The paper proves unique tangent cones for 2D almost minimizing currents.
problem Proving uniqueness of tangent cones for 2D almost minimizing currents.
method Unified approach based on White's theorem for area minimizing currents, with modifications.
result Tangent cones are everywhere unique for 2D almost minimizing currents.
We give a new proof of an old theorem by Banchoff and White 1975 that claims that the writhe of a knot is conformally invariant.
G-framework is presented by Peng [41] for measure risk under uncertainty. In this paper, we define fractional G-Brownian motion (fGBm). Fractional G-Brownian motion is a centered G-Gaussian process with zero mean and stationary increments in the sense of sub-linearity with Hurst index H∈(0,1). This process has sta…
The paper explores triangulations on spheres and tori, extending clock theorems.
problem Investigating triangulations of spheres and tori with colored triangles.
method Analyzing matchings between white and black triangles, focusing on their lattices and state transitions.
result Clock theorems extend to spheres but not to tori, with different lattice structures.
We prove the two theorems of the title, settling two long standing questions in the local theory of singular minimal hypersurfaces. The sharpness of either result is with respect to its hypothesis on the size of the allowable singular sets. The proofs of both theorems rely heavily on the author's recent regularity and …
We propose a fast algorithm for computing the economic capital, Value at Risk and Greeks in the Gaussian factor model. The algorithm proposed here is much faster than brute force Monte Carlo simulations or Fourier transform based methods \cite{MD}. While the algorithm of Hull-White \cite{HW} is comparably fast, it assu…
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is non-regular. The proof relies on a monotonicity formula for expanding solutions and a local regularity result for the network flow in the spirit of B. White's local regularity theorem for mean curvature …
New method for insider trading using white noise theory.
problem Optimal portfolio for an insider with logarithmic utility.
method White noise theory, stochastic forward integrals, Hida-Malliavin calculus, Donsker delta function.
result Developed a new approach to insider trading problem.
Minimal charts with loops have at most 6 white vertices.
problem Properties of minimal charts with loops.
method Analyzing minimal charts with exactly one white vertex per loop.
result There is no loop in a minimal chart with 7 white vertices.
Study analyzes correlation structure in two-factor Hull-White model for XVA calculations.
problem Capturing the correlation structure in two-factor Hull-White model for accurate XVA calculations.
method Combination of approximation formula and Monte-Carlo simulation to investigate correlation structure.
result Hull-White model effectively captures de-correlation of the yield curve under specific parameter conditions.
RIGA watermarks DNNs covertly and robustly with minimal accuracy loss.
problem Watermarking deep neural networks to enable tracing after release.
method Robust white-box GAN watermarking using adversarial training.
result Significantly improves covertness and robustness over state-of-the-art.
Novel 3D U-Net method for fast, reproducible white matter tract segmentation.
problem Challenges in fast and consistent white matter tract segmentation from diffusion tensor MRI.
method Convolutional neural network (3D U-Net) trained on a large DTI dataset.
result Reproducibility and accuracy of tract-specific diffusion measures.
Extends Brakke's local regularity theorem to longer time intervals.
problem Proving smoothness and graphicality of Brakke flows over extended time periods.
method Proving graphicality of Brakke flows with small gradient over time.
result Brakke flows remain graphical for some extended time intervals.
Develops a new flow with free boundary in barrier surfaces.
problem Free-boundary problems in barrier surfaces.
method Develops Brakke flow with free boundary, proves compactness, Gaussian monotonicity, and existence.
result Proves existence of free-boundary Brakke flows.
The paper extends flow theory with free boundaries, proving key bounds and theorems.
problem Mean convex mean curvature flow with free boundary conditions.
method Triple-approximation scheme combining maximum principle and various theorems.
result A priori bound on the ratio of second fundamental form to mean curvature.
No minimal charts with exactly seven white vertices found.
problem Finding minimal charts with specific vertex counts.
method Investigating charts representing embedded surfaces in 4-space.
result No minimal chart with exactly seven white vertices exists.
