# Keyword index H

**h-matrices**- 79/2001 - Data-sparse approximate inverse in elliptic problems: Green's function approach

**H-measures and their characterization**- 111/2007 - Relaxation of three solenoidal wells and characterization of three-phase H-measures

**H-principle**- 96/2007 - Universal spaces for manifolds equipped with a closed integral k-form

**haar basis****Haar Wavelet Method**- 80/2009 - An Operational Haar Wavelet Method for Solving Fractional Volterra Integral Equations.

**hadamard matrices**- 50/2001 - Embeddings of lattices in
**L**^{2}([0,1], Z)

- 50/2001 - Embeddings of lattices in
**Hadamard product****Hadamard space****Hajnal diameter**- 48/2007 - Synchronization of discrete-time dynamical networks with time-varying couplings

**half-Laplacian**- 41/2011 - Saddle-shaped solutions of bistable elliptic equations involving the half-Laplacian

**Hall Coherent States**- 53/2014 - Costratification in terms of coherent states

**hamilton-jacobi equations****Hamiltonian diffeomorphisms**- 16/2009 - The Seidel morphism of cartesian products

**Hamiltonian homeomorphisms**- 13/2016 - Some properties of Hamiltonian homeomorphisms on aspherical closed surfaces

**hamiltonian theory, conservation laws,**- 25/2005 (
*Lecture note*) - Lectures on Quantum Mechanics (nonlinear PDEs point of view)

- 25/2005 (
**Hanarck's inequality**- 16/2008 - Harnack's inequality for some nonlocal equations and application

**hardy-sobolev ineqality**- 28/2003 - Bounds for the Best Constant in an Improved Hardy-Sobolev Inequality

**harmonic function****harmonic map**- 71/2017 - Asymptotic analysis and qualitative behavior at the free boundary for Sacks-Uhlenbeck α-harmonic maps
- 31/2017 - Bubbling analysis for approximate Lorentzian harmonic maps from Riemann surfaces
- 70/2016 - Global existence of the harmonic map heat flow into Lorentzian manifolds
- 38/2016 - Bubbling analysis near the Dirichlet boundary for approximate harmonic maps from surfaces
- 26/2016 - The qualitative behavior at the free boundary for approximate harmonic maps from surfaces
- 90/2014 - Harmonic maps and singularities of period mappings
- 23/2014 - Liouville theorems for f-harmonic maps into Hadamard spaces
- 39/2001 - Harmonic Hopf constructions between spheres II
- 24/2000 - S
^{1}-invariant harmonic maps from S^{3}to S^{2}

**harmonic maps****harmonic mean curvature flow**- 85/2003 - A representation formula for the inverse harmonic mean curvature flow

**harnack inequality**- 96/2003 - Application of The Method of Moving Planes to Conformally Invariant Equations

**hartree-fock****Hartree-Fock calculus**- 14/2016 - Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation

**Hartree-Fock energy**- 29/2009 - Canonical tensor products as a generalization of Gaussian-type orbitals

**Hartree-Fock equation**- 12/2017 - Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach
- 32/2015 - A reduced basis approach for calculation of the Bethe-Salpeter excitation energies using low-rank tensor factorizations
- 62/2014 - Tensor Approach to Linearized Hartree-Fock Equation for Lattice-type and Periodic Systems
- 116/2013 - Grid-based lattice summation of electrostatic potentials by low-rank tensor approximation
- 90/2013 - Black-Box Hartree-Fock Solver by the Tensor Numerical Methods
- 26/2013 - Møller-Plesset (MP2) Energy Correction Using Tensor Factorizations of the Grid-based Two-electron Integrals
- 29/2012 - Tensor-structured factorized calculation of two-electron integrals in a general basis
- 4/2012 - Fast and Accurate 3D Tensor Calculation of the Fock Operator in a General Basis
- 37/2011 - QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations
- 44/2009 - Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format
- 65/2007 - Tensor decomposition in electronic structure calculations on 3D Cartesian grids

