New method predicts quasar continuum near Lyman-α with high precision and accuracy.
problem Precise measurement of quasar red damping wing for epoch of reionization.
method Fully probabilistic approach using conditional neural spline flows.
result Achieved state-of-the-art precision and accuracy in predicting quasar continua.
3D flying wings created for any angle asymptotic cones.
problem Creating 3D steady gradient Ricci solitons with any angle asymptotic cones.
method Constructing 3D flying wings for any angle asymptotic cones.
result 3D flying wings constructed for any angle asymptotic cones.
Researchers discover a new family of 3D solitons that are flying wings.
problem Verifying a conjecture about 3D steady gradient Ricci solitons.
method Analyzing a family of 3D flying wing solitons and proving properties of these solitons.
result 3D flying wing solitons are non-collapsed and have non-zero scalar curvature at infinity.
The paper explores new translating solitons and their relation to Δ-wings.
problem Understanding translating solitons and their properties.
method Description of new annular examples and proving related results.
result Proves several results about translating solitons and their relation to Δ-wings. 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.
Study of red blood cells using elastic surface theory.
problem Understanding the shape of red blood cells.
method Used Helfrich-Canham functional to model red blood cells as elastic surfaces.
result Cassinian ovals, except for the round sphere, do not solve the shape equation.
Finite entropy translating solitons in slabs have quantized entropy and unique structure.
problem Finite entropy translating solitons in slabs with finite genus and finite entropy.
method Analyzing wing numbers and using Morse theory for minimal surfaces.
result Entropy of these solitons is quantized into integer steps and unique structure proven.
This paper presents the recurrent estimation of distributions (RED) for modeling real-valued data in a semiparametric fashion. RED models make two novel uses of recurrent neural networks (RNNs) for density estimation of general real-valued data. First, RNNs are used to transform input covariates into a latent space to …
In this final part of a 3-part paper we introduce the pair of "wings" of the abstract PL-colored complexes Hm⋆, described in the second paper. The wings, via a weight enhanced Tutte's barycentric embedding of a planar map, produce the unexpected reformutation of a 3-dimensionl problem into a 2-dimen…
ReD improves LLM inference efficiency at fixed budget, reducing attempts and cost.
problem Improving LLM inference efficiency at a fixed budget.
method Reset-and-Discard (ReD) query method.
result ReD increases coverage@cost for a given budget, reducing attempts and cost.
Generative ML learns optimal pursuit trajectories in pursuit-evasion games.
problem Optimizing Blue's pursuit trajectory to intercept Red in a game of pursuit-evasion.
method Applying generative machine learning to learn optimal action policies for Blue.
result Generative ML models can learn relevant representations for pursuit-evasion dynamics.
A new method uses higher-order Langevin dynamics with critical damping for better generative modeling.
problem Improving generative models using Langevin dynamics with auxiliary variables.
method Introducing higher-order Langevin dynamics with critical damping, providing closed-form solutions.
result Improved generative models with better performance as measured by FID metric.
RED CoMETS improves multivariate time series classification accuracy.
problem Complexity of multivariate time series classification.
method Ensemble classifier RED CoMETS for symbolically represented multivariate time series.
result RED CoMETS achieves highest reported accuracy on 'HandMovementDirection' dataset.
3D steady gradient Ricci solitons are all O(2)-symmetric.
problem Characterizing 3D steady gradient Ricci solitons.
method Analyzing asymptotic behavior and using O(2) symmetry.
result All 3D steady gradient Ricci solitons are O(2)-symmetric.
TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.
problem Improving the convergence of Denoising Diffusion Probabilistic Models.
method Critically damping the Third-Order Langevin Dynamics (TOLD) forward transition matrix using eigen-analysis.
result TOLD++ converges faster than TOLD, verified on toy and real datasets.
