EMG analysis quantifies bipedal standing quality in SCI patients.
problem Quantifying the quality of bipedal standing in spinal cord injury patients.
method Multi-channel surface EMG recordings during spinal stimulation therapy sessions.
result Multi-channel EMG recording can provide accurate, fast, and robust estimation for standing quality in SCI patients.
Automatically counts microglial cells in rat spinal cord images, providing precise counts and uncertainty estimates.
problem Counting microglial cells in small, heterogeneous datasets is time-consuming and requires extensive training.
method Pre-processing to filter images, designing a non-parametric, non-linear kernel counter, providing uncertainty estimation.
result The method can provide precise counts and uncertainty estimates in small datasets, even with expert opinions.
Redefined cord algebra using Morse Theory for knot invariants.
problem Defining a knot invariant using algebraic methods.
method Using Morse Theory to redefine the cord algebra.
result Proved the cord algebra is a knot invariant.
Study Morse models for torus algebra related to knot homology.
problem Understanding algebraic structures of tori and knots.
method Construct Morse models and use multiple time scale dynamics.
result Identifies Cord(T_K) with Cord(K) and relates to Legendrian contact homology.
TuNet improves glioma segmentation accuracy and efficiency.
problem Accurate and efficient glioma segmentation for early treatment.
method End-to-end cascaded network with hierarchical structure and ResNet-like blocks.
result Improved segmentation accuracy and reduced treatment costs.
New tools classify symplectic fillings of contact 3-manifolds.
problem Classifying symplectic fillings of contact 3-manifolds.
method Spinal open book decompositions and bordered Lefschetz fibrations.
result Symplectic fillings of contact 3-manifolds are deformation equivalent to complements of positive multisections in bordered Lefschetz fibrations.
In Heisenberg group, bisectors are spinal spheres with specific curvature.
problem Understanding bisectors in the Heisenberg group.
method Showed bisectors are spinal spheres and calculated their curvature.
result Metric bisectors in Heisenberg group are spinal spheres with specific curvature.
A common analytical problem in neuroscience is the interpretation of neural activity with respect to sensory input or behavioral output. This is typically achieved by regressing measured neural activity against known stimuli or behavioral variables to produce a "tuning function" for each neuron. Unfortunately, because …
We generalize Ng's two-variable algebraic/combinatorial 0-th framed knot contact homology for framed oriented knots in S3 to knots in S1×S2, and prove that the resulting knot invariant is the same as the framed cord algebra of knots. Actually, our cord algebra has an extra variable, which potentially co…
StageOpt efficiently optimizes safe decisions by separating safety and utility stages.
problem Optimizing unknown utility with safety constraints in sequential decisions.
method Develops StageOpt, a two-stage safe Bayesian optimization algorithm.
result StageOpt is more efficient and applicable to broader problems than existing methods.
Paper uses GPS data and ML to forecast soccer injuries.
problem Injuries in soccer impact team performance and rehabilitation costs.
method Collects GPS training data, constructs injury forecaster using machine learning.
result Injury forecaster is accurate and interpretable, providing practical rules for injury prevention.
J. Boyle classified 1-handles attached to surface-knots, that are closed and connected surfaces embedded in the Euclidean 4-space, in the case that the surfaces are oriented and 1-handles are orientable with respect to the orientations of the surfaces. In that case, the equivalence classes of 1-handles correspond to th…
Study tackles workplace injury prediction and prevention.
problem Rare and imbalanced data makes injury risk prediction challenging.
method Ensemble resampling, transfer learning, and variable analysis.
result Improved injury risk prediction and prevention techniques.
Predictive models of training load data failed to accurately predict injuries in Australian football.
problem Predicting injuries in Australian football using training load data.
method Training load data from GPS, accelerometers, and player ratings were analyzed using various predictive models.
result The best model for hamstring injuries had an AUC of 0.76, but overall predictive performance was poor.
Study shows bounds on symplectic fillings for spinal open book decompositions.
problem Understanding symplectic fillings of contact 3-manifolds.
method Introduced spine removal surgery operation to prove universal bounds.
result Proves a universal bound on the Euler characteristic and signature of minimal symplectic fillings.
New geometric constructions for contact manifolds, not symplectically fillable.
problem Understanding symplectic fillings of contact manifolds with spinal open book decompositions.
method Introducing spine removal surgery to create new contact manifolds.
result Spine removal yields new examples of contact manifolds not symplectically fillable.