Black women and white men have the highest income disparity in the U.S.
problem Income inequality between black women and white men in the USA
method Dynamic microeconomic model, analyzing black and white population income since 1930
result Black females and white males are poles of overall income inequality
Estimates localized complexity of white-matter wiring using GANs.
problem Complexity of white-matter wiring, especially in ambiguous regions, confounds analysis.
method Bayesian estimate of heteroscedastic aleatoric uncertainty through image inpainting.
result Localized wiring complexity quantified, directly reflecting difficulty of lesion inpainting.
The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.
problem Proving lower bounds for Gaussian-weighted \(L^2\)-curvature integrals of self-shrinkers.
method Combining normal coordinate functions with weighted Poincaré inequalities and first-eigenvalue estimates.
result Explicit lower bounds in terms of entropy for closed self-shrinkers, leading to curvature gaps.
CVPR 2018 defenses ineffective against adversarial examples.
problem Vulnerability of neural networks to adversarial examples.
method Evaluated two white-box defenses from CVPR 2018.
result Defenses reduced model accuracy to 0%.
This paper analyzes crypto white papers under MiCAR, highlighting NLP's role.
problem Regulatory changes in crypto white papers under MiCAR.
method Survey of existing NLP applications, analysis of MiCAR changes.
result NLP can assist in regulatory compliance and white paper analysis.
Study shows structural variability in white matter bundles influences brain network function.
problem Understanding how structural variability in white matter bundles affects brain network function.
method Developed a method to measure local integrity of white matter bundles and used statistical approaches to analyze data.
result Variability in the local connectome correlates with variability in functional brain dynamics.
Efficiently distills white-box adversarial attacks into black-box models.
problem Generating efficient adversarial examples for robustness.
method Train a model to emulate white-box attack behavior and distill it into a more efficient black-box model.
result Reduces adversarial example generation time by 19x-39x and transfers to black-box settings.
White-box attacks reveal deep learning model training data records.
problem Privacy leakage in deep learning models.
method Design of white-box inference attacks for both centralized and federated learning.
result Deep models, even well-generalized ones, are susceptible to white-box membership inference attacks.
ODS improves adversarial attacks by maximizing output diversity.
problem Efficiency and effectiveness of adversarial attacks, especially black-box attacks.
method Output Diversified Sampling (ODS) that maximizes diversity in model outputs.
result ODS reduces the number of queries needed for black-box attacks on ImageNet by a factor of two.
Enhances geodesic fiber tracking in white matter using modified metrics and tensor data.
problem Improving the accuracy and robustness of geodesic fiber tracking in white matter.
method Modification of geodesic ray-tracing method using rescaled metrics and fourth-order tensor data.
result More satisfactory results in the construction of white matter tracts as geodesics.
Study the Hull-White model with volatility uncertainty, finding an arbitrage-free term structure.
problem Finding an arbitrage-free term structure in the Hull-White model with volatility uncertainty.
method Representing volatility uncertainty with sublinear expectation and G-Brownian motion; adjusting the model to find an arbitrage-free term structure.
result The resulting term structure is affine with respect to the short rate and the adjustment factor, consistent with the traditional Hull-White model after fitting the yield curve.
We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As a by-product we conclude that the volume of a finite-volume singular s…
Graphical hypersurfaces inside a cylinder become almost graphical after a period.
problem Dealing with mean curvature flow of hypersurfaces inside a cylinder that are initially graphical except for a small set.
method Using White's regularity theorem, proving a lower bound on the period during which the flow remains graphical inside a cylinder of half the radius.
result A mean curvature flow that lies inside a slab and is initially graphical inside a cylinder except for a small set will become graphical inside the cylinder of half the radius.
This paper studies business cycle patterns in UK sectoral output. It analyzes the distinction between white noise processes and their non-white noise counterparts in the frequency domain and further examines the associated features and patterns for the process where white noise conditions are violated. The characterist…
The paper proves smoothness of Brakke flows up to the end-time.
problem Smoothness of Brakke flows up to the end-time.
method Local regularity theorem for Brakke flows, extending White's theorem.
result Smooth extension of Brakke flows up to the end-time.
