MKL-based models outperform complex multi-omics integrative approaches.
problem Integrating diverse omics data sources.
method Supervised multiple kernel learning with different kernel fusion strategies.
result MKL-based models outperform more complex architectures.
We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid i…
Study of multiplicative connections in Lie groupoids.
problem Defining and understanding multiplicative connections in Lie groupoids.
method Definition and study of multiplicative connections satisfying compatibility with the groupoid structure.
result Identification of the obstruction to the existence of a multiplicative connection.
BIDIFAC integrates multi-platform, multi-cohort data for shared and unique patterns.
problem Integration of multi-platform, multi-cohort data for shared and unique patterns.
method BIDIFAC integrates bidimensionally linked matrices into four components: globally shared, row-shared, column-shared, and single-matrix structural components.
result BIDIFAC reveals shared and unique patterns of variability in multi-platform, multi-cohort data.
The paper proves integral formulas for manifolds with multiple orthogonal distributions.
problem Understanding geometric properties of manifolds with multiple orthogonal distributions.
method Develops integral formulas for Riemannian manifolds with k>2 orthogonal complementary distributions. result Generalizes known formulas for k=2 and applies to manifold splitting and immersions. Quantizes Stäckel integrable systems into self-adjoint operators.
problem Quantizing Stäckel integrable systems into self-adjoint operators.
method Constructs commutative self-adjoint operators from quadratic Hamiltonians in involution.
result Proves multiplicative separation of variables for Stäckel integrable systems.
Proposes a multivariate regression model for better analysis of multiple datasets.
problem Insufficient performance of single-dataset analysis in integrative studies.
method Sparse estimation for variable and group selection, alternating direction method of multipliers algorithm.
result Demonstrated improved performance through simulations and real data analysis.
Surveying integrability of Lie algebroids and structures.
problem Integrability of Lie algebroids and structures.
method Survey and recent results on integrability.
result Recent findings on local and global integrability.
The paper solves a pricing problem for a multiple reset put option using integral equations.
problem Valuation of a multiple reset put option with reset rights.
method Formulated as a multiple optimal stopping problem, reduced to single optimal stopping problems, solved by induction and integral equations.
result Characterized optimal reset boundaries as solutions to nonlinear integral equations and derived reset premium representations.
We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce concrete integrations of several geometric stuctures defined infinitesimally. I…
We prove several results on Almgren's multiple valued functions and their links to integral currents. In particular, we give a simple proof of the fact that a Lipschitz multiple valued map naturally defines an integer rectifiable current; we derive explicit formulae for the boundary, the mass and the first variations a…
Partial regularity theorem for geodesic networks in R^n.
problem Proving regularity for geodesic networks in R^n.
method Partial ε-regularity theorem for sequences of integer multiplicity stationary geodesic networks converging to a multiplicity k line. result Proves partial regularity for geodesic networks.
The paper integrates quasi-Poisson manifolds into multiplicative D-valued moment maps.
problem Integrating quasi-Poisson manifolds into a broader geometric framework.
method Develops new aspects of shifted symplectic and Poisson geometry, establishing Lie-type correspondences and systematic constructions.
result Identifies multiplicative D-valued moment maps integrating quasi-Poisson manifolds, extending known constructions.
Motivated by our attempt to recast Cartan's work on Lie pseudogroups in a more global and modern language, we are brought back to the question of understanding the linearization of multiplicative forms on groupoids and the corresponding integrability problem. From this point of view, the novelty of this paper is that w…
The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modellin…
We construct a 2-dimensional twisted nonabelian multiplicative integral. This is done in the context of a Lie crossed module (an object composed of two Lie groups interacting), and a pointed manifold. The integrand is a connection-curvature pair, that consists of a Lie algebra valued 1-form and a Lie algebra valued 2-f…
KLIC combines multiple datasets for clustering, down-weighting noisy data.
problem Robustness of COCA in noisy or conflicting datasets.
method Multiple Kernel Learning for Integrative Clustering.
result KLIC down-weights noisy datasets, improving clustering accuracy.
