Research
Research
Research
Research
3,051+ 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 maintain a $(1+\varepsilon)$-spanner over the disk intersection graph of a dynamic set of disks. We restrict all disks to have their diameter in $[4,\Psi]$ for some fixed and known $\Psi$. The resu…
We revisit the classical transfer matrix solution of the one- and two-dimensional Ising model from the perspective of Clifford and conformal geometric algebras. Building on Kaufman's spinor formulatio…
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 ability to trap a single cell or microparticle in three dimensions is important for biomedical and microfluidic applications. Single-beam acoustic tweezers based on focused waves provide a compact…
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 …
Stepped-wedge cluster randomized trials (SW-CRTs) evaluate interventions rolled out across clusters over time. Standard analyses typically use immediate-treatment (IT) models, which assume effects beg…
Recently, Hausmann and Renner have pointed out that several famous paradoxes relating to black holes have a similar character to various Extended Wigner's Friend paradoxes. In this paper I consider wh…
For any cubic graph in a closed orientable surface and a perfect matching, the Penrose-Kauffman polynomial is a sum of chromatic polynomials of a collection of associated graphs. A knot-theoretic pers…
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 investigate the balanced $M=4$, $p=4$ spin-glass model for a one-dimensional long-range proxy for the finite dimensional short-range $p$-spin glass model to examine the nature of the glass transiti…
Let \(Q \subseteq \mathbb{N}\) be a subset, and let \(\psi\colon \mathbb{N} \to [0, \tfrac{1}{2})\), \(\theta\colon \mathbb{N} \to \mathbb{R}\) be functions. Let \(\{A_q\}\) and \(\{B_q\}\) be sequenc…
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…
We determine the structure of the Kauffman bracket skein module of the connected sum of two genus one handlebodies over the ring of Laurent polynomials $\mathbb Z[q^{\pm 1}]$, thereby proving a conjec…
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…
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