Study shows Nelson-Siegel curves fit well with Ho-Lee and Hull-White models.
problem Fitting observed interest rate term structures with interest rate models.
method Examined Nelson-Siegel curves in the context of Ho-Lee and Hull-White models.
result Extended Nelson-Siegel curves emerge from the forward curve process of the models.
In the last 15 years, White and Huisken-Sinestrari developed a far-reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise description of singularities and of high curvature regions in a mean convex flow.…
New formulas for barrier options in stochastic volatility models with nonzero correlation.
problem Calculating barrier options prices in models with nonzero correlation.
method Derivation of two novel closed-form formulas: Hull and White type and Alòs-like decomposition.
result Closed-form formulas for barrier options in stochastic volatility models with nonzero correlation.
We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White, we prove an abstract genericity result that employs the infinite dimensional Sard--…
A new Frank-Wolfe framework improves efficiency and effectiveness of adversarial attacks.
problem Develop efficient and effective optimization-based adversarial attack algorithms.
method Proposes a Frank-Wolfe algorithm variant for both white-box and black-box adversarial attacks.
result Demonstrates improved efficiency and effectiveness compared to existing methods.
Paper proposes a new Autoencoder for robustly encoding white matter streamlines.
problem Limited Autoencoder architectures ignore global streamline geometry and lack interpretability.
method Introduces Differentiable Vector Quantized Variational Autoencoder (D-VQ-VAE) for entire streamline bundles.
result Demonstrates superior performance in encoding and synthesis compared to state-of-the-art Autoencoders.
Paper proposes using auto-encoders to efficiently purify adversarial perturbations.
problem Vulnerability of machine learning models to adversarial examples.
method Iterative adversarial training on an auto-encoder to purify perturbations.
result The auto-encoder trained model outperforms other methods in protecting models against white-box attacks.
Transfer learning improves model robustness against adversarial attacks.
problem Understanding how transfer learning affects model robustness against adversarial attacks.
method Extensive empirical evaluations of white-box and black-box attacks on fine-tuned transfer learning models.
result Adversarial examples are more transferable when fine-tuning is used than when networks are trained independently.
New method calibrates white-box MI attacks, outperforming previous black-box methods.
problem Calibrating membership inference attacks on white-box models.
method Leveraging model memorization and overfitting features.
result Calibrated attack provides high precision in membership inference.
Paper presents a fast algorithm for pricing Bermudan swaptions under the two-factor Hull-White model.
problem Evaluating Bermudan swaption prices under the two-factor Hull-White model with high computational efficiency.
method Discretization of expected value calculation, Gaussian kernel sums, fast Gauss transform, grid rotation for stability.
result Significant reduction in computation time and improved stability for correlation close to -1.
In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider t…
CRATE-MAE learns structured representations from unlabeled data.
problem Learning structured representations from unlabeled data.
method Structured Diffusion with White-Box Transformers.
result CRATE-MAE achieves highly promising performance on large-scale imagery datasets.
Derives semi-closed form prices for barrier options in the Hull-White model.
problem Calculating prices of barrier options in the Hull-White model with time-dependent parameters.
method Applies generalized integral transform and heat potentials to solve linear Volterra equations of the first kind.
result The method provides more efficient and accurate solutions compared to finite difference methods.
A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order difference ``black and white triangle operators (equations)'' on triangulated surfaces with a black and white coloring or triangles. In this wor…
We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the rel…
ARCH and GARCH models assume either i.i.d. or (what economists lable as) white noise as is usual in regression analysis while assuming memory in a conditional mean square fluctuation with stationary increments. We will show that ARCH/GARCH is inconsistent with uncorrelated increments, violating the i.i.d. and white ass…
The paper defines the time function of stock prices using a mathematical model.
problem Understanding the movement and predictability of stock prices over time.
method Empirical evidence and mathematical modeling of white noise.
result Derives auto-correlation function, displacement formula, and power spectral density of stock price movement.