Mathematical model describes how red blood cells return to equilibrium.
problem How red blood cells regain equilibrium after deformation.
method Gradient flow of the Canham-Helfrich functional, proving global existence and convergence for spheres and axisymmetric tori.
result Global existence and convergence of smooth solutions for spheres and axisymmetric tori under specific energy conditions.
We propose a multi-wing harmonium model for mining multimedia data that extends and improves on earlier models based on two-layer random fields, which capture bidirectional dependencies between hidden topic aspects and observed inputs. This model can be viewed as an undirected counterpart of the two-layer directed mode…
SPT predicts age and mass of red giants from spectra.
problem Challenges in age and mass estimation of red giants using traditional methods.
method SPT framework with Multi-head Hadamard Self-Attention and Mahalanobis distance-based loss function.
result Remarkable age and mass estimations with low errors and uncertainties.
New damping technique improves deep learning models by reducing noise in flat directions.
problem Improving generalization in deep learning models by reducing estimation noise in flat directions.
method Developed a novel random matrix theory based damping learner to reduce the shrinkage coefficient and improve generalization.
result Significant generalization improvements in logistic regression and deep neural networks experiments.
We prove a Weyl-type fractal upper bound for the spectrum of the damped wave equation, on a negatively curved compact manifold. It is known that most of the eigenvalues have an imaginary part close to the average of the damping function. We count the number of eigenvalues in a given horizontal strip deviating from this…
Autoencoder estimates parameters of noisy, multi-component damped signals.
problem Parameter estimation of damped sinusoidal signals under rapid decay and noise.
method Autoencoder-based approach using latent space for frequency, phase, decay, and amplitude estimation.
result High accuracy in parameter estimation, robustness to subdominant components and phase differences.
Quantization and reduction for coisotropic A-branes on Hamiltonian manifolds.
problem Quantization and reduction of coisotropic A-branes.
method Definition and construction of coisotropic A-branes, and a fibration over reduced spaces.
result Quantization commutes with reduction for coisotropic A-branes.
This study uses deep learning to infer stellar parameters from short TESS and K2 observations.
problem Inferring precise stellar parameters from short-duration TESS and K2 observations.
method Developed a machine learning algorithm to infer asteroseismic parameters from one-month-long TESS observations of red giants.
result The algorithm can accurately infer Δν and νmax for approximately 50% of TESS samples and ΔΠ1 for about 200 young red-giants from K2. Unified method for calculating financial option prices from characteristic functions.
problem Calculating financial option prices from characteristic functions in high dimensions.
method Damped Fourier-cosine expansion (COS) method.
result The method converges exponentially if the characteristic function decays exponentially.
Study shows how neural networks learn eigenfunctions of the NTK in underparameterized settings.
problem Understanding the dynamics of MSE optimization in underparameterized neural networks.
method Analysis of gradient flow dynamics, focusing on eigenfunctions of the NTK.
result Eigenfunctions of the NTK determine the learning dynamics in underparameterized networks.
Proposes RPG-RT for red-teaming T2I models without internal access.
problem Evaluating T2I models' security through red-teaming is challenging due to their closed-source nature and unknown defense mechanisms.
method Integrates LLM and rule-based preference modeling to dynamically adapt to unknown defense mechanisms.
result Demonstrates superior and practical approach for red-teaming T2I models.
DistillKac generates images quickly using damped wave equations.
problem Generating high-quality images efficiently.
method Uses damped wave equations and Kac dynamics for finite speed transport.
result Fast image generation with high quality and numerical stability.
New method classifies reticulocytes from red blood cells without labels.
problem Classifying reticulocytes from mature red blood cells without fluorescent labels.
method Unsupervised machine learning on morpho-rheological markers.
result Promising results in classifying reticulocytes from mature red blood cells.
Spatial statisticians and quantitative investors use the same mathematical object: a Schur complement, damped by one parameter.
problem The Schur complement is used in both spatial modeling and portfolio allocation, but the parameters are different.
method The Schur complement is interpreted as reliability shrinkage of a conditional Gaussian.
result The Schur complement is the same in both applications.
