Hyper-SAGNN learns patterns in hypergraphs for complex interactions.
problem Learning patterns in hypergraphs with variable-sized heterogeneous hyperedges.
method Self-attention based graph neural network for homogeneous and heterogeneous hypergraphs.
result Significantly outperforms state-of-the-art methods on various tasks.
This research improves deep neural networks for parameter identification and prediction in stochastic Volterra integral equations.
problem Parameter identification and prediction in Volterra integral equations driven by Gaussian noise.
method Improved deep neural networks framework that incorporates inter-output relationships into the loss function.
result The framework enhances parameter estimation accuracy and provides accurate solutions for modeling stochastic systems.
In this thesis, we draw inspiration from both classical system identification and modern machine learning in order to solve estimation problems for real-world, physical systems. The main approach to estimation and learning adopted is optimization based. Concepts such as regularization will be utilized for encoding of p…
Dan Lovallo and Daniel Kahneman must be commended for their clear identification of causes and cures to the planning fallacy in "Delusions of Success: How Optimism Undermines Executives' Decisions" (HBR July 2003). Their look at overoptimism, anchoring, competitor neglect, and the outside view in forecasting is highly …
Develops a framework for distributional Granger causality
problem Identifying predictive dependence in time series beyond Gaussian settings
method Using finite collection of channel-specific restrictions
result Identifies distributional Granger non-causality through testable hypotheses
The paper explores how to extrapolate from limited data points using causal mechanisms.
problem Handling distribution shifts with limited target samples.
method Formulates the extrapolation problem with a latent-variable model embodying the minimal change principle in causal mechanisms, and identifies conditions for identification.
result Theoretical understanding and practical methods for extrapolation without requiring an on-support target distribution.
FDR criterion simplifies complex causal graphs to a standard front-door setting.
problem Complex causal graphs make identification of causal effects difficult and computationally infeasible.
method Front-door reducibility (FDR) criterion and FDR-TID algorithm.
result Many graphs can be simplified to a standard front-door setting, making causal effect identification simpler and more interpretable.
Paper uses sparse learning to estimate quasi-potential and drift components in stochastic systems.
problem Estimating quasi-potential and drift components in stochastic systems.
method Sparse identification of non-linear dynamics (SINDy) combined with action minimization methods.
result Evaluation of quasi-potential landscape from a single trajectory.
Sharp inequality outside ball proved using Neumann method.
problem Anisotropic isoperimetric inequality for domains outside an Euclidean ball.
method Applied ABP method to Neumann boundary value problem.
result Proved sharp anisotropic isoperimetric inequality.
Optimizes prediction error method for time-varying models.
problem Achieving optimal prediction error rates for time-varying models.
method Nonlinear least squares method for time-varying parametric models.
result First rate-optimal non-asymptotic analysis for time-varying models.
Yelp has been one of the most popular local service search engine in US since 2004. It is powered by crowd-sourced text reviews and photo reviews. Restaurant customers and business owners upload photo images to Yelp, including reviewing or advertising either food, drinks, or inside and outside decorations. It is obviou…
In this paper, we proved the quantum layer over a surface which is ruled outside a compact set, asymptotically flat but not totally geodesic admits ground states.
Uniform bounds on ends for non-branching CD spaces with nonnegative curvature outside a compact set.
problem Bounding the number of ends of non-branching CD spaces with nonnegative curvature outside a compact set.
method Adapting Z.-D. Liu's work to prove a ball covering property.
result Uniform bounds on the number of ends of such spaces.
Study proves quantitative results for isoperimetric problem outside convex bodies in the plane.
problem Quantitative estimates for the relative isoperimetric problem outside convex bodies in the plane.
method Flow approach and Łojasiewicz estimates to prove quantitative stability for minimizers.
result Explicit constants and optimal exponents/rates for Łojasiewicz estimates and rates of convergence for gradient flow.
Constructs initial data for Einstein equations and estimates Bartnik mass outside time-symmetry.
problem Estimating Bartnik mass outside time-symmetry.
method Constructs initial data for Einstein equations and connects Bartnik data to time-symmetric data.
result Obtains estimates for the Bartnik mass outside of time-symmetry.
We introduce generalized Monge-Ampère capacities and use these to study complex Monge-Ampère equations whose right-hand side is smooth outside a divisor. We prove, in many cases, that there exists a unique normalized solution which is smooth outside the divisor.
