OOIR: Observatory of International Research

Papers

(The median citation count of Research in the Mathematical Sciences is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-03-01 to 2024-03-01.)

Article	Citations
Overcoming the curse of dimensionality for some Hamilton–Jacobi partial differential equations via neural network architectures	46
Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy	25
Delay-coordinate maps, coherence, and approximate spectra of evolution operators	13
Modeling of missing dynamical systems: deriving parametric models using a nonparametric framework	12
Free boundary methods and non-scattering phenomena	11
Stability bounds and almost sure convergence of improved particle swarm optimization methods	9
An enriched count of the bitangents to a smooth plane quartic curve	8
Analytical formula for conditional expectations of path-dependent product of polynomial and exponential functions of extended Cox–Ingersoll–Ross process	8
Mean field control problems for vaccine distribution	7
Kolmogorov width decay and poor approximators in machine learning: shallow neural networks, random feature models and neural tangent kernels	7
Time-periodic measures, random periodic orbits, and the linear response for dissipative non-autonomous stochastic differential equations	7
Approximation properties of deep ReLU CNNs	7
Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall	6
Effective forms of the Sato–Tate conjecture	6
Explicit transformations of certain Lambert series	6
Arithmetic statistics on cubic surfaces	6
Semiclassical parametrix for the Maxwell equation and applications to the electromagnetic transmission eigenvalues	6
Modeling illegal logging in Brazil	5
Enhanced Koszul properties in Galois cohomology	5
Zeros of Jensen polynomials and asymptotics for the Riemann xi function	5
Cohomology of complements of toric arrangements associated with root systems	5
Generalized Paley graphs and their complete subgraphs of orders three and four	5
Applications to $${\mathbb {A}}^1$$-enumerative geometry of the $${\mathbb {A}}^1$$-degree	5
New regularity results for Hamilton–Jacobi equations and long time behavior of pathwise (stochastic) viscosity solutions	4
Appell series over finite fields and Gaussian hypergeometric series	4

Superimposing theta structure on a generalized modular relation	4
Multiplicities and mixed multiplicities of arbitrary filtrations	4
Initial investigations of precipitating quasi-geostrophic turbulence with phase changes	4
An error bound for the slender body approximation of a thin, rigid fiber sedimenting in Stokes flow	4
On vanishing near corners of conductive transmission eigenfunctions	4
Harmonic analysis and statistics of the first Galois cohomology group	4
Solving multiscale steady radiative transfer equation using neural networks with uniform stability	4
Motive of the moduli stack of rational curves on a weighted projective stack	4
Stability for quantitative photoacoustic tomography revisited	4
Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals	4
On the modified transmission eigenvalue problem with an artificial metamaterial background	4
Generalization error of GAN from the discriminator’s perspective	4
Laplacian smoothing gradient descent	4
Integral representations of rank two false theta functions and their modularity properties	3
Linear algebraic groups with good reduction	3
Rates of convergence for Laplacian semi-supervised learning with low labeling rates	3
Effective behavior of cooperative and nonidentical molecular motors	3
Hilbert series of parallelogram polyominoes	3
The quaternion Fourier and wavelet transforms on spaces of functions and distributions	3
Split representation of adaptively compressed polarizability operator	3
Semiclassical limit of an inverse problem for the Schrödinger equation	3
Approximation of the inverse scattering Steklov eigenvalues and the inverse spectral problem	3
Period functions associated to real-analytic modular forms	3
Computational graph completion	3
Asymptotics for the twisted eta-product and applications to sign changes in partitions	3
Spectral methods for nonlinear functionals and functional differential equations	3
Axisymmetric solutions of the shallow water equations with bottom topography	2
Fully hyperbolic convolutional neural networks	2
Special foliations on $$\mathbb {CP}^2$$ with a unique singular point	2
$${}_{4}F_{3}$$-Gaussian hypergeometric series and traces of Frobenius for elliptic curves	2
Peacock patterns and resurgence in complex Chern–Simons theory	2
A quaternionic construction of p-adic singular moduli	2
On the simplicial volume and the Euler characteristic of (aspherical) manifolds	2
Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type	2
Tropical Ehrhart theory and tropical volume	2
Ampleness of Schur powers of cotangent bundles and k-hyperbolicity	2
Asymptotic expansions of Stekloff eigenvalues for perturbations of inhomogeneous media	2
Trace minmax functions and the radical Laguerre–Pólya class	2
Uniform approximation rates and metric entropy of shallow neural networks	2
Powers of graphs & applications to resolutions of powers of monomial ideals	2
Improving the prediction of complex nonlinear turbulent dynamical systems using nonlinear filter, smoother and backward sampling techniques	2
Spectral $$\varvec{\zeta }$$-functions and $$\varvec{\zeta }$$-regularized functional determinants for regular Sturm–Liouville operators	2
Infinite families of crank functions, Stanton-type conjectures, and unimodality	2
Spaces of non-degenerate maps between complex projective spaces	2
Existence and uniqueness for solutions of mixed stochastic delay differential equations	2
Powers of componentwise linear ideals: the Herzog–Hibi–Ohsugi conjecture and related problems	2
Uniqueness of conservative solutions for the Hunter–Saxton equation	2
t-SNE, forceful colorings, and mean field limits	2
On sets of maximally commuting and anticommuting Pauli operators	2
Bitangents to plane quartics via tropical geometry: rationality, $$\mathbb {A}^1$$-enumeration, and real signed count	2

