Explanipedia

The future of ageing: science aims to deliver another leap in lifespan Open

Simon Baker · 2025

A quantitative framework for sets of exact approximation order by rational numbers Open

Simon Baker, Benjamin Ward · 2025

In this paper we study a quantitative notion of exactness within Diophantine approximation. Given $Ψ:(0,\infty)\to (0,\infty)$ and $ω:(0,\infty)\to (0,1)$ satisfying $\lim_{q\to\infty}ω(q)=0$, we study the set of points, which we call $E(Ψ…

Trump’s return puts renewables at a crossroads Open

Simon Baker · 2025

On the cardinality and dimension of the slices of Okamoto’s functions Open

Simon Baker, George Bender · 2025

The graphs of Okamoto’s functions, denoted by K_{q} , are self-affine fractal curves contained in [0,1]^{2} , parameterised by q \in (1,2) . In this paper we consider the cardinality and dimension of the intersection of these curves with h…

Hybrid transformer‐based model for mammogram classification by integrating prior and current images Open

Afsana Ahsan Jeny, Sahand Hamzehei, Annie Jin, Simon Baker, Tucker Van Rathe , et al. · 2025

Background Breast cancer screening via mammography plays a crucial role in early detection, significantly impacting women's health outcomes worldwide. However, the manual analysis of mammographic images is time‐consuming and requires speci…

Polynomial Fourier decay for fractal measures and their pushforwards Open

Simon Baker, Amlan Banaji · 2025

We prove that the pushforwards of a very general class of fractal measures $$\mu $$ on $$\mathbb {R}^d$$ under a large family of non-linear maps $$F{:}\,{\mathbb {R}}^d \rightarrow {\mathbb {R}}$$ exhibit polynomial Fourie…

On finitely many base $q$ expansions Open

Simon Baker, George Bender · 2025

Given some integer $m \geq 3$, we find the first explicit collection of countably many intervals in $(1,2)$ such that for any $q$ in one of these intervals, the set of points with exactly $m$ base $q$ expansions is nonempty and moreover ha…

Disintegration results for fractal measures and applications to Diophantine approximation Open

Simon Baker · 2025

In this paper we prove disintegration results for self-conformal measures and affinely irreducible self-similar measures. The measures appearing in the disintegration resemble self-conformal/self-similar measures for iterated function syst…

Recurrence rates for shifts of finite type Open

Demi Allen, Simon Baker, Balázs Bárány · 2024

Approximating elements of the middle third Cantor set with dyadic rationals Open

Simon Baker · 2024

Let C be the middle third Cantor set and μ be the $$\frac{\log\;2}{\log\;3}$$ -dimensional Hausdorff measure restricted to C . In this paper we study approximations of elements of C by dyadic rationals. Our main result implies that…

Can Rule-Based Insights Enhance LLMs for Radiology Report Classification? Introducing the RadPrompt Methodology Open

Panagiotis Fytas, Anna Breger, Ian Selby, Simon Baker, Shahab Shahipasand , et al. · 2024

Developing imaging models capable of detecting pathologies from chest X-rays can be cost and time-prohibitive for large datasets as it requires supervision to attain state-of-the-art performance. Instead, labels extracted from radiology re…

Tidal Range Barrage Design and Construction Open

David Vandercruyssen, Simon Baker, D.C. Howard, George Aggidis · 2024

The west coast of Great Britain has the potential for barrages to create tidal range reservoirs that both facilitate electricity generation and prevent flooding from sea level rise. Seawater flows into and out of the reservoir, or impoundm…

Quantitative recurrence and the shrinking target problem for overlapping iterated function systems Open

Simon Baker, Henna Koivusalo · 2024

In this paper we study quantitative recurrence and the shrinking target problem for dynamical systems coming from overlapping iterated function systems. Such iterated function systems have the important property that a point often has seve…

On the strong separation condition for self-similar iterated function systems with random translations Open

Simon Baker, Derong Kong, Zhiqiang Wang · 2024

Given a self-similar iterated function system $Φ=\{ ϕ_i(x)=ρ_i O_i x+t_i \}_{i=1}^m$ acting on $\mathbb{R}^d$, we can generate a parameterised family of iterated function systems by replacing each $t_i$ with a random vector in $\mathbb{R}^…