The goal of this thesis is to investigate the potential of predictive modelling for football injuries. This work was conducted in close collaboration with Tottenham Hotspurs FC (THFC), the PGA European tour and the participation of Wolverhampton Wanderers (WW). Three investigations were conducted: 1. Predicting the rec…
We define a coalgebra structure for open strings transverse to any framed codimension 2 submanifold. When the submanifold is a knot in R^3, we show this structure recovers a specialization of the Ng cord algebra, a non-trivial knot invariant which is not determined by a number of other knot invariants.
Unsupervised clustering reveals novel TBI phenotypes.
problem Inadequate categorization of traumatic brain injury (TBI) based on symptoms.
method Applied unsupervised learning with GLRM feature selection.
result Identified four novel TBI phenotypes with distinct feature profiles.
This paper classifies symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.
problem Classifying symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.
method Using holomorphic curves and Lefschetz fibrations to classify fillings.
result Symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions can be classified up to deformation equivalence.
Deep learning segments spinal metastases in MR images.
problem Challenges in accurately segmenting spinal metastases in MR images.
method Used a U-Net-like architecture trained on 40 clinical cases.
result Average Dice scores up to 77.6% and mean sensitivity rates up to 78.9%.
New contact manifolds with many fillings found.
problem Contact manifolds with infinite fillings in odd dimensions.
method Spinal open books to construct contact manifolds.
result Contact manifolds with infinitely many different Weinstein fillings constructed.
We prove that the fundamental quandle of the trefoil knot is isomorphic to the projective primitive subquandle of transvections of the symplectic space Z⊕Z. The last quandle can be identified with the Dehn quandle of the torus and the cord quandle on a 2-sphere with four punctures. We also show that the fund…
MRI identifies chronic symptoms in mTBI patients.
problem Chronic symptoms in mTBI patients are hard to characterize.
method Multi-parametric MRI and low-dimensional projection.
result MRI metrics correlate with patient symptoms.
We present a topological interpretation of knot and braid contact homology in degree zero, in terms of cords and skein relations. This interpretation allows us to extend the knot invariant to embedded graphs and higher-dimensional knots. We calculate the knot invariant for two-bridge knots and relate it to double branc…
New theory predicts security prices through a physical law, not randomness.
problem Failed attempts to understand and predict stock price evolution.
method Developed a physicomathematical theory to describe price evolution.
result Security prices are governed by a deterministic physical law, not random.
Model captures neural activity related to behavior while separating internal computations.
problem Capturing neural activity related to behavior from complex brain recordings.
method Behavior-decomposed linear dynamical systems (b-dLDS) model.
result Improves over state-of-the-art models in disentangling behavior-related dynamics.
4-bit quantization reduces U-Net memory by 8x with minimal accuracy loss.
problem Reducing memory and computation time in deep learning models.
method Fixed-point quantization of U-Net architecture.
result 8x reduction in memory usage with minimal accuracy loss.
The paper finds non-contractible loops of Legendrian tori from knot families.
problem Computing non-contractible loops of Legendrian tori from knot families.
method Using cord algebra of knots to compute Legendrian contact homology.
result Obtained an infinite family of non-contractible loops of Legendrian tori.
We study the finitely generated Hausdorff spectrum of spinal automorphism groups acting on rooted trees. Given any α∈[0,1], we construct a branch group Gα such that Gα has a finitely generated subgroup H where H has Hausdorff dimension α in G. Using results by Barnea, Shalev and Klopsch we further de…
Study pochette surgery on 4-manifolds, focusing on 4-spheres.
problem Understanding pochette surgery on 4-spheres and its effects.
method Using linking number of pochette embeddings, compute homology and analyze surgeries.
result Pochette surgery on any homology 4-sphere can be computed via homology, and trivial cord surgeries do not change diffeomorphism type.
We study the relationship between Ng's abelian cord ring and SL(2,C) characters of the two-fold branched cover Σ(K). Augmentations, and their corresponding rank, play a central role in the relationship. Our study also leads to a correspondence between trace-free SL(2,C) characters of a knot complement and augmentatio…
This study uses reinforcement learning to mitigate imminent collisions by controlling car speed and direction.
problem Mitigating imminent collisions on roads.
method Constructed a model using camera images to predict obstacle dynamics. Trained reinforcement learning policies to control braking and steering.
result Both reinforcement learning policies outperform a baseline policy, with the injury model-based policy showing the highest performance.