Divisor-bounded multiplicative functions in short intervals	2
Loop space decompositions of $$(2n-2)$$-connected $$(4n-1)$$-dimensional Poincaré Duality complexes	2
Modified transmission eigenvalues for inverse scattering in a fluid–solid interaction problem	2
The study of certain optimization problems via variational inequalities	2
Side effects of learning from low-dimensional data embedded in a Euclidean space	2
Deep limits of residual neural networks	2
Bayesian inversion for an inverse spectral problem of transmission eigenvalues	2
Problems in arithmetic topology	1
On the reductions of certain two-dimensional crystabelline representations	1
Tropical ideals do not realise all Bergman fans	1
Discontinuous Galerkin method with Voronoi partitioning for quantum simulation of chemistry	1
Quantized convolutional neural networks through the lens of partial differential equations	1
$$L^{1}$$ convergences and convergence rates of approximate solutions for compressible Euler equations near vacuum	1
A double-pivot simplex algorithm and its upper bounds of the iteration numbers	1
On string functions and double-sum formulas	1
Operations on stable moduli spaces	1
Designing rotationally invariant neural networks from PDEs and variational methods	1
Schur–Weyl duality for tensor powers of the Burau representation	1
The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations	1
On sparse geometry of numbers	1
On gluing semigroups in $${\pmb {\mathbb {N}}}^n$$ and the consequences	1
Configuration-mapping spaces and homology stability	1
Explicit transformations for generalized Lambert series associated with the divisor function $$\sigma _{a}^{(N)}(n)$$ and their applications	1
On the dynamical system generated by the Möbius transformation at prime times	1
Derivatives of L-series of weakly holomorphic cusp forms	1
Generative modeling via tree tensor network states	1
Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime	1
A perturbation problem for transmission eigenvalues	1
Weyl formula for the eigenvalues of the dissipative acoustic operator	1
An algebraic lifting invariant of Ellenberg, Venkatesh, and Westerland	1
Indefinite zeta functions	1
Secondary cup and cap products in coarse geometry	1
Deep solution operators for variational inequalities via proximal neural networks	1
Towards the Erdős-Hajnal conjecture for $$P_5$$-free graphs	1
Hypergeometric decomposition of symmetric K3 quartic pencils	1
Learning generative neural networks with physics knowledge	1
Topics on strict closure of rings	1
Multivariable connected sums and multiple polylogarithms	1
A symmetric Bloch–Okounkov theorem	1
Jacobi forms, Saito-Kurokawa lifts, their Pullbacks and sup-norms on average	1
A $$C^{1}-C^{0}$$ conforming virtual element discretization for the transmission eigenvalue problem	1
Cohomology rings of finite-dimensional pointed Hopf algebras over abelian groups	1
Computing $$\mathbb {A}^1$$-Euler numbers with Macaulay2	1
The minimum of the levels of the proper factors of a holomorphic eta quotient	1
Electromagnetic Steklov eigenvalues: existence and distribution in the self-adjoint case	1
The finite and solvable genus of finitely generated free and surface groups	1
Modular knots, automorphic forms, and the Rademacher symbols for triangle groups	1
Torsion in differentials and Berger’s conjecture	1
A second-order nonlocal approximation for Poisson model with Dirichlet boundary	1
A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra	1
Merge trees in discrete Morse theory	1
Linearity of free resolutions of monomial ideals	1
Singularities and vanishing cycles in number theory over function fields	1
On the occurrence of complete intersections in shifted families of numerical semigroups	1
A numerical approach toward the p-adic Beilinson conjecture for elliptic curves over $${\mathbb {Q}}$$	1
Bhargava’s cube and black hole charges	1
Twelve Rational curves on Enriques surfaces	1
$$\lambda $$-Invariant stability in families of modular Galois representations	1
On the notion of sequentially Cohen–Macaulay modules	1
On lattice polarizable cubic fourfolds	1
Nonlinear interaction and turbulence transition in the limiting regimes of plasma edge turbulence	1
Mocking the u-plane integral	1
Automorphism groups and normal forms in Normaliz	1
A stochastic closure for two-moment bulk microphysics of warm clouds: part I, derivations	1
How does momentum benefit deep neural networks architecture design? A few case studies	1
Powers of monomial ideals with characteristic-dependent Betti numbers	1