Study uses Lagrangian approach to prove limiting absorption principle on Riemannian spaces.
problem Proving limiting absorption principle on Riemannian scattering spaces.
method Lagrangian perspective applied to Riemannian scattering spaces.
result Spectral family is Fredholm in function spaces encoding Lagrangian regularity.
The purpose of this paper is to study the property of the resolvent of the Laplace-Beltrami operator on a noncompact complete Riemannian manifold with various ends each of which has a different limit of the growth rate of the Riemannian measure at infinity, in particular, focusing on the limiting absorption principle. …
We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show its dense range in L^2 wh…
Study controlled contagion with state-dependent killing, proving a comparison principle.
problem Analyzing controlled McKean--Vlasov contagion with state-dependent killing.
method Proof of a comparison principle using Wasserstein smooth-gauge comparison and killing-jump absorption estimates.
result Established a comparison principle for the two-population killed-particle HJB.
We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the iden…
Data-driven approach discovers molecular photoswitches with separated electronic absorption bands.
problem Engineering photoswitchable molecules with specific electronic absorption bands remains challenging.
method Data-driven discovery pipeline using Gaussian processes for multitask learning.
result Multioutput Gaussian process (MOGP) trained on four photoswitch transition wavelengths outperforms single-task models and TD-DFT.
We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the identity. By means of the limiting absorption principle, a Fredholm alterna…
The paper analyzes how open-end fund sales affect prices and returns.
problem How open-end fund sales impact prices and returns.
method Continuous-time market-clearing model to derive expected-return restrictions.
result Forced-sale pressure predicts actual fund selling and positive returns.
We study the optimal dividend problem for a firm's manager who has partial information on the profitability of the firm. The problem is formulated as one of singular stochastic control with partial information on the drift of the underlying process and with absorption. In the Markovian formulation, we have a 2-dimensio…
New complete panel dataset for LMICs helps analyze innovation and development.
problem Lack of complete data for empirical analyses in LMICs.
method Predictive Mean Matching multiple imputation technique.
result Created a large dataset of 47 variables for 82 LMICs from 2005-2019.
In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the metho…
New protocol reduces communication costs for heterogeneous bandits over complex networks.
problem Minimizing group regret in a multi-agent, heterogeneous bandit setting over complex networks.
method Flooding with Absorption (FwA) protocol for heterogeneous bandits over complex networks.
result FwA protocol significantly reduces communication costs compared to flooding while maintaining similar regret performance.
New model predicts radiative properties of nanoparticle layers with high accuracy and uncertainty.
problem Predicting radiative properties of nanoparticle embedded layers accurately and with uncertainty.
method Conditional normalizing flows learn conditional distributions of optical outputs given input parameters.
result The model achieves high predictive accuracy and reliable uncertainty estimates.
Paper explores ML for UV spectra, showing transferability in chemical space.
problem Modeling excited states and predicting properties of unseen molecules.
method Adapting charge model for excited states, using SchNarc approach.
result ML models can predict properties of unseen molecules and different excited states.
The paper calibrates shrinkage covariance estimators for spectral functionals in high dimensions.
problem Calibrating shrinkage covariance estimators for spectral functionals in high dimensions.
method Derives first-order null laws, distribution-free Davis-Kahan bands, and calibrated tests for spectral functionals under shrinkage.
result Calibrated tests and intervals for spectral functionals are provided, addressing the issue of estimation noise and shrinkage bias.
This paper explains how low-precision arithmetic causes loss spikes in deep learning models.
problem Loss spikes during long-term training of deep neural networks.
method Analyzes the impact of floating-point precision limits on gradient updates and feature means.
result Numerical Feature Inflation (NFI) explains loss spikes and rapid parameter norm growth.
A low-cost, robust, and simple mechanism to measure hemoglobin would play a critical role in the modern health infrastructure. Consistent sample acquisition has been a long-standing technical hurdle for photometer-based portable hemoglobin detectors which rely on micro cuvettes and dry chemistry. Any particulates (e.g.…
Study on liquidation games with market drop-out, proving unique equilibria.
problem Analyzing portfolio liquidation with market drop-out constraints.
method Proves existence and uniqueness of equilibria using integral equations.
result Existence and uniqueness of equilibria in both mean-field and finite-player games.
Enhanced X-ray polarimetry with deep learning for better exposure times.
problem Improving sensitivity of X-ray telescopic observations with imaging polarimeters.
method A weighted maximum likelihood combination of predictions from a deep ensemble of ResNet convolutional neural networks trained on Monte Carlo event simulations.
result Improves effective exposure times by ~45% for power-law source spectra.
MethaneMapper detects methane emissions with high accuracy and reduced model size.
problem Challenges in detecting and quantifying methane emissions from AVIRIS-NG data.
method Spectral absorption wavelength aware transformer network, introducing two novel modules.
result Achieves 0.63 mAP in detection and reduces model size by 5x.
Paper improves gas species identification in complex mixtures using neural networks.
problem Identifying gas species in multi-gas mixtures with high accuracy.
method Multi-label neural networks with optimal thresholding for IR spectroscopy.
result Optimal thresholding improves classification performance over conventional methods.
The paper studies the dimension of limit sets using variational principles and stationary measures.
problem Calculating the Hausdorff dimension of limit sets of Anosov representations and the Rauzy gasket.
method Established variational principles for affinity exponents and Rauzy gaskets, combined with dimension formulas of stationary measures.
result Yields the equality between the Hausdorff dimensions and affinity exponents in both settings.
We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology o…
Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show tha…
A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.
problem Tackling the indistinguishability of spectral line profiles under scalar summaries.
method Introduces a geometric representation of line profiles using rough path theory, mapping profiles to a common velocity grid and defining descriptors from path properties.
result Compact descriptors separate morphologies with similar scalar summaries, revealing ordered line structures.
