We compare various notions of weak subsolutions to degenerate complex Monge-Amp{è}re flows, showing that they all coincide. This allows us to show that the viscosity solution coincides with the envelope of pluripotential subsolutions. Dedicated to Duong Hong Phong on the occasion of his 65th birthday.
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The paper constructs invariant Calabi-Yau structures on complexified symmetric spaces.
problem Constructing invariant Calabi-Yau structures on complexified symmetric spaces.
method Solutions of a Monge-Ampère type equation.
result Existence of solutions to the Monge-Ampère type equation.
Continuity of complex Monge-Ampère potentials on Kähler manifolds.
problem Continuity of solutions to complex Monge-Ampère equations on compact Kähler manifolds.
method Extending DiNezza-Lu's approach to big cohomology classes, proving continuity on Zariski open sets.
result Singular Kähler-Einstein metrics have continuous potentials on the ample locus outside of the non-klt part.
We establish a stability result for elliptic and parabolic complex Monge-Amp{è}re equations on compact K{ä}hler manifolds, which applies in particular to the K{ä}hler-Ricci flow. Dedicated to Jean-Pierre Demailly on the occasion of his 60th birthday.
We develop a parabolic pluripotential theory on compact K{ä}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{è}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{ä}hler-Ricci flow on varieties with log te…
Study solves complex equation on specific types of manifolds.
problem Solving complex Monge-Ampère equation on Kähler manifolds.
method Flow-based arguments to establish existence of smooth solutions.
result Existence of smooth solutions under decreasing right-hand side.
K{ä}hler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functionalmath.DG
We introduce a class of almost homogeneous varieties contained in the class of spherical varieties and containing horospherical varieties as well as complete symmetric varieties. We develop K{ä}hler geometry on these varieties, with applications to canonical metrics in mind, as a generalization of the Guillemin-Abreu-D…
We obtain a necessary and sufficient condition of existence of a K{ä}hler-Einstein metric on a -equivariant Fano compactification of a complex connected reductive group in terms of the associated polytope. This condition is not equivalent to the vanishing of the Futaki invariant. The proof relies on the …
We develop the first steps of a parabolic pluripotential theory in bounded strongly pseudo-convex domains of Cn. We study certain degenerate parabolic complex Monge-Amp{è}re equations, modelled on the K{ä}hler-Ricci flow evolving on complex algebraic varieties with Kawamata log-terminal singularities. Under natural ass…
N. V. Efimov \cite{Ef1} proved that there is no complete, smooth surface in with uniformly negative curvature. We extend this to isometric immersions in a 3-manifold with pinched curvature: if has sectional curvature between two constants and , then there exists such that $M…
Study complex Monge-Ampère flows on Kähler manifolds using Perron method.
problem Complex Monge-Ampère flows in big cohomology classes.
method Perron method for pluripotential subsolutions.
result Upper envelope of subsolutions is a unique pluripotential solution with regularity.
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while the Hessian is approximated by automatic differentiation of the gradient…
We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations - the generalised Monge-Amp`ere equation, the almost Hitchin system, and the Calabi-Yang-Mills equations. These are all perturbations of already existing equations. Our construction for the g…
The paper studies mean curvature flow of Lagrangian graphs in pseudo-Euclidean space.
problem Mean curvature flow of Lagrangian graphs in pseudo-Euclidean space.
method Analyzes the parabolic equation and Monge-Ampère type equation, proving smooth solutions and convergence to self-expanding solutions.
result Smooth solutions for specific nonlinear equations and convergence to self-expanding solutions.
In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \cite{klw,hdl}. For the first hyperbolic flow, as in \cite{klw}, by using support function, we reduce it to a hyperbolic Monge-Ampre equation …
Solves complex Monge-Ampère equations on Kähler manifolds.
problem Behavior of singularities in solutions to degenerate equations.
method Analyzes singularities of solutions to degenerate complex Monge-Ampère equations.
result Resolves unresolved problem from Yau's work.
Attention to entropic communication improves message decoding and cooperation.
problem Improper weighting in attention mechanisms hinders optimal communication.
method Combining attention and relative entropy (RE) for optimal message encoding and decoding.
result Proper attention communication emerges via weighted RE, aiding optimal protocols.
RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments c…
It is natural to ask: what kinds of matrices satisfy the Restricted Eigenvalue (RE) condition? In this paper, we associate the RE condition (Bickel-Ritov-Tsybakov 09) with the complexity of a subset of the sphere in , where is the dimensionality of the data, and show that a class of random matrices with indep…
We implement a method for re-ranking top-10 results of a state-of-the-art question answering (QA) system. The goal of our re-ranking approach is to improve the answer selection given the user question and the top-10 candidates. We focus on improving deployed QA systems that do not allow re-training or re-training comes…
We analyze different re-ranking algorithms for diversification and show that majority of them are based on maximizing submodular/modular functions from the class of parameterized concave/linear over modular functions. We study the optimality of such algorithms in terms of the `total curvature'. We also show that by adj…
High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularizationstat.ML
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively investigated during the last decades and have found applications in optimization, o…
New research challenges the flatness-generalization link in deep neural networks.
problem The correlation between flatness of the loss landscape and generalization in deep neural networks is questioned.
method The study examines various flatness measures and popular SGD variants, finding some break the flatness-generalization link. It proposes using , a global quantity, as a predictor of generalization.
result The log of Bayesian prior upon initialization, , is a significantly more robust predictor of generalization than flatness measures.
Given a complex analytic function f on a Whitney stratified complex analytic variety of complex dimension n, whose real part Re(f) is Morse, we prove the existence of a stratified gradient-like vector field for Re(f) such that the unstable set of a critical point p on a stratum S of complex dimension s has real dimensi…
RES improves robustness in Bayesian optimization.
problem Finding robust solutions in Bayesian optimization with adversarial perturbations.
method Robust Entropy Search (RES) acquisition function.
result RES reliably finds robust optima, outperforming state-of-the-art algorithms.
An on-going debate in the energy economics and power market community has raised the question if energy-only power markets are increasingly failing due to growing feed-in shares from subsidized renewable energy sources (RES). The short answer to this is: No, they are not failing. Energy-based power markets are, however…
Topological equivalence of smooth functions with isolated critical points on a closed surfacesmath.GT
We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Re for the some nonnegative integer k. The full topological invariant of such functions is constructed.
This paper addresses detection of a reverse engineering (RE) attack targeting a deep neural network (DNN) image classifier; by querying, RE's aim is to discover the classifier's decision rule. RE can enable test-time evasion attacks, which require knowledge of the classifier. Recently, we proposed a quite effective app…
Beta-SOD detects and corrects noisy object re-identification using cosine similarity and Beta mixtures.
problem Noisy object re-identification in image datasets.
method Reframed Re-ID as a similarity task, using Siamese networks and Beta mixture models.
result Superior performance in noisy conditions compared to state-of-the-art methods.
LITE models improve query-document relevance with learnable late interactions.
problem Improving query-document relevance with lower latency and storage.
method Proposes learnable late-interaction models (LITE) that use factorized query and document embeddings followed by a learnable scorer.
result Empirically, LITE outperforms previous late-interaction models in re-ranking tasks.
We compare the isoperimetric profiles of $S^2 \times \re^3$ and of $S^3 \times \re^2$ with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the Yamabe constants of $S^2 \times \re^3$ and $S^3 \times \re^2$. Explicitly we show that $Y(S^3 \times \re^2, [g_0^3 +dx^2…
PyKEEN 1.0 simplifies KGE model creation and optimization.
problem Training and evaluating knowledge graph embeddings (KGEs).
method Composes KGEMs with various interaction models, training approaches, and loss functions. Implements automatic memory optimization and extensive HPO functionalities.
result PyKEEN 1.0 streamlines KGE model creation and optimization.
Re-initializing neural networks improves generalization but not as much as other techniques.
problem Understanding when and how re-initialization improves neural network performance.
method Empirical comparison of re-initialization with standard training and various regularization techniques.
result Re-initialization is beneficial for generalization but not as much as other techniques, especially when combined with careful tuning of hyperparameters.
Model predicts wound and episode-level readmission risk and time to re-admit.
problem Identify patients at high risk of re-admission to prevent wound recurrences and reduce healthcare costs.
method Data-driven analysis of wound care and episode-level patient data.
result Model achieves high recall and precision for predicting re-admission risk and time.
