Minimal surfaces from simple polynomials solve a geometric problem.
problem Constructing minimal surfaces using Traizet's method.
method Using polynomials that satisfy a hypergeometric differential equation.
result Simple minimal surfaces are described by these polynomials.
Researchers prove the existence of new doubly periodic minimal surfaces with specific properties.
problem Proving the existence of new doubly periodic minimal surfaces with specific properties.
method Using Traizet's regeneration method, the researchers constructed families of embedded, doubly periodic minimal surfaces.
result For each positive integer n, there is a family of embedded, doubly periodic minimal surfaces with parallel ends in Euclidean space of genus 2n-1 and 4 ends in the quotient by the maximal group of translations.
Using Traizet's regeneration method, we prove the existence of many new 3-dimensional families of embedded, doubly periodic minimal surfaces. All these families have a foliation of 3-dimensional Euclidean space by vertical planes as a limit. In the quotient, these limits can be realized conformally as noded Riemann sur…
We give a positive answer to M. Traizet's open question about the existence of complete embedded minimal surfaces with Scherk-ends without planar geodesics. In the singly periodic case, these examples get close to an extension of Traizet's result concerning asymmetric complete minimal submanifolds of Euclidean space wi…
Machine learning predicts gene involvement in axon regeneration.
problem Predicting gene involvement in specific biological processes.
method Extracted 31 features from databases, trained five machine learning models (Random Forest Classifier with 50 submodels), achieved 85.71% test score.
result Models have some predictive capability for gene involvement in axon regeneration.
Starting from works by Scherk (1835) and by Enneper-Weierstraß\ (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see \cite{Karcher1,Karcher}). In the singly periodic case, Karcher's examples of positive genera had been unique until Traizet obtained new ones in 1996 (see \cite{Traizet}).…
We prove that a closed 3-orbifold that fibers over a hyperbolic polygonal 2-orbifold admits a family of hyperbolic cone structures that are viewed as regeneration of the polygon, provided that the perimeter is minimal.
In 1996 M. Traizet obtained singly periodic minimal surfaces with Scherk ends of arbitrary genus by desingularizing a set of vertical planes at their intersections. However, in Traizet's work it is not allowed that three or more planes intersect at the same line. In our paper, by a {\it saddle-tower} we call the desing…
Model predicts road traffic using high-dimensional time-series with L1-penalization.
problem Predicting high-dimensional road traffic data with limited observations.
method Vector autoregressive model with L1-penalization for high-dimensional regression.
result The approach identifies the most important road sections and is competitive in prediction.
Minimal twin surfaces are found in material science, resembling crystal twins.
problem Finding mathematical and physical existence of twin surfaces.
method Employed Brakke's Surface Evolver to construct and analyze minimal twin surfaces.
result Strong evidence for the existence of D and G twins, and new cubic polyhedral models for G twins.
This paper provides statistical guarantees for WAE's latent space regeneration.
problem Lack of statistical analysis for Autoencoders, especially WAE.
method Utilizes Vapnik Chervonenkis (VC) theory and Optimal Transport of measures under the Wasserstein metric.
result WAE achieves the target distribution in the latent space and regenerates the input distribution.
Complete conjecture on rational curves on K3 surfaces.
problem Existence of infinitely many rational curves on K3 surfaces.
method Two new techniques: regeneration and marked point trick.
result Existence of integral curves of unbounded degree for any projective K3 surface.
This paper classifies Heisenberg structures on orbifolds and computes their deformation spaces.
problem Classifying Heisenberg structures on orbifolds and computing their deformation spaces.
method Analyzes the geometry of the Heisenberg group acting on the plane and considers the deformation and regeneration of Heisenberg structures on orbifolds.
result Closed orbifolds admitting Heisenberg structures are classified, and their deformation spaces are computed.
We describe Venture, an interactive virtual machine for probabilistic programming that aims to be sufficiently expressive, extensible, and efficient for general-purpose use. Like Church, probabilistic models and inference problems in Venture are specified via a Turing-complete, higher-order probabilistic language desce…
Given a tiling T of the plane by straight edge polygons, which is invariant by two independent translations, we construct a family of embedded triply periodic minimal surfaces which desingularizes T×R. For this purpose, inspired by the work of Martin Traizet, we open the nodes of s…
A stochastic model helps maintain insufficiently funded pension funds.
problem Maintaining pension funds that are underfunded and require external financing.
method A time-homogeneous diffusion process with a barrier is used to model the unrestricted reserves value, and a renewal-reward process models the financing effort.
result Expected values and cost evaluations of maintenance are derived, and the approach is applied to a generalized Brownian motion process.
