Research
Research
Research
Research
3,137+ open-access research outputs.
In finance, portfolio management is a traditional yet difficult problem that has drawn attention from practitioners and researchers for many years. However, there are still difficult technological pro…
In this paper, we study the rigidity properties of compact Kahler manifolds. Given a smooth family of compact Kahler manifolds X over the unit disk, we show that all the fibers are mutually isomorphic…
For every $n \geq 5$, we show that the Kneser graph of triangulations of a convex $n$-gon contains a Hamiltonian cycle.…
We prove that the information complexity (i.e., the inverse) of the classical spherical cap $L_2$ discrepancy on the $d$-dimensional sphere $\mathbb{S}^d$ decreases with dimension $d$, indicating a ``…
We study the edge-expansion of the graph of a random $0/1$ polytope $P^d_p$, defined as the convex hull of a random subset of the points in $\{0,1\}^d$ where every point is retained independently and …
We present the Multi-Block DC (BDC) class, a rich class of structured nonconvex functions that admit a DC ("difference-of-convex") decomposition across parameter blocks. This multi-block class not onl…
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a p…
Semiclassical analysis and noncommutative geometry are two pillars of quantum theory. It's only recently that bridges between them have been emerging. In this monograph, we combine various techniques …
We study the smallest convex lattice generated by a finite set of points. To analyze this structure, we introduce the notion of a point configuration, defined via the relative lattice. Under a suitabl…
In AI-rich higher education, polished written mathematics has become easier to produce than trustworthy evidence of understanding. This article develops a human-scale methodology for service mathemati…
In this paper, we clarified the relationship between continued fractions, determinants, and identities, making it easier to apply these methods systematically in other settings. In particular, we stud…
We introduce the notion of invariant vectors of a game and develop the Invariance Reduction Process, which first uses reduction of positions via invariance and then zero and merge reductions of games …
We derive a stochastically-constrained Koiter shell model in line with the SALT (Stochastic Advection by Lie Transport) approach introduced by Holm [Proc. A. 471 (2015)]. First, we deduce the stochast…
We investigate the relationship between two interpretations of equivariant Riemann-Roch defects of complex spaces with conic singularities; as (i) equivariant $\eta_{T}$ and $\xi_{T}$ invariants, and …
We prove a law of large numbers and a functional central limit theorem for the empirical density of a Marcus-Lushnikov model. The limiting density turns out to be the solution of a Smoluchowski equati…
Inspired by the MacDowell-Mansouri formulation of four-dimensional General Relativity, we study a class of four-dimensional gauge-theoretic functionals obtained from the Pontryagin density of a G-conn…
In this paper, we study Clairaut generic Riemannian map from a nearly Kahler manifold to a Riemannian manifold. Further, we obtain a condition for a Clairaut generic Riemannian map to be a totally geo…
Consider a parabolic SPDE \[ \partial_t u = \Delta u + \sigma(u)\eta, \] on $(0\,,\infty)\times\mathbb{R}^d$, where $\eta$ is a centered, generalized Gaussian noise with $\text{Cov}[\eta(t\,,x)\…
We consider random walk polynomial sequences $(P_n(x))_{n\in\mathbb{N}_0}\subseteq\mathbb{R}[x]$ given by recurrence relations of the form $P_0(x)=1$, $P_1(x)=x$ and $x P_n(x)=a_n P_{n+1}(x)+c_n P_{n-…
Solving mixed-integer nonlinear programs (MINLPs) typically relies on constructing relaxations that are easier to tackle than the original problem. Recently, global parabolic (PARA) relaxations were i…
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