New framework for ranking distributions using variable fractional parameters.
problem Ordering distributions with varying steepness and local non-concavities.
method Introducing a function γ:Ro[0,1] to replace the fixed parameter in fractional SD. result Enables ranking of a broader range of distributions and incorporates dynamic greediness.
New graph feedback model for bandits with improved regret bounds.
problem Understanding how graph structure affects regret in bandit problems.
method Introduced fractional weak domination number and k-packing independence number to capture upper and lower bounds on regret. Used strong duality theorem to derive upper and lower bounds. result Proved general upper and lower bounds on regret for various graph structures, showing tightness up to a logarithmic factor.
Proposes new rule for ranking investment prospects over long horizons.
problem Ranking investment prospects over long horizons considering bounded risk aversion.
method Introduces asymptotic fractional-order stochastic dominance with bounded relative risk aversion.
result Establishes equivalent conditions for the new rule under lognormal returns without mean non-negativity constraint.
Study rough volatility models using path-dependent PDEs and fractional Brownian motions.
problem Modeling and analyzing rough volatility in financial markets.
method Showed conditional expectations are unique classical solutions to path-dependent PDEs derived from functional Itô formula. Leverage these to study weak rates of convergence for discretized stochastic integrals.
result Obtained optimal weak error rates for approximating log-stock prices in rough volatility models.
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
method Used Euler type scheme with integrated kernels to study weak convergence rate.
result Obtained weak convergence rate of min(3α−1,1) for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model. We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.
Study vortex flows on Riemann surfaces, proving dominated splitting and Anosov properties.
problem Investigate flow properties on Riemann surfaces.
method Associate flow to vortex equations, investigate properties of flow.
result Show that flow always admits a dominated splitting and identify special cases of Anosov flow.
The paper discusses fractional Sobolev immersions of flat domains into 3D space.
problem Developing C1 regularity and isometric immersions of flat domains with fractional Sobolev regularity. method Analysis of weak Codazzi-Mainardi equations, study of $W^{2, rac2s}$ planar deformations, and properties of the distributional Jacobian determinant.
result Generalization of isometric immersions with local fractional Sobolev regularity.
We introduce a new paradigm that is important for community detection in the realm of network analysis. Networks contain a set of strong, dominant communities, which interfere with the detection of weak, natural community structure. When most of the members of the weak communities also belong to stronger communities, t…
Improved volatility models for option pricing with weak error rates.
problem Improving volatility models to fit market data better.
method Developed a weak convergence analysis for the Euler method applied to linear rough volatility models.
result Proved weak convergence rates of 1/2 + H for linear models and 1 for quadratic payoffs.
Study examines surfaces with bounded fractional mean curvature, proving control over local parametrization.
problem Understanding surfaces with bounded fractional mean curvature.
method Investigates bounded L^p-norm of fractional mean curvature, proving control over local parametrization.
result Proves control over local parametrization, leading to lower Ahlfors-regularity, weak Michael-Simon type inequality, and stability application.
Paper approximates fractional harmonic maps with numerical methods.
problem Approximating fractional harmonic maps with constraints and nonlocality.
method Weak compactness results and numerical methods for various PDEs.
result Convergence of numerical approximations for fractional harmonic maps.
Study on error rates for approximating rough volatility models.
problem Simulation of rough volatility models with fractional Brownian motion.
method Analysis of weak error rates for numerical schemes, focusing on fBm and cubic test functions.
result Convergence rates for approximations are (3H+21)∧1 for exact left-point discretization and H+21 for hybrid schemes. Study improves weak error estimates for rough volatility models.
problem Efficient numerical schemes for non-Markovian stochastic processes with rough volatility.
method Analyzes weak rates for a class of stochastic processes with rough stochastic volatility.
result Weak rate is of order min{3H+0.5, 1} for a large class of test functions.
Finite-time extinction and smoothing effects in fractional fast diffusion on manifolds.
problem Finite-time extinction and smoothing effects in fractional fast diffusion equations.
method Nonlinear semigroups techniques, weighted Lp spaces, fractional Green function. result Sharp extinction rates and pointwise lower bounds for solutions.