Prefix consistency improves model reliability by weighting answers based on their reproducibility.
problem Improving the reliability of large language models' reasoning traces.
method Use prefix consistency to weight candidate answers based on their reproducibility during regeneration.
result Prefix consistency is the best correctness predictor, reaching Standard MV plateau accuracy with up to 21x fewer tokens.
New RL theory reduces sample complexity for mixing MDPs.
problem Optimal sample complexity for reinforcement learning in mixing MDPs.
method Regeneration-type ideas to analyze mixing times.
result Optimal sample complexity depends on mixing time, not just discount factor.
The study finds area estimates for specific surface types in a flat 3-torus.
problem Finding surfaces with constant mean curvature in a flat 3-torus.
method Analyzes closed surfaces with specific genus and constant mean curvature in a closed flat 3-torus.
result Establishes area estimates for surfaces with constant mean curvature, contrasting with minimal surfaces.
We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are close, then the solution locally resembles an entire solution discovered by Haus…
New minimal surfaces derived from helicoids.
problem Existence of minimal surfaces with specific symmetries.
method Balance equations and nodal limit analysis.
result Existence of new screw motion invariant minimal surfaces.
Given a closed orientable Euclidean cone 3-manifold C with cone angles less than or equal to pi, and which is not almost product, we describe the space of constant curvature cone structures on C with cone angles less than pi. We establish a regeneration result for such Euclidean cone manifolds into spherical or hyperbo…
The Viterbi process can be extended indefinitely in a pairwise Markov model.
problem Estimating hidden chains in pairwise Markov models.
method Construction of barriers to ensure Viterbi path goes through states.
result The Viterbi process is regenerative in the PMM.
We investigate the local contribution of the braid monodromy factorization in the context of the links obtained by the closure of these braids. We consider plane curves which are arrangements of lines and conics as well as some algebraic surfaces, where some of the former occur as local configurations in degenerated an…
Let T be a complex torus, and X the surface CP^1 x T. If T is embedded in CP^{n-1} then X may be embedded in CP^{2n-1}. Let X_Gal be its Galois cover with respect to a generic projection to CP^2. In this paper we compute the fundamental group of X_Gal, using the degeneration and regeneration techniques, the Moishezon-T…
Let O be a three-dimensional Nil-orbifold, with branching locus a knot Sigma transverse to the Seifert fibration. We prove that O is the limit of hyperbolic cone manifolds with cone angle in (pi-epsilon, pi). We also study the space of Dehn filling parameters of O-Sigma. Surprisingly it is not diffeomorphic to the defo…
Deep learning boosts micro-CT image resolution and texture recovery.
problem Compensating for image resolution trade-offs in micro-CT imaging.
method EDSRGAN trained on a diverse dataset of uCT images.
result EDSRGAN outperforms other methods in texture recovery and resolution.
We describe a 3-parametric family K of properly embedded minimal tori with four parallel ends in quotients of R3 by two independent translations, which we will call the \textit{Standard Examples.} These surfaces generalize the examples given by Karcher, Meeks and Rosenberg in \cite{ka4,ka6,mr3}.…
Generative approach learns hash functions for efficient binary search.
problem Challenges in learning discrete hash functions for fast search.
method Generative approach using Minimum Description Length principle and stochastic distributional gradient.
result Significantly better retrieval results than existing methods.
In 1988, Karcher generalized the family of singly periodic Scherk minimal surfaces by constructing, for each natural n≥2, a (2n−3)-parameter family of singly periodic minimal surfaces with genus zero and 2n Scherk-type ends in the quotient, called {\it saddle towers}. They have been recently classified by Pér…
AV-CPL uses continuous pseudo-labels for AVSR combining labeled and unlabeled data.
problem Improving AVSR performance with labeled and unlabeled data.
method Semi-supervised method using continuous pseudo-labels generated by the same AVSR model.
result Significant improvements in VSR performance on LRS3 dataset.
This work provides statistical guarantees for VAEs using PAC-Bayesian theory.
problem Theoretical properties of VAEs remain open questions.
method PAC-Bayesian theory to derive statistical guarantees.
result Upper bounds on Wasserstein distance between input and generative model.
