Study of hyperbolic polyhedral surfaces with regular faces.
problem Understanding the properties of hyperbolic polyhedral surfaces with regular faces.
method Combinatorial and geometric analysis of hyperbolic polyhedral surfaces with regular faces.
result There is a gap between the areas of non-smooth hyperbolic polyhedral surfaces and smooth hyperbolic surfaces.
MO-GP models fill gaps in biophysical data with across-domain info transfer.
problem Gap filling of biophysical parameters LAI and fAPAR over rice areas.
method Multi-output Gaussian Processes (MO-GP) based on Linear Model of Coregionalization (LMC).
result MO-GP models successfully predict biophysical variables even in high missing data regimes.
Deep-Gap predicts crowdsourcing supply-demand gaps using deep learning.
problem Balancing supply and demand in mobile crowdsourcing.
method Residual learning-based deep neural networks trained on time series data and external factors.
result Deep-Gap achieves lowest forecasting errors compared to state-of-the-art methods.
In the first part we use Gromov's K--area to define the K--area homology which stabilizes into singular homology on the category of pairs of compact smooth manifolds. The second part treats the questions of certain curvature gaps. For instance, the L∞--curvature gap of complex vector bundles on a compact manif…
Minimal surfaces in hyperbolic space have a renormalized area criterion.
problem Minimal surfaces in hyperbolic space
method Renormalized area criterion
result Y must be a totally geodesic disk
The paper characterizes gaps in minimal foliations on tori using energy criteria.
problem Characterizing gaps in minimal foliations on tori.
method Introduced an energy to study min-max theory and applied it to Almgren-Pitts min-max theory.
result For a generic metric, if a lamination contains a gap, there exists a non-area-minimizing minimal hypersurface inside the gap.
We prove the existence of metrics maximizing the first eigenvalue normalized by area on closed, non-orientable surfaces assuming two spectral gap conditions. These spectral gap conditions are proved by the authors in \cite{MS3}.
The equatorial disk in a ball has the smallest area.
problem Finding the minimal area of free boundary minimal surfaces in a ball.
method Comparing excess of surfaces with excess of cones over the boundary.
result Existence of a gap in the area of minimal surfaces.
New method fuses optical and SAR data to fill LAI gaps during cloudy periods.
problem Cloudy periods mask key crop growth stages, leading to unreliable yield predictions.
method Multi-Output Gaussian Process (MOGP) regression for fusing Sentinel-1 RVI and Sentinel-2 LAI time series.
result MOGP provides improved LAI estimations even during cloudy periods, especially for long gaps.
Since n-dimensional λ-hypersurfaces in the Euclidean space Rn+1 are critical points of the weighted area functional for the weighted volume-preserving variations, in this paper, we study the rigidity properties of complete λ-hypersurfaces. We give a gap theorem of complete λ-hypersurfaces with po…
The study proves optimal spectral gaps for hyperbolic surfaces.
problem Proving optimal spectral gaps for hyperbolic surfaces.
method Proving the absence of eigenvalues in a specific range for random covers of hyperbolic surfaces.
result The first non-zero eigenvalue of the Laplacian on a sequence of closed hyperbolic surfaces tends to 1/4.
Introduces fractional k-dimensional measure bridging fractional length and area.
problem Defining fractional measures for dimensions between 0 and n-1.
method Introduces a parameterized fractional measure σ that converges to Hausdorff measure. result Fractional measure converges to Hausdorff measure with a known constant factor.
New offline RL method works with limited data and function approximators.
problem Sample efficiency with limited data and weak function approximators.
method Pessimistic algorithm based on version space formed by marginalized importance sampling (MIS), with gap assumption.
result Guarantees sample efficiency for simple algorithm under specific assumptions.
Uniform spectral gap for convex cocompact hyperbolic surfaces and expanders.
problem Spectral gap for convex cocompact hyperbolic surfaces and their covers.
method Using thermodynamic formalism for twisted Selberg zeta functions.
result Uniform resonance-free regions for convex cocompact hyperbolic surfaces and expanders.
A new topological gap theorem improves the systole of 3-manifolds with positive scalar curvature.
problem Improving the systole of 3-manifolds with positive scalar curvature.
method Weak inverse mean curvature flow.
result The systole of 3-manifolds is no greater than an improved constant c ≈ 5.44π.
The paper bounds the index of CMC surfaces with capillary boundary.
problem Bounding the index of CMC surfaces with capillary boundary.
method Comparison of second variations of area and energy, derived second variation formulae.
result The index is bounded linearly by genus, boundary components, and contact angle.