Method predicts spinal deformity progression using 3D models and machine learning.
problem Predicting the progression of spinal deformities in scoliosis patients.
method Discriminative probabilistic manifold embedding for 3D spine models.
result 81% classification rate and 2.1° prediction difference in curve angulation.
Gauge theory applied to foliations yields insights into their moduli spaces.
problem Understanding the moduli space of codimension-k framed foliations. method Applying gauge theory to study the space of foliations and using quotient spaces and cohomology.
result The quotient of Maurer-Cartan elements forms a moduli space that includes foliations.
Study identifies key MRI features for predicting cognitive performance after mTBI.
problem Identify relevant diffusion MRI metrics for cognitive functions in mTBI patients.
method Proposes a novel feature selection method combining best-first search with genetic algorithm crossover.
result Achieves significantly more accurate predictions than other feature selection algorithms.
Natural language processing predicts AKI onset in ICU patients.
problem Early detection of AKI in ICU patients to improve outcomes.
method Clinical notes were processed to generate word and concept embeddings. Five classifiers and a deep learning model were used to predict AKI.
result The best model achieved an AUC of 0.779 for predicting AKI onset.
Bayesian method for estimating functional graphical models from neuroimaging data.
problem Estimating dependence structures from functional data in neuroscience.
method Fully Bayesian regularization scheme, including direct Bayesian analog of functional graphical lasso and graphical horseshoe.
result Insight into brain compensation after traumatic brain injury.
The conormal Lagrangian LK of a knot K in R3 is the submanifold of the cotangent bundle T∗R3 consisting of covectors along K that annihilate tangent vectors to K. By intersecting with the unit cotangent bundle S∗R3, one obtains the unit conormal ΛK, and the Legendrian…
New representation connects two link invariants.
problem Link invariants of different types.
method Augmentation representation of link group.
result Connects two types of link invariants.
A new method quantifies uncertainty in brain injury simulations.
problem High computational cost and high-dimensional inputs/outputs limit traditional UQ methods for biofidelic head models.
method Two-stage, data-driven manifold learning framework using Gaussian kernel-density estimation, diffusion maps, and Grassmannian diffusion maps.
result Surrogate models reduce computational cost while providing highly accurate approximations of the computational model.
This paper automates mining of COVID-19 scholarly articles using machine learning.
problem Time-consuming and impractical manual extraction of relevant COVID-19 research articles.
method Used machine learning approaches, specifically clustering and parallel one-class support vector machines (OCSVMs), on the CORD-19 dataset.
result Parallel OCSVMs outperform other methods for both original and reduced feature space.
We prove that if a contact manifold (M,ξ) is supported by a planar open book, then Euler characteristic and signature of any Stein filling of (M,ξ) is bounded. We also prove a similar finiteness result for contact manifolds supported by spinal open books with planar pages. Moving beyond the geography of Stein filli…
Automated brain CT image retrieval from traumatic brain injury cohorts using deep neural networks.
problem Manual image retrieval of whole brain CT scans from large clinical cohorts is time-consuming and resource-intensive.
method Proposes a deep convolutional neural network (dMIR) for automated classification of 2D montage images.
result Achieved high accuracy (f1=1.0) for validation and testing data sets.
Improved AI model predicts construction safety outcomes from incident reports.
problem Predicting safety outcomes from incident reports using AI.
method Extracted attributes from incident reports using NLP, trained machine learning models (XGBoost, linear SVM), used model stacking, analyzed per-category attribute importance.
result Attributes are highly predictive of safety outcomes, injury severity is well predicted.
Deep CNN models simulate cognitive deficits from neurodegenerative diseases and TBI.
problem Limited ability to assess damaged neurons in vivo for accurate diagnosis and prognosis.
method Used convolutional neural networks (CNNs) to damage simulated brain connections based on biophysically relevant data on FAS.
result Damage to simulated brain connections leads to human-like cognitive mistakes and quantifiable accuracy reductions.
EdgeLite detects hazardous supermarket floors, improving safety.
problem Detecting hazardous conditions on supermarket floors to prevent injuries.
method Developed a lightweight deep learning model, EdgeLite, for edge devices.
result EdgeLite outperformed state-of-the-art models in detecting hazards on supermarket floors.
Proposes a framework for personalized treatment recommendations using observational data.
problem Estimating patient-level treatment effects from observational data.
method Integrates existing methods for learning patient-level causal models.
result Improves patient outcomes in heart failure patients with acute kidney injury.