A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…
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48 results for “constructive methods”
Modified curve shortening flow constructs -Angenent curve.
problem Constructing -Angenent curve.
method Modified curve shortening flow
result Constructs -Angenent curve.
Unified framework for constructing nonconvex sparse recovery methods.
problem Constructing valid nonconvex regularization functions remains open.
method Unified framework based on probability density function, using Weibull distribution.
result New nonconvex sparse recovery method based on Weibull distribution.
We constructed physically stable sp2 negatively curved cubic carbon structures which reticulate a Schwarz P-like surface. The method for constructing such crystal structures is based on the notion of the standard realization of abstract crystal lattices. In this paper, we expound on the mathematical method to construct…
Survey on constructing manifolds over simple polytopes using Lickorish's method.
problem Classifying manifolds over simple convex polytopes with torus action.
method Lickorish type construction over simple polytopes with torus action.
result Many classical classification results can be interpreted using this construction.
Risk diversification is one of the dominant concerns for portfolio managers. Various portfolio constructions have been proposed to minimize the risk of the portfolio under some constrains including expected returns. We propose a portfolio construction method that incorporates the complex valued principal component anal…
Method constructs Bryant surfaces in hyperbolic space.
problem Constructing Bryant type surfaces in hyperbolic space.
method Bianchi-Calo type construction method
result Constructs Bryant type surfaces in hyperbolic space.
In this article we introduce a method to construct -instantons on -manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing ASD instantons over ALE spaces to flat bundles on -orbifolds of the form . We use this construction to produce non-trivia…
Method constructs orthogonal curvilinear coordinates in constant curvature spaces.
problem Creating orthogonal coordinates in spaces of constant curvature.
method Modification of Krichever's method for Euclidean space, applied to constant curvature spaces.
result Examples of orthogonal coordinate systems on the sphere and hyperbolic plane constructed.
Paper constructs multivalued harmonic functions on R^3 using twistor methods.
problem Constructing multivalued harmonic functions on R^3.
method Twistor methods to construct multivalued harmonic functions.
result Found a family of multivalued harmonic functions with branching sets as ellipses and quadratic growth at infinity.
Quantum character varietiesmath.QA
Quantum character varieties unify four construction methods.
problem No specific problem stated; unification of approaches.
method Four different approaches to construction.
result Unified understanding of quantum character varieties.
New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.
problem Constructing Birkhoff sections for pseudo-Anosov flows with specific properties.
method Uses connection between pseudo-Anosov flows and veering triangulations to explicitly construct sections with controlled complexity.
result Shows that any transitive pseudo-Anosov flow has a Birkhoff section with two boundary components.
Method uses network biology to construct gene expression models for cancer.
problem Building models for cancer phenotypes using gene expression data.
method Unsupervised construction of computational graphs based on protein-protein networks.
result The method outperforms other models in cancer phenotype analysis.
Unified Long-Moody and Katz methods for constructing local systems.
problem Constructing representations of braid groups and local systems.
method Katz-Long-Moody functor unifying Long-Moody and Katz methods.
result Extends Katz algorithm to various topological spaces.
Minimal annuli constructed in PSL2 via variational method.
problem Constructing minimal annuli in a non-symmetric 3-manifold.
method Variational method, foliations by minimal surfaces, limit of compact minimal annuli.
result Existence of complete, embedded minimal annuli asymptotic to vertical planes.
Method constructs special Lagrangian submanifolds using symmetries.
problem Constructing special Lagrangian submanifolds in Calabi-Yau manifolds.
method Using generalized perpendicular symmetries and moment maps of Lie group actions.
result Constructs non-flat Calabi-Yau manifolds with Stenzel metrics.
New methods for equity fund selection and portfolio construction using mutual fund top holdings.
problem Classic equity fund selection and portfolio construction problems.
method Propose an easy-to-implement framework to produce a long-short portfolio from mutual fund top holdings.
result Generate impressive results and show statistical evidence.
We construct constant mean curvature surfaces in euclidean space with genus zero and n ends asymptotic to Delaunay surfaces using the DPW method.
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.
The Ward equation, also called the modified 2+1 chiral model, is obtained by a dimension reduction and a gauge fixing from the self-dual Yang-Mills field equation on . It has a Lax pair and is an integrable system. Ward constructed solitons whose extended solutions have distinct simple poles. He also used a li…
We investigate a method of construction of Calabi--Yau manifolds, that is, by smoothing normal crossing varieties. We develop some theories for calculating the Picard groups of the Calabi--Yau manifolds obtained in this method. Some applications are included, such as construction of new examples of Calabi--Yau 3-folds …
Constructs surfaces with conical singularities using variational methods.
problem Creating Hamiltonian Stationary Surfaces with specific singularities.
method Variational methods and convergence process similar to Ginzburg-Landau analysis.
result Obtained surfaces with prescribed conical singularities related to optimal Wente constants.
Analog ensemble data assimilation and a method for constructing analogs with variational autoencodersphysics.comp-ph
Analog methods improve forecast accuracy in complex models.
problem Improving forecast accuracy in complex models like Lorenz-96.
method Constructing analogs using variational autoencoders for ensemble data assimilation.
result Constructed analogs perform as well as a full ensemble square root filter.
