Enhances NOAA's Geospace model with machine learning for predicting ground magnetic perturbations.
problem Predicting the probability of ground magnetic field changes.
method Combining physics-based model with machine learning (boosted ensemble of classification trees).
result The ML-enhanced model consistently improves probabilistic forecast metrics.
In this paper, we present a new location fingerprinting database comprised of Wi-Fi received signal strength (RSS) and geomagnetic field intensity measured with multiple devices at a multi-floor building in Xi'an Jiatong-Liverpool University, Suzhou, China. We also provide preliminary results of localization and trajec…
New model predicts particle precipitation from magnetosphere to ionosphere.
problem Improving prediction of electron particle precipitation from magnetosphere to ionosphere.
method Compilation of new database, use of machine learning (ML) tools, neural network (PrecipNet).
result PrecipNet achieves >50% reduction in errors and better captures dynamic changes.
New method uses DTW to evaluate neural network forecasts of geomagnetic indices.
problem Evaluation metrics fail to capture persistence behavior in neural network forecasts.
method Dynamic Time Warping (DTW) to measure time series similarity, training neural networks to remove persistence.
result DTW reveals persistence behavior in neural network forecasts, confirming visual inspection.
Neural Bayes methods simplify fitting complex bivariate extremal models.
problem Inference on complex multivariate extremal dependence models with computationally expensive likelihood functions.
method Use neural networks to approximate Bayes estimators and classifiers for model selection.
result Proposed neural Bayes methods enable routine implementation of complex extreme-value dependence models.
Develops non-parametric tests for group symmetry in data.
problem Lack of statistical tests for group symmetry in data.
method Formulates and implements non-parametric tests for distributional symmetry under specified groups.
result Develops tests for conditional invariance/equivariance and applies them to real-world data.
2L-FUSE enhances feature sparsity through kernel learning.
problem Sparsity and feature selection in regression tasks.
method 2-Layered kernel machines for learning a shape matrix and feature direction identification.
result Minimal yet informative feature sets are identified without losing predictive performance.
Machine learning detects and characterizes whistler radio waves for real-time monitoring of the plasmasphere.
problem Detect and characterise whistler radio waves generated by lightning strokes for real-time monitoring of the plasmasphere.
method Developed a machine learning model using image classification and localisation on spectrogram data to identify and localise whistlers.
result The proposed detectors achieve a misdetection and false alarm rate of less than 15% on Marion's dataset.
We show that any semi-calibration of degree 2 is locally induced by a smooth almost complex structure. We provide some applications of this result in the regularity theory for semi-calibrated 2-currents
The paper studies how certain currents can induce metric structures from Kähler-Ricci flows.
problem Understanding metric structures induced by currents from Kähler-Ricci flows.
method Analyzes sufficient conditions for a closed, positive (1,1)-current to induce a metric structure from Kähler-Ricci flows.
result Shows that certain currents can induce metric structures from Kähler-Ricci flows, including Alexandrov surfaces.
The note proves positive currents induced by VKE with mixed singularities.
problem Variation of Kahler-Einstein metrics with mixed singularities.
method Fiberation between compact Kahler manifolds with generic smooth log canonical pairs.
result Current induced by VKE with mixed cone and Poincare singularities is positive.
Slender marine structures such as deep-water marine risers are subjected to currents and will normally experience Vortex Induced Vibrations (VIV), which can cause fast accumulation of fatigue damage. The ocean current is often three-dimensional (3D), i.e., the direction and magnitude of the current vary throughout the …
Periodic Floer homology (PFH) is a Gromov-Floer type invariant for fibered three-manifolds with Hamiltonian structures. The cobordism maps on periodic Floer homology induced by symplectic cobordisms are currently only defined indirectly by using Seiberg-Witten theory. In this paper, we investigate the cobordism maps in…
Compactifies a component by studying metric degeneration.
problem Compactify the SO(2,3)-Hitchin component.
method Study metric degeneration on a surface in pseudo-hyperbolic space.
result Establish closure in projectivized geodesic currents space.
