We study the poset of normalized ideals of a numerical semigroup with multiplicity three.

Commutative Algebra Combinatorics 20M14, 20M12

Sequential excavation is common in shallow tunnel engineering, especially for large-span tunnels.

Numerical Analysis Numerical Analysis Complex Variables

A related problem is estimating the minimal altitude an aircraft needs to glide to a given airfield in the presence of obstacles.

Optimization and Control Numerical Analysis Systems and Control Systems and Control Numerical Analysis

We develop a heuristic for the density of integer points on affine cubic surfaces.

Number Theory 11G35 (11D25, 11G50, 14G12)

The inversion graph of a graph $G$, denoted by $\mathcal{I}(G)$, is the graph whose vertices are orientations of $G$ in which two orientations $\overrightarrow{G_1}$ and $\overrightarrow{G_2}$ are adjacent if and only if there is an inversion $X$ transforming $\overrightarrow{G_1}$ into $\overrightarrow{G_2}$.

Combinatorics

We develop a first-order (pseudo-)gradient approach for optimizing functions over the stationary distribution of discrete-time Markov chains (DTMC).

Optimization and Control

We prove that, as the number of training points increases, the empirical risk minimization problem converges (in the sense of Gamma-convergence) to the expected risk minimization problem.

Optimization and Control Functional Analysis Statistics Theory Statistics Theory 65J20, 65K10, 46N10, 52A05

In this paper, we study Physics-Informed Neural Networks (PINN) to approximate solutions to one-dimensional boundary value problems for linear elliptic equations and establish robust error estimates of PINN regardless of the quantities of the coefficients.

Numerical Analysis Numerical Analysis Analysis of PDEs Primary: 34B05, 35A15, Secondary: 68T07, 65L10

In this paper we consider bound-constrained mixed-integer optimization problems where the objective function is differentiable w. r. t.\ the continuous variables for every configuration of the integer variables.

Optimization and Control 90C11, 90C26, 90C30

On a compact Riemannian manifold $M,$ we show that the Riemannian distance function $d(x, y)$ can be explicitly reconstructed from suitable asymptotics of the expected signature of Brownian bridge from $x$ to $y$.

Probability