Researchers recover material parameters in transversely isotropic media from travel times of qP and qSV waves.
problem Recovering material parameters in transversely isotropic media from travel times of qP and qSV waves.
method Using parabolic type operators and stability estimates for travel times of qP and qSV waves.
result Stability estimates for recovering material parameters from travel times of qP and qSV waves.
We prove that the boundary distance map of a smooth compact Finsler manifold with smooth boundary determines its topological and differentiable structures. We construct the optimal fiberwise open subset of its tangent bundle and show that the boundary distance map determines the Finsler function in this set but not in …
Consider a Riemannian manifold in dimension n≥3 with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem is closely related with elastic \textit{qP}-wave tomography. Under the condition …
Efficiently solves heterogeneous QPs by reducing variables using instance-specific projections.
problem Solving high-dimensional quadratic programming problems efficiently.
method Data-driven framework with a graph neural network generating projections tailored to each QP instance.
result Produces high-quality solutions with reduced computation time, outperforming existing methods.
Unified description of p-brane QP-manifolds connects two recent tensor hierarchy descriptions.
problem Connecting two recent tensor hierarchy descriptions of p-brane QP-manifolds.
method Presented a duality-covariant version of p-brane QP-manifolds based on a specific QP-manifold construction.
result Solutions to constraints correspond to 1/2-BPS p-branes, suggesting a new incarnation of a brane scan.
QP perspective on Poisson-Lie T-duality topology changes.
problem Understanding Poisson-Lie T-duality through QP manifolds.
method QP manifolds and canonical transformations for symplectic reductions.
result Canonical transformations mediate Poisson-Lie T-duality.
In this paper we show that in anisotropic elasticity, in the particular case of transversely isotropic media, under appropriate convexity conditions, knowledge of the qSH wave travel times determines the tilt of the axis of isotropy as well as some of the elastic material parameters, and the knowledge of qP and qSV tra…
Constructs brane current algebras from QP-manifolds, generalizing string currents.
problem Constructing brane current algebras from QP-manifolds.
method Using Poisson algebra and QP-manifolds (symplectic L∞-algebroids), the paper derives a universal geometric form for Poisson brackets of brane currents. result Derives a universal expression for 't Hooft anomaly in the presence of fluxes.
Defines formal exponentials for graded manifolds and linearizes QP-manifolds.
problem Formal exponentials and linearizations of QP-manifolds.
method Definition of formal exponential maps, Grothendieck connections, and connections on tangent bundles.
result Linearizes QP-manifolds at points, giving formal tangent spaces L∞-algebra structures. We know SGAN may have a risk of gradient vanishing. A significant improvement is WGAN, with the help of 1-Lipschitz constraint on discriminator to prevent from gradient vanishing. Is there any GAN having no gradient vanishing and no 1-Lipschitz constraint on discriminator? We do find one, called GAN-QP. To construct a …
We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of M data p…
In this paper, we give the notion of a CLWX 2-algebroid and show that a QP-structure of degree 3 gives rise to a CLWX 2-algebroid. This is the higher analogue of the result that a QP-structure of degree 2 gives rise to a Courant algebroid. A CLWX 2-algebroid can also be viewed as a categorified Courant algebroid. We sh…
QP improves Gaussian process inference by minimizing Wasserstein distance.
problem Approximate inference in Gaussian processes using KL divergence is inadequate.
method Quantile Propagation (QP) minimizes Wasserstein distance instead of KL divergence.
result QP outperforms EP and variational Bayes in classification and Poisson regression.
Generalized current algebras introduced by Alekseev and Strobl in two dimensions are reconstructed by a graded manifold and a graded Poisson brackets. We generalize their current algebras to higher dimensions. QP manifolds provide the unified structures of current algebras in any dimension. Current algebras give rise t…
A rational projective plane (QP2) is a simply connected, smooth, closed manifold M such that H∗(M;Q)≅Q[α]/⟨α3⟩. An open problem is to classify the dimensions at which such a manifold exists. The Barge-Sullivan rational surgery realization theorem provides necessar…
Tail-Safe hedging uses reinforcement learning with a safety layer to manage financial risks.
problem Managing financial risks in derivatives trading with robustness and explainability.
method Combines distributional reinforcement learning with a CBF-QP safety layer to enforce financial constraints.
result Improves risk management without degrading central performance and avoids hard constraint violations.
