Classifies components of strata of k-differentials on Riemann surfaces.
problem Classifying connected components of strata of k-differentials.
method Developed new techniques to study connected components of strata of k-differentials for general k.
result Complete classification of connected components of the strata of quadratic differentials with arbitrary poles.
The paper describes a cover of strata of k-differentials with a formula for fiber cardinality.
problem Understanding the ramification locus and cardinality of fibers in strata of k-differentials.
method Intersection calculations on multi-scale compactification and flat geometry.
result A formula for the cardinality of each fiber involving the k-factorial function.
A k-differential on a Riemann surface is a section of the k-th power of the canonical line bundle. Loci of k-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification of the moduli space of k-differentials. In this paper we give a complete description for the compa…
Study meromorphic k-differentials with prescribed singularities on Riemann surfaces.
problem Understanding local invariants of meromorphic k-differentials on Riemann surfaces.
method Analyzing orders of zeros and poles, and k-residues at poles.
result For a given pattern of zeros, there exists a primitive holomorphic k-differential with these zeros.
Researchers solved a number-theoretic hypothesis to determine the spin parity of k-differentials.
problem Determining the spin parity of k-differentials on Riemann surfaces of genus zero and one.
method Proved a number-theoretic hypothesis (Conjecture A.10) by reformulating it in terms of Jacobi symbols and reducing it to a combinatorial identity.
result The spin parity of k-differentials on Riemann surfaces of genus zero and one was completely determined.
We study the local invariants that a meromorphic k-differential on a Riemann surface of genus g≥0 can have. These local invariants are the orders of zeros and poles, and the k-residues at the poles. We show that for a given pattern of orders of zeroes, there exists, up to a few exceptions, a primitive k-diff…
Paper defines quasi-Strebel structures for meromorphic k-differentials and proves their existence.
problem Existence of quasi-Strebel structures for meromorphic k-differentials.
method Introduced quasi-Strebel structures and proved their existence for meromorphic k-differentials.
result Every differential of even order k > 2 satisfying certain conditions admits a quasi-Strebel structure.
Classifies components of k-differentials and their orbit closures.
problem Classifying components of strata of k-differentials and their orbit closures.
method Algebraic approach using multiscale compactification.
result Complete classification of components of strata of holomorphic and meromorphic k-differentials.
Connected boundaries of strata of differentials are always connected in various compactifications.
problem Understanding the connectedness of boundaries of differentials' strata in various compactifications.
method Explicit degeneration techniques, algebraic compactifications, and properties of Teichmüller curves.
result The boundaries of differentials' strata are always connected in any complete algebraic compactification.
For g≥2, j=1,…,g and n≥g+j we exhibit infinitely many new rigid and extremal effective codimension j cycles in Mg,n from the strata of quadratic differentials and projections of these strata under forgetful morphisms and show the same holds for k-differentials with $k\geq …
Flat surfaces that correspond to k-differentials on compact Riemann surfaces are of finite area provided there is no pole of order k or higher. We denote by \textit{flat surfaces with poles of higher order} those surfaces with flat structures defined by a k-differential with at least one pole of order at least $k…
In the first part we extend the construction of the smooth normal-crossing divisors compactification of projectivized strata of abelian differentials given by Bainbridge, Chen, Gendron, Grushevsky and Moeller to the case of k-differentials. Since the generalized construction is closely related to the original one, we m…
Study automorphisms of smooth curve graphs on surfaces.
problem Understanding automorphisms of fine curve graphs.
method Examined automorphisms of continuously differentiable curves on surfaces.
result Automorphisms on surfaces of genus ≥ 2 are induced by homeomorphisms.
Novel neural network solves PDEs with multi-scale resolution.
problem Solving time-dependent PDEs with varying spatial and temporal scales.
method Multi-scale message passing neural network with temporal and spatial gating modules.
result Outperforms baselines on PDEs with diverse scales.
This study presents a new lossy image compression method that utilizes the multi-scale features of natural images. Our model consists of two networks: multi-scale lossy autoencoder and parallel multi-scale lossless coder. The multi-scale lossy autoencoder extracts the multi-scale image features to quantized variables a…
The present paper shows that for a given integer k greater than 2 it is possible to construct an at least k-differentiable Riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal. Moreover, we show that this construction can be extended to the case of Finsler sp…
Paper introduces multi-scale methods to improve CATE estimation from EO data.
problem Challenges in balancing fine-grained and contextual information in EO-based causal inference.
method Multi-Scale Representation Concatenation, combining Vision Transformer and Causal Forests.
result Multi-scale approach captures effect heterogeneity better than single-scale models.
