The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.
problem Determining planar curves for constant-speed motion under specific force conditions.
method Analyzing the motion of a particle under friction and a central force field.
result Every solution to the constant-speed motion problem approaches either a circle or a logarithmic spiral.
New binary approach for multiclass classification scales logarithmically with classes.
problem Efficient multiclass classification for large number of classes.
method Proves a boosting theorem and translates it into an algorithm.
result Exponential speed improvements for large number of classes.
FastForest boosts Random Forest speed by 24%.
problem Efficiency in processing speed for Random Forest.
method Subsample Aggregating, Logarithmic Split-Point Sampling, Dynamic Restricted Subspacing.
result Average 24% increase in processing speed with accuracy maintained.
A new interpolation method speeds up neural ODE training.
problem Efficiently approximating gradients in neural ODEs.
method Interpolation-based technique to approximate gradients.
result Our method trains neural ODEs faster than the reverse dynamic method.
The paper studies foliation flows with logarithmic speeds and finds convergence to translating solutions.
problem Flowing foliations with specific curvature speeds and analyzing convergence behavior.
method Analyzes foliations of Rn+1∖{0} with speeds −log(F/f), focusing on uniformly convex hypersurfaces. result There is a distinct leaf MΘ∗ such that flows starting from it converge to a translating solution. Study improves privacy-preserving online prediction from experts with speed-ups.
problem Privacy-preserving online prediction from experts with speed-ups.
method Differentially private federated online prediction algorithms.
result Achieves m-fold regret speed-up with low-loss expert in federated setting. CNNs improve wind speed forecasts in the Netherlands.
problem Limited spatial patterns in current post-processing methods.
method Convolutional Neural Networks (CNNs) for spatial wind speed information.
result CNNs produce better probabilistic forecasts with higher Brier skill scores.
Quantum computing speeds up training Gaussian processes exponentially.
problem Training Gaussian processes efficiently.
method Quantum algorithms for computing the logarithm of the determinant and matrix inversion.
result Exponential improvement in estimating the marginal likelihood of Gaussian processes.
The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein-Uhlenbeck process. We focus on the optimal strategy with a logarithmic utility functi…
We prove that almost all geodesics on a noncompact locally symmetric space of finite volume grow with a logarithmic speed -- the higher rank generalization of a theorem of D. Sullivan (1982). More generally, under certain conditions on a sequence of subsets An of a homogeneous space G/Γ (G a semisimple Lie group…
New MCMC algorithms speed up sampling from polytope distributions.
problem Sampling from uniform distributions over polytopes efficiently.
method Vaidya walk and John walk based on interior point methods.
result Vaidya walk mixes significantly faster than Dikin walk.
Two new feature selection algorithms improve on RFE.
problem Optimal feature selection for faster and more accurate models.
method Fibonacci and k-Subsecting Recursive Feature Elimination.
result Faster feature selection with comparable predictive performance.
Compact scheme solves American put options with regime-switching using finite differences and Hermite interpolation.
problem Pricing American put options with regime-switching model.
method Logarithmic transformation, compact finite difference scheme, Hermite interpolation.
result The scheme provides an accurate and fast solution compared to other methods.
Quantum algorithm speeds up Gibbs partition function estimation.
problem Estimating partition functions in sublinear time.
method Sublinear-time quantum algorithm using quantum phase and amplitude estimation.
result First sublinear-time speed-up for partition function estimation.
SCAFFLSA reduces communication complexity for federated learning with heterogeneous clients.
problem Quantifying and reducing communication complexity in federated learning with heterogeneous clients.
method Proposes SCAFFLSA, a variant of FedLSA using control variates to correct for client drift.
result SCAFFLSA achieves logarithmic communication complexity for statistically heterogeneous agents, scaling with the inverse of the desired accuracy.
Nystrom approximation speeds up kernel model training.
problem Slow convergence in kernel models due to poor conditioning.
method Spectral preconditioning with Nystrom approximation for scalability.
result Nystrom approximation accelerates gradient descent nearly as well as exact preconditioner.