Data-driven optimization improves mean-variance portfolios by penalizing norms.
problem Estimation error in mean-variance optimization.
method Augment MVO with norm penalties, use neural networks for optimization, and compute derivatives implicitly.
result Data-driven optimization reduces portfolio risk compared to standard MVO.
Neural network discovers exact solutions to QP with linear constraints.
problem Discovering exact solutions to Quadratic Programs (QP) with linear constraints using neural networks.
method Proposes a neural network modeling approach that analytically derives model parameters from problem coefficients, ensuring closed-form solutions without training.
result The closed-form NN model produces exact solutions for every critical region of the QP solution function, outperforming DNNs and commercial solvers in terms of optimality and feasibility.
MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence…
Develops a new fuzzy model using QPs and ewl2 regularization to improve local region behavior.
problem Inability of constant and linear functions to accurately describe local regions in fuzzy models.
method Applied Fuzzy C-Means for structure identification, used QPs as consequents, introduced ewl2 regularization.
result Improved model's ability to describe local regions without overfitting.
New method uses neural nets to control systems safely with disturbances.
problem Designing safe control laws for systems with disturbances.
method Imitation learning to train neural network controllers that satisfy CBF constraints.
result Demonstrated on a unicycle model with external disturbances.
Simplified approach to portfolio risk management and hedging in practice.
problem Challenges in applying academic portfolio risk management and hedging in real-world business settings.
method A straightforward approach using convex optimization and quadratic programming.
result Demonstrates how to solve portfolio risk management and hedging problems with CVXOPT.
We define \textit{graded manifolds} as a version of supermanifolds endowed with an additional Z-grading in the structure sheaf, called \textit{weight} (not linked with parity). Examples are ordinary supermanifolds, vector bundles over supermanifolds, double vector bundles, iterated constructions like TTM, e…
We study the problem of computing the minimum adversarial perturbation of the Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on continuous approximations of NN models or search for the perturbation by some heuristic methods. In this paper, we propose the first algorithm that is able to comp…
The paper prices a new life insurance policy for couples, considering various contingent benefits.
problem Valuation of life insurance policies for dependent coupled lives.
method Employed the QP-rule combining real-world and risk-neutral measures for pricing. result Explicit pricing expressions for the new insurance policy were derived and analyzed.
Partial label learning deals with the problem where each training instance is assigned a set of candidate labels, only one of which is correct. This paper provides the first attempt to leverage the idea of self-training for dealing with partially labeled examples. Specifically, we propose a unified formulation with pro…
The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the ℓ1-regularized (possibly not strongly) convex QP that terminate at an optimal solution in a finite numb…
New algorithms solve large-scale convex regression problems.
problem Large-scale convex regression with subgradient regularization.
method Active set type algorithm on dual QP, approximate optimization, randomized augmentation.
result Solves problems with n=10^5 and d=10 in minutes.
PriceAggregator optimizes hotel price fetching to increase Agoda's bookings.
problem Limited QPS from suppliers causes many user searches to be ignored.
method Intelligently determines queries to suppliers for price fetching.
result PriceAggregator increases Agoda's bookings significantly.
Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
problem Interaction of three impulsive gravitational waves in Einstein vacuum equations.
method Geometric estimates and wave estimates to prove local solution and continuity.
result Local solution to Einstein vacuum equations with three impulsive gravitational waves, Lipschitz continuity.
New Galilean spacetimes found as pp-wave reductions.
problem Understanding isotropic homogeneous Galilean spacetimes.
method Null reductions of pp-wave spacetimes.
result Found novel torsional Galilean spacetimes.