Boosting theory explains why multi-scale GNNs work.
problem Over-smoothing in graph neural networks.
method Gradient boosting and transductive learning analysis.
result Test error bound decreases with more node aggregations.
In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs…
CAST improves spectral clustering for multi-scale data by integrating reachability similarity.
problem Applying spectral clustering to multi-scale data where clusters vary in size and density.
method CAST integrates reachability similarity with distance-based similarity to derive a coefficient matrix, then applies trace Lasso regularization.
result CAST provides excellent performance and robustness across various multi-scale data test cases.
The analysis of temporal networks has a wide area of applications in a world of technological advances. An important aspect of temporal network analysis is the discovery of community structures. Real data networks are often very large and the communities are observed to have a hierarchical structure referred to as mult…
Strata of k-differentials on smooth curves parameterize sections of the k-th power of the canonical bundle with prescribed orders of zeros and poles. Define the tautological ring of the projectivized strata using the κ and ψ classes of moduli spaces of pointed smooth curves along with the tautological class η…
Framework for multi-scale clustering using phase transitions.
problem Clustering datasets with multi-scale structures.
method Cascade of phase transitions in simulated annealing of Expectation-Maximisation algorithm with weighted local covariance.
result Approximation of the number and size of clusters at different scales.
We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with normal crossing boundary. Locally, our compactification can be described as the norm…
EvoMSN tackles time series forecasting under distribution shifts by evolving multi-scale normalization.
problem Accurate long-term time series forecasting under complex distribution shifts.
method EvoMSN framework with multi-scale statistics prediction and adaptive ensembling for collaborative updating.
result Improves forecasting performance of five mainstream methods on benchmark datasets.
New PINN architectures learn high-frequency features using Fourier features.
problem PINNs struggle with high-frequency or multi-scale features.
method Employ spatio-temporal and multi-scale random Fourier features.
result Effective PINN models for multi-scale PDEs.
Proposes OC4Seq for detecting anomalies in discrete event sequences.
problem Challenges in detecting anomalies in discrete event sequences, including data imbalance, discrete events, and sequential nature.
method Integrates anomaly detection with recurrent neural networks (RNNs) to embed sequences into latent spaces and designs a multi-scale RNN framework to capture multi-scale sequential patterns.
result OC4Seq consistently outperforms various baselines on three benchmark datasets.
Paper tackles leverage effect estimation from noisy data.
problem Estimating leverage effect from high-frequency data with microstructure noise.
method Holistic multi-scale framework operating directly on leverage effect, using Subsampling-and-Averaging Leverage Effect (SALE) and Multi-Scale Leverage Effect (MSLE) estimators.
result Holistic multi-scale framework achieves substantial efficiency gains over existing benchmarks.
New method improves robustness of large models without sacrificing accuracy.
problem Improving robustness of large pre-trained models without accuracy loss.
method Multi-scale diffusion denoised smoothing, selectively applying smoothing at multiple noise scales.
result Strong certified robustness at high noise levels with accuracy close to non-smoothed classifiers.
Deep generative modeling using flows has gained popularity owing to the tractable exact log-likelihood estimation with efficient training and synthesis process. However, flow models suffer from the challenge of having high dimensional latent space, the same in dimension as the input space. An effective solution to the …
DRFormer uses dynamic tokenization and multi-scale transformer to forecast long time series.
problem Forecasting long-term time series data across diverse scales.
method Dynamic tokenizer, multi-scale transformer, dynamic sparse learning, rotary position encoding.
result DRFormer outperforms existing methods in forecasting accuracy.
We construct a new map from a convex function to a distribution on its domain, with the property that this distribution is a multi-scale exploration of the function. We use this map to solve a decade-old open problem in adversarial bandit convex optimization by showing that the minimax regret for this problem is $\tild…
CrossAD detects anomalies in time series data by considering cross-scale associations and cross-window modeling.
problem Anomaly detection in time series data is challenging due to varying patterns at different scales and fixed window sizes.
method CrossAD incorporates cross-scale reconstruction and a query library to capture dynamic cross-scale associations and comprehensive context.
result CrossAD achieves state-of-the-art performance in anomaly detection across multiple real-world datasets.
