Research
Research
Research
Research
26,416+ open-access research outputs.
We consider a class of nonlinear parabolic equations \[ \dfrac{\partial}{\partial t} b(u)-\nabla \cdot (A(x,t,u,\nabla u))+H(x,t,\nabla u)=f , \] where $H$ is a nonlinear lower order term sati…
In this paper we study when the origin $(0,0)$ is a regular (or irregular) boundary point for the so-called soda can domains of the type \[ \Theta_{l,\theta}:= \{(x,t) \in \mathbf{R}^{n+1}: 0<-t < \th…
3D shapes from scanning, reconstruction, or AI-generated content often lack simple quad mesh layouts -- critical for efficient editing and modeling. Existing quad-remeshing techniques typically produc…
To accommodate classical communication systems with progressively increasing transmission rates, quantum access networks (QAN) have undergone systematic and protocol-level optimizations in recent year…
Learning rate scheduling has evolved from the single global fixed rate of early SGD to sophisticated layer-wise adaptive strategies. We systematize this evolution into five generations: (Gen1) global …
We discovered generalized structures, named astrocytes due to their shape, that constitute a defined region characterizing regular behavior within the parameter plane (PP) of dynamical systems (DSs). …
Hill functions, dominant in gene regulatory network modeling, carry fundamental limitations: at non-integer cooperativity exponents, routine when fitting dose-response data, derivatives diverge at the…
Circadian rhythms are endogenous oscillations that regulate various physiological processes and their disruption has been linked to many diseases, making it important to determine how gene-expression …
A convex polyhedron is Rupert if a hole can be cut into it (making its genus $1$) such that an identical copy of the polyhedron can pass through the hole. Resolving a conjecture of Jerrard-Wetzel-Yuan…
In the previous work [Interfaces Free Bound., 19, 351--369, 2017], de Queiroz and Shahgholian established the optimal $C^{1,\log}_{\mathrm{loc}}$ regularity of solutions for the obstacle problem with …
Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$. Early work by Friedland and Stanley addressed so…
The evolutionary origins of structural features in reconstructed gene-regulatory networks (GRNs) remain poorly understood, especially given the random aspects of gene expression. Here, we extend a cla…
Identifying genes associated with diseases is crucial to understanding disease mechanisms and developing therapies. However, identification of individual genes associated with a disease often needs to…
We study the occurrence of curved three-point configurations in fractal subsets of the real line. We prove that if \(E \subset [0,1]\) is a compact set with sufficiently large Hausdorff dimension, the…
The start of a human's life can be characterized by two lotteries: that of your genes (nature) and the family you were born into (nurture). These set in motion a trajectory, from birth onward, in heal…
Large Language Models (LLMs) have shown strong potential for narrative generation, but their use in complex, multi-layered role-playing game (RPG) worlds is still limited by issues of coherence, contr…
We compute the Atiyah Real $K$-theory of $C_2$-equivariant projective spaces and construct immersions of such spaces into multiples of the regular representation. These computations are made tractable…
T-cells are central to SARS-CoV-2 clearance and immunological memory, yet their contribution to the persistence of post-acute sequelae of COVID-19 (PASC) remains poorly understood. The immunological f…
Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to sig…
Melanoma is an aggressive form of skin cancer. Survival rates are excellent if it is detected early but fall markedly if it metastasises. A key step in early tumour progression is the formation of cel…
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