**Hartree-Fock method**- 66/2008 - Density fitting scheme for pseudo-potentials
- 4/2008 - On Tensor Approximation of Green Iterations for Kohn-Sham Equations
- 3/2008 - Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling
- 60/2005 - Best N-term approximation in electronic structure calculations.I. One-electron reduced density matrix

**Hartree-Fock operator**- 25/2009 - Computation of the Hartree-Fock Exchange by the Tensor-structured Methods

**Hartree-Fock solver****hausdorff dimension**- 73/2001 - Pathologies in Aleksandrov spaces of curvature bounded above

**Hausdorff space**- 6/2008 - Some remarks on the strong maximum principle arising in nonlocal operators

**HDD method**- 5/2006 (
*Technical report*) - Documentation for the HDD method

- 5/2006 (
**heat asymptotics**- 38/2002 - Heat asymptotics with spectral boundary conditions II

**heat content asymptotics**- 63/2005 - Heat content asymptotics for Riemannian manifolds with Zaremba boundary conditions
- 81/2002 - Heat content asymptotics for spectral boundary conditions
- 60/2002 - Heat content asymptotics with transmittal and transmission boundary conditions
- 48/2002 - Heat content asymptotics for oblique boundary conditions

**heat engine**- 40/2016 - A Resource Theory for Work and Heat

**heat equation****heat equation asymptotics**- 57/2000 - Heat trace asymptotics of a time dependent process

**heat flow**- 70/2016 - Global existence of the harmonic map heat flow into Lorentzian manifolds
- 26/2016 - The qualitative behavior at the free boundary for approximate harmonic maps from surfaces
- 30/2015 - Dirac-geodesics and their heat flows
- 55/2014 - The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces
- 26/2003 - Maps With Prescribed Tension Fields

**heat kernel****heat kernel estimate**- 60/2016 - Heat kernel upper bounds for interacting particle systems

**heat trace asymptotics**- 104/2002 - Supertrace divergence terms for the Witten Laplacian
- 100/2002 - Divergence terms in the supertrace heat asymptotics for the de Rham complex on a manifold with boundary
- 86/2002 - Duality symmetry of the p-form effective action and super trace of the twisted de Rham complex
- 74/2002 - Chiral Bag Boundary Conditions on the Ball
- 70/2002 - Heat trace asymptotics defined by transfer boundary conditions

**heat transport**- 6/2011 - Rayleigh--B\'enard convection: Improved bounds on the Nusselt number

**heat ﬂow**- 38/2016 - Bubbling analysis near the Dirichlet boundary for approximate harmonic maps from surfaces

**heavy tails**- 62/2003 - Approach to self-similarity in Smoluchowski's coagulation equations

**Heintze-Karcher inequality**- 54/2014 - A generalization of Reilly's formula and its applications to a new Heintze-Karcher type inequality

**hele-shaw flow****Helffer-Sjöstrand representation**- 2/2008 - Strict convexity of the free energy for non-convex gradient models at moderate β

**helmholtz equation****Helmholtz machines****Hermitian manifold**- 135/2006 - Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold

**Heron's algorithm**- 3/2009 - On the Efficient Computation of High-Dimensional Integrals and the Approximation by Exponential Sums

**Hessian discriminant**- 88/2019 - The Hessian discriminant

**Heston stochastic volatility process****heterogeneous agents**- 75/2016 - The Coconut Model with Heterogeneous Strategies and Learning

**hidden Markov models**- 8/2008 - On the Generative Nature of Prediction

**hierarchical bases****hierarchical block partioning**- 22/1999 - A sparse -Matrix Arithmetic, Part II: Application to Multi-Dimensional Problems

