Research
Research
Research
Research
1,826+ open-access research outputs.
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…
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…
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 …
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 …
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…
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…
A problem proposed by Erd\H{o}s, Fajtlowicz and Staton asks for the smallest $n$ for which every graph on $n$ vertices contains a regular induced subgraph of order at least $k$. A variation is to ask …
The notion of asymptotic space for an unbounded metric space has been introduced by Micha Gromov in 1980s. It is intended to capture the structure of a metric space at infinity. The most comprehensive…
We give a categorical proof of the projectivity of $N$ in the free topos -- in proof-theoretic terms, the rule of countable choice for intuitionistic higher-order logic -- based on the unpublished pro…
The notion of $\ast$-measure on a compact Hausdorff space can be defined for arbitrary continuous triangular norm $\ast$. The well-known Hutchinson-Barnsley theory deals with the iterated function sys…
To model amplification Polymerase Chain Reaction (PCR) techniques targeting DNA sequences of several types, we introduce a multitype PCR branching process as a generalized version of the Michaelis-Men…
We establish an equivalence between massive spinning particle models in four spacetime dimensions coupled to electromagnetism or gravity, within the spin-magnitude-preserving sector. Four representati…
The renowned theorem of Dirac states that if $G$ is a graph with minimum degree at least $n/2$ then $G$ has a Hamilton cycle. A natural generalisation asks what properties of an edge-colouring of $G$ …
Oriented graph discrepancy problems focus on finding specific subgraphs within a given oriented graph $G$ that contain a significant number of edges in one direction. This concept was first introduced…
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