Uniform RC-positivity results for direct image bundles.
problem Understanding the relation between rational connectedness and RC-positivity.
method Analyzing vector bundles and their direct images, using weak RC-positivity as a starting point.
result Uniform RC-positivity of direct image bundles under weak RC-positivity conditions.
RCS-YOLO improves brain tumor detection speed and accuracy.
problem Efficiently detecting brain tumors with high accuracy and speed.
method Proposes RCS-YOLO, a fast and accurate brain tumor detector using YOLO with Reparameterized Convolution and channel Shuffle.
result RCS-YOLO outperforms other YOLO versions in speed and accuracy on brain tumor detection.
Recurrent convolution (RC) shares the same convolutional kernels and unrolls them multiple steps, which is originally proposed to model time-space signals. We argue that RC can be viewed as a model compression strategy for deep convolutional neural networks. RC reduces the redundancy across layers. However, the perform…
Combining LETKF and RC improves chaotic system prediction from noisy, sparse data.
problem Improving chaotic system prediction from imperfect observations and models.
method Combining LETKF and RC to predict spatio-temporal chaotic systems from noisy and sparsely distributed observations.
result The proposed method using LETKF and RC outperforms LETKF in predicting chaotic systems from noisy and sparse observations.
The paper proves rational connectedness for certain Kähler manifolds.
problem Rational connectedness of compact Kähler manifolds.
method Uniform weak RC-positivity of the tangent bundle.
result Compact Kähler manifolds with uniformly weakly RC-positive tangent bundles are projective and rationally connected.
In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric ω such that (TX,ω) is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective manifold X is rationally connected, then the tautological line bundle $\mathscr{O}_{T…
The paper extends Schwarz's lemma to RC-positivity and complex manifolds.
problem Comparing metrics with RC-positivity in complex manifolds.
method Establishing Schwarz lemmas for RC-positivity and applying them to complex manifolds.
result New diameter and volume comparison theorems.
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…
RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
Reservoir Computing (RC) is a popular methodology for the efficient design of Recurrent Neural Networks (RNNs). Recently, the advantages of the RC approach have been extended to the context of multi-layered RNNs, with the introduction of the Deep Echo State Network (DeepESN) model. In this paper, we study the quality o…
In this paper, we introduce a concept of RC-positivity for Hermitian holomorphic vector bundles and prove that, if E is an RC-positive vector bundle over a compact complex manifold X, then for any vector bundle A, there exists a positive integer cA=c(A,E) such that $$H^0(X,\mathrm{Sym}^{\otimes \ell}E^*\otimes…
The paper models network formation using mixed logit models.
problem Modeling network formation in various fields.
method Mixed logit models, specifically the repeated-choice (RC) model.
result The RC model outperforms the multinomial logit (MNL) model in estimating network formation.
Reservoir Computing (RC) refers to a Recurrent Neural Networks (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a classifier (the hidden-output readout layer). Here we focus on the sequence lear…
Reservoir Computing (RC) provides an efficient way for designing dynamical recurrent neural models. While training is restricted to a simple output component, the recurrent connections are left untrained after initialization, subject to stability constraints specified by the Echo State Property (ESP). Literature condit…
A new sampling method, RC-LMC, reduces computational cost for high-dimensional log-concave distributions.
problem High computational cost of LMC in high dimensions.
method RC-LMC updates only one coordinate at a time, adding noise.
result RC-LMC is more efficient than LMC in high dimensions, especially for skewed distributions.
A new sampling method reduces computational cost for high-dimensional log-concave distributions.
problem High computational cost of ULMC in high dimensions.
method Random Coordinate ULMC (RC-ULMC) selects a single coordinate per iteration.
result RC-ULMC is cheaper than classical ULMC, especially in highly skewed and high-dimensional problems.
Reduced reservoir size for faster edge computing.
problem Efficiently reducing computational resources for reservoir computing.
method Concatenating past or drifting states of the reservoir to the output layer.
result Reduced reservoir size up to one tenth without significant error increase.
