Smooth Schubert varieties are rigid in rational homogeneous manifolds.
problem Classifying and understanding rigidity of Schubert varieties.
method Classification and analysis of homology classes.
result Smooth Schubert varieties are rigid unless they are linear.
Identifies root causes of outliers in unknown cyclic graphs.
problem Outliers in unknown cyclic graphs with linear structural equations.
method Identifies a short list of potential root causes based on strong perturbation and structural equations.
result The shortlist includes true root causes and their parents on the cycle.
In this paper we study tangentially degeneracy of the orbits of s-representations in the sphere. We show that an orbit of an s-representation is tangentially degenerate if and only if it is through a long root, or a short root of restricted root system of type G_2. Moreover these orbits provide many new examples of tan…
New identities link Frobenius elements to Jones-Wenzl projectors at roots of unity.
problem Understanding relationships between Frobenius elements and Jones-Wenzl projectors at roots of unity.
method Obtained skein identities relating Frobenius elements to Jones-Wenzl projectors in the Kauffman bracket skein module.
result Skein identities provide new proofs of the existence of the Chebyshev-Frobenius homomorphism.
The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are…
Study on eigenvalues of Laplace operator on 1-forms for symmetric spaces.
problem Investigating the first eigenvalue of the Laplace operator on 1-forms in compact inner symmetric spaces.
method Analyzing the Casimir eigenvalue of the highest root for the isotropy representation.
result The first eigenvalue of the Laplace operator on 1-forms is the Casimir eigenvalue of the highest root.
The purpose of this paper is to study the generalized Fong--Vasicek two-factor interest rate model with stochastic volatility. In this model the dispersion of the stochastic short rate (square of volatility) is assumed to be stochastic as well and it follows a non-negative process with volatility proportional to the sq…
Deep neural networks predict electricity consumption accurately.
problem Predicting future electricity consumption for better management.
method Used Recurrent Neural Networks (RNN) and Long Short Term Memory (LSTM) networks to predict electricity consumption based on past data.
result Both RNN and LSTM achieved an average Root Mean Square error of 0.1.
TRP uses tree-based approach for market-neutral portfolios.
problem Creating non-binary, market-neutral portfolios with signed signals.
method Tree-based portfolio construction with minimum-spanning-tree and sector-anchored variants.
result TRP outperforms HRP in preserving signal direction and managing exposures.
Two families of Sp(2,R) symmetric G2 structures found in 7D.
problem Identifying Sp(2,R) symmetric G2 structures in 7D. method Analyzing homogeneous spaces and root diagrams of sp(2,R). result Found two families of Sp(2,R) symmetric G2 structures with distinct properties. Study bounds changes in hyperbolic 3-manifold structures after drilling short geodesics.
problem Bounding changes in complex projective structures after drilling short geodesics.
method Analyzes L2-bounds on changes in conformally compact hyperbolic 3-manifolds. result Change is bounded by a universal constant times the square root of the length of the drilled geodesics.
Paper uses LSTM neural networks to forecast commodity prices.
problem Forecasting accuracy of traditional methods like ARIMA.
method Long Short-Term Memory (LSTM) neural networks complement traditional methods.
result Forecast averaging of LSTM and ARIMA models improves forecast accuracy.
Algorithm generates realistic metaorders from public trade data.
problem Generating realistic metaorders from public data.
method Novel algorithm that recovers stylized facts of metaorders impact.
result Average realized short-term price impact has a mechanical origin.
The paper examines the short-time implied volatility of additive processes and finds key parameters.
problem Characterizing the short-time implied volatility of equity markets.
method Examined pure jump exponential additive processes with power-law scaling parameters.
result The implied volatility is consistent with equity market characteristics if and only if β=1 and δ=-1/2.
Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomog…
In this short paper, we re-derive the Bochner formula for the Laplacian by considering local variations of volume. The derivation is rooted in the fact that the Laplacian of a function measures the volume variation along the flow of the gradient vector of the function. Possible extensions of this approach/technique are…
The Garside group, as a generalization of braid groups and Artin groups of finite types, is defined as the group of fractions of a Garside monoid. We show that the semidirect product of Garside monoids is a Garside monoid. We use the semidirect product Z⋉Gn of the infinite cyclic group Z and…
New asymptotic formula for option prices with interest rates and dividend yield effects.
problem Deriving option prices with interest rates and dividend yield effects in the local volatility model.
method Developed a new asymptotic limit for short-maturity option prices, including interest rates and dividend yield effects.
result Generalized the Berestycki-Busca-Florent formula to all orders in n for interest rates and dividend yield effects. We study optimal liquidation of a trading position (so-called block order or meta-order) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the unaffected asset price while simultaneously ruling out short sales. In this setting the l…
Research develops a water quality prediction model using LSTM.
problem Global degradation of water resources and need for optimal water quality monitoring.
method Developed a multivariate water quality prediction model using LSTM and historical data.
result Multiple step LSTM model achieved RMSE of 0.227 mg/L.
Estimates long-term effects of new treatments using historical and short-term data.
problem Estimating long-term effects of novel treatments with limited historical data.
method Surrogate indices, dynamic treatment effect estimation, and double machine learning combined in a unified pipeline.
result Consistent and asymptotically normal estimates of long-term effects under Markovian assumption.
Study predicts diabetes biomarkers using wearable data.
problem Understanding and predicting diabetes progression.
method Wide and deep neural network with LSTM structure.
result Model predicts biomarkers with low error rates.
The paper defines Dirichlet domains for Anosov subgroups in Lie groups.
problem Finding finite-sided Dirichlet domains for Anosov subgroups in Lie groups.
method Introducing a sufficient condition for finite-sided Dirichlet domains in semisimple Lie groups for polyhedral Finsler metrics.
result Finitely generated subgroups of semisimple Lie groups can have finite-sided Dirichlet domains under certain conditions.