Person Re-identification (re-id) faces two major challenges: the lack of cross-view paired training data and learning discriminative identity-sensitive and view-invariant features in the presence of large pose variations. In this work, we address both problems by proposing a novel deep person image generation model for…
Re-calibrating Photometric Redshift Probability Distributions Using Feature-space Regressionastro-ph.IM
New method calibrates photometric redshift PDFs more accurately.
problem Inaccurate photometric redshift uncertainties lead to systematic errors.
method Local re-calibration using feature-space regression of Probability Integral Transform (PIT) distributions.
result Calibrated PDFs are more accurate at all locations in feature space.
This work aims at solving the problems with intractable sparsity-inducing norms that are often encountered in various machine learning tasks, such as multi-task learning, subspace clustering, feature selection, robust principal component analysis, and so on. Specifically, an Iteratively Re-Weighted method (IRW) with so…
Paper proves Reshetikhin-Turaev link invariants appear in higher order terms of re-normalized link invariants for plumbed links.
problem Proving relations between Reshetikhin-Turaev and re-normalized link invariants for links.
method Analyzing higher order terms of re-normalized link invariants for plumbed links.
result Reshetikhin-Turaev link invariants appear in higher order terms of re-normalized link invariants for plumbed links.
Generator and Critic: A Deep Reinforcement Learning Approach for Slate Re-ranking in E-commercecs.LG
A deep reinforcement learning approach for slate re-ranking in e-commerce.
problem Improving user satisfaction in e-commerce by optimizing the ranking of items in a slate.
method Generator and Critic approach, using reinforcement learning and a Full Slate Critic model.
result The Generator and Critic approach significantly outperforms existing methods in slate evaluation and efficiency.
An elementary model of price dynamics in a financial market: Distribution, Multiscaling & Entropyphysics.soc-ph
Stylized facts of empirical assets log-returns include the existence of (semi) heavy tailed distributions and a non-linear spectrum of Hurst exponents . Empirical data considered are daily prices of 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is…
Develops RES metrics for stable rare-event forecasting evaluation.
problem Challenges in evaluating forecasts of rare events.
method Rare-event-stable (RES) metrics designed to maintain stable thresholds under extreme rarity.
result RES metrics maintain stable thresholds, consistent model rankings, and near-complete prevalence invariance.
Paper proves BGW tau-function can be represented as Q-polynomials.
problem Enumerative geometric interpretations of BGW tau-function.
method Proves BGW tau-functions are hypergeometric tau functions of BKP hierarchy.
result Original BGW tau-function can be represented as a linear combination of Schur Q-polynomials.
By the Fox's re-embedding theorem, any compact submanifold of the 3-sphere can be re-embedded in the 3-sphere so that it is unknotted. It is unknown whether the Fox's re-embedding can be replaced with twistings. In this paper, we will show that any closed 2-manifold embedded in the 3-sphere can be unknotted by twisting…
Examines climate financing for renewable energy projects using structured funds.
problem Valuation of structured climate financing on diverse renewable energy asset pools.
method Bottom-up Gaussian copula framework with LH++ model for diversification analysis.
result Shows how the mix of indirect and direct RE investments affects the sensitivity of the senior tranche.
Understanding deep neural networks is a major research objective with notable experimental and theoretical attention in recent years. The practical success of excessively large networks underscores the need for better theoretical analyses and justifications. In this paper we focus on layer-wise functional structure and…
RE enhances DL by learning model behavior, enabling iterative self-improvement.
problem Static data representations limit DL's potential for evolving models.
method RE uses multiple mappings of data through identical deep architectures, analyzing internal representations and performance signals.
result Models can gain insight from predecessors, leading to iterative self-improvement.
Comparison and Adaptation of Automatic Evaluation Metrics for Quality Assessment of Re-Speakingcs.CL
Re-speaking is a mechanism for obtaining high quality subtitles for use in live broadcast and other public events. Because it relies on humans performing the actual re-speaking, the task of estimating the quality of the results is non-trivial. Most organisations rely on humans to perform the actual quality assessment, …