Adapts manifold structure for better clustering performance.
problem Lack of consideration for local manifold structure in existing multiple kernel k-means methods.
method Adopts manifold adaptive kernel to integrate local manifold structure of kernels.
result Proposed method outperforms state-of-the-art methods.
In this paper we introduce multiplicative Dirac structures on Lie groupoids, providing a unified framework to study both multiplicative Poisson bivectors (i.e., Poisson group(oid)s) and multiplicative closed 2-forms (e.g., symplectic groupoids). We prove that for every source simply connected Lie groupoid G with Lie …
SMTM improves MCMC sampling in high dimensions with multiple proposals and stereographic integration.
problem Improving MCMC performance in high-dimensional sampling.
method Integrating multiple-try Metropolis with stereographic MCMC framework.
result SMTM outperforms classical MTM and other methods in high-dimensional sampling.
Proposes a new method for medical image segmentation.
problem Medical image segmentation challenges.
method Decompose-and-Integrate Learning.
result Improves segmentation performance on multiple datasets.
We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac manifolds.
InVA models image outcomes from multiple modalities, outperforming standard VAEs.
problem Understanding relationships across multiple imaging modalities in neuroimaging.
method Integrative Variational Autoencoder (InVA) framework for image-on-image regression.
result InVA accurately predicts PET scans from structural MRI, outperforming conventional models.
Develops theory of weightings for Lie groupoids and algebroids.
problem Understanding differential geometry of weightings for Lie groupoids and algebroids.
method Extending work on weighted manifolds, defining weighted submanifolds, and developing theories of linear weightings and multiplicative weightings.
result Characterizes infinitesimally multiplicative weightings for Lie algebroids and classifies multiplicative weightings of Lie groupoids.
Proves singular set of certain integral hypercurrents has measure zero.
problem Characterizing singular sets of specific integral hypercurrents.
method Proof based on varifold stationarity.
result Singular set has measure zero.
Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according t…
Special Legendrian Integral Cycles in S5 are the links of the tangent cones to Special Lagrangian integer multiplicity rectifiable currents in Calabi-Yau 3-folds. We show that such Special Legendrian Cycles are smooth except possibly at isolated points.
Formula for Milnor triple linking number in link diagrams with multiple crossings.
problem Calculating Milnor triple linking number for complex link diagrams.
method Polyak-Viro type formula with explicit computation of configuration space integral.
result Formula applicable to diagrams with triple or more crossings.
A new method integrates multi-label and multi-view features for image classification.
problem Combining multi-label and multi-view information for effective image classification.
method Introduces MV3MR, a method that exploits the complementary property of different features and discovers intrinsic local geometry. result MV3MR outperforms existing methods on PASCAL VOC' 07 and MIR Flickr datasets. We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known integration results related to Poisson geometry. We also revisit multiplicative…
This research improves asset life prediction by integrating deep learning with mixture distributions.
problem Predicting residual useful life for assets with multiple failure modes.
method Integrates mixture (log)-location-scale distribution with deep learning.
result Proposed models outperform existing methods in predicting residual useful life.
Protein function prediction is the important problem in modern biology. In this paper, the un-normalized, symmetric normalized, and random walk graph Laplacian based semi-supervised learning methods will be applied to the integrated network combined from multiple networks to predict the functions of all yeast proteins …
We prove that 2 dimensional Integral currents (i.e. integer multiplicity 2 dimensional rectifiable currents) which are almost complex cycles in an almost complex manifold admitting locally a compatible symplectic form are smooth surfaces aside from isolated points and therefore are J-holomorphic curves.
