This paper introduces new Lagrangian branes in stable generalized complex manifolds.
problem Understanding stable generalized complex manifolds and their properties.
method Using log symplectic geometry and Floer theory techniques.
result Lagrangian branes with boundary are introduced and their properties are studied.
GC Stein manifolds characterized with embeddings and functions.
problem Characterize GC Stein manifolds using embeddings and functions.
method Extended Cartan's Theorem A and B, defined L-plurisubharmonic functions, established GH embeddings. result Characterized GC Stein manifolds via L-plurisubharmonic exhaustion functions and GH embeddings. Develops SGH bundles and theories for GC manifolds.
problem No specific problem stated; focuses on new bundle theory.
method Introduces SGH bundles, develops cohomology, and establishes theories.
result Established a Chern-Weil theory and Hodge theory for SGH bundles.
Generalized complex structures on certain torus bundles are explored.
problem Exploring generalized complex structures on specific torus bundles.
method Analyzing principal torus bundles over complex manifolds with even dimensional fibers and characteristic class of type (1,1).
result Generalized complex structures on these bundles are equivalent to products of complex and symplectic structures in tubular neighborhoods of fibers.
We investigate the formal deformation theory of (rank 1) branes on generalized complex (GC) manifolds. This generalizes, for example, the deformation theory of a complex submanifold in a fixed complex manifold. For each GC brane B on a GC manifold (X,J), we construct a formal (pointed) groupoid $…
In the quatenions ($\H$, $\H'$, $\H^{C}$) and octonions ($\gC$, $\gC^\prime$, $\gC^C$), we show some results on the conjugacy of two pure imaginary non-zero elements with same norm.
Reinterprets Granger causality with causal Bayesian networks and Reichenbach's principles.
problem Lack of a rigorous causal foundation in Granger causality.
method Reinterpreting Granger causality through Reichenbach's principles and causal Bayesian networks, implementing as c-GC.
result c-GC provides a more principled framework for causal discovery in observational datasets.
Deep learning aligns GC-MS peaks for biomarker discovery.
problem Aligning retention times of GC-MS peaks across different samples.
method ChromAlignNet, a deep learning model for peak alignment.
result ChromAlignNet outperforms existing methods on complex data sets.
A neural network approach uncovers Granger causality without explicit variable selection.
problem Capturing complex associations in multivariate time series data.
method A deep learning model with proper regularization to learn the true Granger Causality structure.
result A neural network can learn the true Granger Causality structure from data without explicit variable selection.
We show how the classical Moser Lemma from symplectic geometry extends to generalized complex structures (GCS) on arbitrary Courant algebroids. For this, we extend the notion of Lie derivative to sections of the tensor bundle (⊗iE)⊗(⊗jE∗) with respect to sections of the Courant algebroid E us…
We define the thin fundamental categorical group P2(M,∗) of a based smooth manifold (M,∗) as the categorical group whose objects are rank-1 homotopy classes of based loops on M, and whose morphisms are rank-2 homotopy classes of homotopies between based loops on M. Here two maps are rank-n homotop…
New metric invariant GC connects to TC, with applications in robotics.
problem Understanding motion planning in metric spaces.
method Introducing geodesic complexity (GC) as a new invariant.
result GC and topological complexity (TC) coincide in many cases but can be distinguished.
New neural network models improve Granger Causality detection in non-linear systems.
problem Mischaracterization of Granger Causality in non-linear systems using traditional linear models.
method Proposes Learned Kernel VAR (LeKVAR) and decoupled penalties for GC estimation and lag selection.
result Improves GC detection in non-linear systems with computational efficiency.
New method models portfolios with leptokurtic risk factors using Gram-Charlier expansions.
problem Modeling portfolios with excess kurtosis.
method GC-like expansions of the hyperbolic-secant law to account for leptokurtosis.
result Portfolio distribution with risk factors modeled as GC-like expansions of the HS law.
We notice that a generic nonsingular gradient field v=∇f on a compact 3-fold X with boundary canonically generates a simple spine K(f,v) of X. We study the transformations of K(f,v) that are induced by deformations of the data (f,v). We link the Matveev complexity c(X) of X with counting the …
In conventional Differential Geometry one studies manifolds, locally modelled on Rn, manifolds with boundary, locally modelled on [0,∞)×Rn−1, and manifolds with corners, locally modelled on [0,∞)k×Rn−k. They form categories ${\bf Man}\subset{\bf Man^b}\sub…
Optimal GCP selects GCs for ACGs, reducing memory usage.
problem Limited GPU memory in deep learning training.
method Optimal algorithms for selecting Gradient Checkpoints (GCs) for arbitrary computation graphs (ACGs).
result Achieves maximal memory cut-offs for ACGs, outperforming existing methods.