Paper tackles multivariate shape-constrained convex regression problems.
problem Fitting a convex function to data with component-wise monotonicity and uniform Lipschitz continuity.
method Least squares estimator via solving a constrained convex quadratic programming problem. Efficient algorithms designed: sGS-ADMM and pALM.
result Both proposed algorithms outperform state-of-the-art methods in numerical experiments.
Analyzes Gerstner's trochoidal waves and their geometric properties.
problem Understanding the geometry and kinematics of trochoidal waves.
method Derives velocity and arc length conditions for cycloidal, curtate, and prolate trochoids using Galilean transformations.
result Conditions for arc lengths of prolate and curtate trochoids to coincide over a wave cycle.
Wave fronts on certain surfaces become dense.
problem Density of wave fronts on surfaces.
method Proof of density for specific surfaces.
result Wave fronts become dense on flat torus, square billiard, Klein bottle, and cube surface.
Analyzes properties of stiffness tensors for elastic wave imaging.
problem Characterizing stiffness tensor fields for elastic wave imaging.
method Finsler-geometric methods applied to anisotropic stiffness tensor fields.
result Conditions for Finsler-geometric methods to be applicable.
Deep learning model predicts wind-wave relationship.
problem Characterize ocean wave climate for engineering applications.
method Two-stage deep learning model: CNN for spatial features, LSTM for temporal dependencies.
result Predicts spatio-temporal relationship between wind and significant wave height.
Impulsive waves contradict a 1962 conjecture about pp-waves.
problem The failure of the Ehlers--Kundt conjecture in the impulsive case.
method Summarized completeness results for impulsive wave spacetimes.
result Impulsive pp-waves are complete, contradicting the conjecture.
Extends Penrose limit to Finsler spacetimes.
problem Extending Penrose limit to Finsler spacetimes.
method Introducing lightlike coordinates and adapting Lorentzian pp-wave definition.
result New examples of Finsler pp-waves presented.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
problem Classifying Lorentz homogeneous spaces of dimension 3, focusing on plane waves.
method Revisiting and relaxing usual completeness assumptions, characterizing homogeneous plane waves.
result Non-unimodular elliptic plane waves are unique and non-extendable, geodesically complete only if symmetric.
Classifies solutions to vacuum weighted Einstein equations on pr-waves.
problem Classifying solutions to vacuum weighted Einstein field equations on pr-waves.
method Classifying solutions using smooth metric measure spacetimes of dimension 4.
result Provides examples of solutions with special geometric properties.
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton e…
Study compact plane waves, showing they are essentially standard.
problem Understanding the topology and dynamics of compact plane waves.
method Analyzing quotients of homogeneous plane waves by discrete subgroups.
result Compact quotients of homogeneous plane waves are essentially standard.
New method finds precise late-time behavior of wave equations.
problem Analyzing late-time behavior of wave equations with inverse-square potentials.
method Physical-space-based method for deriving late-time asymptotics.
result Sharp, uniform decay estimates in time for asymptotic late-time tails.
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric invariants of the initial wave fronts.
Paper explores non-uniqueness and uniqueness class for wave equations on graphs.
problem Non-uniqueness of solutions to wave equations on infinite graphs.
method Analyticity of solutions in the uniqueness class, extension to a wide class of linear evolution equations.
result Sharp uniqueness class for solutions of wave equations on graphs.
The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
New metrics link Kähler and pp-wave spacetimes.
problem Connecting Kähler and pp-wave spacetimes.
method Constructing families of complete almost Kähler metrics by deforming pp-waves.
result Established a one-to-one correspondence between almost Kähler metrics and pp-wave spacetimes.
New method detects spike-and-wave epileptiform discharges using Kendall's Tau-b.
problem Detecting spike-and-wave epileptiform discharges in EEG signals.
method Proposes a new method based on Kendall's Tau-b coefficient.
result High Specificity and rule in (SpPIn) for spike-and-wave discharge detection.