolds with positive Ricci curvature.
BSA reduces network data by interpreting feature subspaces.
problem Interpreting feature subspaces of unlabeled network data.
method Barycentric Subspace Analysis (BSA) for unlabeled networks.
result BSA provides a more interpretable approach compared to PCA.
CNN detects phase transitions in Potts models without prior knowledge.
problem Detecting phase transitions in q-state Potts models using deep learning. method Trained a deep CNN on Ising model spin configurations and temperatures, then tested on Potts model images.
result Deep CNN accurately detects phase transitions in Potts models, including high- and low-temperature regions.
We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the underlying conservation laws (i.e., for mass, momentum, and energy) to infer hid…
Hospital Readmissions within 30 days after discharge following Coronary Artery Bypass Graft (CABG) Surgery are substantial contributors to healthcare costs. Many predictive models were developed to identify risk factors for readmissions. However, majority of the existing models use statistical analysis techniques with …
ECGDetect uses deep learning to detect ischemia in heart ECGs.
problem Detecting early signs of acute coronary syndrome in patients.
method Developed a deep learning model using the LTST database.
result Deep neural network achieved 90.31% ROC-AUC, 89.34% sensitivity, 87.81% specificity.
IntraVascular UltraSound (IVUS) is one of the most effective imaging modalities that provides assistance to experts in order to diagnose and treat cardiovascular diseases. We address a central problem in IVUS image analysis with Fully Convolutional Network (FCN): automatically delineate the lumen and media-adventitia b…
Machine learning improves CAD management outcomes.
problem Current CAD guidelines do not account for patient-specific characteristics.
method Developed binary classifiers and regression models using patient data.
result Improved health outcomes by 24.11% compared to standard care.
Paper calculates the benefit of unlabeled data in semi-supervised learning for Gaussian mixtures.
problem Improving performance in semi-supervised learning with unlabeled data.
method Analytical computation of Bayes risk gap between supervised and semi-supervised approaches for Gaussian mixture models.
result Quantifies the accuracy increase due to unlabeled data in a Bayesian setting.
String-net models explore non-spherical fusion categories, revealing new spin structures and representations.
problem Investigating string-net models in non-spherical fusion categories.
method String-net models associate vector spaces to surfaces in terms of graphs decorated by objects and morphisms of a pivotal fusion category.
result String-net spaces count r-spin structures and carry representations of the mapping class group.
Non-invasive detection of cardiovascular disorders from radiology scans requires quantitative image analysis of the heart and its substructures. There are well-established measurements that radiologists use for diseases assessment such as ejection fraction, volume of four chambers, and myocardium mass. These measuremen…
The compact exceptional Lie groups F4, E6, E7 and E8 have spinor groups as a subgroup as follows: E8 \supset Ss(16) \supset Spin(15) \supset Spin(14) \supset Spin(13), E7 \supset Spin(12) \supset Spin(11), E6 \supset Spin(10), F4 \supset Spin(9) \supset Spin(8) \supset Spin(7) \supset \cdot \cdot \cdot \supset Spin(1) …
The paper explores spin^h structures and their obstructions.
problem Understanding which manifolds are spin^h.
method Analyzing the fifth Stiefel-Whitney class and constructing generalised spin structures.
result Every compact orientable manifold of dimension 7 or lower is spin^h, and there are higher-dimensional manifolds that are not.
Study mSpin(7)-dDT connections on manifolds with mSpin(7)-structures.
problem Understanding moduli spaces of mSpin(7)-dDT connections. method Introduced and studied mSpin(7)-dDT connections using fully nonlinear PDEs. result Moduli space MmSpin(7)′ has finite expected dimension and smoothness under certain conditions. New Spin(7)-instantons constructed on Joyce's manifold.
problem Constructing Spin(7)-instantons on Joyce's compact manifold. method Gluing non-flat connections on local model spaces to a flat connection on the Spin(7)-orbifold. result More than 20,000 new four-parameter families of Spin(7)-instantons. This is an introduction to the construction of higher-dimensional knots by spinning methods. Simple spinning of classical knots was introduced by E. Artin in 1926, and several generalizations have followed. These include twist spinning, superspinning or p-spinning, frame spinning, roll spinning, and deform spinning. We…
New spin frame transformations affect Dirac equations without preserving metric structures.
problem Extending spin structures to spin manifolds with fixed signature.
method Defining spin frames and studying their effects on connections and Dirac equations.
result New transformations affect Dirac equations more generally than usual spin transformations.