Unified treatment of RC in stochastic and deterministic settings.
problem Understanding and generalizing reservoir computing in both deterministic and stochastic contexts.
method Investigation of state-space systems, analysis of fading memory and solution stability, introduction of stochastic echo states.
result Generality of fading memory and solution stability in state-space systems, even without the echo state property.
EIDGM model estimates DE parameters from RCS data.
problem Estimating DE parameters from RCS data with heterogeneities.
method Physics-informed neural network emulator + Wasserstein GAN parameter generator.
result EIDGM accurately captures diverse parameter distributions.
New topologies for star-shaped sets without boundedness.
problem Defining convergence for unbounded star-shaped sets.
method Introducing radial distance functionals and new topologies.
result New topologies τWr and τAWr for star-shaped sets. Pyramidal GNN combines RC and pooling for efficient graph embeddings.
problem Efficiently embedding graphs while maintaining accuracy.
method Alternates RC layers with pooling to reduce complexity.
result Formally shows how pooling reduces complexity and speeds convergence.
In this paper, we show that every harmonic map from a compact Kähler manifold with uniformly RC-positive curvature to a Riemannian manifold with non-positive complex sectional curvature is constant. In particular, there is no non-constant harmonic map from a compact Kähler manifold with positive holomorphic sectional c…
New loss function handles uncertain constraints in CSLO problems.
problem Handling uncertain inequality constraints in CSLO with machine learning predictions.
method Introduces SPO-RC loss and SPO-RC+ surrogate, trains on truncated datasets, corrects bias.
result SPO-RC+ effectively manages constraint uncertainty and improves performance.
Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes g…
This paper investigates the role of sparsity in Reservoir Computing networks.
problem Designing efficient Recurrent Neural Networks (RNNs) with hidden recurrent layers.
method Empirical investigation of sparsity in input-reservoir connections and recurrent connections.
result Sparsity, particularly in input-reservoir connections, enhances the network's temporal memory and dimensionality.
New characterizations of partial positivity using Hörmander's L2-estimate.
problem Characterizing partial positivity in complex geometry.
method Using a twisted version of Hörmander's L2-estimate. result New characterizations of partial positivity, including uniform q-positivity and RC-positivity. Rapid identification of object from radar cross section (RCS) signals is important for many space and military applications. This identification is a problem in pattern recognition which either neural networks or support vector machines should prove to be high-speed. Bayesian networks would also provide value but requi…
Vanishing theorems show holomorphic tensor fields on certain Kähler manifolds are trivial.
problem Understanding properties of holomorphic tensor fields on Kähler manifolds.
method Established vanishing theorems for uniformly rational connected (RC) k-positive Hermitian holomorphic vector bundles. result Holomorphic tangent bundles of Kähler manifolds with positive k-Ricci curvature are uniformly RC k-positive. The paper examines positivity properties of singular Hermitian metrics.
problem Investigating positivity for singular Hermitian metrics.
method Exploring Griffiths, ω-trace, and RC positivity.
result These positivity notions imply cohomology vanishing and rational connectedness.
Machine learning predicts dam-break flood wave behavior accurately.
problem Predicting long-term wave behavior in dam-break floods.
method Solved Saint-Venant equations using Lax-Wendroff scheme, trained RC-ESN with flow depth data.
result RC-ESN model predicts 286 time-steps ahead with RMSE < 0.01, outperforming LSTM.
Efficient CV for ESNs improves time series predictions.
problem Lack of CV in time series modeling, especially for ESNs.
method Two-level optimizations for k-fold CV of ESNs. result Proposed CV schemes give better and more stable test performance.
We construct normal rationally connected varieties (of arbitrarily large dimension) not containing any smooth rational curves.
EuSN uses Euler discretization for stable, non-dissipative reservoir computing.
problem Designing stable and efficient reservoir computing models.
method Forward Euler discretization and antisymmetric recurrent matrices.
result EuSN outperforms standard RC models in long-term memory tasks and time-series classification.
