Stability of chiral rings in N=1 theories linked to K-stability of X.
problem Understanding the stability of chiral rings in N=1 theories.
method Introducing test chiral rings and generalized maximization, studying N=1 field theory derived from D3 branes probing a three-fold singularity X.
result K-stability of X is equivalent to the stability of chiral ring of the corresponding field theory.
Extends flat spacetimes with BTZ singularities, preserving key properties.
problem Describing globally hyperbolic singular flat spacetimes.
method Lorentzian geometry, Teichmüller space, BTZ singularities.
result BTZ extensions preserve Cauchy-maximality and Cauchy-completeness.
4-manifolds with specific trisections are 3-fold covers of S^4.
problem Understanding 4-manifolds with (g;k1,k2,0)-trisections. method Proving 4-manifolds with certain trisections are irregular 3-fold covers of S4. result Any 4-manifold with a (g;k1,k2,0)-trisection is an irregular 3-fold cover of S4. Paper proves structure of compact Kähler 3-folds with specific bundles.
problem Characterizing compact Kähler 3-folds with nef anti-canonical bundles.
method Minimal Model Program, positivity of direct image sheaves, Q-conic bundles, orbifold vector bundles.
result Compact Kähler 3-folds with nef anti-canonical bundles are essentially one of three types.
Existence proved for complex 3-folds equation on a specific phase range.
problem Existence of solutions for a specific equation on complex 3-folds.
method New continuity path and Monge-Ampère equation with mixed sign coefficients.
result Existence result for the deformed Hermitian Yang-Mills equation on compact complex three-folds.
New G2-holonomy manifolds from 5d N=1 theories domain walls.
problem Geometrizing domain walls in 5d N=1 theories.
method Constructing 7-manifolds by fibering a Calabi-Yau over a real line.
result 7-manifolds with G2-holonomy from domain walls in 5d theories. In this paper we construct Mabuchi LωM functional and Aubin-Yau functionals IωAY,JωAY on any compact complex three-folds. The method presented here will be used in the forthcoming paper \cite{L1} on the construction of those functionals on any compact complex m…
Deligne and Mostow constructed a class of lattices in PU(2,1) using monodromy of hypergeometric functions. Later, Thurston reinterpreted them in terms of cone metrics on the sphere. In this spirit we construct a fundamental domain for all lattices with three fold symmetry in Deligne-Mostow list. This is a generalisatio…
Paper derives normal approximations for singular subspaces with i.i.d. noise.
problem Normal approximation of singular subspaces under i.i.d. noise.
method Explicit representation formula, expected projection distance calculation, non-asymptotic normal approximation, bias corrections.
result Non-asymptotic normal approximation with optimal SNR condition and comprehensive simulation results.
Study dualities between G2-manifolds and string theories.
problem Determine dualities between M-theory and heterotic string theories on G2-manifolds.
method Analyze K3-fibered G2-manifolds and their dual heterotic and F-theory realizations.
result Identify dual heterotic and F-theory realizations for a large class of G2-manifolds.
We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-paramete…
For any alternating knot, it is known that the double branched cover of the 3-sphere branched over the knot is an L-space. We show that the three-fold cyclic branched cover is also an L-space for any genus one alternating knot.
In the previous papers \cite{L1, L2} the author constructed Mabuchi and Aubin-Yau functionals over any complex surfaces and three-folds, respectively. Using the method in \cite{L2}, we construct those functionals over any complex manifolds of the complex dimension bigger than or equal to 2.
We describe an action of U(1)×Sp(1) on HP7 that allows to obtain a Z2-quotient of CAYLEY (the Grassmannian of oriented 4-planes in R8 closed under the three-fold cross product) by quaternionic Kähler reduction.
Calculates Laplacian spectra on Calabi-Yau hypersurfaces.
problem Computing the spectrum of the Laplacian on complex manifolds.
method Numerical computation of eigenvalues and eigenmodes for line bundles.
result Agreement with exact results for P3 and a torus, first numerical results for Fermat quintic. Develops optimal transport in Lorentzian spaces with synthetic curvature bounds.
problem Synthetic curvature bounds for Lorentzian spaces.
method Optimal transport, convexity analysis of entropy functionals.
result Synthetic notion of timelike Ricci curvature lower bounds.