Investigates Meyer risk measures and their applications in finance.
problem Existence and structure of Meyer risk measures.
method Fractional stochastic dominance and Meyer's utility function.
result Existence and structure of risk measures respecting v-SD order. Paper introduces a new optimization method for imbalanced datasets.
problem Overfitting in imbalanced datasets, especially in financial fraud detection.
method Fractional Weyl Integral optimization algorithm.
result Significantly improved performance in financial fraud detection (40% improvement in PR-AUC).
We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be handled delicately. We introduce a modified constraint operator to absorb the first order change of the metric in the dominant energy condit…
Researchers study fractional porous medium equation on hyperbolic space.
problem Analyzing the fractional porous medium equation on hyperbolic space.
method Existence results for solutions in weak sense, using fractional Laplacian and Green's function.
result Proves different smoothing effects for solutions.
Study nonnegative solutions on Riemannian manifolds using fractional porous medium equation.
problem Analyzing solutions to fractional porous medium equation on noncompact Riemannian manifolds.
method Existence and smoothing estimates for weak solutions in L1 and weighted spaces. result Results hold for Euclidean and hyperbolic spaces, including larger data classes.
Improved machine learning models outperform their simpler counterparts by using imperfect labels.
problem Improving model performance using imperfect labels.
method Random feature ridge regression (RFRR) with a deterministic equivalent for excess test error.
result The student model can outperform the teacher model regardless of the teacher's scaling law, achieving the minimax optimal rate.
Study of Dirac-Witten operator on Lorentzian manifolds under dominant energy condition.
problem Detecting non-trivial homotopy groups in spaces of initial data under strict dominant energy condition.
method Use index theory and Lorentzian Hitchin's α-invariant to analyze Dirac-Witten operator.
result Kernel of Dirac-Witten operator is non-trivial only if fundamental group is virtually solvable of derived length at most 2.
Study non-Weinstein Liouville geometry via hyperbolic dynamics, proving rigidity results.
problem Characterize non-Weinstein Liouville geometry with persistent transverse skeleton.
method Anosov 3-flows, Liouville Interpolation Systems, non-singular partially hyperbolic flows, hyperbolic dynamics.
result Mitsumatsu's examples characterize 4D non-Weinstein Liouville geometry with 3D persistent transverse skeleton.
This note removes technical assumptions and characterizes relatively dominated representations.
problem Geometrically finiteness and Anosov conditions in higher-rank settings.
method Characterization using eigenvalue gaps and limit maps.
result Relatively dominated representations are characterized using eigenvalue gaps and limit maps.
Develops Poisson structures on weak Sobolev loop spaces for integrable systems.
problem Analyzing integrable systems on low regularity loop spaces.
method Extending Mokhov's constructions to weak Sobolev spaces, constructing presymplectic and Poisson structures.
result Valid Poisson structures and deformations for weak Sobolev loops, extending Hamiltonian formalisms.
Fractional porous media equations yield q-Gaussian solutions for stock price returns.
problem Modeling stock price returns using fractional porous media equations.
method Analyzed three types of fractional extensions of the porous media equation.
result Local and non-local fractional extensions fit S&P 500 data better than classical models.
The Knowledge Gradient (KG) policy was originally proposed for online ranking and selection problems but has recently been adapted for use in online decision making in general and multi-armed bandit problems (MABs) in particular. We study its use in a class of exponential family MABs and identify weaknesses, including …
New conjectures link SU(r) Vafa-Witten invariants to Ramanujan's continued fractions.
problem Exploring new expressions for SU(r) Vafa-Witten partition functions.
method Combining S-duality, Gholampour-Thomas's theory, and Ramanujan's continued fractions.
result Conjectural expressions for SU(r) Vafa-Witten invariants in terms of theta functions and Seiberg-Witten invariants.
Study forecasts U.S. bond index using deep learning, finding persistence is key.
problem Forecasting U.S. aggregate bond index with deep learning methods.
method Constructed a stationary but maximally persistent representation of the bond index, evaluated using MLPs and CNNs.
result Deep learning models outperform traditional methods in short-horizon forecasting of bond indices.
Study on fractional mass for codimension-two currents, proving equi-coercivity and Γ-convergence.
problem Defining and studying fractional mass for codimension-two currents on manifolds.
method Energy minimization with Jacobian constraint, equi-coercivity, Γ-convergence, weak linking.
result Equivalence of two formulations of fractional mass, improved regularity for s-harmonic maps. The paper proves a comparison principle for complex Monge-Ampère flows and solves a uniqueness problem.
problem Proving uniqueness of weak solutions to the pluripotential Cauchy-Dirichlet problem.
method Proving a comparison principle for the pluripotential complex Monge-Ampère flows.
result Proves the uniqueness of the weak solution to the pluripotential Cauchy-Dirichlet problem.