Researchers propose a non-monotone quantum natural gradient for quantum systems.
problem Applying natural gradient methods to quantum systems without monotonicity.
method Introducing a non-monotone quantum natural gradient (QNG) and demonstrating its superiority over conventional QNG.
result Non-monotone QNG outperforms conventional QNG in terms of convergence speed.
Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spectral algorithm to perform inference in HSMMs. Unlike expectation maximization (EM), our approach cor…
Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded because they do not represent topological 3-manifolds. In this paper we show how …
Quantum algorithm speeds up nested expectation estimation by nearly quadratically.
problem Estimating repeatedly nested expectations with quantum computing.
method Proposes a quantum algorithm achieving nearly quadratic speedup over classical methods.
result Achieves nearly quadratic speedup for RNEs, up to logarithmic factors.
In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…
Study traveling waves in hyperbolic space for Fisher-KPP equations.
problem Understanding wave behavior in hyperbolic space for Fisher-KPP equations.
method Analyzes the Cauchy problem in hyperbolic space for heat equation with Fisher-KPP forcing term.
result Proves new results on the dichotomy of solution propagation or vanishing based on diffusion and reaction strength.
New algorithm speeds up solving saddle-point problems with large condition numbers.
problem Solving saddle-point problems with large condition numbers.
method Proposes a stochastic proximal point algorithm that accelerates variance reduction methods.
result Reduces logarithmic term of condition number for iteration complexity.
Develops RF-softmax for faster training with softmax cross entropy.
problem High computational cost of training with softmax cross entropy.
method Random Fourier Features for efficient sampling from approximate softmax distribution.
result RF-softmax provides low bias in estimating both softmax distribution and its gradient.
Cover trees speed up MRI fingerprint recovery by reducing computation.
problem Efficiently reconstructing MRI fingerprint signals from compressed sensing data.
method Use cover trees for fast approximate nearest neighbor searches in IPG algorithm.
result Achieves 2-3 orders of magnitude reduction in computations.
New method solves ∂ˉ-equations for logarithmic forms on Kahler manifolds.
problem Solving ∂ˉ-equations for logarithmic forms on Kahler manifolds. method Using harmonic integral theory for currents on Kahler manifolds.
result Constructs the extension for logarithmic (n,q)-forms on the central fiber. Study rigidity by logarithmic capacity and related functions.
problem Rigidity phenomena in kernel functions and capacities.
method Exploration of Bergman kernel, logarithmic capacity, Green's function, and Euclidean distance/volume.
result Established rigidity theorems by logarithmic capacity.
Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.
problem Bounding invariant hypersurfaces and testing log canonicity of singularities.
method Introduce excess logarithmic residues, prove residue formula, derive Poincaré-type bound, and use them to recover log discrepancies.
result Componentwise logarithmic residues of a lifted foliation along the exceptional divisor recover log discrepancies of singularities.
Logarithmic connections on principal bundles over normal varieties are studied.
problem Existence and properties of logarithmic connections on principal bundles over normal varieties.
method Introducing logarithmic connections, showing equivalence to covariant derivatives, and proving existence conditions.
result Existence of logarithmic connections on principal bundles over normal varieties is equivalent to certain conditions on the associated vector bundles and adjoint bundles.
Study real logarithms of semi-simple matrices, focusing on differential structure.
problem Understanding the differential structure of real logarithms of semi-simple matrices.
method Examines the differential structure of real logarithms of semi-simple matrices under specific matrix types.
result Characterizes the differential structure of real logarithms of semi-simple matrices.
Introduces logarithmic Cartan geometry on complex manifolds with singularities.
problem Holomorphic Cartan geometry with singularities.
method Definition and study of logarithmic Cartan geometry on complex manifolds with polar part supported on a normal crossing divisor.
result Push-forward of a Cartan geometry constructed using a finite Galois ramified covering is a logarithmic Cartan geometry.
Optimistic search speeds up change point detection in large datasets.
problem Efficiently detecting change points in large-scale data with high computational demands.
method Adaptive logarithmic queries to reduce evaluation complexity.
result Asymptotic minimax optimality and fast localization rates for change point detection.