New framework assesses LLM security risks in BFSI.
problem Lack of domain-specific security evaluation for LLMs in BFSI.
method Risk-aware evaluation framework combining taxonomy, automated red-teaming, and ensemble judging.
result Higher decoding stochasticity and adaptive interaction lead to more severe disclosures.
The paper studies bowl solitons and their asymptotic expansions.
problem Understanding the behavior of bowl solitons under curvature flows.
method Asymptotic expansion analysis for a large class of fully nonlinear curvature flows.
result Uniqueness of bowl-type solitons in their asymptotic class and construction of wing-like solitons.
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from thi…
In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regul…
The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP conver…
A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.
problem Efficiently pricing multi-asset options in Lévy models.
method Optimized damping parameters and hierarchical adaptive quadrature.
result Significant speed-up in computational time for up to six dimensions.
In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversio…
RED-2400 is a public benchmark of trading events from a Solana exchange, labeled by algorithmic rejection.
problem Analyzing algorithmically-rejected trading events for insights into market dynamics.
method Public dataset of 6,660 algorithmically-rejected trading events, linked to post-rejection price and liquidity trajectories.
result First window of a planned series of datasets extending the time horizon and enabling regime-stratified analysis.
Scenario discovery is the process of finding areas of interest, known as scenarios, in data spaces resulting from simulations. For instance, one might search for conditions, i.e., inputs of the simulation model, where the system is unstable. Subgroup discovery methods are commonly used for scenario discovery. They find…
Develops geometric framework for dissipative field equations.
problem Dissipative field equations and their geometric analysis.
method Canonical k-contact manifolds, k-contactifications, splitting results, regularity conditions, criteria for PDEs. result Explicit Hamiltonian descriptions for various nonlinear PDEs.
After shortly recalling the construction of the Khovanov-Kuperberg algebras, we give a characterisation of indecomposable web-modules. It says that a web-module is indecomposable if and only if one can deduce it directly from the Kuperberg bracket (via a Schur lemma argument). The proofs relies on the construction of i…
We introduce \textcolor{red}{general} new techniques for computing the geometric index of a link L in the interior of a solid torus T. These techniques simplify and unify previous ad hoc methods used to compute the geometric index in specific examples \textcolor{red}{ and allow the simple computation of geometric i…
RED detects sleep EEG events using deep neural networks, outperforming previous methods.
problem Manual detection of sleep EEG events is time-consuming and variable.
method Deep Recurrent Neural Networks (RNNs) with convolutional and recurrent components.
result RED outperforms state-of-the-art methods in sleep spindle and K-complex detection.
In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dy…
We determine the distribution of size and growthrates of German business firms in 1987-1997. We find a log-normal size distribution. The distribution of growth rates has fat tails. It can be fitted to an exponential in a narrow central region and is dominated by finite-sample-size effects far in its wings. We study the…
We introduce an efficient method for training the linear ranking support vector machine. The method combines cutting plane optimization with red-black tree based approach to subgradient calculations, and has O(m*s+m*log(m)) time complexity, where m is the number of training examples, and s the average number of non-zer…
Traditional anatomical analyses captured only a fraction of real phenomic information. Here, we apply deep learning to quantify total phenotypic similarity across 2468 butterfly photographs, covering 38 subspecies from the polymorphic mimicry complex of Heliconius erato and Heliconius melpomene. E…
The energy in a square membrane Ω subject to constant viscous damping on a subset ω⊂Ω decays exponentially in time as soon as ω satisfies a geometrical condition known as the "Bardos-Lebeau-Rauch" condition. The rate τ(ω) of this decay satisfies τ(ω)=2min(−μ(ω),g(ω)) (see Lebeau [Math. Phys. Stud. …
Unified ODE model explains residual and non-residual networks.
problem Unclear relationship between residual and non-residual networks.
method Introducing a damping term in an ODE model to interpolate between ResNet and CNN architectures.
result Unified framework for understanding residual and non-residual networks.