Develops active learning for scale-bridging simulations.
problem Quantitative predictions in nanoporous media and inertial confinement fusion.
method Active learning approach to optimize fine-scale simulations for coarse-scale hydrodynamics.
result Optimizes use of fine-scale simulations for coarse-scale predictions.
We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: (1) a scale mixture of normals with respect to an alpha-stable random variable; and (2) a mixture of Bartlett--Fejer kernels (or triangle densities) with r…
I2SB learns nonlinear diffusion processes between images.
problem Image restoration tasks, especially with limited structural information.
method Conditional diffusion models, Schrödinger bridge approach.
result I2SB outperforms standard models in various image restoration tasks. Unified framework to bridge human and LLM judgments.
problem Systematic discrepancies between human and LLM evaluations.
method Latent human preference score and linear transformations of covariates.
result Higher agreement with human ratings and exposure of systematic gaps.
New algorithm solves complex mean-field Schrödinger bridge problem.
problem Designing a controller for diffusion processes with nonlocal interaction.
method Generalized Hopf-Cole transform and Sinkhorn-type algorithm.
result Convergence guarantees for the proposed algorithm under mild assumptions.
Paper introduces a new generative learning model using Schrödinger bridge diffusion in latent space.
problem Learning distributions from divergent data distributions.
method Pre-training with large-scale models, Schrödinger bridge diffusion model in latent space.
result Effective control of second-order Wasserstein distance between generated and target distributions.
This work bridges two views of feature learning in neural networks.
problem The relationship between kernel scale changes and data-adaptive feature learning in neural networks remains unresolved.
method Using statistical mechanics, the work derives analytical expressions for network output statistics across scaling regimes.
result Kernel adaptation can be reduced to an effective kernel rescaling, but multi-scale adaptive approach provides richer insights.
Machine learning has begun to play a central role in many applications. A multitude of these applications typically also involve datasets that are distributed across multiple computing devices/machines due to either design constraints (e.g., multiagent systems) or computational/privacy reasons (e.g., learning on smartp…
Localized sampler tackles high-dimensional sampling with fewer samples.
problem Sampling from unknown distributions with limited data.
method Combining Schrödinger bridges and plug & play Langevin samplers with localization strategy.
result Localized sampler reduces dimensionality, making sampling more efficient.
A new sampler for FLMs improves token-level decoding controls.
problem Sampling from FLMs using standard methods collapses marginals and produces invalid sequences.
method Samples clean one-hot endpoints from FLM token marginals and uses Ornstein-Uhlenbeck bridges conditioned on these endpoints.
result The method preserves token-wise posterior-predictive marginals and improves quality-diversity tradeoff.
New algorithm improves on existing methods for solving transport problems.
problem Finding a map to transport one distribution to another.
method Iterative Markovian Fitting (IMF) and Diffusion Schrödinger Bridge Matching (DSBM).
result DSBM significantly improves over previous SB numerics and recovers various transport methods.
We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the lab…
Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.
problem Nonparametric estimation of Schrödinger bridge drifts from single time interval data.
method Direct Nadaraya-Watson plug-in estimator based on kernelized numerator and denominator terms.
result Uniform non-asymptotic bound, CLT under undersmoothing, and adaptive bandwidth selector.
Generative model uses Schrödinger bridges for stable sampling.
problem Sampling from unknown distributions with limited training samples.
method Combines Schrödinger bridges and Langevin dynamics.
result Effective stability and generation of samples within convex hull.
Developed a new thresholding method that connects soft and hard thresholding.
problem Connecting soft and hard thresholding methods in data analysis.
method Scaled soft thresholding method with empirical scaling values.
result Found two sources of over-fitting in the scaled soft thresholding method.
Current system thermal-hydraulic codes have limited credibility in simulating real plant conditions, especially when the geometry and boundary conditions are extrapolated beyond the range of test facilities. This paper proposes a data-driven approach, Feature Similarity Measurement FFSM), to establish a technical basis…
We propose a novel framework to investigate lead-lag relationships between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure …
Federated CTMC model estimates bridge deterioration hazards without sharing raw data.
problem Bridge inspection data privacy and cross-organizational data sharing constraints.
method Federated CTMC hazard model with local optimization and FedAvg aggregation.
result Federated model converges on global benchmark parameters without data transfer.
Generative models accelerate molecular dynamics by four orders of magnitude.
problem Femtosecond time steps limit access to slow molecular processes.
method Deep generative modeling framework that accelerates sampling.
result Quantitative characterization of equilibrium ensembles and dynamical relaxation processes.
ASBS improves sampling from Boltzmann distributions without importance weighting.
problem Sampling from Boltzmann distributions with known energies but unknown samples.
method Adjoint Schrödinger Bridge Sampler using kinetic-optimal transportation.
result ASBS achieves scalable and efficient sampling without importance weighting.
We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale …
New examples of knots with special bridge positions found.
problem Understanding special types of bridge positions for knots.
method Derived examples of knots with unperturbed weakly reducible non-minimal bridge positions.
result Connected sum of unperturbed bridge positions is unperturbed (a new conjecture).
HyperAgent improves RL exploration in large-scale problems.
problem Efficient exploration in large-scale reinforcement learning problems.
method Hypermodel framework for incremental posterior approximation without conjugacy.
result HyperAgent achieves logarithmic per-step computational complexity and sublinear regret.
The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.
problem Characterizing and finding examples of keen weakly reducible bridge spheres.
method Analyzing bridge spheres and their properties in terms of compressing disks and width complex.
result Infinitely many examples of keen weakly reducible bridge spheres for links in b-bridge position.
We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.