**hierarchical Cholesky**- 95/2006 - Domain decomposition based -matrix preconditioners for the skin problem

**hierarchical matrices**- 10/2008 (
*Technical report*) - HLIBpro C Language Interface - 9/2008 (
*Technical report*) - HLIBpro User Manual - 27/2005 (
*Lecture note*) - An Introduction to Structured Tensor-Product Representation of Discrete Nonlocal Operators. - 21/2003 (
*Lecture note*) - Hierarchical Matrices - 100/2019 - Semi-Automatic Task Graph Construction for H-Matrix Arithmetic
- 13/2014 - Hierarchical matrices and the High-Frequency Fast Multipole Method for the Helmholtz Equation with Decay
- 5/2014 - ℋ-LU Factorization on Many-Core Systems
- 59/2012 - Partial evaluation of the discrete solution of elliptic boundary value problems
- 33/2011 - Rapid error reduction for block Gauss-Seidel based on p-hierarchical bases
- 81/2008 - Application of hierarchical matrices for computing the Karhunen-Lo\`eve expansion
- 65/2008 - Performance of H-LU Preconditioning for Sparse Matrices
- 11/2007 - On the Robustness of Elliptic Resolvents Computed by means of the Technique of Hierarchical Matrices
- 61/2006 - Hierarchical Matrix Techniques for a Domain Decomposition Algorithm
- 38/2006 - Tensor-Product Approximation to Multi-Dimensional Integral Operators and Green's Functions
- 115/2005 - Parallel Black Box Domain Decomposition Based -LU Preconditioning
- 114/2005 - Adaptive variable-rank approximation of general matrices
- 112/2005 - Approximate Iterations for Structured Matrices
- 84/2005 - Nonlinear multigrid for the solution of large scale Riccati equations in low-rank and -matrix format
- 78/2005 - On the numerical solution of convection-dominated problems using hierarchical matrices
- 44/2005 - Data-sparse approximation of non-local operators by
^{2}-matrices - 30/2005 - Low-Rank Kronecker Product Approximation to Multi-Dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators
- 29/2005 - Low-Rank Kronecker-Product Approximation to Multi-Dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-Variate Functions
- 17/2005 - - and
^{2}-matrices for low and high frequency Helmholtz equation - 8/2005 - Why approximate LU decompositions of finite element discretizations of elliptic operators can be computed with almost linear complexity
- 4/2005 - Structured Data-Sparse Approximation to High Order Tensors Arising from the Deterministic Boltzmann Equation
- 79/2004 - Adaptive Galerkin Boundary Element Methods with Panel Clustering
- 68/2004 - Hybrid Cross Approximation of Integral Operators
- 62/2004 - -matrix preconditioners in convection-dominated problems
- 47/2004 -
^{2}-matrix arithmetics in linear complexity - 29/2004 - Parallel -Matrix Arithmetics on Shared Memory Systems
- 28/2004 - Hierarchical LU decomposition based preconditioners for BEM
- 19/2004 - Adaptive Geometrically Balanced Clustering of -Matrices
- 18/2004 - Approximation of integral operators by
^{2}-matrices with adaptive bases - 17/2004 - Adaptive Recompression of -Matrices for BEM
- 16/2004 - Hierarchical Kronecker tensor-product approximation to a class of nonlocal operators in high dimensions
- 10/2004 - Fast Parallel Solution of Boundary Integral Equations and Related Problems
- 90/2003 - Efficient Computation of Lead Field Bases and Influence Matrix for the FEM-based EEG and MEG Inverse Problem. Part I: Complexity Considerations
- 83/2003 - Hierarchical Tensor-Product Approximation to the Inverse and Related Operators for High Dimensional Elliptic Problems
- 71/2003 - Panel Clustering Techniques and Hierarchical Matrices for BEM and FEM
- 35/2003 - Hierarchical Kronecker tensor-product approximations
- 33/2003 - Fast Evaluation of Boundary Integral Operators arising from an Eddy Current Problem
- 7/2003 -
^{2}-matrices — Multilevel methods for the approximation of integral operators - 5/2003 - Approximation of boundary element operators by adaptive
^{2}-matrices - 2/2003 - Hierarchical Matrices based on a Weak Admissibility Criterion
- 103/2002 - Construction and Arithmetics of -Matrices
- 82/2002 - Approximation of Integral Operators by Variable-Order Interpolation
- 62/2002 - Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices
- 23/2002 - Direct Domain Decomposition using the Hierarchical Matrix Technique
- 21/2002 - Existence of -Matrix Approximants to the Inverse FE-Matrix of Elliptic Operators with L
^{∞}-Coefficients - 18/2002 - Introduction to Hierarchical Matrices with Applications
- 106/2001 - Adaptive refinement and clustering of -matrices
- 105/2001 - An introduction to hierarchical matrices
- 86/2001 - Data-sparse approximation by adaptive -Matrices
- 15/2000 - Towards -matrix approximation of linear complexity
- 66/1999 - A sparse -matrix arithmetic: general complexity estimates
- 54/1999 - -matrix approximation on graded meshes
- 50/1999 - On H
^{2}-Matrices - 22/1999 - A sparse -Matrix Arithmetic, Part II: Application to Multi-Dimensional Problems