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{σ^2|n}\propto \ev{n|A}^{2α}$ with 1/2≥α≥1 when a parameter A (usually the system size) is varied. A can be the strength of the nod…
The objective of this paper is to fill a gap in the literature on internationalization, in relation to the absence of objective and measurable performance indicators on the process of how firms sequentially enter external markets. To that end, this research develops a quantitative tool that can be used as a performance…
We study λ-hypersurfaces that are critical points of a Gaussian weighted area functional ∫Σe−4∣x∣2dA for compact variations that preserve weighted volume. First, we prove various gap and rigidity theorems for complete λ-hypersurfaces in terms of the norm of the second fundamental form ∣A∣. Sec…
New bound limits generalization gap for large models, independent of model complexity.
problem Understanding generalization gap in large-scale machine learning models.
method Established a model-independent upper bound for generalization gap using Rényi entropy.
result Generalization gap can be maintained with arbitrarily large models if data entropy is sufficient.
We study the distribution of resonances for geometrically finite hyperbolic surfaces of infinite area by countting resonances numerically. The resonances are computed as zeros of the Selberg zeta function, using an algorithm for computation of the zeta function for Schottky groups. Our particular focus is on three aspe…
Paper integrates ML with physics models for engineering and environmental challenges.
problem Complex science and engineering problems require new methodologies combining physics-based models and ML.
method Structured overview of integrating physics-based models with ML techniques.
result Taxonomy of existing techniques and potential research gaps identified.
Study characterizes compact Einstein-type manifolds with boundary.
problem Characterize compact Einstein-type manifolds with nonempty boundary.
method Proved a sharp boundary estimate, obtained Hawking mass bounds, and provided a topological classification for the boundary.
result Obtained a gap result for compact Einstein-type manifolds with boundary.
Framework explains deep learning generalization by comparing real and ideal worlds.
problem Understanding why deep models generalize well in practice.
method Integrates real-world empirical loss with ideal population loss to decompose test error.
result The gap between real and ideal worlds is small in deep learning, suggesting robust optimization leads to good generalization.
Paper closes the gap in MP-MAB problems with novel adaptive communication and exploration.
problem Closing the gap between decentralized MP-MAB and natural centralized lower bound.
method BEACON: Batched Exploration with Adaptive COmmunicatioN, incorporating ADC and batched exploration.
result Proves logarithmic regret for a generalized MP-MAB problem.
We study the SL(2,R)-infimal lengths of simple closed curves on half-translation surfaces. Our main result is a characterization of Veech surfaces in terms of these lengths. We also revisit the "no small virtual triangles" theorem of Smillie and Weiss and establish the following dichotomy: the virtual triangle area spe…
The paper provides uniform length estimates for trajectories on flat cone surfaces.
problem Estimating the length of trajectories on flat cone surfaces.
method Using self-intersection numbers and constants depending only on the flat metric, the paper focuses on convex flat cone spheres with a positive curvature gap and a fixed number of singularities.
result Uniform two-sided estimates for trajectory lengths on convex flat cone spheres are obtained.
This paper reviews digital transformation research from 2011-2024, focusing on corporate finance.
problem Lack of systematic review in digital transformation from corporate finance perspective.
method Combines bibliometric and content analysis methods.
result Emerging and rapidly growing focus on digital transformation, particularly in developed countries.
Improves hierarchical clustering in Euclidean space using autoencoders.
problem Lack of unsupervised methods for learning hierarchical structure in Euclidean space.
method Variational autoencoder with Gaussian mixture prior, rescaling latent space, and Ward's linkage.
result Improved dendrogram purity and Moseley-Wang cost function results.
Employs granular data to create a multilayer network for euro area banks, revealing distinct risk patterns.
problem Lack of comprehensive, granular data integration for systemic risk assessment in euro area banks.
method Constructs an empirically grounded multilayer network integrating various supervisory and statistical datasets, each layer representing a distinct transmission channel.
result Cross-layer heterogeneity in connectivity and centrality reveals economically relevant structure and misidentifies systemically important institutions.
The paper stratifies projective measured laminations and identifies a group of transformations.
problem Stratifying the space of projective measured laminations.
method Introducing a natural stratification and proving rigidity results.
result The group of self-homeomorphisms preserving the stratification is identified with the extended mapping class group.
New dataset for UAV gesture recognition in outdoor settings.
problem Lack of public outdoor UAV gesture recognition datasets.
method Recorded 13 gestures in an outdoor setting, created 119 HD video clips, annotated with body joints and gesture classes.
result Baseline gesture recognition performance of 91.9% using P-CNN.
