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.
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.
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. 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.
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…
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.
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.
Generalized complex (GC) geometry interpolates between ordinary symplectic and complex geometry. Stable generalized complex manifolds (first introduced by Cavalcanti, Gualtieri in 2015) carry a Poisson structure which is generically symplectic, but degenerates on a (real) codimension-2 submanifold. Up to gauge equivale…
We present ChromAlignNet, a deep learning model for alignment of peaks in Gas Chromatography-Mass Spectrometry (GC-MS) data. In GC-MS data, a compound's retention time (RT) may not stay fixed across multiple chromatograms. To use GC-MS data for biomarker discovery requires alignment of identical analyte's RT from diffe…
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.
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.
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.
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 …
Deep Neural Networks(DNNs) require huge GPU memory when training on modern image/video databases. Unfortunately, the GPU memory is physically finite, which limits the image resolutions and batch sizes that could be used in training for better DNN performance. Unlike solutions that require physically upgrade GPUs, the G…
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.
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 $…
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.
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.
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…
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…
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.
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 …
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 focus on the commonly used synchronous Gradient Descent paradigm for large-scale distributed learning, for which there has been a growing interest to develop efficient and robust gradient aggregation strategies that overcome two key system bottlenecks: communication bandwidth and stragglers' delays. In particular, R…
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…
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…
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.
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.
There are different problems for resolution of complex LC-MS or GC-MS data, such as the existence of embedded chromatographic peaks, continuum background and overlapping in mass channels for different components. These problems cause rotational ambiguity in recovered profiles calculated using multivariate curve resolut…
E2GC optimizes energy efficiency in DNNs by balancing computational and data movement costs.
problem Imbalance between computational complexity and data reuse in GConv leads to suboptimal energy efficiency.
method Developed an optimum group size model and proposed E2GC module with constant group size.
result E2GC modules improve energy efficiency by 10.8% and 4.73% on P100 and P4000 GPUs, respectively.
Study of 13,456 hot stellar systems reveals multi-layered grouping.
problem Understanding physical and evolutionary properties of Hot Stellar Systems.
method Used stellar mass, effective radius, and mass-to-luminosity ratio to group HSS into eight homogeneous ellipsoidal groups, then merged them through a multi-phased syncytial algorithm.
result Identified two complex-structured groups of HSS, one older and smaller, the other brighter and younger.
Let $X\hookrightarrow \cpn $ be a smooth complex projective variety of dimension n. Let λ be an algebraic one parameter subgroup of $G:=\gc$. Let 0≤l≤n+1. We associate to the coefficients Fl(λ) of the normalized weight of λ on the mth Hilbert point of X new energies $F_{\om,l}(\vp)$. The (loga…
Study cohomology of GL₂n(Z) and graph complexes using Pfaffian forms.
problem Cohomology of GL₂n(Z) and related graph complexes.
method Use Pfaffian forms on symmetric spaces and dual Laplacians on graphs.
result First cocycle gives a non-trivial class in H⁻⁶(GC₃).
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…
Study of weighted nonlinear flags in symplectic geometry.
problem Understanding the geometry of weighted nonlinear flags.
method Generalizing weighted nonlinear Grassmannians to Frechet manifolds and using them to describe coadjoint orbits.
result Description of coadjoint orbits of Hamiltonian diffeomorphisms using weighted isotropic nonlinear flags.