Research
Research
Research
Research
2,818+ open-access research outputs.
We establish a half-space theorem \`a la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.…
Most galaxies have supermassive black holes (SMBH) at their centres, surrounded by stars with binary systems also present in this environment. We use two schemes - post-Newtonian (PN) and a scalar per…
In 2014, Michal Lewicki and Andrzej Olbry\'s proved that if a real valued function $f$ defined on the real line satisfies the conditional functional equation \[ f(tx + (1-t)y) = t f(x) + (1-t) f(y),\q…
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…
Christoph, Dragani\'{c}, Gir\~{a}o, Hurley, Michel, and M\"{u}yesser conjectured that, when $d\mid n$, the expected number of cycles in a uniformly random cycle-factor of a directed $d$-regular graph …
Network Slice as a Service (NSaaS) is a key enabler of Beyond Fifth Generation (5G) and Sixth Generation (6G) networks, supporting next-generation applications such as extended reality (XR), immersive…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal valu…
We prove that on a semisimple Lie algebra $\mathfrak{g}$ over a finite field of large characteristic, if a complex-valued invariant function $f$ and its Fourier transform $\hat f$ are both supported i…
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 …
For the fixed-size Brualdi--Hoffman--Turan problem forbidding the fish graph $H(4,3)$, Zheng and Zhang proved that every $H(4,3)$-free graph of even size $m \ge 38$ without isolated vertices satisfies…
The Nobel Prize in literature 1965 was awarded Mikhail Sholokhov (1905-1984), for the epic novel Tikhij Don about Cossack life and the birth of a new Soviet society (And Quiet Flows the Don, or The Qu…
The extent to which the geometry of an object is determined by some associated spectral data is a longstanding problem. We investigate this problem in the context of the Steklov spectrum, focusing on …
This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties o…
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dimensional or structur…
Biochemical signalling cascades transduce extracellular stimuli into cellular responses through sequences of discrete, node-to-node activations. While signal fidelity depends critically on local inter…
Federated Learning (FL) enables collaborative model training across distributed clients without sharing raw data, thereby preserving privacy. However, FL often suffers from significant communication a…
We present a computational platform for modeling chemical reactions in complex molecular environments, focused on ligand-protein binding in drug discovery. The platform implements our new quantum-in-q…
A 0/1-polytope is the convex hull of a subset $V\subseteq \{0,1\}^n$. A celebrated conjecture of Mihail and Vazirani asserts that the graph of every 0/1-polytope has edge-expansion at least 1. In this…
For a set of $n$ points $V \subseteq \mathbb{R}$ let $G(V, p)$ be the random graph on $V$ where each possible edge is present independently with probability $p$. We call a subset $U \subseteq V$ {\emp…
Cell-Free Massive Multiple-Input Multiple-Output (CF-MaMIMO) in Open Radio Access Network (O-RAN) promises high spectral efficiency but is limited by frequent Channel State Information (CSI) exchanges…
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