A new formula connects supersymmetric path integrals to Chern-Simons theory.
problem Constructing a rigorous path integral for supersymmetric theories on spin manifolds.
method Using Chen differential forms and non-commutative geometry, a Chern-Simons transgression formula is derived.
result The supersymmetric path integral induces a differential topological invariant.
We show that for k at least 3, given any matrix in GL(k,Z), there is a hyperbolic fully irreducible automorphism of the free group of rank k whose induced action on Z^k is the given matrix.
Study Blaschke metrics to compactify Hitchin component.
problem Compactify the SL(3,R)-Hitchin component.
method Study degeneration of Blaschke metrics on equivariant affine spheres.
result Establish closure in projectivized geodesic currents space.
New examples show flat singular sets can be arbitrarily complex.
problem Understanding the structure of singular sets in almost-minimizing currents.
method Construction of specific examples of area almost-minimizing currents.
result Flat singular sets can contain any closed empty interior subset of a plane.
A new method selects inducing points to optimize high-throughput Bayesian optimisation.
problem Current inducing point selection methods sacrifice high-fidelity modeling of promising regions.
method Information-theoretic criterion to select inducing points maximizing global and maximum value uncertainties.
result Surrogate models support high-precision high-throughput Bayesian optimisation.
In human cognition, the expansion of perceived between-category distances and compression of within-category distances is known as categorical perception (CP). There are several hypotheses about the causes of CP (e.g., language, learning, evolution) but no functional model. Whether CP is essential to categorisation or …
Study examines homology of contact CR-submanifolds in complex Euclidean space.
problem Investigating the homology of contact CR-submanifolds.
method Analyzes stable integral currents and homology groups of contact CR-submanifolds in Cm. result Nonexistence of stable integral currents and vanishing theorems for homology groups.
In this paper we discuss the twistor equation in Lorentzian spin geometry. In particular, we explain the local conformal structure of Lorentzian manifolds, which admit twistor spinors inducing lightlike Dirac currents. Furthermore, we derive all local geometries with singularity free twistor spinors that occur up to di…
New characterization of geodesic currents via curve functionals.
problem Characterize geodesic currents using curve functionals.
method Purely axiomatic and combinatorial approach.
result Characterization of curve functionals dual to geodesic currents.
Witt algebra acts on categorified quantum groups in type A.
problem Action of Witt algebra on categorified quantum groups.
method Construction of action on categorified quantum group and foams.
result Action of Witt algebra on foams recovers previous results.
New method approximates hyperbolic lattices using cube complexes.
problem Metric approximation of hyperbolic lattices by cubulations.
method Study of co-geodesic currents and their intersection number.
result Isometric actions of hyperbolic lattices can be approximated by geometric actions on CAT(0) cube complexes.
Study of random sections on complex spaces converging to equilibrium metrics.
problem Understanding the behavior of random holomorphic sections on complex spaces.
method Analyzing the convergence of normalized Fubini-Study currents and integration currents to the equilibrium metric's curvature.
result The normalized currents of integration along zero divisors converge almost surely to the curvature current of the equilibrium metric.
The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
problem Conditions for linearity of the conditional mean estimator in vector Poisson noise.
method Analyzes prior distributions and their impact on the conditional mean estimator's linearity.
result The only prior distribution that induces linearity is a product gamma distribution, and non-zero dark current parameter prevents linearity.
We prove uniform north-south dynamics type results for the action of φ∈Out(FN) on the space of projectivized geodesic currents PCurr(S)=PCurr(FN), where φ is induced by a pseudo-Anosov homeomorphism on a compact surface S with boundary such that π1(S)=FN. As an appli…
New algorithms improve GP inference without approximations, achieving better results.
problem Inexact stochastic optimization methods in Gaussian Processes leading to biased results.
method Exact stochastic inference for GPs with finite dimensional RKHS, extending to infinite dimensions.
result Achieves better experimental results than existing methods in constrained resource settings.
Survey of Bayesian nonparametric space partition models and their applications.
problem Partitioning high-dimensional spaces into homogeneous regions.
method Various strategies for generating partitions in a D-dimensional space.
result Review of current progress in BNSP research.
Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs). We generalize the current NNGP to first include a larger number of hyperparameters and subsequently train the model…
This paper presents a Bayesian approach to symbol and phase inference in a phase-unsynchronized digital receiver. It primarily extends [Quinn 2011] to the multi-symbol case, using the variational Bayes (VB) approximation to deal with the combinatorial complexity of the phase inference in this case. The work provides a …
The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces the manifold topology. We show when warped products of low regularity and globally…
In this paper, we propose a generalized scale mixture family of distributions, namely the Power Exponential Scale Mixture (PESM) family, to model the sparsity inducing priors currently in use for sparse signal recovery (SSR). We show that the successful and popular methods such as LASSO, Reweighted ℓ1 and Reweigh…
Compact models learn photocurrent dynamics from radiation-induced excess carrier density.
problem Accurate but computationally expensive physics-based photocurrent models for semiconductor devices.
method Dynamic Mode Decomposition (DMD) for learning reduced order models from internal state data.
result Physics-aware, compact delayed photocurrent models accurately approximate internal excess carrier dynamics.
We give a simple proof of a result on the ∂∂ˉ-lemma property under a blow-up transformation by Deligne--Griffiths--Morgan--Sullivan's criterion. Here, we use an explicit blow-up formula for Dolbeault cohomology given in our previous work, which can be induced by a morphism expressed on the level of…
A trace formula for foliated flows on closed manifolds.
problem Establishing a trace formula for foliated flows on closed manifolds.
method Using leafwise currents and cohomologies, a trace formula is derived involving infinitesimal data from closed orbits and preserved leaves.
result A trace formula is proven for foliated flows on closed manifolds, solving a conjecture by C. Deninger.
Large batch sizes reduce gradient variance in DP-SGD, improving privacy.
problem Understanding why large batch sizes work in DP-SGD.
method Decomposed total gradient variance into subsampling and noise-induced variances, proving batch size independence in the limit.
result Large batch sizes reduce effective total gradient variance, improving privacy in DP-SGD.
The Riemannian hemisphere has a lower bound for its mass.
problem Estimating the mass of surfaces spanning a circle.
method Constructing a differential form with a stationary comass norm on the hemisphere.
result The mass of surfaces spanning a circle has a lower bound of 2π plus a second-order term. Given a family f:X→S of canonically polarized manifolds, the unique Kähler-Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle KX/S. We use a global elliptic equation to show that this metric is strictly positive on X, unless the fam…
Sharp criteria for 2-varifolds to be induced by smooth immersions.
problem Regularity of integral 2-varifolds with square integrable mean curvature.
method Fine analysis of Hausdorff density and recent local regularity results.
result Optimal threshold for Willmore energy leading to curvature varifolds.
We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compactification of Teichmüller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to the Gardiner-Masur boundary. Using the embedding of flat metrics into th…
Study first-order locally convex Lie algebroids in Bastiani calculus.
problem Define and study first-order locally convex Lie algebroids.
method Define sheaves of Lie algebroid forms and morphisms, prove category structure, study representations and cohomology.
result First-order locally convex Lie algebroids form a category and have applications in Lie II theorems.
TILT improves target domain performance by penalizing an auxiliary component on unlabeled target inputs.
problem Improving performance on target domain under covariate shift.
method TILT uses a novel objective function to decompose the source predictor and penalize an auxiliary component on unlabeled target inputs.
result TILT improves target domain performance over source-only training and other baselines.
Decision forests are widely used for classification and regression tasks. A lesser known property of tree-based methods is that one can construct a proximity matrix from the tree(s), and these proximity matrices are induced kernels. While there has been extensive research on the applications and properties of kernels, …
Current state-of-the-art nonparametric Bayesian text clustering methods model documents through multinomial distribution on bags of words. Although these methods can effectively utilize the word burstiness representation of documents and achieve decent performance, they do not explore the sequential information of text…
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections between the geometric properties of the induced manifold and statistical properti…
If (X,J) is an almost complex manifold, then a function u is said to be plurisubharmonic on X if it is upper semi-continuous and its restriction to every local pseudo-holomorphic curve is subharmonic. As in the complex case, it is conjectured that plurisubharmonicity is equivalent to the fact that the (1,1)-cur…