Polynomial Fourier decay for fractal measures and their pushforwards Open

Simon Baker, Amlan Banaji · 2024

We prove that the pushforwards of a very general class of fractal measures $μ$ on $\mathbb{R}^d$ under a large family of non-linear maps $F \colon \mathbb{R}^d \to \mathbb{R}$ exhibit polynomial Fourier decay: there exist $C,η>0$ such that…

North–south publishing data show stark inequities in global research Open

Simon Baker · 2023

Tidal range electricity generation into the twenty-second century Open

David Vandercruyssen, Simon Baker, D.C. Howard, George Aggidis · 2023

Tidal range electricity generation schemes are designed to have a minimum operational life of at least 120 years, making it important to plan for changes such as sea-level rise (SLR). Earlier studies have shown that schemes can maintain th…

On the cardinality and dimension of the slices of Okamoto's functions Open

Simon Baker, George Bender · 2023

The graphs of Okamoto's functions, denoted by $K_q$, are self-affine fractal curves contained in $[0,1]^2$, parameterised by $q \in (1,2)$. In this paper we consider the cardinality and dimension of the intersection of these curves with ho…

Metric results for numbers with multiple $q$-expansions Open

Simon Baker, Yuru Zou · 2023

Let M be a positive integer and q\in (1, M+1] . A q -expansion of a real number x is a sequence (c_i)=c_1c_2\cdots with c_i\in \{0,1,\ldots, M\} such that x=\sum_{i=1}^{\infty}c_iq^{-i} . In this paper we study the set \mathcal{U}_q^j cons…

Overlapping Iterated Function Systems from the Perspective of Metric Number Theory Open

Simon Baker · 2023

In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation which shows that for a family of limsup sets, their L…

Spectral gaps and Fourier dimension for self-conformal sets with overlaps Open

Simon Baker, Tuomas Sahlsten · 2023

We prove a uniform spectral gap for complex transfer operators near the critical line associated to overlapping $C^2$ iterated function systems on the real line satisfying a Uniform Non-Integrability (UNI) condition. Our work extends that …

Quantitative recurrence and the shrinking target problem for overlapping iterated function systems Open

Simon Baker, Henna Koivusalo · 2023

In this paper we study quantitative recurrence and the shrinking target problem for dynamical systems coming from overlapping iterated function systems. Such iterated function systems have the important property that a point often has seve…

Intrinsic Diophantine approximation for overlapping iterated function systems Open

Simon Baker · 2023

In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine’s theorem for these sets. We then apply this result to the topic of intrinsic Diophantine Approxi…

Overcoming the obstacles to invention Open

Simon Baker · 2022

A note on dyadic approximation in Cantor’s set Open

Demi Allen, Simon Baker, Sam Chow, Han Yu · 2022

We consider the convergence theory for dyadic approximation in the middle-third Cantor set, , for approximation functions of the form (). In particular, we show that for values of beyond a certain threshold we have that almost no point in …

Tidal range electricity generation: A comparison between estuarine barrages and coastal lagoons Open

David Vandercruyssen, Simon Baker, D.C. Howard, George Aggidis · 2022

The potential power from coastal tidal range is becoming better appreciated due to the need to mitigate global warming. Great Britain (GB) is ideally situated to exploit tidal power but currently has no operational systems. Historically, e…

Harnessing AI and robotics for science and society Open

Simon Baker · 2022

Recurrence rates for shifts of finite type Open

Demi Allen, Simon Baker, Balázs Bárány · 2022

Let $Σ_{A}$ be a topologically mixing shift of finite type, let $σ:Σ_{A}\toΣ_{A}$ be the usual left-shift, and let $μ$ be the Gibbs measure for a Hölder continuous potential that is not cohomologous to a constant. In this paper we study re…

A note on dyadic approximation in Cantor's set Open

Demi Allen, Simon Baker, Sam Chow, Yu Han · 2022

We consider the convergence theory for dyadic approximation in the middle-third Cantor set, $K$, for approximation functions of the form $ψ_τ(n) = n^{-τ}$ ($τ\ge 0$). In particular, we show that for values of $τ$ beyond a certain threshold…

Approximating elements of the middle third Cantor set with dyadic rationals Open

Simon Baker · 2022

Let $C$ be the middle third Cantor set and $μ$ be the $\frac{\log 2}{\log 3}$-dimensional Hausdorff measure restricted to $C$. In this paper we study approximations of elements of $C$ by dyadic rationals. Our main result implies that for $…

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