New methods for assessing and visualizing feature groups in machine learning models.
problem Lack of methods for interpreting feature groups in machine learning models.
method Permutation-based, refitting, and Shapley-based techniques for grouped feature importance. Introduced a sequential procedure for identifying stable feature combinations. Developed a combined features effect plot.
result Effective methods for assessing and visualizing the importance and effect of feature groups in machine learning models.
Survey examines challenges and tools for integrating multiple types of omics data.
problem Integrating multiple types of omics data for healthcare applications.
method Categorizes fusion approaches, collects open-source tools, explores datasets.
result Identifies challenges and gaps in multimodal learning for multi-omics.
Automated strategies improve model adaptation efficiency.
problem Manual adaptation strategies are time-consuming and costly.
method Flexible adaptive mechanism deployment for automated adaptation strategies.
result Automated strategies achieve better or comparable performance.
T-EMDE bridges the heterogeneity gap between image and text modalities.
problem Finding similarities between image and text modalities with non-related feature spaces.
method Inspired by EMDE, T-EMDE uses sketches for multimodal operations, avoiding self-attention's quadratic complexity.
result T-EMDE achieves state-of-the-art results and reduces model latency.
Algorithm improves wildlife protection patrols.
problem Balancing exploration and exploitation in patrolling vast protected areas.
method Formulated as a stochastic multi-armed bandit problem, leveraging smoothness and decomposability.
result Algorithm LIZARD improves performance on real-world poaching data.
SMAC benchmarks StarCraft II multi-agent micromanagement challenges.
problem Benchmarking cooperative multi-agent reinforcement learning.
method Proposes StarCraft Multi-Agent Challenge (SMAC) for evaluation.
result SMAC provides a standard benchmark for multi-agent RL.
Challenge forecasts EV charging station usage accurately.
problem Better understanding of EV charging behaviors needed.
method Hierarchical forecasting of EV charging station occupancy.
result Hierarchical forecasting improves EV charging station occupancy predictions.
The study finds invariants of smooth metrics on surfaces through embeddings into spheres.
problem Understanding invariants of smooth metrics on surfaces through embeddings into spheres.
method Defining the Willmore functional over Nash isometric embeddings and analyzing its infimum.
result The study identifies unique conformal classes of metrics with specific invariants and lower bounds.
CAT method learns causal structure of directed trees efficiently.
problem Learning causal structure from directed trees.
method Chu-Liu-Edmonds algorithm for fast and scalable structure learning.
result Consistency in asymptotic regime with vanishing identifiability gap for Gaussian errors.
While the interpretability of machine learning models is often equated with their mere syntactic comprehensibility, we think that interpretability goes beyond that, and that human interpretability should also be investigated from the point of view of cognitive science. The goal of this paper is to discuss to what exten…
The cooperative hierarchical structure is a common and significant data structure observed in, or adopted by, many research areas, such as: text mining (author-paper-word) and multi-label classification (label-instance-feature). Renowned Bayesian approaches for cooperative hierarchical structure modeling are mostly bas…
Method for creating synthetic multi-fidelity data sets.
problem Lack of representative synthetic datasets for multifidelity optimisation benchmarks.
method Systematic generation of synthetic fidelities from preexisting datasets.
result Allows systematic investigation of lower fidelity proxies' influence.
Examines AI regulation in finance, highlighting risks and gaps in current laws.
problem Rapid AI adoption in finance introduces risks and compliance challenges.
method Reviews current legislation, industry guidelines, and real-world use cases.
result Need for adaptive, technology-neutral policies to balance innovation and consumer protection.
Foundation models outperform supervised methods in time series forecasting across various operational regimes.
problem Lack of domain-specific training and ongoing maintenance in supervised learning for time series forecasting.
method Evaluation of foundation models against standard supervised approaches across four operational regimes: periodic, physically constrained, stochastic, and demand forecasting.
result Foundation models are optimal for cold-start or long-tail scenarios and perform well in domains with transferable periodic structures.
Adapts ISO 26262 for machine learning in automotive software.
problem Conflict between innovation and safety in automotive software development.
method Detailed assessment and adaptation of ISO 26262 for machine learning, analyzing and proposing new requirements.
result Adapted ISO 26262 for machine learning, addressing safety and innovation in automotive software.
The paper explores gaps in curvature-related metrics and rigidity.
problem Understanding gaps in curvature-related metrics and rigidity.
method Analyzes three types of gaps: spectral, metric-rigidity, and topological-rigidity.
result Proposes open problems in the field.