- 10/2008 (
**Hierarchical matrix****hierarchical model****hierarchical models****Hierarchical Quadrature**- 70/2012 - Tensor Structured Evaluation of Singular Volume Integrals

**hierarchical representation**- 4/2018 - Numerical Tensor Techniques for Multidimensional Convolution Products

**hierarchical solution**- 61/2014 - A hierarchical extension scheme for solutions of the Wright–Fisher model

**Hierarchical Tensor Format****hierarchical tensor representation****Hierarchical Tucker**- 57/2010 - Black Box Approximation of Tensors in Hierarchical Tucker Format

**hierarchy of exponential families**- 52/2000 - An information geometric approach to a theory of pragmatic structuring

**higd-dimensional dynamics**- 95/2005 - Persistent chaos in high dimensions

**higgs bundles**- 17/2003 - Quantization of a Moduli Space of Parabolic Higgs Bundles

**Higgs Mass**- 21/2006 - Dirac Type Gauge Theories and the Mass of the Higgs Boson

**high dimensional tensors**- 27/2005 (
*Lecture note*) - An Introduction to Structured Tensor-Product Representation of Discrete Nonlocal Operators.

- 27/2005 (
**high dimensions****high frequency solutions**- 1/2005 - Oscillatory Solutions of Soliton Equations; Phase Transitions and Variational Problems

**high space dimensions**- 83/2003 - Hierarchical Tensor-Product Approximation to the Inverse and Related Operators for High Dimensional Elliptic Problems

**high spatial dimension****high--dimensional problems****high-dimensional dynamical systems****high-dimensional dynamics**- 92/2005 - Routes to chaos in high-dimensional dynamical systems: a qualitative numerical study

**high-dimensional PDEs**- 108/2014 - Tensor Numerical Methods for Multidimensional PDEs: Theoretical Analysis and Initial Applications

**high-dimensional problems**- 10/2013 - Alternating minimal energy methods for linear systems in higher dimensions. Part I: SPD systems
- 43/2011 - Quantized-TT-Cayley transform to compute dynamics and spectrum of high-dimensional Hamiltonians
- 19/2011 - Solution of linear systems and matrix inversion in the TT-format
- 18/2011 - Superfast Fourier transform using QTT approximation
- 69/2010 - DMRG+QTT approach to computation of the ground state for the molecular Schr\"odinger operator
- 21/2010 - Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances
- 55/2009 - O(dlog N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling
- 48/2003 - Existence and Computation of a Low Kronecker-Rank Approximant to the Solution of a Tensor System with Tensor Right-Hand Side

**High-frequency**- 147/2006 - Analysis of multiple scattering iterations for high-frequency scattering problems. \\ II: The three-dimensional scalar case

**high-order tensors**- 9/2010 - Tensor-Structured Galerkin Approximation of parametric and stochastic Elliptic PDEs

**higher dimensions****higher integrability**- 70/2004 - Convex integration and the L
^{p}theory of elliptic equations.

- 70/2004 - Convex integration and the L
**higher order jacobi operator**- 96/2002 - Nilpotent Szabo Osserman and Ivanov-Petrova Pseudo-Riemannian Manifolds

**higher order nonlinear degenerate parabolic equations****Higher-order Riccati equations**- 39/2009 - Higher-order Abel equations: Lagrangian formalism, Darboux polynomials and constants of the motion

**higher-order correlations**- 58/2014 - Maximizing the divergence from a hierarchical model of quantum states

**higher-order finite elements**- 33/2011 - Rapid error reduction for block Gauss-Seidel based on p-hierarchical bases

**higher-order parabolic equations**- 1/2014 - Well-posedness for the Navier-Slip Thin-Film Equation in the Case of Complete Wetting

