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.
Stability proven for complex equations on Kähler manifolds.
problem Stability of solutions to complex Monge-Ampère equations.
method Elliptic and parabolic complex Monge-Ampère equations on compact Kähler manifolds.
result Stability result applies to Kähler-Ricci flow.
Study shows various weak solutions to complex flows match, proving viscosity equals pluripotential.
problem Comparing weak solutions to complex Monge-Ampère flows.
method Examined various notions of weak subsolutions and showed they coincide.
result Viscosity solution equals pluripotential solution.
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.
Develops theory for Kähler-Ricci flow on singular varieties.
problem Analyzing Kähler-Ricci flow on varieties with log terminal singularities.
method Parabolic pluripotential theory and complex Monge-Ampère equations.
result Establishes a parabolic theory analogous to Bedford-Taylor's.
N. V. Efimov \cite{Ef1} proved that there is no complete, smooth surface in R3 with uniformly negative curvature. We extend this to isometric immersions in a 3-manifold with pinched curvature: if M3 has sectional curvature between two constants K2 and K3, then there exists K1<min(K2,0) such that $M…
New methods solve complex equations, proving some have solutions.
problem Solving complex equations in infinite dimensions.
method Infinite-dimensional prequantum line bundles and moment maps.
result Proves some perturbed equations have solutions for small parameters.
Kähler-Einstein metrics found on compactifications of groups.
problem Existence of Kähler-Einstein metrics on group compactifications.
method Continuity method, real Monge-Ampère equation, invariance under maximal compact subgroup.
result Necessary and sufficient condition for existence of Kähler-Einstein metrics.
Method solves high-dimensional nonlinear PDEs using neural networks.
problem Solving high-dimensional fully nonlinear PDEs.
method Backward induction with multi-layer neural networks to estimate solution and its gradient, with Hessian approximated by automatic differentiation.
result Method extends previous work on semi-linear PDEs to fully nonlinear cases, demonstrating accuracy on various examples.
Develops parabolic pluripotential theory for complex flows.
problem Complex Monge-Ampère equations in degenerate settings.
method Study of semi-concave envelopes and unique solutions.
result Shows semi-concave envelopes as unique solutions.
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 u(x,t) for specific nonlinear equations and convergence to self-expanding solutions. 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.
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-Ampeˋre equation …
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.
Develops Kähler geometry on new varieties for canonical metrics.
problem No specific problem stated; focuses on new varieties.
method Introduces new varieties, develops Kähler geometry, associates convex functions with metrics.
result Provides expression for Mabuchi functional and combinatorial sufficient condition of properness.
Compute equation for Kenyon-Smillie (2,3,4) Teichmüller curve.
problem Find algebraic equation for Kenyon-Smillie (2,3,4)-Teichmüller curve. method Compute algebraic equation and use Picard-Fuchs equation.
result Found algebraic equation describes a Teichmüller curve.
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…
Re-examines classical mechanics with superdegrees of freedom.
problem Classical mechanics with both commuting and anticommuting degrees of freedom.
method Defines phase dynamics as an implicit differential equation on supermanifolds.
result Defines phase dynamics on arbitrary supermanifolds.
We investigate how to obtain various flows of Kähler metrics on a fixed manifold as variations of Kähler reductions of a metric satisfying a given static equation on a higher dimensional manifold. We identify static equations that induce the geodesic equation for the Mabuchi's metric, the Calabi flow, the pseudo-Calabi…
The presentation of supergravity theories of our previous paper "Super-Poincare' algebras, space-times and supergravities (I)" is re-formulated in the language of Berezin-Leites-Kostant theory of supermanifolds. It is also shown that the equations of Cremmer, Julia and Scherk's theory of 11D-supergravity are equivalent…
Let (Mm,g) be a closed Riemannian manifold (m≥2) of positive scalar curvature and (Nn,h) any closed manifold. We study the asymptotic behaviour of the second Yamabe constant and the second N−Yamabe constant of (M×N,g+th) as t goes to +∞. We obtain that $\lim_{t \to +\infty}Y^2(M\times N,[…
The paper studies conditions for graphs connecting level sets of harmonic polynomials.
problem Conditions for graphs connecting level sets of harmonic polynomials.
method Algebraic properties and Kempf-Ness functional construction.
result Stability condition equivalent to the existence of a solution to the deformed Hermitian-Yang-Mills equation.
New method combines Monte Carlo and tensor networks for solving complex equations.
problem Solving high-dimensional partial differential equations efficiently.
method Uses Monte Carlo simulations and tensor train sketching for updates and re-estimations.
result Demonstrates versatility and efficacy in solving specific equations.