A method to fix radius distortion in generative models on curved spaces.
problem Distortion in geodesic radius measurements across different charts on Riemannian manifolds.
method Radial Compensation (RC) adjusts the tangent-space base distribution to match the geodesic radius law, improving model stability and interpretability.
result RC ensures that the model's geodesic radius matches the intended distribution, improving numerical stability and curvature interpretation.
SIMPLE-RC method tests group membership profiles in large networks with weak signals.
problem Testing group membership profiles in large networks with weak signals.
method Random coupling technique to construct maximum SIMPLE tests for subsampled node pairs.
result Asymptotic distributions of SIMPLE-RC test are derived, enabling delicate analysis.
EPD method accurately captures parameter distributions from RCS data.
problem Limitations of traditional methods in estimating parameter distributions from RCS data.
method EPD method generates synthetic trajectories, estimates parameters, and selects parameters based on discrepancy.
result EPD provides accurate distribution of parameters without data loss.
Offline RL tackles resource-constrained online deployment with improved policy transfer.
problem Training policies with limited online features using a rich offline dataset.
method Introduce a policy transfer algorithm that first trains a teacher agent with full offline features and then transfers knowledge to a student agent with limited online features.
result Consistent improvement in performance over baseline methods on resource-constrained datasets.
In this paper, we study gradient Ricci expanding solitons (X,g) satisfying Rc=cg+D2f, where Rc is the Ricci curvature, c<0 is a constant, and D2f is the Hessian of the potential function f on X. We show that for a gradient expanding soliton (X,g) with non-negative Ricci curvature, the scalar curva…
Deep Echo State Networks (DeepESNs) recently extended the applicability of Reservoir Computing (RC) methods towards the field of deep learning. In this paper we study the impact of constrained reservoir topologies in the architectural design of deep reservoirs, through numerical experiments on several RC benchmarks. Th…
Reservoir Computing enhances climate predictability studies.
problem Improving climate predictability using machine learning.
method Reservoir Computing applied to climate data.
result Reservoir Computing outperforms traditional LIM in predicting climate variables.
Let M and N be two compact complex manifolds. We show that if the tautological line bundle OTM∗(1) is not pseudo-effective and OTN∗(1) is nef, then there is no non-constant holomorphic map from M to N. In particular, we prove that any holomorphic map from a compact complex mani…
We show for a complete noncompact steady Ricci soliton that there exists a sequence {x_i} of points tending to infinity such that |Rc|(x_i) limits to zero.
New method constructs solution operators for PDEs with prescribed support properties.
problem Constructing solution operators for under/overdetermined PDEs with specific support properties.
method Using a recovery on curves condition and taking smooth averages over curves, we obtain integral solution operators and representation formulas.
result Our method leads to integral representation formulas for overdetermined PDEs and solution operators for underdetermined PDEs.
Ring-reservoir networks simplify graph embeddings efficiently.
problem Efficient graph embeddings using deep neural networks.
method Progressive simplification of Reservoir Computing models to ring topology.
result Ring-reservoir networks show consistent advantages in predictive performance.
In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir computing, RC-ESN), deep feed-forward artificial neural n…
In this article we study any 4-dimensional Riemannian manifold (M,g) with harmonic curvature which admits a smooth nonzero solution f to the following equation \begin{eqnarray} \label{0002bx} \nabla df = f(Rc -\frac{R}{n-1} g) + x Rc+ y(R) g. \end{eqnarray} where Rc is the Ricci tensor of g, x is a constant a…
Paper breaks down risk contribution into inherent and correlation risk components.
problem Understanding the sources of risk in portfolio contributions.
method Leave-one-out decomposition approach to separate inherent and correlation risk contributions.
result The decomposition reveals distinct contributions of position volatility and correlation to portfolio risk.
Study predicts climate data at distant locations using machine learning.
problem Predict climate variables at distant locations where comprehensive data collection is not feasible.
method Uses reservoir computing and vector autoregression models for prediction.
result Machine learning improves prediction accuracy for highly correlated data.