**higher-order singular value decomposition**- 51/2016 - Perturbation of higher-order singular values

**higher-order singular value decomposition (HOSVD)**- 17/2012 - L
^{∞}estimation of tensor truncations

- 17/2012 - L
**highest eigenvalue**- 1/2003 - Convexity of the Joint Numerical Range: Topological and Differential Geometric Viewpoints

**highientropy**- 95/2005 - Persistent chaos in high dimensions

**Hilbert lattices**- 50/2016 - Quantum logic is undecidable

**hilbert space**- 50/2001 - Embeddings of lattices in
**L**^{2}([0,1], Z)

- 50/2001 - Embeddings of lattices in
**Hilbert tensor**- 25/2018 - Tucker tensor analysis of Matérn functions in spatial statistics

**Hilbert-Burch matrices**- 46/2020 - Canonical Hilbert-Burch matrices for power series

**History of chemistry****HIV**- 10/2007 - The probability of HIV infection in a new host and its reduction with microbicides

**HNN-extensions**- 62/2012 - Linear and Projective Boundaries in HNN-Extensions and Distortion Phenomena

**Hodge theory****Hodgkin-Huxley**- 13/2012 - Analysis of inverse stochastic resonance and long-term firing in Hodgkin-Huxley neurons

**Hodgkin-Huxley model****Hoelder shadowing**- 106/2013 - Hölder Shadowing on Finite Intervals

**Hofer geometry**- 50/2010 - A comparison of symplectic homogenization and Calabi quasi-states

**hölder continuity****Holder regularity**- 50/2012 - Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations

**Holder shadowing**- 107/2014 - Shadowing in linear skew product

**Holevo quantity**- 20/2013 - Universal upper bound for the Holevo information induced by a quantum operation

**holonomy**- 57/2005 - Generalized plane wave manifolds

**homogeneous spaces****homogenisation**- 59/2012 - Partial evaluation of the discrete solution of elliptic boundary value problems

**homogenization**- 5/2020 - Quantitative homogenization for the case of an interface between two heterogeneous media
- 102/2018 - Some quantitative homogenization results in a simple case of interface
- 11/2015 - Correlation structure of the corrector in stochastic homogenization
- 61/2013 - On the general homogenization and Γ-closure for the equations of von Kármán plate from 3D nonlinear elasticity
- 40/2013 - Homogenization of the nonlinear bending theory for plates
- 34/2013 - A note on the derivation of homogenized bending plate model
- 33/2013 - Derivation of a homogenized von Kármán shell theory
- 61/2012 - Derivation of a Homogenized Von-Kármán Plate Theory from 3d Nonlinear Elasticity
- 74/2011 - Rigorous derivation of a homogenized bending-torsion theory for inextensible rods from 3d elasticity
- 73/2010 - Commutability of homogenization and linearization at identity in finite elasticity and applications
- 34/2008 - Diffractive geometric optics for Bloch wave packets
- 29/2008 - Damage as Gamma-limit of microfractures in anti-plane linearized elasticity
- 27/2008 - Damage as Gamma-limit of microfractures in linearized elasticity under the non-interpenetration constraint
- 103/2007 - Diffractive behavior of the wave equation in periodic media: weak convergence analysis
- 88/2005 - Traveling wave speeds in rapidly oscillating media
- 38/2005 - Gamma-convergence of the Allen-Cahn energy with an oscillating forcing term
- 49/2004 - Examples of nonlinear homogenization in plane strain involving degenerate energies

**homogenization error****homology**- 61/2004 - Realizing homology classses by symplectic submanifolds

**Homology Theory****homomorphism**- 112/2007 - Arithmetic and Polynomials over Fuzzy Rings

**homotopy continuation**- 104/2020 - Epsilon local rigidity and numerical algebraic geometry

**homotopy group finiteness**- 57/1999 - Geometric Diffeomorphism Finiteness in Low Dimensions and Homotopy Group Finiteness