Solves equality case in isoperimetric inequality for non-convex domains.
problem Equality case in relative isoperimetric inequality outside convex sets.
method Analyzes non-convex domains to settle the equality case.
result Solves the equality case for relative isoperimetric inequality outside arbitrary convex sets.
Deep learning models generalize by extending decision boundaries outside the convex hull of training data.
problem Understanding how deep learning models generalize beyond their training data.
method Investigation of decision boundaries inside and outside the convex hull of training sets, using various neural network architectures and training regimes.
result Over-parameterization is necessary for deep learning models to extend decision boundaries outside the convex hull of their training data.
In this paper we prove that a capillary minimal surface outside the unit ball in R3 with one embedded end and finite total curvature must be either part of the plane or part of the catenoid. We also prove that a capillary minimal surface outside the unit ball with one end asymptotic to the end of the Ennep…
The paper proves conditions for compact complex manifolds to be Kahler outside analytic subsets.
problem Conditions for compact complex manifolds to be Kahler outside an analytic subset.
method Analyzes balanced manifolds and uses Hironaka's examples to prove theorems.
result Compact complex manifolds that are Kahler outside an analytic subset are balanced.
This paper explores how theories of the planning fallacy and the outside view may be used to conduct quality control and due diligence in project management. First, a much-neglected issue in project management is identified, namely that the front-end estimates of costs and benefits--used in the business cases, cost-ben…
Let Mn, n≥3, be a compact differentiable manifold with nonpositive Yamabe invariant σ(M). Suppose g0 is a continuous metric with V(M,g0)=1, smooth outside a compact set Σ, and is in Wloc1,p for some p>n. Suppose the scalar curvature of g0 is at least σ(M) outside Σ. We prove that $g_0…
Absolute index theorem for warped product manifolds.
problem Equivariant index computation for manifolds with warped product structures.
method Warped product structure, Fredholm operator, Atiyah-Segal-Singer index theorem.
result Equivariant relative index theorem for manifolds with warped product structures.
Constructs Poisson structures with compact support on manifolds.
problem Creating Poisson structures with compact support on manifolds.
method Explicit construction of Poisson structures with polynomial coefficients and modification outside open balls.
result Even-dimensional manifolds can be equipped with Poisson structures that vanish to infinite order at codimension one subsets.
Finite graphs with specific curvature have limited harmonic functions and ends.
problem Graphs with nonnegative curvature outside a finite subset.
method Introducing discrete Gromov-Hausdorff convergence to study bounded harmonic functions.
result The space of bounded harmonic functions is finite dimensional, and the number of non-parabolic ends is finite.
The paper classifies stable free boundary minimal hypersurfaces outside a ball.
problem Classifying stable free boundary minimal hypersurfaces outside a ball.
method Proved a Bôcher type result for positive Jacobi functions and used a symmetrization procedure.
result Stable free boundary minimal hypersurfaces outside a ball are catenoidal.
Paper explores using EEG for better speaker identification, even in noisy environments.
problem Speaker identification performance degrades in background noise.
method Uses EEG signals to enhance speaker identification systems, comparing with acoustic features.
result Speaker identification system using only EEG features outperforms one using only acoustic features in high background noise.
In this paper we examine inefficiencies and information disparity in the Japanese stock market. By carefully analysing information publicly available on the internet, an `outsider' to conventional statistical arbitrage strategies--which are based on market microstructure, company releases, or analyst reports--can never…
The paper constructs manifolds without smooth psc metrics but with L∞-metrics that are psc outside singular points.
problem Constructing manifolds without smooth positive scalar curvature metrics.
method Constructing manifolds with point singularities and L∞-metrics that are psc outside the singular set. result Examples of manifolds with point singularities that do not admit smooth psc metrics but do admit L∞-metrics that are psc outside the singular set. It is expected that matter composed of a perfect fluid cannot be at rest outside of a black hole if the spacetime is asymptotically flat and static (non-rotating). However, there has not been a rigorous proof for this expectation without assuming spheical symmetry. In this paper, we provide a proof of non-existence of …
An outsider's overview of Anosov flows in 3D.
problem Understanding Anosov flows in 3D and their interactions.
method Overview and discussion of main results and questions.
result Highlighting the interaction with topology and symplectic geometry.
