Generalizations of the Weierstrass formulae to generic surface immersed into , and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.
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48 results for “multidimensional space”
Paper analyzes multidimensional PIDEs for financial modeling, proving existence and uniqueness in Bessel spaces.
problem Analyzing solutions of non-local nonlinear PIDEs in multidimensional spaces.
method Employing abstract semilinear parabolic equations theory in Bessel potential spaces.
result Existence and uniqueness of solutions for a wide class of Lévy measures in multidimensional spaces.
UAPCA projects uncertain data to low dimensions using GMMs.
problem Uncertain multidimensional data not well described by normal distributions.
method Model data with Gaussian mixture models, derive UAPCA projection from general formulation.
result Low-dimensional projections better represent multidimensional distributions.
We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discr…
Multidimensional scaling (MDS) is a class of projective algorithms traditionally used in Euclidean space to produce two- or three-dimensional visualizations of datasets of multidimensional points or point distances. More recently however, several authors have pointed out that for certain datasets, hyperbolic target spa…
4 greedy algorithms for approximating dataset diameter efficiently.
problem Finding the diameter of large multidimensional datasets.
method Greedy algorithms based on minimum/maximum l2 norms, hill climbing, Tabu search, and Beam search.
result Efficiency proven through experiments on machine learning datasets.
Extends multidimensional scaling to analyze three-way asymmetric proximities.
problem Analyzing asymmetric and three-way proximities in a Euclidean space.
method Unified h-plot methodology for three-way asymmetric proximities, including symmetric and conditional frameworks.
result Identification of archetypal profiles and clustering structures.
Extends Bayesian theory to handle complex interdependencies in multidimensional event spaces.
problem Complex interdependencies between events and hypotheses sets in real-world systems.
method Developed a mathematical formalism for modeling complex relationships through rigorous derivation and validated using analytical proofs, simulations, and case studies.
result MDSE theory improves prediction accuracy by 15-20% compared to standard Bayesian methods in high interdimensionality datasets.
A new tensor regression model preserves multidimensional data structure.
problem Complex multidimensional data loses intrinsic connections and parameter explosion.
method Developed a parsimonious tensor regression model using Tucker structure and shrinkage penalization.
result The model outperforms benchmark models in forecasting.
A novel algorithm for the decomposition of non-stationary multidimensional and multivariate signalsmath.NA
New algorithm for decomposing multidimensional, non-stationary signals.
problem Handling complex, non-stationary signals in multidimensional and multivariate data.
method Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) algorithm.
result Extracts Intrinsic Mode Functions (IMFs) from complex signals varying in space and time.
New method visualizes brain activity changes over time.
problem Understanding representational dynamics in neural responses.
method Procrustes-aligned Multidimensional Scaling (pMDS) on RDM movies.
result Multidimensional scaling alignment captures representational dynamics.
This paper deals with multidimensional dynamic risk measures induced by conditional -expectations. A notion of multidimensional -expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem and…
This paper improves conditional multidimensional scaling for incomplete data.
problem Handling missing data in known features for multidimensional scaling.
method Proposes a method to learn low-dimensional configurations with missing known feature values.
result Can learn low-dimensional configurations and impute missing values.
Modified multidimensional scaling improves clustering in noisy high-dimensional data.
problem Improving clustering accuracy in noisy high-dimensional data.
method Unified framework of multidimensional scaling, modified with nonlinear transformation.
result Modified multidimensional scaling achieves exact recovery of cluster labels with high probability.
We develop a new statistical test for comparing variables with varying scales.
problem Comparing variables with different scales in multidimensional spaces.
method Order based on expectations of random variables, generalized stochastic dominance (GSD) order, regularized statistical test, linear optimization, imprecise probability models.
result Validated through multidimensional data from various fields.
The paper explores multidimensional critic output in GANs, improving convergence and diversity.
problem Underexplored in GANs literature, multidimensional critic output.
method Generalized Wasserstein GAN framework, SRVT block, maximal p-centrality discrepancy.
result High-dimensional critic output improves GAN performance in convergence and diversity.
Improved algorithm for multidimensional scaling reduces stress.
problem Stress in multidimensional scaling.
method Proposed modifications of the smacof algorithm.
result Convergent majorization algorithm for Kruskal's stress formula two.
A method to visualize multidimensional local subspaces using implicit differentiation.
problem Understanding the effect of multidimensional projection on local subspaces.
method Implicit function differentiation to analyze local subspaces shaped by multidimensional ellipses.
result Visualization of local subspaces provides insights into the global structure of data.
In this note, we consider European options of type depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger \cite{Breeden} on the relation between derivatives of the call price and the risk-neutral density of the underlying asse…
A new method for aligning datasets without known correspondences.
problem Aligning datasets from different domains without labeled correspondences.
method Integrates MDS and Wasserstein Procrustes for joint optimization of embeddings and correspondences.
result Maps datasets to a common low-dimensional space without labeled correspondences.
Paper analyzes classical multidimensional scaling for cluster recovery.
problem Cluster recovery from noisy data.
method Classical multidimensional scaling followed by distance-based clustering.
result Scaling conditions for high probability cluster recovery.
Paper proposes conditional multidimensional scaling for better data reduction.
problem Mapping high-dimensional data to low-dimensional space with known features.
method Developed a broad class of methods called conditional multidimensional scaling (MDS) with an optimization algorithm.
result Conditional MDS improves estimation quality and simplifies visualization and knowledge discovery.
Global minima found for multidimensional scaling with penalties.
problem Finding global minima in multidimensional scaling.
method Combining stress loss function with a quadratic penalty term to find minimizers.
result Trajectory of minimizers leads to global minima.