We consider the local analytic behavior for a family of holomorphic differentials on a family of degenerating annuli. Three results and discussion are presented. The first is the normal families Lemma 1. The second is an isomorphism of sheaves, formula (3), giving a direct description of families of regular k-differe…
Novel framework for systemic risk analysis in financial markets.
problem Systemic risk in financial markets.
method Multi-scale network dynamics, transfer entropy networks, agent-based modeling, wavelet decomposition, Model Context Protocol (MCP).
result Multi-scale approach reveals hidden systemic risk patterns.
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a possible explanation for the complex dynamics of markets' returns. Scaling and m…
Space2Vec learns multi-scale spatial representations from grid cell insights.
problem Encoding spatial features with varying scales from GIS data.
method Proposes Space2Vec, a multi-scale representation learning model using grid cell insights.
result Space2Vec outperforms baselines in predicting POI types and image classification with geo-locations.
Federated learning improves CRC grading accuracy and privacy.
problem Inter-observer variability and data privacy in CRC grading.
method Multi-scale federated learning framework integrating ResNetRS50.
result Framework achieves 83.5% accuracy, outperforming centralized models.
MCFNet recovers spatial detail and fuses it with semantic information for real-time segmentation.
problem Recovering spatial detail information and fusing it with semantic information in real-time.
method Proposes a new architecture (MCFNet) with feature refinement and fusion modules, and a gating unit.
result Achieves competitive performance with high speed (75.5% mIOU, 151.3 FPS on Cityscapes).
Langevin Dynamics speeds up mixing time with manifold hypothesis and multi-scale approach.
problem Langevin Dynamics struggles in high dimensions and nonconvex landscapes.
method Utilizes manifold hypothesis to reduce mixing time and employs multi-scale approach to improve image generation quality.
result Mixing time depends on intrinsic dimension rather than ambient dimension, significantly reducing computational complexity.
Locally adaptive clustering for tree delineation.
problem Tree delineation from distance data.
method Locally adaptive hierarchical cluster termination.
result Multi-scale alternative to conventional termination criteria.
Improves speaker verification for variable-duration utterances using a feature pyramid module.
problem Improving robustness for variable-duration utterances in speaker verification.
method Integrates a feature pyramid module into multi-scale aggregation to enhance speaker-discriminative information from multiple layers.
result Improves performance for both short and long utterances compared to state-of-the-art approaches.
Model for directed synthesis of audio textures using multi-scale RNNs.
problem Challenges in modeling complex audio textures with traditional methods.
method Combining multi-scale RNNs with a conditioning strategy for user-directed synthesis.
result Demonstrated improved performance on various audio texture datasets.
Neural HMM with AGA captures multi-scale dynamics in financial markets.
problem Capturing multi-scale temporal dynamics in financial markets.
method Parallel multi-resolution encoders, adaptive gating, and multi-head attention.
result Outperforms fixed-resolution baselines in predicting price movements and liquidity shocks.
Affine varieties among all algebraic varieties have simple structures. For example, an affine variety does not contain any complete algebraic curve. In this paper we study affine related properties of strata of k-differentials on smooth curves which parameterize sections of the k-th power of the canonical line bund…
Improved recurrent neural networks learn long-term dependencies through multi-scale memory.
problem Capturing long-term dependencies in recurrent neural networks.
method Incremental training of a modular RNN architecture with multi-scale hidden states.
result Incremental training and multi-scale memory enhance RNNs' ability to learn long-term dependencies.
Proposes MSTD-RCNN for improved financial time-series classification.
problem Combining Multi-Scale and Temporal Dependency for better financial time-series classification.
method Multi-Scale Temporal Dependent Recurrent Convolutional Neural Network (MSTD-RCNN).
result Achieves state-of-the-art performance in trend classification and simulated trading.
Study abelian varieties' Weil-Petersson metric asymptotics.
problem Asymptotic behavior of Weil-Petersson metric on abelian varieties.
method Linking asymptotic with multi-scale collapsing limits of parametrized flat tori.
result Refined description of Weil-Petersson metric on abelian varieties.