Research
Research
Research
Research
17,576+ open-access research outputs.
We study how long the SIRS process persists or how quickly it reaches extinction across various network topologies. Our results provide a three-part characterization of this process: In finite sparse …
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…
Let $M$ be a smooth manifold without boundary and let $\mathcal{T}$ be a countable collection of manifolds with corners, each equipped with a smooth map to $M$. We show that the singular simplicial se…
In modern parametric model training, full-batch gradient descent (and its variants) suffers due to progressively stronger biasing towards the exact realization of training data; this drives the system…
The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consi…
This paper is a continuation work of Ren et al. (2026) aiming to further devise q-learning algorithms for mean-field control (MFC) with controlled common noise. Based on the relaxed control formulatio…
This paper studies whether solutions of a class of nonlinear feedback systems remain bounded over time. The systems we consider arise naturally in synthetic biology, where the antithetic feedback cont…
We study some interesting hypersurfaces that naturally arise when studying the period map on the moduli space of hypersurfaces, in the context of Sung Gi Park's recent work on studying the GIT moduli …
The Immersed Boundary Method has long served as a robust computational framework for fluid-structure interactions, yet the rigorous analysis of 1D Peskin filaments anchored to rigid boundaries remains…
It is a fundamental question in epidemiology to estimate, model and predict the growth rate of a pandemic. Analogously, analysing the diffusion of innovation, (fake) news, memes, and rumours is of key…
The problem of characterizing graphs with a prescribed number of main eigenvalues is a long-standing problem in spectral graph theory. Although some constructions are known, only a few produce infinit…
We show that under $\mathsf{ZF} + \mathsf{CC}_{\mathbb R}$, if the Ramsey property holds for all sets in a good pointclass $\Gamma$, then there is no MAD family in $\Gamma$, proving a long-standing co…
We study random matrices whose entries are obtained by applying consistent rank correlations, such as Hoeffding's $D$, pairwise to a high-dimensional random vector with mutually independent components…
Coisotropic A-branes were introduced by Kapustin--Orlov to enlarge the Fukaya category of a symplectic manifold in a way that aligns with predictions from homological mirror symmetry. From a mathemati…
We obtain a complete classification of components of strata of holomorphic and meromorphic k-differentials. We show that, when genus is at least two and outside of explicit exceptions when k < 4, ther…
We explore the nonlinear dynamics of classical field theories containing ghost degrees of freedom, focusing on two coupled scalar fields with opposite kinetic terms in (1+1) and (2+1) dimensional Mink…
The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct…
We study the deterministic recursion $n_{j+1} = n_j - \tau(n_j)$, where $\tau(n)$ denotes the divisor function, and the associated orbit length $a(x)$. Heuristics based on the average order of $\tau(n…
Based on discrete observations $X_0,X_{\Delta},\dots, X_{n\Delta}$ for $\Delta=n^{-\gamma}$ with $\gamma\in [0,1)$ of the null-recurrent dynamic $dX_t = \sigma(X_t)dW_t$ with a Brownian motion $W$ and…
Genome-Scale Metabolic Models (GEMs) describe the interactions between genes, proteins, and the biochemical reactions that underpin an organism's metabolism aiming to computationally simulate function…
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