The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in N=2 supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces…
We consider a generalised complex Monge-Ampère equation on a compact Kähler manifold and treat it using the method of continuity. For complex surfaces, we prove an easy existence result. We also prove that (for three-folds and a related real PDE in a ball), as long as the Hessian is bounded below by a pre-determined co…
We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In parti…
Null Kähler metrics are characterized by Painlevé I or II ODEs.
problem Characterizing null-Kähler metrics in four dimensions.
method Cohomogeneity-one anti-self-dual null-Kähler metrics, twistor methods, Painlevé I and II ODEs.
result Cohomogeneity-one anti-self-dual null-Kähler metrics are generically characterized by solutions to Painlevé I or Painlevé II ODEs.
Let X be a complex four-dimensional compact Calabi-Yau manifold equipped with a Kähler form ω and a holomorphic four-form Ω. Under certain assumptions, we define Donaldson-Thomas type deformation invariants by studying the moduli space of the solutions of Donaldson-Thomas equations on the given Calabi-Yau manifol…
Study links public concern in Italy to financial markets worldwide.
problem Understanding public concern's impact on financial markets during pandemics.
method Used Google Trends data from YouTube, News, and Search to measure public concern and correlate it with stock index returns.
result Public concern in Italy drives concerns in other countries and explains stock index returns of multiple nations.
New explicit constructions of unbalanced Ramanujan bipartite graphs.
problem Constructing bipartite Ramanujan graphs with specified degrees and avoiding certain edges.
method Presented explicit constructions and discussed known methods for Ramanujan graph construction.
result Affirmative answer to constructing unbalanced Ramanujan bipartite graphs under certain conditions.
An irreducible representation of the free group on two generators X,Y into SL(2,C) is determined up to conjugation by the traces of X,Y and XY. We study the diagonal slice of representations for which X,Y and XY have equal trace. Using the three-fold symmetry and Keen-Series pleating rays we locate those groups which a…
Adaptive IHS improves sketching for large-scale data.
problem Efficiently modeling large-scale data with iterative Hessian sketch.
method Deterministic A-optimal subsampling for improved IHS.
result A-optimal IHS outperforms existing accelerated IHS methods.
Study on positivity properties of vector bundle Monge-Ampère equation.
problem Analyzing positivity in vector bundle Monge-Ampère equation.
method Investigates MA-positivity and MA-semi-positive solutions for different ranks of holomorphic bundles over complex surfaces and manifolds.
result Positivity preservation in rank-two holomorphic bundles but not in higher ranks.
This paper simplifies OPE in large state spaces using state abstractions.
problem Accurately evaluating policies offline in large state spaces.
method Developed a backward-model-irrelevance condition and an iterative state abstraction procedure.
result Deeply-abstracted states substantially simplify OPE sample complexity.
Study on information-theoretic measures in deep neural networks.
problem Understanding the relationship between compression and generalization in deep neural networks.
method Heuristic statistical physics methods and adaptive interpolation method.
result The relationship between compression and generalization remains elusive in the studied setting.
High-dimensional regression models struggle with resampling methods.
problem Estimating uncertainty in high-dimensional supervised regression tasks.
method Investigation of bootstrap, subsampling, and jackknife methods in high-dimensional generalized linear models.
result Resampling methods exhibit double-descent behavior and are inconsistent in high dimensions.
Discusses handling intercurrent events in clinical trials with time-to-event outcomes.
problem Handling intercurrent events in clinical trials with time-to-event outcomes.
method Defines estimands and six ICE handling strategies, including new competing-risk strategy.
result Novel methods for handling intercurrent events in clinical trials with time-to-event outcomes.
Method for conditional sampling with pre-trained normalizing flows.
problem Conditional sampling for incomplete observations.
method Variational Schur conditional sampling with normalizing flows.
result Successfully applied to invertible residual networks for inference and classification.
Paper proposes a new method for efficient hyperparameter optimization.
problem Challenging task of optimizing hyperparameters in machine learning.
method Sequential Uniform Design (SeqUD) strategy for adaptive and efficient exploration of hyperparameter space.
result The proposed SeqUD strategy outperforms existing methods in hyperparameter optimization.
Unified framework for robust ordinal embedding from contaminated comparisons.
problem Inconsistent relative comparisons in ordinal data.
method Jointly identifies and corrects contaminated comparisons, learning embeddings directly.
result Unified framework alleviates sub-optimality and provides a robust solution.