The paper analyzes optimal statistical arbitrage strategies for co-integrated stocks.
problem Finding optimal portfolio weights for co-integrated stocks.
method Solving a Hamilton-Jacobi-Bellman (HJB) partial differential equation for optimal portfolio weights.
result The proposed co-integrated model with eigenportfolios can generate stable growth rates over a long time horizon.
New technologies have enabled the investigation of biology and human health at an unprecedented scale and in multiple dimensions. These dimensions include a myriad of properties describing genome, epigenome, transcriptome, microbiome, phenotype, and lifestyle. No single data type, however, can capture the complexity of…
The study examines stationary integral varifolds near multiplicity 2 planes, proving regularity under specific conditions.
problem Understanding the structure of stationary integral varifolds near multiplicity 2 planes.
method Investigates the structure of varifolds close to planes with multiplicity 2, proving an ε-regularity theorem under certain conditions.
result In B1/2(0), V is represented by the graph of a Lipschitz 2-valued function over P0 with small Lipschitz constant; all tangent cones at singular points are unique and comprised of stationary unions of 4 half-planes. Study minimal surfaces with finite curvature in a specific manifold.
problem Understanding minimal surfaces with finite total curvature in a Hadamard manifold.
method Developed a formula to compute total curvature using topological, geometrical, and conformal data.
result Total curvature is an integral multiple of \(2\pi\).
Integral foliated simplicial volume is zero for certain amenable covers.
problem Calculating the integral foliated simplicial volume of specific manifolds.
method Using open amenable covers and fixed price property of fundamental groups.
result Integral foliated simplicial volume is zero for manifolds with multiplicity at most n.
New proof of Lie algebroid action equivalence and integrability.
problem Equivalence between Lie algebroid action and integrability.
method Double Lie groupoids and multiplicative foliations.
result Simple characterization of double Lie groupoids inducing Lie groupoid structures.
AICov integrates population covariates for better COVID-19 forecasting.
problem Forecasting COVID-19 with broader social context.
method Integrative deep learning framework with LSTM and multiple data sources.
result Improved prediction of COVID-19 cases and deaths with population risk factors.
The paper integrates multiple Gaussian process predictions using Monte Carlo sampling.
problem Accurate prediction of variables using multiple models.
method Log-linear pooling of Gaussian process predictions, combined with Monte Carlo sampling.
result The log-linear pooling method improves prediction accuracy compared to linear pooling.
In this paper it is shown that multiplicative cohomology theories that are rationally even -- a technical condition that is often satisfied -- the Hopkins-Singer construction of generalized differential cohomology has a unital, graded commutative multiplicative structure. To this end, an explicit integration and a diff…
Researchers prove uniqueness of certain cylindrical tangent cones for special Lagrangians.
problem Proving uniqueness of cylindrical tangent cones for special Lagrangians.
method Analyzing exact special Lagrangian submanifolds with multiplicity one and cylindrical tangent cones.
result The cylindrical tangent cones are unique under specific conditions.
Classifies 3D F-manifolds with or without Euler fields.
problem Local classification of 3D F-manifolds.
method Integrability condition on multiplication in holomorphic tangent bundle.
result Local classification of 3D F-manifolds.
Q-NETs use neural networks to estimate integrals of low-dimensional functions efficiently.
problem Estimating integrals of multidimensional functions with costly evaluations.
method Fixed neural networks (Q-NETs) that operate on proxy function parameters to calculate exact integrals over subsets of dimensions.
result Q-NETs can calculate integrals over any subset of dimensions without resampling or retraining the proxy.
We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex multiplicities (in the multivalued ''Darboux'' case). We specify normal forms in e…
We study the properties of the multiplicative structure on valuations on convex sets. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss related problems of integral geometry. Then we formulate a conjectural analogue of this result for odd valuations.
Improves accuracy of SMCI estimators without expanding sum regions.
problem Intractable multiple summations in evaluating expectations on the Ising model.
method Combining multiple SMCI estimators using generalized least squares (GLS).
result The proposed method can improve accuracy without combinatorial explosion.