**Homotopy of Links****homotopy theory**- 27/2002 - Local minimizers and quasiconvexity - the impact of Topology

**hopf algbera**- 10/2006 - Renormalization : A number theoretical model

**hopf algebra****hopf algebras**- 52/2004 - Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple

**hopf bifurcation****hopf construction**- 39/2001 - Harmonic Hopf constructions between spheres II

**hopf invariant**- 24/2000 - S
^{1}-invariant harmonic maps from S^{3}to S^{2}

- 24/2000 - S
**Horn’s problem**- 93/2019 - A variant of Horn's problem and the derivative principle

**HOSVD**- 62/2015 - On the interconnection between the higher-order singular values of real tensors

**HOSVD truncation**- 29/2018 - Truncation of Tensors in the Hierarchical Format

**hp-finite element methods****hp-finite elements**- 38/2007 - Convolution of hp-functions on locally refined grids - extended version

**Hurwitz form**- 88/2019 - The Hessian discriminant

**hydrogen atom, lie algebra, rotation group, spin**- 25/2005 (
*Lecture note*) - Lectures on Quantum Mechanics (nonlinear PDEs point of view)

- 25/2005 (
**hyper-k\"ahler manifold**- 22/2005 - New examples of indefinite hyper-K\"ahler symmetric spaces

**hyperbolic**- 35/2019 - Topology and curvature of metric spaces

**hyperbolic boundary**- 73/2001 - Pathologies in Aleksandrov spaces of curvature bounded above

**hyperbolic model**- 34/2003 - Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit

**hyperbolic monge-ampere**- 53/2003 - Rigidity for the hyperbolic Monge-Ampere equation

**hyperbolic monge-ampere equation**- 16/2003 (
*Lecture note*) - Rigidity and Geometry of Microstructures

- 16/2003 (
**hyperbolic space**- 79/2007 - Finite Area and Volume of Pointed k-Surfaces

**hyperbolic systems****hyperbolic, nonlinear, symmetry group**- 24/2005 (
*Lecture note*) - Lectures on Global Attractors of Hamilton Nonlinear Wave Equations

- 24/2005 (
**hyperbolic-elliptic system**- 15/2015 - Blowup and Global Solutions in a Chemotaxis-Growth System

**hypercomplex automorphic forms**- 95/2013 - Applications of hypercomplex automorphic forms in Yang-Mills gauge theories

**hypercomplex manifolds**- 63/1999 - Special complex manifolds

**hyperconvex**- 35/2019 - Topology and curvature of metric spaces

**hypercube**- 35/1999 - Hyperplane arrangements separating arbitrary vertex classes in n-cubes

**hypergraph C*-algebra**- 73/2018 - Curious properties of hypergraph C*-algebras

**hypergraphs**- 1/2006 - Discrepancy of Symmetric Products of Hypergraphs

**hyperplane arrangement****hypersingular integrals**- 40/2002 - Discrete-to-continuum limit of magnetic forces

**Hyperspace**- 73/2020 - Factor maps of collective dynamics and hyperspace entropy

**hypersurface**- 32/2008 - Regularity for weakly Dirac-harmonic maps to hypersurfaces

**hypoelliptic**- 53/2008 - On hypoellipticity of generators of L\'{e}vy processes

**hysteresis**- 10/2016 - Rattling in spatially discrete diffusion equations with hysteresis
- 87/2008 - Energy barriers and hysteresis in martensitic phase transformations
- 77/2001 - Low energy domain patterns in soft ferromagnetic films
- 80/2000 - Numerical analysis of a relaxed variational model of hysteresis in two-phase solids

**Hysteresis in magnetism**- 40/2011 - The Formation and Coarsening of the Concertina Pattern

**H^2-matrix**- 85/2007 - Approximation of solution operators of elliptic partial differential equations by - and
^{2}-matrices

- 85/2007 - Approximation of solution operators of elliptic partial differential equations by - and
**h^∗ -polynomial**- 59/2018 - Arithmetic aspects of symmetric edge polytopes

**H²-matrix**- 92/2007 - Construction of data-sparse
^{2}-matrices by hierarchical compression

- 92/2007 - Construction of data-sparse