New method makes CNN interpretations robust to adversarial attacks.
problem Adversarial attacks on CNN interpretation maps.
method Renyi Differential Privacy (RDP) for robust interpretation.
result Certifiable top-k robustness and improved experimental robustness. Constructs explicit nontrivial cycles in Habiro cohomology of smooth varieties.
problem Describing and constructing nontrivial cycles in Habiro cohomology.
method Using either the Picard-Fuchs equation or push-forward of elements of the Habiro ring.
result Explicit classes for 1-parameter Calabi-Yau families and q-holonomic modules.
New Spin(7)-manifolds constructed via generalized connected sums.
problem Creating compact Spin(7)-manifolds for geometric engineering.
method Generalized connected sum of Calabi-Yau four-fold and G2-holonomy manifold.
result Construction of new compact Spin(7)-manifolds with holonomy.
MNIST-NET10 fusion improves MNIST classification to 0.1% error rate.
problem Improving MNIST classification accuracy.
method Complex heterogeneous fusion architecture using degree of certainty aggregation.
result MNIST-NET10 achieves 0.1% error rate with 10 misclassifications.
Study of stability conditions on 3-folds, focusing on walls and intersections.
problem Understanding stability conditions and numerical walls on 3-folds.
method Differential geometry analysis of numerical walls, proving intersections and maximum turning points.
result Gieseker semistability equivalent to asymptotic semistability along paths in the upper half plane.
Paper proposes an adversarial sampling method for efficient extreme classification.
problem Training classifiers over many classes is computationally expensive.
method Adversarial sampling to draw negative samples from an adversarial model.
result Significantly reduces training time by an order of magnitude.
With the rapid development of social media sharing, people often need to manage the growing volume of multimedia data such as large scale video classification and annotation, especially to organize those videos containing human activities. Recently, manifold regularized semi-supervised learning (SSL), which explores th…
This paper uses cPF to build recommender systems from raw count data.
problem Sparse, over-dispersed and bursty count data make direct use in recommender systems challenging.
method Compound Poisson Factorization (cPF) with a unified framework (dcPF) and adaptive algorithm.
result dcPF achieves better recommendation scores than Poisson Factorization on raw or binarized data.
Study improves stock price prediction by integrating international markets using deep learning.
problem Complex cross-correlation between international stock markets.
method Multimodal deep learning to forecast stock prices.
result Early and intermediate fusion models outperform late fusion and single modality models.
ReGAN uses GANs for improved text sequence generation.
problem Limited use of GANs for text sequence generation, especially for longer sequences.
method ReGAN employs GANs with efficient policy gradient estimators and unbiased low variance techniques.
result Improved sequence generation quality and training stability.
Study shows how classifiers can approach Bayes error in high-dimensional settings.
problem Generalization error in high-dimensional perceptrons.
method Proved a formula for generalization error using convex optimization and observed that logistic and hinge regression can approach Bayes error closely.
result Logistic and hinge regression can approach Bayes-optimal generalization error closely in high-dimensional settings.
Twistor theory connects space-time to complex curves, solving physics equations.
problem Solving equations in mathematical physics using twistor theory.
method Encoding solutions into twistor cohomology and using twistor correspondences.
result Explicit examples of Yang-Mills and gravitational instantons.
Research combines econometric, machine learning, and deep learning models for financial forecasting.
problem Improving financial time series forecasting accuracy.
method Hybrid models combining ARIMA, SVM, XGBoost, and LSTM.
result Effective hybrid models outperform individual components and the Buy&Hold strategy.
This work tackles slate-based recommender systems using RL, optimizing long-term user engagement.
problem Optimizing long-term user engagement in slate-based recommender systems.
method Developed SLATEQ, a decomposition of RL methods for slate-based recommendations, and outlined a practical methodology.
result SLATEQ decomposes long-term value of a slate into component item-wise long-term values under mild assumptions.
Proposes a method to estimate treatment effects using instruments.
problem Estimating treatment effects from observational data is challenging when unconfoundedness is violated.
method Leverages instruments to estimate bounds on conditional average treatment effect (CATE) through a mapping to a discrete representation space and a two-step procedure.
result Demonstrates theoretical validity and reduced estimation variance in finite-sample settings.