Deep learning attacks chaos-based image encryption.
problem Chaos-based image encryption vulnerability.
method Project encrypted images to low-dimensional space, use deconvolutional generator to regenerate images.
result Proposes a key-independent, end-to-end trained method to attack chaos-based encryption.
InfoSFT improves LLMs by focusing on informative, medium-confidence tokens.
problem Overfitting to unlikely samples and degradation of prior capabilities in SFT.
method InfoSFT uses a principled weighting scheme to concentrate learning signals on medium-confidence tokens.
result InfoSFT improves generalization and preserves pre-existing capabilities over vanilla SFT and likelihood-weighted baselines.
Parallel decoding improves machine translation efficiency and accuracy.
problem Efficiently generating translations from left to right.
method Conditional masked language modeling for parallel decoding.
result Improves translation performance by over 4 BLEU points.
This paper introduces NPR, a technique to improve Bayesian inference for multi-modal, high-dimensional simulations.
problem Challenges in Bayesian inference for multi-modal, high-dimensional simulations.
method Introduces Neural Posterior Regularization (NPR) to enforce exploration of input parameter space.
result Empirically validated that NPR significantly improves performance on various simulation tasks.
Paper improves privacy for language models against reconstruction attacks.
problem Reconstruction attacks can regenerate training data from language models.
method Uses Rényi differential privacy with optimized privacy budgets.
result Better privacy guarantees for extraction of rare secrets.
New technique trains DNNs with fewer weights, saving memory and energy.
problem Training deep neural networks requires many weights, increasing memory and energy costs.
method Constrain weight updates to those with highest gradients, regenerating others.
result Pruned networks maintain accuracy while significantly reducing weight count and memory usage.
A new method selects features for clustering using a block model.
problem Finding high-quality features for clustering in linked data.
method Building a block model on the graph and using it for feature selection.
result BMGUFS outperforms state-of-the-art methods in clustering performance.
Paper tackles non-Markovian control problems with new learning methods.
problem Non-Markovian stochastic control problems with unknown parameters.
method Off-model training and importance sampling for deep neural network approximation.
result Quantitative error bounds for adaptive learning under model uncertainty.
Proposes CCCVAE for better single-cell clustering with cell-cell communication.
problem Improving single-cell RNA sequencing clustering by incorporating cell-cell communication.
method Integrates cell-cell communication into a variational autoencoder framework.
result Empirical results show CCCVAE outperforms standard VAEs in clustering performance.
Adversarial autoencoders improve speech-based emotion recognition.
problem Improving speech-based emotion recognition accuracy.
method Adversarial autoencoders map feature vectors to different noise PDFs, allowing synthetic sample generation.
result Adversarial autoencoders can encode high-dimensional feature vectors into a compressed space with minimal loss of emotion class discriminability.
Model predicts stock prices using GAN and RoI Pooling.
problem Predicting stock prices influenced by macroeconomic factors.
method Markov Decision Process, GAN, RoI Pooling.
result Identifies macroeconomic factors' influence on stock prices.
Kolmogorov-Arnold network improves GW catalog posterior construction.
problem Efficiently constructing posterior distributions for GW catalogs.
method Using the Kolmogorov-Arnold network to create lightweight neural density estimators.
result Kolmogorov-Arnold network achieves superior interpretability and accuracy in posterior construction.
Blind Source Separation (BSS) has proven to be a powerful tool for the analysis of composite patterns in engineering and science. We introduce Convex Analysis of Mixtures (CAM) for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the convex data scatter p…
Paper studies CLT rates for dependent data in Wasserstein-p distance.
problem CLT rates for multivariate dependent data in Wasserstein-p distance.
method Analyzes locally dependent sequences and geometrically ergodic Markov chains.
result Establishes optimal W1 CLT rates and Wp (p≥2) rates for dependent data. Improves many-shot learning by optimizing and generating influential examples.
problem Limited performance in many-shot in-context learning (ICL).
method Iterative optimization and generation of influential examples.
result Significant improvements across various tasks using BRIDGE.
S-VQ-VAE learns interpretable class-specific representations.
problem Learning interpretable representations of data.
method Supervised Vector Quantized Variational AutoEncoder (S-VQ-VAE).
result S-VQ-VAE learns interpretable class-specific representations.