GC-FCP provides efficient federated CP with group-conditional coverage guarantees.
problem Uncertainty quantification in federated settings with distributed calibration data.
method Group-conditional federated conformal prediction (GC-FCP) using group-stratified coresets.
result GC-FCP offers efficient aggregation and calibration compared to centralized methods.
A novel framework uses goal-conditioned reinforcement learning to generate diverse samples.
problem Generating high-quality, diverse samples from generative models.
method Two agents: GC-agent learns to reconstruct the training set, S-agent learns to imitate GC-agent without knowing the goals.
result Empirically, the method generates diverse and high-quality samples in image synthesis.
Paper uses time series transformers to predict investment success.
problem Optimizing investment sourcing in VC and GC.
method Transformer-based Multivariate Time Series Classifier (TMTSC).
result TMTSC improves decision making in VC and GC investments.
It has been shown recently that the geometry of D-branes in general topologically twisted (2,2) sigma-models can be described in the language of generalized complex structures. On general grounds such D-branes (called generalized complex (GC) branes) must form a category. We compute the BRST cohomology of open strings …
Currents on cusped hyperbolic surfaces have a denseness property similar to compact surfaces.
problem Proving denseness of rational currents on cusped hyperbolic surfaces.
method Using geodesic currents and subset currents, proving denseness through examples and continuous extension.
result Denseness of rational currents on cusped hyperbolic surfaces, including geodesics connecting cusps.
A new method selects regions of interest in GC-MS data without prior target selection.
problem Challenges in GC-MS data analysis due to fragmentation and shared fragment ions.
method Uses a pseudo F-ratio moving window (ψFRMV) to automatically select regions of interest. result Algorithm can accurately identify signal regions in GC-MS data.
We propose a new heavy-tailed distribution --- Gaussian-Chain (GC) distribution, which is inspirited by the hierarchical structures prevailing in social organizations. We determine the mean, variance and kurtosis of the Gaussian-Chain distribution to show its heavy-tailed property, and compute the tail distribution tab…
Unified framework for uniform signal recovery in nonlinear GCS with 1-bit/quantized measurements.
problem Uniform recovery guarantees for nonlinear generative compressed sensing.
method Unified framework using generalized Lasso and Lipschitz approximation.
result Uniform recovery of all signals in the ball up to an error of ε using approximately O(k/ε^2) samples.
Robust machine learning models improve DNA regulatory sequence prediction under various shifts.
problem Real-world applications of DNA regulatory sequence prediction involve shifts not captured by standard i.i.d. assumptions.
method Introduces a robustness framework combining simulation benchmarks and real data analysis.
result Models remain accurate and calibrated under mild shifts but show higher error and miscalibration under strong shifts.
We prove that all the Tonelli Hamiltonians defined on the cotangent bundle $T^*\T^n$ of the n-dimensional torus that have no conjugate points are C0 integrable, i.e. $T^*\T^n$ is C0 foliated by a family $\Fc$ of invariant C0 Lagrangian graphs. Assuming that the Hamiltonian is C∞, we prove that there …
GC-Flow uses graph flows for better clustering than traditional GCNs.
problem Traditional GCNs miss useful clustering information.
method Designing normalizing flows to replace GCN layers, creating a generative model.
result GC-Flow produces well-separated clusters while maintaining predictive power.
Study optimizes GCS operations with deep learning and reinforcement learning.
problem Maximizing storage performance in GCS with resource-efficient simulations.
method Introduces MLD model for fast flow prediction and well control optimization, combining deep learning and reinforcement learning.
result Achieves highest NPV while reducing computational resources by over 60%.
FNO model predicts GCS pressure fields with 81% less data, even with limited high-fidelity data.
problem Accurate prediction of complex physical behaviors in large-scale 3D geological carbon storage problems with limited data.
method Multi-fidelity Fourier Neural Operator (FNO) for efficient training with multi-fidelity datasets.
result Multi-fidelity FNO model predicts pressure fields with reasonable accuracy even with limited high-fidelity data.
Proposes QGC to distinguish between lower and upper tail connectivity in financial networks.
problem Identifying systemically important firms using financial data.
method Quantile Granger Causality (QGC) using Lasso penalized quantile regressions.
result QGC networks detect systemic risk more accurately than mean-based networks.
Deep learning speeds up pressure prediction in carbon storage reservoirs.
problem Accurately forecasting reservoir pressure in geologic carbon storage projects with sparse well data.
method Combining InSAR surface displacement data with deep learning and data assimilation techniques.
result Workflow can predict reservoir pressure with high efficiency and uncertainty quantification.
