KZImputer improves time series data quality with adaptive imputation for short to medium-sized gaps.
problem Missing data in time series analysis.
method Adaptive imputation method for univariate time series with tailored strategies for different gap positions.
result KZImputer achieves strong performance, especially for high missingness rates and high-sparsity regimes.
In this short note, we find a new gap phenomena on Riemannian manifolds, which says that for any complete noncompact Riemannian manifold with nonnegative Ricci curvature, if the scalar curvature decays faster than quadratically, then it is Ricci flat.
Study shows gaps in Bitcoin order book are linked to returns but only in the short term.
problem Understanding the relationship between gaps and returns in Bitcoin order books.
method Examined the dynamics of gaps and returns in a Bitcoin order book without considering long-term causation.
result The causal relationship between gaps and returns is limited to instantaneous causation.
Notes a flaw in a proof about embedding graphs.
problem A flaw in proving Sachs' conjecture about graph embeddings.
method Analyzing Stanfield's proof for gaps.
result Identifies a significant error in the proof.
Geodesically convex functions are continuous on Riemannian manifolds.
problem Continuity of geodesically convex functions on Riemannian manifolds.
method Proof of continuity using geodesic convexity and addressing a gap in existing proof.
result All geodesically convex functions are continuous in the interior of their domain on Riemannian manifolds.
Margin trading and short selling boost green tech innovation in China.
problem Encouraging green technology innovation in Chinese companies.
method Quasi-experimental research using panel data of Chinese listed companies, double difference model.
result Margin trading and short selling increase green tech innovation significantly.
In this short note, using Günther's volume comparison theorem and Yokota's gap theorem on complete shrinking gradient Ricci solitons, we prove that for any complete shrinking gradient Ricci soliton (Mn,g,f) with sectional curvature K(g)<A and Volf(M)≥v for some uniform constant A,v, there exists…
High-dimensional curved diffusions show abrupt convergence at a critical time.
problem Understanding abrupt convergence in high-dimensional curved diffusions.
method Functional inequalities and spectral rigidity.
result Abrupt convergence (cutoff) occurs in high dimensions, linked to spectral rigidity.
TimeBridge addresses non-stationarity in long-term time series forecasting.
problem Non-stationarity in multivariate time series leads to spurious regressions and obscures long-term relationships.
method TimeBridge segments series into patches, applying Integrated Attention for short-term non-stationarity and Cointegrated Attention for long-term cointegration.
result TimeBridge achieves state-of-the-art performance in both short-term and long-term forecasting.
Reservoir computers and RNNs fall short of optimal prediction for stochastic PDFA.
problem Predicting stochastic processes generated by probabilistic deterministic finite-state automata.
method Generalized linear models, Reservoir computers, and Long Short-Term Memory (LSTM) RNNs were tested.
result Each method can fall short of maximal predictive accuracy by up to 50% after training.
Improved homological dimension for certain subgroups in Lie groups.
problem Determining homological dimensions of discrete subgroups in Lie groups.
method Using recent results and properties of injectivity radius, the homological dimension gap is calculated.
result Infinite volume torsion-free subgroups of higher rank Lie groups have a homological dimension gap of at least 1/8 of the real rank.
The aim of this short note is to fill in a gap in our earlier paper [16] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [15]. We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [13, 23] in the so--called G−framework…
The purpose of this paper is two-fold: On the one side we would like to close a gap on the classification of vector bundles over 5-manifolds. Therefore it will be necessary to study quaternionic line bundles over 5-manifolds which are in 1−1 correspondence to elements in the first cohomotopy group $π^4(M)=[M,S^4]…
In this short note we consider a dynamic assortment planning problem under the capacitated multinomial logit (MNL) bandit model. We prove a tight lower bound on the accumulated regret that matches existing regret upper bounds for all parameters (time horizon T, number of items N and maximum assortment capacity K)…
Generative adversarial network improves audio inpainting for long gaps.
problem Generating missing audio content in long-range gaps using WGAN.
method Proposed WGAN architecture with short-range and long-range neighboring borders.
result The proposed model outperforms classical WGAN in reconstructing high-frequency content.
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.
In the seminal work [9], several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment decisions, a concise mathematical description of their dynamics has been missing. W…
The paper proves a gap theorem for almost non-negatively curved manifolds.
problem Proving a gap theorem for almost non-negatively curved manifolds.
method Two novel technical tools: controlling the spreading of minimal geodesics and Ricci flow smoothing.
result Closed manifolds with bounded geometry are diffeomorphic to torus bundles.
Paper tackles non-stationary bandits with various examples.
problem Non-stationary stochastic bandit problem with specific cases.
method Proposes a single algorithm for multiple non-stationary bandit problems.
result Unified solution for four different bandit problems.
A reverse Riesz estimate and spectral gap imply a Poincaré inequality.
problem Establishing a Poincaré inequality using a reverse Riesz estimate and spectral gap.
method Combining a reverse Riesz estimate and spectral gap condition to prove a Poincaré inequality.
result A Poincaré inequality is derived from a reverse Riesz estimate and spectral gap condition.
A new machine learning method for spatial regression.
problem Spatial/temporal regression with scattered data and arbitrary dimensions.
method Modified Planar Rotator (MPRS) method, a non-parametric model with distance-dependent interactions.
result MPRS predictions are competitive with standard interpolation methods and superior in handling rough and non-Gaussian data.