Local logarithmic Brunn-Minkowski holds for zonoids.
problem Logarithmic Brunn-Minkowski conjecture for zonoids
method Bochner method variant
result Local form of conjecture proven for zonoids
A new method solves American put options with high accuracy and speed.
problem Solving American put options with high accuracy and speed.
method Adaptive fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme.
result The method provides a more accurate solution and better performance in terms of computational speed.
New framework for logarithmically divergent integrals on manifolds with corners.
problem Logarithmically divergent integrals on manifolds with corners.
method Introduces new geometric framework and morphisms in logarithmic geometry.
result Functorial characterization of regularized integration.
Directly proves logarithmic systolic growth for all hyperbolic surfaces.
problem Proving logarithmic systolic growth for all hyperbolic surfaces.
method Using original Brooks/Buser-Sarnak surfaces through a direct approach.
result Directly proves logarithmic systolic growth for all hyperbolic surfaces.
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
problem Understanding hierarchical structure in hyperbolic groups with logarithmic separation.
method Proving groups with logarithmic separation split over cyclic groups and providing counterexamples.
result Not all groups with hierarchical structure have logarithmic separation profile.
Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.
problem Proving logarithmic Sobolev inequalities on manifolds with nonnegative curvature.
method Employing the ABP method developed by Brendle.
result Sharp L2 and Lp logarithmic Sobolev inequalities established. The paper explores how gradient descent trains associative memories, revealing oscillations and convergence issues.
problem Training dynamics of associative memories in overparameterized and underparameterized settings.
method Reduction to particle system dynamics, theory, and experiments.
result Oscillatory transitory regimes and benign loss spikes in overparameterized settings, suboptimal memorization in underparameterized settings.
Investment and consumption strategy optimized under uncertain conditions.
problem Optimal investment and consumption under logarithmic utility and uncertainty model.
method Characterized using quadratic BSDE.
result Optimal solution found.
The paper constructs a Saito basis for a specific class of divisors and applies it to logarithmic Poisson geometry.
problem Investigating a class of non-quasi-homogeneous free divisors and their logarithmic vector fields.
method Explicitly constructing a Saito basis for the module of logarithmic vector fields and applying it to logarithmic Poisson geometry.
result The construction of the Saito basis and the Lie-Rinehart algebra structure on the sheaf of logarithmic 1-forms.
Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.
problem Deviation of U-statistics with heavy-tailed samples.
method Exponential tail bounds and Large Deviation Principle (LDP) for U-statistics.
result Obtained an exponential upper bound for U-statistics tail decay, showing two regions of decay.
Extended logarithm for solvable elements in mapping class groups.
problem Logarithm of Johnson map extension to solvable elements.
method Extension to exponential solvable elements in mapping class groups using solvable Lie groups.
result Solvability of extended logarithm.
Functorial correspondence found between logarithmic connections and abelian connections.
problem Establishing a relationship between logarithmic sl2-connections and abelian connections. method Constructing inverse functors and a canonical cocycle.
result Functorial correspondence proved between logarithmic sl2-connections and abelian connections. Solves logarithmic ∂-equation on Kähler manifolds with smooth divisors.
problem Closedness of logarithmic forms and injectivity theorems.
method Cyclic covering trick to solve ∂-equation.
result Unobstructed deformations for smooth divisors.
Study of conformal logarithmic Laplacian on sphere, connecting Yamabe problems and Sobolev spaces.
problem Yamabe-type problems and Sobolev spaces on the sphere.
method Detailed spectral analysis, conformal invariance, and Hilbert space introduction.
result Established precise connection between sphere and \(\mathbb{R}^N\) logarithmic Laplacian.
In this work, we give a formula for the logarithmic invariant of knots in terms of certain derivatives of the colored Jones invariant. This invariant is related to the logarithmic conformal field theory, and was defined by using the centers in the radical of the restricted quantum group at root of unity. A relation bet…
Paper finds necessary condition for logarithmic Minkowski problem in higher dimensions.
problem Logarithmic Minkowski problem in higher dimensions.
method Established a necessary condition through generalization and refinement of previous work.
result Generalizes and refines necessary condition for logarithmic Minkowski problem.