New mSpinh-manifolds studied for their properties.
problem Understanding new manifold classifications.
method Exploring mSpinh-manifolds as a new category. result Highlights of mSpinh-manifolds discussed. Study on harmonic flow of Spin(7)-structures in 8D manifolds.
problem Comparing isometric Spin(7)-structures.
method Developed a notion of harmonicity for Spin(7)-structures and studied the harmonic flow.
result Analytical properties of the harmonic flow of Spin(7)-structures presented.
Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
problem Understanding higher spin Killing spinors on 3D manifolds.
method Definition and detailed study of higher spin Killing spinors in arbitrary dimension, focusing on 3D manifolds. Rigidity result and explicit expressions for 3-sphere and 3-hyperbolic space.
result Proved a rigidity result for 3D manifolds admitting higher spin Killing spinors and provided explicit expressions for these spinors.
We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups Spin(d,d)×R+ for which the generalised tangent space transforms in a spinor representation of the group. In …
The paper characterizes new invariant spinr spinors on projective spaces.
problem Characterizing new invariant spinr spinors on projective spaces. method Adapting spin representation via exterior forms to the generalised spinr context. result Complete description of the space of invariant spinr spinors for CPn, HPn, and OP2. Spin-harmonic structures on low-dimensional manifolds.
problem Defining geometric structures on low-dimensional manifolds.
method Introducing spin-harmonic structures defined by harmonic unitary spinors.
result Spin-harmonic structures are equivalent to balanced Spin(7) structures in dimension 8.
New relation between quantum groups and BPS series.
problem Connecting quantum groups at roots of unity and generic q.
method Proposing and proving a precise relation between invariants.
result Bridging non-semisimple and semisimple TQFTs.
Spin(7) geometry linked to multisymplectic geometry.
problem Understanding Spin(7) structures through multisymplectic geometry.
method Utilized Spin(7) identities to prove non-degeneracy of Cayley four-form in multisymplectic context.
result Spin(7) geometry is a special case of multisymplectic geometry.
Suppose that Σ=∂M is the n-dimensional boundary of a connected compact Riemannian spin manifold (M,⟨,⟩) with non-negative scalar curvature, and that the (inward) mean curvature H of Σ is positive. We show that the first eigenvalue of the Dirac operator of the boundary corresponding to…
We explore differential and algebraic operations on the exterior product of spinor representations and their twists that give rise to cohomology, the spin cohomology. A linear differential operator d is introduced which is associated to a connection ∇ and a parallel spinor ζ, ∇ζ=0, and the algebraic o…
Rigidity of elliptic genera proven for non-spin manifolds with S1-action.
problem Rigidity of elliptic genera for non-spin manifolds with S1-action. method Analysis of universal covering spin condition and π2(M) for rigidity. result Rigidity of elliptic genera is proven for spin universal coverings but not for non-spin universal coverings.
Proves almost flat spin^c manifolds bound compact manifolds.
problem Proving almost flat spin^c manifolds bound compact manifolds.
method Long-standing conjecture of Farrell--Zdravkovska and S. T. Yau settled.
result Every almost flat spin^c manifold bounds a compact orientable manifold.
First non-trivial examples of deformed Spin(7)-instantons constructed.
problem Constructing deformed Spin(7)-instantons and connections.
method Constructing on cotangent bundles of CP2 and cones over 3-Sasakian 7-manifolds. result First non-trivial examples of deformed Spin(7)-instantons.
Study shows certain spin manifolds can't meet DEC condition.
problem Non-existence of spin fill-ins meeting DEC condition.
method Analyzes spin Riemannian manifolds and generalized mean curvature functions.
result Closed spin manifolds cannot satisfy DEC if curvature is large.