We construct new topological invariants of three-dimensional manifolds which can, in particular, distinguish homotopy equivalent lens spaces L(7,1) and L(7,2). The invariants are built on the base of a classical (not quantum) solution of pentagon equation, i.e.algebraic relation corresponding to a ``2 tetrahedra to 3 t…
In this paper we describe how to include funding and margining costs into a risk-neutral pricing framework for counterparty credit risk. We consider realistic settings and we include in our models the common market practices suggested by the ISDA documentation without assuming restrictive constraints on margining proce…
We study and generalize in various ways the model of rational expectation (RE) bubbles introduced by Blanchard and Watson in the economic literature. First, bubbles are argued to be the equivalent of Goldstone modes of the fundamental rational pricing equation, associated with the symmetry-breaking introduced by non-va…
Investigates surface immersions in normed spaces using affine differential geometry.
problem Differential geometry of immersed surfaces in normed spaces.
method Endows surface with a Riemannian metric related to normal curvature, re-calculates curvatures in terms of ambient affine distance functions, and characterizes minimal surfaces.
result Characterizes minimal surfaces as solutions to a differential equation and identifies conditions for affine normal and Birkhoff normal vector fields to coincide.
New PFPPs based on rank-dependent utility for better performance control.
problem Improving performance prediction in systems with short-term control.
method Introduces rank-dependent PFPPs, solves integral equations via Volterra theory.
result Existence of rank-dependent PFPPs under specific market conditions.
A deep learning method solves nonlinear filtering problems efficiently.
problem Nonlinear filtering problem
method Deep splitting method combined with energy-based neural network approximation
result Computational efficiency and performance comparable to Kalman and bootstrap filters
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.
Generates realistic person images for re-id, overcoming pose variations.
problem Lack of cross-view paired training data and pose variations in person re-identification.
method Pose-normalization GAN (PN-GAN) for generating images conditioned on pose.
result Synthesized images enable learning invariant features free of pose variations.
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…
We mathematically analyze a simple market model where trading at each point in time involves only two agents with the sum of their money being conserved and with neither parties resulting with negative money after the interaction process. The exchange involves random re-distribution among the two players of a fixed fra…
Paper extends method to detect reverse engineering attacks on DNN classifiers.
problem Detecting reverse engineering attacks on deep neural network image classifiers.
method Extend ADA approach to detect RE attacks (ADA-RE).
result Successfully detects 'stealthy' RE attacks before they launch test-time evasion attacks.
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.
Improved QA system by re-ranking top-10 results using machine learning.
problem Enhance deployed QA systems without re-training.
method Learn similarity function using n-gram features; implement neural sentence embeddings.
result Mean reciprocal rank improves by 9.15%.
This paper compares automatic metrics for re-speaking quality assessment.
problem Estimating the quality of re-speaking results is challenging.
method Comparing and adapting automatic evaluation metrics (BLEU, EBLEU, NIST, METEOR, etc.) to re-speaking quality.
result Automatic metrics are compared to human-derived NER metric for re-speaking quality.
ASTPN improves video-based person re-identification by jointly attending to spatial and temporal features.
problem Video-based person re-identification in surveillance and HCI.
method Joint Spatial and Temporal Attention Pooling Network (ASTPN).
result ASTPN outperforms state-of-the-art methods on multiple datasets.
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.
We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of orders with different prices. We then perform a re-scaling procedure leading to a …
In this thesis, we consider the suitability of using the charged cold fluid model in the description of ultra-relativistic beams. The method that we have used is the following. Firstly, the necessary notions of kinetic theory and differential geometry of second order differential equations are explained. Then an averag…
DBNs improve accuracy of biological ODE models with missing data.
problem Uncertainty in biological ODE models with missing data.
method Converted ODE models to DBNs and used Particle Filtering for parameter estimation.
result DBNs can accurately infer model variables with missing data.
Repulsive ensembles improve uncertainty estimates in PINNs for differential equations.
problem Improving uncertainty estimates in PINNs for differential equations.
method Employing repulsive ensembles (RE-PINN) with a repulsive term in the loss function.
result Repulsive ensembles produce more accurate uncertainty estimates and higher sample diversity.
We investigate bi-Hamiltonian structures and mKdV hierarchies of solitonic equations generated by (semi) Riemannian metrics and curve flows of non-stretching curves. There are applied methods of the geometry of nonholonomic manifolds enabled with metric-induced nonlinear connection (N-connection) structure. On spacetim…
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.
Some problems with the recent stimulating proposal of a ``Gauge Theory of Finance'' by Ilinski and collaborators are outlined. First, the derivation of the log-normal distribution is shown equivalent both in information and mathematical content to the simpler and well-known derivation, dating back from Bachelier and Sa…
A new method to improve image restoration by re-fitting standard methods.
problem Systematic errors in popular restoration algorithms for image processing.
method Developing a re-fitting approach that preserves covariant information and Jacobian of original estimators.
result Improved image restoration results on numerical simulations.