We present methods to construct interesting surfaces of general type via -Gorenstein smoothing of a singular surface obtained from an elliptic surface. By applying our methods to special Enriques surfaces, we construct new examples of a minimal surface of general type with , $π_1=\mathbb{Z}/2\mathbb{…
Improved Markowitz method handles uncertainty in return forecasts.
problem Uncertainty in return statistics forecasts.
method Convex optimization with practical constraints.
result Handles uncertainty gracefully and efficiently.
We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC metho d itself. It turns out that autocorrelations between the data generated …
Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to a concrete construction of some natural equivariant operators that a…
New hyperbolic 3-manifolds with multiple cusps are found that sound the same but look different.
problem Finding hyperbolic 3-manifolds with multiple cusps that are isospectral but not isometric.
method Used Sunada's method and the Strong Approximation Theorem of Nori and Weisfeiler.
result Constructed hyperbolic 3-manifolds with multiple cusps that are isospectral but not isometric.
In this paper we investigate Uludag's method for constructing new curves whose fundamental groups are central extensions of the fundamental group of the original curve by finite cyclic groups. In the first part, we give some generalizations to his method in order to get new families of curves with controlled fundamenta…
Paper proves new method for constructing initial data in general relativity.
problem Proving the existence of solutions for initial data in general relativity.
method Using the Banach fixed point theorem to prove existence, with guarantees of uniqueness and explicit construction.
result Guaranteed uniqueness and explicit construction of solutions to the conformal method equations.
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and constructing a uniform confidence subgraph. Due to the presence of unknown marginal trans…
Method to create rational Seifert surfaces for knots in Lens space.
problem Creating rational Seifert surfaces for knots in Lens space.
method Assuming a regular projection, construct rational Seifert surface on twist toroidal diagram.
result A method to construct rational Seifert surfaces for knots in Lens space.
New method constructs surfaces with constant mean curvature.
problem Constructing surfaces with specific curvature properties.
method Combining DPW method and opening nodes.
result Embedded surfaces with positive constant mean curvature.
Motivated by an abstract notion of low-level edge detector filters, we propose a simple method of unsupervised feature construction based on pairwise statistics of features. In the first step, we construct neighborhoods of features by regrouping features that correlate. Then we use these subsets as filters to produce n…
New method constructs graphs from data efficiently, suitable for large datasets.
problem Memory and runtime limitations of traditional TMFG for large datasets.
method Uses k-Nearest Neighbors Graphs and memory management for scalable graph construction.
result Provides a parsimonious way to construct graphs for learning tasks.
A simple method constructs Lefschetz fibrations on compact Stein surfaces.
problem Constructing Lefschetz fibrations on compact Stein surfaces.
method From a 2-handlebody decomposition, yields PALF's with small genus.
result Minimal genus of regular fibers bounded by (N - 1)/2.
We describe a glueing construction for the Yang-Mills equations in dimension . Our method is based on a construction of approximate solutions, and a detailed analysis of the linearized operator near an approximate solution.
New method constructs Floer homologies without hard analysis.
problem Constructing homological invariants in infinite dimensions.
method Soft, finite-dimensional tools to avoid hard analysis.
result Demonstrates construction of Floer homologies without PDE.
New methods detect and create Brunnian links efficiently.
problem Detecting and constructing Brunnian links when each component is known to be an unknot.
method Two practical methods based on observation and handwork.
result Established a general way to construct new Brunnian links in bulk.
By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CP^n and C^n.
Joint learning framework for clustering and graph construction.
problem Graph construction not fitting clustering requirements.
method Joint learning framework to learn graph and clustering simultaneously.
result Improved clustering accuracy on 10 datasets.
Paper develops a method to construct confidence regions for model parameters using batch means method.
problem Constructing confidence regions for model parameters in stochastic gradient descent.
method Batch means method to cancel out covariance matrix, using Polyak-Ruppert averaging.
result Established process-level functional central limit theorem for stochastic gradient descent estimators.
NNK algorithm improves neighborhood and graph construction for machine learning.
problem Ad hoc selection of k and ε parameters in kNN and ε-neighborhood methods.
method NNK algorithm for better sparse signal approximation.
result NNK leads to superior performance in local neighborhood and graph-based machine learning tasks.
Approximate vanishing ideal is a concept from computer algebra that studies the algebraic varieties behind perturbed data points. To capture the nonlinear structure of perturbed points, the introduction of approximation to exact vanishing ideals plays a critical role. However, such an approximation also gives rise to a…
This paper uses rank correlation methods to construct MSTs from financial returns, finding them more stable and robust.
problem Stability and robustness of MSTs constructed from financial correlation matrices.
method Pearson, Spearman, and Kendall's rank correlation methods applied to daily financial returns.
result Rank MSTs are more stable and robust than MSTs constructed using Pearson correlation.
In this paper, we construct families of nonisometric hyperbolic orbifolds that contain the same isometry classes of nonflat totally geodesic subspaces. The main tool is a variant of the well-known Sunada method for constructing length-isospectral Riemannian manifolds that handles totally geodesic submanifolds of multip…
Survey of G2-holonomy manifold constructions.
problem Finding compact Riemannian 7-manifolds with G2 holonomy.
method Two methods: resolving orbifolds and gluing asymptotically cylindrical pieces.
result Examples of compact G2-holonomy manifolds constructed.
This study evaluates methods for constructing prediction intervals with neural networks.
problem Lack of confidence measures in neural network predictions limits their applicability.
method Two-step experiment using bootstrapping and conformal inference methods.
result Cross-conformal method provides best performance with reasonable computational burden.