We propose and study the known-compensation multi-arm bandit (KCMAB) problem, where a system controller offers a set of arms to many short-term players for T steps. In each step, one short-term player arrives to the system. Upon arrival, the player aims to select an arm with the current best average reward and receiv…
We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an illustration of the contents of the paper, we prove that metrics whose curvature operator has eigenvalues greater than −1 can be evolve…
This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP graph representations and output tours in a non-autoregressive manner via highly parallelized beam search. Our approach ou…
Perpetual futures offer leverage without maturity, with prices influenced by funding rates.
problem Understanding and pricing perpetual futures with funding rates.
method Derive no-arbitrage prices and bounds in markets with trading costs. Empirically analyze deviations and Sharpe ratios of implied arbitrage strategies.
result Implied arbitrage strategies in crypto markets yield high Sharpe ratios, indicating significant pricing inefficiencies.
This paper establishes the existence of a gap for the stable length spectrum on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive e there is a positive d depending only on n and on e such that an element of pi_1(M) with stable commutator length less than d is represented by a geodesic with leng…
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.
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.
Predicts local AQI using mobile sensor data, improving accuracy by 71.654 MSE.
problem Inaccurate AQI data from sparse sensors in developing countries.
method Spatio-temporal GNNs for fine-grained AQI forecasting.
result Significant improvement in AQI prediction accuracy (71.654 MSE reduction).
Paper combines machine learning and model averaging for robust parameter estimation.
problem Estimating structural parameters with partially unknown functional forms.
method Pairing double/debiased machine learning with stacking for model averaging.
result DDML with stacking is more robust to unknown functional forms than single learners.
RER improves sample complexity by updating in reverse order.
problem Theoretical analysis limits RER's convergence rate.
method Tighter analysis for larger learning rates and longer sequences.
result RER converges faster with larger learning rates and longer sequences.
We provide here a counter-example to the second inequality of Corollary (19.10) in the Clay Institute Monograph by J.Morgan and G.Tian entitled "Ricci Flow and the Poincare Conjecture". We had announced the existence of this counter-example in our paper "Five Gaps in Mathematics", Advanced Non-linear Studies, vol 15, N…
A method for multidimensional probabilistic electricity market forecasting is proposed.
problem Uncertainty in simultaneous multivariate predictions of electricity markets.
method Repeated resampling to estimate uncertainty of simultaneous multivariate predictions.
result The method provides highly accurate predictions and gains are largest when considering functions of variables.
This paper challenges the conventional wisdom about temporal difference learning's superiority in stitching experience.
problem The effectiveness of temporal difference learning in stitching experience across different reinforcement learning methods.
method Empirical study comparing Monte Carlo and temporal difference learning methods in stitching experience.
result Monte Carlo methods can also achieve experience stitching, challenging the conventional wisdom.
NeuralProphet improves forecast accuracy by 55-92% for short-term forecasts.
problem Challenges in explainable, scalable forecasting for business decisions.
method Hybrid framework combining classical methods and deep learning, with auto-regression and covariate modules.
result NeuralProphet outperforms Prophet on real-world datasets and short-term forecasts.
We prove that a compact RCD∗(0,N) (or equivalently RCD(0,N)) metric measure space, (X,d,m), with $\diam X \le d$ and its first (nonzero) eigenvalue of the Laplacian (in the sense of Ambrosio-Gigli-Savaré) , λ1=d2π2, has to be a circle or a line segment with diameter, π. This compl…
New framework explains normalizing flows' power and limitations.
problem Understanding the expressive power and limitations of normalizing flows.
method Theoretical framework for well-conditioned coupling-based normalizing flows and volume-preserving flows.
result RealNVP is distributionally universal, but volume-preserving flows are not.
Combines spline interpolation and ARIMA for stock market forecasting.
problem Limited predictive performance of ARIMA in noisy data.
method Integrates cubic spline interpolation and ARIMA for time series forecasting.
result Demonstrates guidance for short-term stock market forecasting.
Enhances VC startup success predictions using graph augmented time series models.
problem Challenges in predicting startup success due to limited financial data and subjective forecasts.
method Integrates inter-company relationships into time series analysis using GraphRAG.
result Significantly outperforms previous models in startup success predictions.
Feature engineering remains a major bottleneck when creating predictive systems from electronic medical records. At present, an important missing element is detecting predictive regular clinical motifs from irregular episodic records. We present Deepr (short for Deep record), a new end-to-end deep learning system that …
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.
Study gap-dependent regret bounds for risk-sensitive RL.
problem Risk-sensitive reinforcement learning with entropic risk measure.
method Propose cascaded gaps to adapt to problem structures, derive regret bounds.
result Exponential improvement over existing bounds in appropriate settings.
ACL improves robustness with unlabeled data, and we analyze its generalization using Rademacher complexity.
problem Improving robustness of deep networks against adversarial attacks using unlabeled data.
method We analyze the generalization performance of Adversarial Contrastive Learning (ACL) using Rademacher complexity.
result The average adversarial risk of the downstream tasks can be upper bounded by the adversarial unsupervised risk of the upstream task.
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large integrality gap, due to frustrated cycles. One way to tighten the relaxation is to intr…
{\em Riemannian cubics} are curves in a manifold M that satisfy a variational condition appropriate for interpolation problems. When M is the rotation group SO(3), Riemannian cubics are track-summands of {\em Riemannian cubic splines}, used for motion planning of rigid bodies. Partial integrability results are know…
Improves video search by balancing text and visual modalities.
problem Modality imbalance in video search models, focusing mainly on text matching.
method Proposes MBVR with MS samples and DM to balance modalities.
result Empirically shows significant improvement in modality balance and search effectiveness.
A graph model improves short text classification by integrating sentence relationships.
problem Sparse features in short text classification due to limited text length.
method PathWalk model combining graph networks and short sentences.
result PathWalk achieves state-of-the-art results on four datasets.
Study compares short vs long strategies for equity factors, finds short strategy better.
problem Determining the best market-neutral implementation of equity factors.
method Revisited the relative predictability of short and long legs, diversification, and costs.
result Long-Short implementation yields superior risk-adjusted returns compared to Hedged Long-Only.