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.
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…
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…
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…
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 …
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…
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.
The grid integration of intermittent Renewable Energy Sources (RES) causes costs for grid operators due to forecast uncertainty and the resulting production schedule mismatches. These so-called profile service costs are marginal cost components and can be understood as an insurance fee against RES production schedule u…
A new system combines vision and language for person re-identification.
problem Real-world surveillance lacks visual data for person re-identification.
method Two-stream CNN framework with shared logits, CCA for modalities, multi-modal testing protocol.
result 22% improvement in re-identification performance with multi-modal queries.
This paper improves fairness in recommendation systems by learning individual preferences across multiple dimensions.
problem Fairness in recommender systems, especially in areas with social impact.
method Opportunistic multi-aspect re-ranking approach that learns individual preferences and enhances provider fairness.
result Achieves a better trade-off between accuracy and fairness across multiple fairness dimensions.
We show that the coefficients of the re-normalized link invariants of the paper "Multivariable link invariants arising from Lie superalgebras of type I" are Vassiliev invariants which give rise to a canonical family of weight systems.
Feed in tariff (FiT) is one of the most efficient ways that many governments throughout the world use to stimulate investment in renewable energies (REs) technology. For governments, financial management of the policy is very challenging as that it needs a considerable amount of budget to support RE producers during th…
We consider the problem of efficient "on the fly" tuning of existing, or {\it legacy}, Artificial Intelligence (AI) systems. The legacy AI systems are allowed to be of arbitrary class, albeit the data they are using for computing interim or final decision responses should posses an underlying structure of a high-dimens…
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.
For a compact connected 3-submanifold with connected boundary in the 3-sphere, we relate the existence of a Seifert surface system for a surface with a Dehn surgery along a null-homologous link. As its corollary, we obtain a refinement of the Fox's re-embedding theorem.
DeepBark improves tree bark re-identification accuracy.
problem Challenging illuminations make tree bark hard to re-identify.
method Used a large dataset of 2,400 bark images to train DeepBark and SqueezeBark.
result DeepBark achieves 87.2% mAP in retrieving relevant bark images.
In addition to constraining bilateral exposures of financial institutions, there are essentially two options for future financial regulation of systemic risk (SR): First, financial regulation could attempt to reduce the financial fragility of global or domestic systemically important financial institutions (G-SIBs or D…
Paper proposes a method for weather-informed probabilistic forecasting and scenario generation in power systems.
problem Challenges of integrating renewable energy sources into power grids due to their stochasticity and uncertainty.
method Combines probabilistic forecasting and Gaussian copula for day-ahead prediction and scenario generation of load, wind, and solar power.
result Demonstrates superior performance of the proposed weather-informed Temporal Fusion Transformer (WI-TFT) model.
About Some Applications of Kolmogorov Equations to the Simulation of Financial Institutions Activityq-fin.GN
The goal of this article is to describe the concepts of system dynamics and its applications to the simulation modeling of financial institutions daily activity. The hybrid method of the re-engineering of banking business processes based upon combination of system dynamics, queuing theory and tools of ordinary differen…
Federated Learning is a distributed learning paradigm with two key challenges that differentiate it from traditional distributed optimization: (1) significant variability in terms of the systems characteristics on each device in the network (systems heterogeneity), and (2) non-identically distributed data across the ne…
We propose a neural information processing system which is obtained by re-purposing the function of a biological neural circuit model, to govern simulated and real-world control tasks. Inspired by the structure of the nervous system of the soil-worm, C. elegans, we introduce Neuronal Circuit Policies (NCPs), defined as…
The goal of this research was to find a way to extend the capabilities of computers through the processing of language in a more human way, and present applications which demonstrate the power of this method. This research presents a novel approach, Rhetorical Analysis, to solving problems in Natural Language Processin…
Study reveals geometric context of second-order superintegrable systems.
problem Understanding second-order superintegrable systems and their Weylian geometry.
method Re-examined second-order maximally conformally superintegrable Hamiltonian systems, revealing their Weyl structure.
result Extended conformal superintegrability to Weyl structures, interpreting systems as semi-Weyl structures.
Adaptive ML learns complex time-varying systems without new data.
problem Applying ML to time-varying systems with shifting distributions.
method Mapping high-dimensional inputs to low-dimensional latent space, actively tuning latent space based on feedback.
result Learning correlations and tracking system evolution in real-time without new data.
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.
We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, w…
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…
MLtuner automatically tunes settings for training tunables (such as the learning rate, the momentum, the mini-batch size, and the data staleness bound) that have a significant impact on large-scale machine learning (ML) performance. Traditionally, these tunables are set manually, which is unsurprisingly error-prone and…
Type system captures CI relationships for probabilistic models.
problem Challenges in inference for models with mixed discrete and continuous parameters.
method Information flow type system for probabilistic programming.
result Well-typed programs guarantee certain CI relationships.
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.
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system inference, such as Boltzmann machines, MLE requires the arduous computation of pa…
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…
Many retailers today employ inventory management systems based on Re-Order Point Policies, most of which rely on the assumption that all decreases in product inventory levels result from product sales. Unfortunately, it usually happens that small but random quantities of the product get lost, stolen or broken without r…
Early Prediction of 30-day ICU Re-admissions Using Natural Language Processing and Machine Learningcs.LG
ICU readmission is associated with longer hospitalization, mortality and adverse outcomes. An early recognition of ICU re-admission can help prevent patients from worse situation and lower treatment cost. As the abundance of Electronics Health Records (EHR), it is popular to design clinical decision tools with machine …
Researchers dissect Neural ODEs to understand their dynamics.
problem Understanding the inner workings of Neural ODEs.
method Developing continuous-depth formulation to clarify design choices.
result Clarified the influence of design choices on Neural ODE dynamics.
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions. We convert mathematical ODE models of three benchmark biological systems to Dyn…