Research
Research
Research
Research
6,438+ open-access research outputs.
We develop a harmonic gauge on the space of Riemannian metrics and study its role in the variational and flow-theoretic structure of geometric analysis. We prove that the harmonic gauge eliminates div…
Optimization of quadratic functions and the quotient of those are relevant in subspace and iterative optimization methods. In this paper, the calculation of the generalized operator norm and extremal …
An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^3$. We establish an equivariant analogue of the work of Carter and Saito aimed at studying equivariant …
We establish a direct connection between the analytic data of weakly isolated mixed singularities and the topology of their associated links. More precisely, we prove that the existence of essential t…
We compute the $k$-colored $\mathfrak{sl}(N)$ homology of the torus knot $T(2,2m+1)$, and we show that it stabilizes as $m\to\infty$ to the integral homology of the free loop space of the complex Gras…
We study the Ehrhart $h^\ast$-polynomial of (the boundary of) a lattice polytope via regular unimodular triangulations and Gr\"obner degenerations of toric ideals. Our main result is a boundary analog…
As a vital link between group theory and graph theory, Cayley graphs provide a geometric framework for encoding algebraic structures. This study explores the properties of Cayley graphs derived from c…
This paper focuses on the multi-agent synchronization problem with an open-loop unstable leader and followers under the switching topologies. For this issue, the typical approach is intermittent commu…
We consider large-scale traffic assignment problems and develop a path-based compression framework. In particular, we partition paths into major and minor paths according to a set of nominal flows and…
This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of…
For a germ $(X,0)$ of a normal complex analytic surface, let $E:=H^0({}^p_+IC_X\mathbb Z)_0$, where ${}^pIC_X\mathbb Z$ and ${}^p_+IC_X\mathbb Z$ denote the ordinary and dual middle-perversity interse…
We establish a relationship between error terms appearing in estimates for the counting functions of smooth and rough numbers. We then apply this link to obtain an explicit upper bound for the error t…
We define branched bending deformations as deformations supported on a piecewise totally geodesic complex of $(n-1)$-dimensional faces meeting along $(n-2)$-dimensional branching loci. These are a gen…
In this paper, we define real link Floer homology for strongly invertible and doubly periodic links in closed real $3$-manifolds with connected fixed sets, which generalizes real Heegaard Floer homolo…
We record a Lean-certified theorem package for the four-point Heil--Ramanathan--Topiwala configuration \[ \Lambda=\{0,a,b,\nu\}\subset \R^2, \qquad \Lzero=\Z a+\Z b, \qquad \nu=r a+s b, \] with $a$ an…
We study the complexity of the Thouless-Anderson-Palmer (TAP) free energy for Ising spin glasses with a general mixed p-spin covariance, working with the generalized TAP functional of Chen, Panchenko,…
Classical work of Thurston and Gabai shows that finitely many taut sutured manifold hierarchies determine the Thurston norm of a compact oriented irreducible $3$-manifold with toroidal boundary. We gi…
Terminal airspace congestion remains a major bottleneck in the global air traffic network. Although the Aircraft Sequencing and Scheduling Problem (ASSP) has been widely studied, many methods rely on …
We study in detail an A4-symmetric tensegrity appearing in Connelly's catalog. The realizable configurations form a one-parameter family that can be parametrized by points on the elliptic curve with C…
We introduce joint exclusivity (JE), a form of extremal negative dependence that extends the classical notion of mutual exclusivity. The JE structure is analytically tractable and is defined by the ex…
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