Research
Research
Research
Research
16,403+ open-access research outputs.
We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system le…
A self-contained introduction to infinite dimensional representations over a tame hereditary algebra is provided, assuming a basic knowledge of the category of finite dimensional representations. This…
Recent results have shown that for a linear tilt to a reference measure, the scores that would be produced under convolution with a normal variable can be expressed in terms of convolutions of the ori…
We develop a calculus for counting pseudoholomorphic disks with boundary in tropical Lagrangians contained in almost toric manifolds, using our previous work with Venugopalan. The results are mostly i…
Many well-known theorems establish sufficient criteria for linearizability of a vector field in terms of the eigenvalues of its linear approximation. By attaching weights to coordinates so that some d…
The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxatio…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). I…
This paper presents a projection-based technique to mitigate the impact of modeling errors related to domain truncation, changes in the optode coupling coefficients, and misspecified optical parameter…
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Max…
The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraint…
A graph is Schur-positive if its chromatic symmetric function expands non-negatively in the Schur basis. We determine a full Schur-positivity classification for complete multipartite graphs by showing…
Discrete variational methods show excellent performance in numerical simulations of mechanical systems. In this paper, we adapt discrete variational integrators for the case of mechanical systems with…
This paper presents a high-order bound-preserving oscillation-eliminating discontinuous Galerkin (BP-OEDG) scheme for simulating gas-gas and gas-liquid two-phase flows governed by the Kapila five-equa…
In this paper, we propose a novel Physics-Informed Neural Network (PINN) framework based on the Cord\`{e}s condition for solving both linear and fully nonlinear partial differential equations (PDEs) i…
While the positive Grassmannian is deeply understood through the rich combinatorics of plabic graphs and positroid cells, its tropical counterpart, the positive tropical Grassmannian Trop$_{>0}G(k,n)$…
This paper provides second-order optimality conditions for optimization problems with generalized equation constraints (GEPs), a framework that encompasses several important and challenging models in …
The combination of data and models, enhanced by AI methodologies, leads to the paradigm called Digital Twins. This concept is expected to bring unprecedented support to personalized medicine. The comb…
The higher Bruhat orders are partial orders that generalize the weak order on the symmetric group $S_n$, and the second higher Bruhat order is a poset on commutation classes of reduced words for the l…
Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we cons…
A gyration is an operation on Poincar\'{e} Duality complexes that arises from a certain surgery on the product of a given complex $N$ and a sphere, parametrised by a chosen twisting. Of particular rec…
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