Study shows flow convergence to smooth K-Ricci outside a divisor with cusp singularity.
problem Behavior of conical Kähler-Ricci flow as cone angle approaches zero.
method Analysis of limit behavior of conical Kähler-Ricci flow as cone angle tends to zero.
result Flow converges to a unique Kähler-Ricci flow with cusp singularity along the divisor.
Paper proposes a new method to improve BART model predictions outside training data range.
problem Improving prediction and prediction intervals for BART models at extrapolation points.
method Gaussian processes are added to BART leaf nodes for extrapolation.
result The new method outperforms standard BART and frequentist resampling methods in simulations.
In the present paper we study interval identification systems of order three. We prove that the Rauzy induction preserves symmetry: for any symmetric interval identification system of order three after finitely many iterations of the Rauzy induction we always obtain a symmetric system. We also provide an example of sym…
Simplified identification methods for causal inference with arbitrary interventional distributions.
problem Estimating cause-effect relationships from data with experimental interventions.
method Using Single World Intervention Graphs and nested model factorization, we provide algorithms for identifying causal parameters from mixed observational and interventional distributions.
result Our algorithms are complete for certain types of interventional marginal distributions.
Let H=Δ+V be a Schrödinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of H implies the existence of a function φ solution of Hφ=0 outside a compact set. This has consequences for minimal surfaces and for the finitenes…
Cyclic coordinate descent identifies models in finite time and converges linearly.
problem Model identification in composite nonsmooth optimization problems.
method Cyclic coordinate descent for a wide class of functions.
result Explicit local linear convergence rates for coordinate descent.
In this paper we extend Efimov's Theorem by proving that any complete surface in R3 with Gauss curvature bounded above by a negative constant outside a compact set has finite total curvature, finite area and is properly immersed. Moreover, its ends must be asymptotic to half-lines. We also give a partial so…
Study on identifying and inferring nonlinear dynamics on unknown networks.
problem Identifying network structure in nonlinear dynamic systems with unknown interactions.
method Showed network structure is not generically identified, requiring sufficient spectral heterogeneity. Developed necessary and sufficient conditions for identification and proposed a semiparametric estimator.
result Necessary and sufficient conditions for identification of network structure in nonlinear dynamic systems.
New findings on complexity limits in fixed budget bandit identification.
problem Determining the best possible error rate for fixed budget bandit identification.
method Analyzing the best non-adaptive sampling procedures and showing the existence of complexities.
result No fixed complexity for certain bandit identification tasks.
Wi-Fi signals-based person identification attracts increasing attention in the booming Internet-of-Things era mainly due to its pervasiveness and passiveness. Most previous work applies gaits extracted from WiFi distortions caused by the person walking to achieve the identification. However, to extract useful gait, a p…
Polyconvex energies with conformal invariance have smooth stationary points outside a discrete set.
problem Stationary points of conformally invariant polyconvex energies
method Proving smoothness of stationary points
result Smooth stationary points outside a discrete set
Study shows death ratio of COVID-19 deaths increases financial volatility.
problem Impact of COVID-19 deaths on financial markets.
method Analysis of VIX index based on daily case reports and death ratios.
result Death ratio positively influences financial volatility.
Bayesian methods reduce variance in subspace identification for small data sets.
problem High variance in traditional subspace identification methods for large models or small sample sizes.
method Investigation of Bayesian estimation solutions (regularized and shrinkage estimators) for subspace identification.
result Bayesian estimators reduce estimation risk by up to 40% compared to traditional methods.
Let (X,g0) be a simply connected, complete, negatively curved Riemannian manifold. We prove local and infinitesimal rigidity results for compactly supported deformations of the metric g0. For any negatively curved metric g equal to g0 outside a compact, the identity map of X induces a natural boundary map…
Obtaining reliable uncertainty estimates of neural network predictions is a long standing challenge. Bayesian neural networks have been proposed as a solution, but it remains open how to specify their prior. In particular, the common practice of an independent normal prior in weight space imposes relatively weak constr…
We compute the space of L2 harmonic forms (outside the middle degrees) on negatively curved Kaehler manifolds of finite volume.
Driver identification has emerged as a vital research field, where both practitioners and researchers investigate the potential of driver identification to enable a personalized driving experience. Within recent years, a selection of studies have reported that individuals could be perfectly identified based on their dr…