Any 2-bridge knot in the 3-sphere has a bridge sphere from which any other bridge surface can be obtained by stabilization, meridional stabilization, perturbation and proper isotopy.
Paper bridges statistical inference for DP-SGD, a privacy-preserving machine learning method.
problem Asymptotic statistical inference for Differentially Private Stochastic Gradient Descent (DP-SGD).
method Established asymptotic properties of SGD under randomized subsampling, extended to DP-SGD, proposed methods for constructing valid confidence intervals.
result Valid confidence intervals for DP-SGD output achieve nominal coverage rates while maintaining privacy.
Suppose a knot in a 3-manifold is in n-bridge position. We consider a reduction of the knot along a bridge disk D and show that the result is an (n−1)-bridge position if and only if there is a bridge disk E such that (D,E) is a cancelling pair. We apply this to an unknot K, in n-bridge position with re…
We define and compare several natural ways to compute the bridge number of a knot diagram. We study bridge numbers of crossing number minimizing diagrams, as well as the behavior of diagrammatic bridge numbers under the connected sum operation. For each notion of diagrammatic bridge number considered, we find crossing …
This study examines cores within superclusters, highlighting their transitional nature and dynamical state.
problem Understanding the morphology and dynamical properties of cores within superclusters.
method Projected and radial velocity distributions of galaxies, morphological analysis, entropy and mass estimates.
result Cores are transitional structures that evolve towards virialisation but remain gravitationally bound.
New method finds infinitely many surface knots with specific bridge numbers.
problem Finding numerical invariants for surface links.
method Colorings of surface links by keis to prove bridge number existence.
result Existence of infinitely many surface knots with bridge number n for n ≥ 4.
A new calibration metric bridges testability and actionability.
problem Combining testability and actionable insights for forecast probabilities.
method Cutoff Calibration Error (CCE) that assesses calibration over intervals of forecasted probabilities.
result Cutoff Calibration Error is both testable and actionable.
Researchers found infinite links with specific bridge positions.
problem Finding links with minimal bridge positions.
method Applying Takao et al.'s criterion to create links with locally minimal n-bridge and globally minimal m-bridge positions. result Provided an infinite family of links with specific bridge positions.
The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.
problem Nonlinear dynamics of minimal resistance in radial fields.
method Analysis of two non-equilibrium scenarios: scale-invariant free expansion and incompressible source flow.
result Incompressible flow acts as a structural regularizer, admitting unique, smooth, and strictly concave solutions.
We show that if K is a knot in S3 and Σ is a bridge sphere for K with high distance and 2n punctures, the number of perturbations of K required to interchange the two balls bounded by Σ via an isotopy is n. We also construct a knot with two different bridge spheres with 2n and 2n−1 bridges respecti…
We show that for every integer b≥3, there exists a link in a b-bridge position with respect to a critical bridge sphere. In fact, for each b, we construct an infinite family of links which we call square whose bridge spheres are critical.
Two-bridge ribbon knots have symmetric union presentations.
problem Characterizing two-bridge ribbon knots.
method Symmetric union presentations and partial knot analysis.
result Symmetric union presentations for various two-bridge ribbon knots.
We give a locally minimal, but not globally minimal bridge position of a knot, that is, an unstabilized, nonminimal bridge position of a knot. It implies that a bridge position cannot always be simplified so that the bridge number monotonically decreases to the minimal.
Paper explores link and plat presentations, showing equivalence under bridge isotopy.
problem Relationship between links in bridge position and plat presentations.
method Established equivalence between Hilden double coset classes of plat presentations and bridge positions up to isotopy.
result Revealed equivalence of Hilden double coset classes for n-bridge unknot and torus knots in plat position.
We give a complete characterization of those essential simple loops on 2-bridge spheres of 2-bridge links which are null-homotopic in the link complements. By using this result, we describe all upper-meridian-pair-preserving epimorphisms between 2-bridge link groups.
Bridge positions of handlebody-knots are equivalent when stable.
problem Equivalence of bridge positions in handlebody-knots.
method Demonstrated stability of bridge positions.
result Bridge positions of handlebody-knots are stably equivalent.
SIAN bridges simple models to neural networks by identifying necessary feature combinations.
problem The gap between simple models and powerful neural networks in performance.
method Feature interaction detection and sparse selection algorithm.
result Competitive performance across multiple tabular datasets with optimal tradeoff.
Paper refines generating function for 2-bridge knot groups.
problem Determining the number of epimorphisms between 2-bridge knot groups.
method Refined generating function considering genus and crossing number.
result Improved formula for epimorphisms between 2-bridge knot groups.
The study calculates braid indices for two-bridge knots and proves inequalities.
problem Calculating the braid index of two-bridge knots.
method Proved inequalities and provided average braid index for knots of a given crossing number.
result Average braid index for two-bridge knots with a given crossing number.
We show that there exists an infinite family of knots, each of which has, for each integer k>=0, a destabilized (2k+5)-bridge sphere. We also show that, for each integer n>=4, there exists a knot with a destabilized 3-bridge sphere and a destabilized n-bridge sphere.
For any given number of crossings c, there exists a formula to determine the number of 2-bridge knots of c crossings, and indeed it is a simple matter to actually construct presentations of these knots. However, the determination of whether a given (prime) knot is a 2-bridge knot remains a nontrivial exercise, and …
In this paper and its prequel, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to be homotopic in the orbifold. We also give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even …
Perturbing non-minimal bridge positions of a knot ensures similar behavior for its cable links.
problem Ensuring similar non-minimal bridge positions for cable links.
method Perturbing non-minimal bridge positions of a knot K and analyzing (2,2q)-cable links L. result Every non-minimal bridge position of a (2,2q)-cable link L is perturbed.