New method identifies sepsis-related patient features in EMR data.
problem Identify sepsis-related patient features in EMR data.
method Linear multivariate Hawkes process model with ReLU link function, coupled with gradient-based method.
result Identifies several interpretable GC chains that precede sepsis.
GC 2022 challenges real-time trend detection in financial tick data.
problem Efficiently detect trading trends in high-volume financial tick data.
method Real-time complex event processing of tick data, focusing on trend indicators and patterns.
result Participants must build reusable and practical solutions for real-life trading decisions.
The paper explores how different patterns of heterophily affect Graph Neural Networks.
problem Understanding the impact of heterophily on Graph Neural Networks.
method Theoretical analysis and experiments with Heterophilous Stochastic Block Models (HSBM).
result The impact of heterophily on classification depends on the Euclidean distance of neighborhood distributions and the averaged node degree.
We invoke a Gaussian mixture model (GMM) to jointly analyse two traditional emission-line classification schemes of galaxy ionization sources: the Baldwin-Phillips-Terlevich (BPT) and WHα vs. [NII]/Hα (WHAN) diagrams, using spectroscopic data from the Sloan Digital Sky Survey Data Release 7 and SEAGal/STARLI…
Unified kernel-based methods improve nonlinear causal discovery.
problem Identifying nonlinear causal relationships between time series variables.
method Unified Kernel Principal Component Regression (KPCR) and Gaussian Process score-based model with Smooth Information Criterion.
result Improved performance in time series nonlinear causal discovery.
CodedReduce combines tree topology and gradient coding for efficient and resilient gradient aggregation.
problem Efficient and robust gradient aggregation in distributed learning.
method CodedReduce combines tree topology and gradient coding to overcome bandwidth bottlenecks and straggler delays.
result CodedReduce achieves up to 27.2x speedup over benchmarks GC and RAR.
LCMQR improves prediction intervals by adapting to local heteroscedasticity.
problem Efficient and adaptive prediction intervals for local heteroscedasticity.
method LCMQR combines multi-quantile information with kernel-based localization.
result LCMQR constructs tighter intervals than prior methods, especially in heterogeneous environments.
We specify a result of Yokoi \cite{yo} by proving that if G is an abelian group and X is a homogeneous metric ANR compactum with dimGX=n and Hˇn(X;G)=0, then X is an (n,G)-bubble. This implies that any such space X has the following properties: Hˇn−1(A;G)=0 for every closed…
GC-KAN uses KANs to detect Granger causality in time series data.
problem Detecting causal relationships in nonlinear time series data.
method Developed GC-KAN framework using Kolmogorov-Arnold networks for Granger causality detection.
result KANs outperform MLPs in identifying sparse Granger causal relationships.
The paper examines how stable solutions of elliptic problems affect the geometry of manifolds.
problem Characterizing manifolds with stable solutions of elliptic problems.
method Analyzing geometric rigidity under stability conditions and non-negative Ricci curvature.
result Characterization and splitting results for manifolds with stable solutions.
The study explores stable diffeomorphism groups in 4-manifolds using localisation and invariants.
problem Understanding stable diffeomorphism groups in 4-manifolds.
method Localisation of n-manifolds, inverting connected sum construction, using Bauer--Furuta invariants.
result K3-stable Bauer--Furuta invariants determine S^2xS^2-stable invariants.
New findings on stable minimal hypersurfaces in curved 4-manifolds.
problem Nonexistence of complete stable minimal hypersurfaces in positively curved 4-manifolds.
method Combination of non-negative sectional curvature and strict positivity of scalar curvature.
result Rigidity of complete stable minimal hypersurfaces in 4-manifolds with positive curvature.
Constructs operations on stable moduli spaces to compare manifold cohomology.
problem Comparing cohomology of moduli spaces of closed manifolds.
method Constructs operations on stable moduli spaces and uses them to compare cohomology.
result Obtains isomorphisms in a stable range for all primes not invertible in coefficients.
Paper improves privacy and utility of SGD with bounded domain and smooth losses.
problem Lack of tight privacy bounds and practical assumptions in DPSGD.
method Rigorous privacy characterization for DPSGD with general L-smooth and non-convex loss functions, tracking privacy loss over iterations.
result Privacy loss converges without convexity assumption for bounded domain, improving utility.
Researchers study the geometric properties of a specific type of stable processes.
problem Understanding the information geometry of tempered stable processes.
method Derivation of α-divergence, Fisher information matrices, and α-connections.
result Obtained Fisher information matrices and α-connections for statistical manifolds.
Characterizes hyperbolic links with stable maps to the plane.
problem Understanding hyperbolic links through stable maps.
method Characterization of hyperbolic links via stable maps to the plane.
result Complete characterization of hyperbolic links with specific stable maps.