Sliced Inverse Regression reduces parameter space for estimating complex financial models.
problem High-dimensional parameter space in stochastic differential equations.
method Sliced Inverse Regression for dimension reduction.
result Reduced computational costs in estimating parameters.
Study uses multidimensional SE-NBD process to analyze default portfolios and identify shock amplification.
problem Analyzing interactions and shock propagation in default portfolios with multiple sectors.
method Applied multidimensional self-exciting negative binomial distribution (SE-NBD) process to 13 sectors.
result Identified upstream and downstream sectors, showing shock amplification in default portfolios.
Adaptive tensor modeling preserves continuity in multidimensional data.
problem Discretization of continuous multidimensional data loses important information.
method Functional Tucker decomposition (FTD) with RKHS modeling.
result FTD enables adaptive and expressive tensor modeling.
Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequen…
Efficiently recovers piecewise linear functions from noisy samples.
problem Recovering a piecewise linear function from noisy samples with unknown segmentation.
method Iterative merging approach for multidimensional segmented regression.
result First sample and computationally efficient algorithm in any fixed dimension.
BMTI method estimates densities without bins, outperforming traditional estimators.
problem Nonparametric, robust, and data-efficient density estimation in high-dimensional spaces.
method BMTI integrates log-density differences between neighboring points, weighted by uncertainties, using a maximum-likelihood formulation.
result BMTI reconstructs smooth profiles in high-dimensional spaces, outperforming traditional estimators.
We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in terms of a flat connection in the jet bundle. We extend it to supercase using a part…
We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly define a change surface in combination with expressive spectral mixture kernels to …
We study one extremal problem on the product of power of generalized inner radii of non-overlapping domains in .
A Multiclass ROC Curvestat.ME
Novel method for multiclass ROC curves using multidimensional Gini index.
problem Multiclass performance evaluation, especially for imbalanced datasets.
method Extends ROC curve methodology to multiclass settings using multidimensional Gini index.
result Validated through case studies in health care and finance.
Shortfall Risk Approximations for American Options in the multidimensional Black--Scholes Modelq-fin.CP
We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we conside…
Bayesian hyperbolic MDS improves tree-like data representation.
problem Representing tree-like structures in high-dimensional data.
method Bayesian approach to hyperbolic MDS for low-dimensional manifold.
result Bayesian hyperbolic MDS reduces computational complexity and improves accuracy.
A novel online framework for analyzing multidimensional functional data.
problem Analysis of multidimensional functional data streams poses significant challenges.
method Online functional principal component analysis using tensor product splines on a Stiefel manifold with Riemannian stochastic gradient descent.
result Efficient and scalable modeling of multidimensional functional data.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
Paper presents adaptive minimax risk classifiers for multidimensional concept drift.
problem Multidimensional concept drift in supervised classification.
method Adaptive minimax risk classifiers (AMRCs) tracking multivariate and high-order distribution changes.
result AMRCs provide computable tight performance guarantees and improve classification.
Whitney type examples of maps for a maximal possible real , and multidimensional space-filling curves with special properties are constructed.
Uniform proof for ultradifferentiability in various classes and dimensions.
problem Generalizing ultradifferentiability conditions to multidimensional cases and infinite dimensional spaces.
method Uniform proof approach that works in all cases and dimensions, including infinite dimensional Banach spaces and convenient vector spaces.
result Characterization of ultradifferentiability for general analytic germs and functions.
We analyze small price impacts in a multidimensional utility maximization problem using PDEs.
problem Small nonlinear price impacts in a multidimensional utility maximization problem.
method Asymptotic expansion using nonlinear PDEs related to ergodic control and linear parabolic PDEs.
result Leading order correction to the value function is characterized by a nonlinear second order PDE.
sWk-means clusters multidimensional financial time series into distinct market regimes.
problem Classifying distinct market regimes in multidimensional financial time series.
method Approximated multidimensional Wasserstein distance as sliced Wasserstein distance for clustering.
result sWk-means successfully identifies distinct market regimes in real financial data.
New boundary treatment improves accuracy for complex PDEs.
problem Order reduction in high-order IMEX schemes for multidimensional PDEs.
method Novel boundary treatment algorithms for Cartesian meshes, treating implicit-explicit stages similarly to interior points.
result Recovery of designed order of convergence by numerical verification.
Improved image ranking model using ordinal distance metric learning and multidimensional scaling.
problem Ranking images based on known ranked images.
method Proposes an improved linear ordinal distance metric learning approach using multidimensional scaling.
result Demonstrates improved ranking performance and speed over the linear distance metric learning model.
Quaternion neural networks improve speech recognition efficiency.
problem Improving speech recognition systems with fewer parameters.
method Investigating quaternion-valued convolutional and recurrent neural networks.
result Quaternion neural networks outperform real-valued models with fewer parameters.
Simulation of Multidimensional Diffusions with Sticky Boundaries via Markov Chain Approximationmath.PR
New method simulates sticky boundaries in multidimensional diffusions.
problem Simulating sticky boundaries in multidimensional diffusions.
method Approximate sticky diffusion by a Markov chain, using either finite difference or matching local moments.
result Validates both construction methods for first-order simulation schemes.
Extends Carathéodory's theorem to multidimensional domains with constant curvature.
problem Characterizing biholomorphic domains with constant holomorphic curvature.
method Using Bergman representative coordinates and Calabi's diastasis.
result Provides sufficient conditions for the boundary of a biholomorphic ball to be a topological sphere.
New method learns psychological similarity spaces for unseen stimuli.
problem Generalizing psychological similarity spaces to new stimuli.
method Learn mapping from raw stimuli to similarity space using ANNs.
result ANNs can successfully map raw stimuli into similarity spaces.