The Soil Moisture Active Passive (SMAP) mission has delivered valuable sensing of surface soil moisture since 2015. However, it has a short time span and irregular revisit schedule. Utilizing a state-of-the-art time-series deep learning neural network, Long Short-Term Memory (LSTM), we created a system that predicts SM…
What return should you expect when you take on a given amount of risk? How should that return depend upon other people's behavior? What principles can you use to answer these questions? In this paper, we approach these topics by exploring the consequences of two simple hypotheses about risk. The first is a common-sense…
LSTM predicts COVID-19 growth patterns from global data.
problem Forecasting the spread of COVID-19 using big data and machine learning.
method Used multivariate long short-term memory (LSTM) to learn correlations over time.
result LSTM outperformed RNN in predicting COVID-19 growth with lower validation error.
Two-root Riemannian manifolds have no odd-dimensional examples.
problem Characterizing Riemannian manifolds with specific eigenvalues of the Jacobi operator.
method Investigation of k-root manifolds, focusing on one-root and two-root cases. result There are no two-root Riemannian manifolds of odd dimension.
A new learning framework reduces PV-Battery system costs by 3.6%.
problem Optimizing PV-Battery systems for cost savings with accurate forecasts.
method Decision-focused learning framework integrating optimization and prediction.
result Decision-focused method reduces average electricity costs by 3.6%.
In this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a generalized m-th root metric is conformal to a m-th root metric, then both of them redu…
iKF method uncovers complex variable interactions for scientific discovery.
problem Limited interpretability of existing models in decision-making applications.
method Iterative Kings' Forests (iKF) method to uncover multi-order interactions.
result iKF provides strong interpretive power for explainable modeling.
We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order, that consistently generalizes previously proposed pro…
New definition of patient-specific root causes of disease using counterfactuals.
problem Lack of rigorous mathematical formulation for automatic detection of root causes.
method Proposes a counterfactual definition matching clinical intuition and uses Shapley values for causal contribution scores.
result Adapts to disease prevalence, accounts for noisy labels, and admits fast computation.
The paper calibrates geophysical predictions using marginal distributions and machine learning.
problem Sensitivity to initial conditions in geophysical systems leads to large deviations in long-term forecasts.
method The method introduces a calibration algorithm based on normalization and Kernelized Stein Discrepancy (KSD) to enhance ML predictions.
result The method improves the fidelity of ML predictions to known physical distributions, ensuring consistency with non-local statistical structures.
Uniqueness of quasi-roots explored in right-angled Artin groups.
problem Uniqueness of quasi-roots in right-angled Artin groups.
method Introducing quasi-roots and studying their uniqueness.
result Uniqueness of quasi-roots established in right-angled Artin groups.
We show that if the variety of minimal rational tangents (VMRT) of a uniruled projective manifold at a general point is projectively equivalent to that of a symplectic or an odd-symplectic Grassmannian, the germ of a general minimal rational curve is biholomorphic to the germ of a general line in a presymplectic Grassm…
Study differential properties of matrix square roots in specific cases.
problem Understanding matrix square roots in semi-simple, symmetric, and orthogonal cases.
method Analysis of differential and metric structures of real square roots of matrices under specific conditions.
result Differential properties of matrix square roots in semi-simple, symmetric, and orthogonal cases.
A model predicts solar irradiance without local data using satellite and weather forecasts.
problem Forecasting solar irradiance without local measurements for geographically dispersed solar generators.
method Uses satellite data and weather forecasts with a deep neural network trained on a subset of ground data.
result Proposed model performs as well or better than local models across 25 locations and prediction horizons.
D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary number-theoretic conditions that describe the values of n for which an nth root exis…
LSTM models outperform traditional ARIMA in S&P 500 forecasting.
problem Forecasting volatile financial data with non-linear dependencies.
method Compared LSTM and ARIMA models using historical data and technical indicators.
result LSTM models outperformed ARIMA in accuracy and error metrics.
Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
WSqD extends learning rate schedules for large model training without fixed horizons.
problem Fixed learning rate schedules limit training horizon extension.
method WSqD replaces constant stable phase with a shifted inverse-square-root base, retaining linear cooldown.
result WSqD achieves minimax-optimal convergence rate and horizon-independence.
CROC identifies the earliest-changing stream as the root cause in multi-stream data.
problem Distribution-free root cause analysis in multi-stream data with unknown distributional changes.
method Conformal p-values and finite-sample valid confidence sets.
result CROC efficiently isolates the root cause under minimal assumptions.
Bayesian theory explains market impact of large trades.
problem Reduction of price impact from large trades.
method Bayesian approach incorporating all trade information.
result Recovery of market impact laws including square-root and linear regimes.
Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable surface N_g of genus g. We explore the existence of roots and, following the work of …
New model identifies patient-specific disease root causes.
problem Identifying root causes of complex diseases varying between patients.
method Generalized Root Causal Inference (GRCI) algorithm for heteroscedastic noise model.
result GRCI accurately extracts patient-specific root causes.
This paper uses GAN and ERMSE to improve stock price movement prediction accuracy.
problem Predicting stock price movement direction is challenging due to complex, incomplete, and fuzzy information.
method The paper proposes a deep learning model using GAN and ERMSE to forecast stock market trends.
result The GAN model outperformed LSTM in predicting stock price movement direction with a 4.35% improvement.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
Enhanced ROOT-SGD optimizes stochastic optimization with diminishing stepsizes.
problem Improving statistical efficiency in stochastic optimization.
method Integrates a diminishing stepsize strategy into ROOT-SGD.
result Achieves optimal convergence rates with improved stability and precision.