GANPOP uses deep learning to estimate optical properties from single images, improving accuracy over existing methods.
problem Estimating optical properties from single wide-field images.
method Conditional generative adversarial networks trained on paired images and optical property maps.
result GANPOP estimates optical properties with 58% higher accuracy than single-snapshot optical property technique in human gastrointestinal specimens.
Deep neural networks' infinite-width behavior approximated by Gaussian models.
problem Understanding the behavior of deep neural networks in the limit of infinite width.
method Using the Lindeberg exchange principle to approximate weights by Gaussian random variables.
result Quantitative bounds on the 2-Wasserstein distance between deep neural networks and Gaussian limits.
A new framework models multi-state events and biomarkers.
problem Limited representation of complex multi-state trajectories.
method General multi-state joint modeling framework.
result Accurate parameter recovery and personalized predictions.
We establish large deviation principles for convolutional neural networks.
problem Understanding the behavior of convolutional neural networks in the infinite-channel limit.
method We establish large deviation principles for convolutional neural networks under Gaussian prior and posterior distributions.
result We provide a large deviation principle for the sequence of conditional covariance matrices and the posterior distribution.
MEP-Net uses MEP to generate solutions from limited data.
problem Generating solutions to scientific problems with incomplete information.
method Combines MEP with neural networks to learn complex distributions from moment constraints.
result Demonstrates MEP-Net's effectiveness in modeling biochemical reaction networks and generating complex distributions.
Study shows superdiffusive behavior in geodesic flows on curved surfaces.
problem Understanding the statistical behavior of geodesic flows on curved surfaces.
method Proved nonstandard central limit theorem with superdiffusive normalisation (tlogt)1/2 for geodesic flows on nonpositively curved surfaces. result Geodesic flows exhibit superdiffusive behavior with correlations decaying at rate t−1. Mean field game with defaultable agents and systemic risk quantified.
problem Modeling systemic risk in a financial system with defaultable agents.
method Introduced a mean field game with default, provided an explicit solution, and derived an equation for default probability evolution.
result Systemic risk is described by the evolution of default probability.
Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to …
We prove a Lorentzian splitting theorem with weakened curvature conditions.
problem Proving a Lorentzian splitting theorem under weakened Ricci curvature conditions.
method Using achronal limits and geometric maximum principles.
result Strengthened a related result in [29] by removing a boundedness condition on Ricci curvature.
A principle for specialized decision-making divides complex problems into manageable parts.
problem Complex decision-making problems beyond individual capabilities.
method An on-line learning rule that learns a partitioning of the problem space for specialized linear policies.
result The approach solves problems that exceed individual decision-makers' capabilities.
We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the distances-to-default of financial institutions and absorption at zero correspon…
We derive a semi-analytic formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main…
Background: Pharmacokinetic evaluation is one of the key processes in drug discovery and development. However, current absorption, distribution, metabolism, excretion prediction models still have limited accuracy. Aim: This study aims to construct an integrated transfer learning and multitask learning approach for deve…
Paper establishes a new formula for Atiyah-Patodi-Singer index using eta invariants.
problem Calculating the Atiyah-Patodi-Singer index without invertibility of boundary operator.
method Using an asymptotic gluing formula for eta invariants and a splitting principle.
result Formula expressing index in terms of eta invariants of domain-wall massive Dirac operators.
Study optimal reward schemes for inducing desired player performance in risky contests.
problem Designing optimal rewards to encourage desired performance levels in risky contests.
method Analyzed the optimal reward schemes for inducing average and specific rank performance.
result Optimal reward schemes can have surprising shapes, not just related to inequality.
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 …
Reinterprets Granger causality with causal Bayesian networks and Reichenbach's principles.
problem Lack of a rigorous causal foundation in Granger causality.
method Reinterpreting Granger causality through Reichenbach's principles and causal Bayesian networks, implementing as c-GC.
result c-GC provides a more principled framework for causal discovery in observational datasets.
Study uses deep learning to quickly estimate tissue properties for personalized radio-frequency dosimetry.
problem Time-consuming tissue segmentation limits personalized radio-frequency dosimetry.
method Developed a learning-based approach using Convolutional Neural Networks (CNN) for magnetic resonance images.
result Smooth distribution of dielectric properties improves SAR distribution consistency.
Two firms compete in a financial market, choosing dividend strategies to avoid default and maximize profits.
problem Strategic interaction between two financially constrained firms in a market with default risk.
method Construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control.
result Explicit identification of optimal strategies and equilibrium payoffs for different initial conditions.
Constructs expanding gradient Ricci solitons with unique properties.
problem Creating expanding gradient Ricci solitons with specific characteristics.
method Combining previous work with localized maximum principle.
result Constructs various examples of expanding gradient Ricci solitons with positive curvature and exotic curvature decay.
New method tests conditional independence using spectral representations.
problem Untestable conditional independence in many settings.
method Spectral representations of partial covariance operators, bi-level contrastive learning.
result Asymptotic validity and power guarantees for CI testing.
Researchers reveal how neural networks implicitly favor low-frequency functions.
problem Why deep neural networks generalize well despite having more parameters than samples.
method Proposed a linear F-Principle dynamics to predict and explain the learning of two-layer ReLU NNs.
result Explicitly penalizing higher frequencies in the optimization process improves generalization.
Study on spectral gaps of hyperbolic surfaces as genus increases.
problem Understanding differences in eigenvalues for large genus hyperbolic surfaces.
method Analysis of the Laplacian on degenerating hyperbolic surfaces, min-max principle.
result Supremum of spectral gaps has infimum limit of at least 1/4 as genus increases.