Given a compact manifold Nn⊂Rν, s≥1 and 1≤p<∞, we prove that the class of smooth maps on the cube with values into Nn is strongly dense in the fractional Sobolev space Ws,p(Qm;Nn) when Nn is ⌊sp⌋ simply connected. For sp integer, we prove weak den…
Majorizing measures control sequential complexities for online learning.
problem Extending classical empirical processes theory to sequential cases.
method Generic chaining, majorizing measures, fractional covering numbers.
result Sharp control of worst-case sequential Rademacher complexity.
Study on W2S generalization with spurious correlations, proposing remedies.
problem Understanding and improving W2S generalization with spurious correlations.
method Theoretical analysis and algorithmic remedies for W2S fine-tuning.
result W2S always happens with sufficient pseudolabels when group fractions match, but may fail otherwise.
W2S FT often outperforms weak teachers due to low intrinsic dimensionality.
problem Understanding why weak-to-strong finetuning outperforms weak models.
method Analyzing W2S in ridgeless regression setting, focusing on variance reduction.
result Weak teacher's variance is inherited by strong student in shared feature subspace, reduced in discrepancy subspace.
Jackknife variance estimation validated for generalized U-statistics.
problem Uncertainty quantification for subsampling-based estimators.
method Jackknife variance estimation for generalized U-statistics with row-wise Lr weak law. result Jackknife and delete-d variance estimators are ratio-consistent for generalized U-statistics. We provide approximations for VIX futures and options in forward variance models.
problem Modeling VIX futures and options in forward variance models.
method Weak approximations and explicit formula derivation for VIX futures and options.
result Explicit combinations of Black-Scholes prices and greeks for option price approximations.
We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modell…
New algorithm improves convergence of gradient boosting trees.
problem Global convergence of Newton boosting in tabular machine learning.
method Introduces Gradient Regularized Newton Descent for GBDTs, proving linear convergence for smooth, strongly convex losses and O(k21) rate for general convex losses. result Achieves globally convergent second-order GBDT algorithm with rate matching first-order boosting.
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured b…
The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold M of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric Hs of order 0≤s<21 on the Lie algebra Xc(M) of vector fields with compact …
Diagnosing basal cell carcinomas (BCC), one of the most common cutaneous malignancies in humans, is a task regularly performed by pathologists and dermato-pathologists. Improving histological diagnosis by providing diagnosis suggestions, i.e. computer-assisted diagnoses is actively researched to improve safety, quality…
Bayesian priors improve neural network performance on weak signals.
problem Challenges in encoding domain knowledge for weak signals in neural networks.
method Proposed a new joint prior over local scale parameters for feature sparsity and signal-to-noise ratio, optimized with Stein gradient.
result Improved prediction accuracy on various datasets, including genetics applications with weak and sparse signals.
Unified model explains volatility memory in stocks and forex.
problem Understanding the components of volatility memory in financial markets.
method Developed a three-dimensional decomposition of volatility memory into level, shape, and tempo.
result Unified model shows that volatility memory is state-dependent, with different gates prevailing in equities and forex.
Consider a smooth, projective family of canonically polarized varieties over a smooth, quasi-projective base manifold Y, all defined over the complex numbers. It has been conjectured that the family is necessarily isotrivial if Y is special in the sense of Campana. We prove the conjecture when Y is a surface or threefo…
We consider the class of measurable functions defined in all of Rn that give rise to a nonlocal minimal graph over a ball of Rn. We establish that the gradient of any such function is bounded in the interior of the ball by a power of its oscillation. This estimate, together with previously known…
Learning new tasks with few samples using related task evaluations.
problem Learning a new task with limited data and related task evaluations.
method Modeling task relatedness through weak monotonicity and leveraging it in transfer learning and model selection aggregation.
result Pruning the model class based on monotonicity and hedging on the task frontier.
The paper explores how score-driven models can approximate rough volatility.
problem Modeling rough volatility with long memory structures.
method Extending score-driven models to include infinite-lag structures and heavy-tailed decay.
result Score-driven models converge to fractional Ornstein-Uhlenbeck processes under appropriate scaling.