John R. Doyle
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View article: Mitigating the Impact of Dysregulation on Learning Outcomes for Autistic Pupils.
Mitigating the Impact of Dysregulation on Learning Outcomes for Autistic Pupils. Open
Lay AbstractThis study looks at how autistic children manage their emotions at school and how teachers can help them feel more in control. Emotional regulation is important for learning, and it’s a key part of education, but most research …
View article: Bridging the gap: empowering patients as research partners through a structured training program
Bridging the gap: empowering patients as research partners through a structured training program Open
The training program emphasized clear expectations, accessibility, and providing resources to build the capacity of patient partners. Trust was established through a dedicated support person, a collaborative group dynamic, and regular enga…
View article: Unicritical polynomials over $abc$-fields: from uniform boundedness to dynamical Galois groups
Unicritical polynomials over $abc$-fields: from uniform boundedness to dynamical Galois groups Open
Let $K$ be a function field of characteristic $p\geq0$ or a number field over which the $abc$ conjecture holds, and let $ϕ(x)=x^d+c \in K[x]$ be a unicritical polynomial of degree $d\geq2$ with $d \not\equiv 0,1\pmod{p}$. We completely cla…
View article: The Furstenberg-Sárközy theorem for polynomials in one or more prime variables
The Furstenberg-Sárközy theorem for polynomials in one or more prime variables Open
We establish upper bounds on the size of the largest subset of $\{1,2,\dots,N\}$ lacking nonzero differences of the form $h(p_1,\dots,p_{\ell})$, where $h\in \mathbb{Z}[x_1,\dots,x_{\ell}]$ is a fixed polynomial satisfying appropriate cond…
View article: Galois groups and prime divisors in random quadratic sequences
Galois groups and prime divisors in random quadratic sequences Open
Given a set $S=\{x^2+c_1,\dots,x^2+c_s\}$ defined over a field and an infinite sequence $\gamma$ of elements of S , one can associate an arboreal representation to $\gamma$ , generalising the case of iterating a single polynomial. We study…
View article: Quadratic points on dynamical modular curves
Quadratic points on dynamical modular curves Open
Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This yields a classification statement on preperiodic points for quadratic polynomials over qu…
View article: New families satisfying the Dynamical Uniform Boundedness Principle over function fields
New families satisfying the Dynamical Uniform Boundedness Principle over function fields Open
We extend a technique, originally due to the first author and Poonen, for proving cases of the Strong Uniform Boundedness Principle (SUBP) in algebraic dynamics over function fields of positive characteristic. The original method applied t…
View article: Polynomials with many rational preperiodic points
Polynomials with many rational preperiodic points Open
In this paper we study two questions related to exceptional behavior of preperiodic points of polynomials in $\mathbb{Q}[x]$. We show that for all $d\geq 2$, there exists a polynomial $f_d(x) \in \mathbb{Q}[x]$ with $2\leq \mathrm{deg}(f_d…
View article: Stochastic Equidistribution and Generalized Adelic Measures
Stochastic Equidistribution and Generalized Adelic Measures Open
We study the dynamics of stochastic families of rational maps on the projective line. As such families can be infinite and may not typically be defined over a single number field, we introduce the concept of generalized adelic measures, ge…
View article: Galois groups and prime divisors in random quadratic sequences
Galois groups and prime divisors in random quadratic sequences Open
Given a set $S=\{x^2+c_1,\dots,x^2+c_s\}$ defined over a field and an infinite sequence $γ$ of elements of $S$, one can associate an arboreal representation to $γ$, generalizing the case of iterating a single polynomial. We study the proba…
View article: Dynamical moduli spaces and polynomial endomorphisms of configurations
Dynamical moduli spaces and polynomial endomorphisms of configurations Open
A portrait is a combinatorial model for a discrete dynamical system on a finite set. We study the geometry of portrait moduli spaces, whose points correspond to equivalence classes of point configurations on the affine line for which there…
View article: Dynatomic polynomials, necklace operators, and universal relations for dynamical units
Dynatomic polynomials, necklace operators, and universal relations for dynamical units Open
Given a generic polynomial $f(x)$, the generalized dynatomic polynomial $Φ_{f,c,d}(x)$ vanishes at precisely those $α$ such that $f^c(α)$ has period exactly $d$ under iteration of $f(x)$. We show that the shifted dynatomic polynomials $Φ_{…
View article: Dynatomic polynomials, necklace operators, and universal relations for\n dynamical units
Dynatomic polynomials, necklace operators, and universal relations for\n dynamical units Open
Given a generic polynomial $f(x)$, the generalized dynatomic polynomial\n$\\Phi_{f,c,d}(x)$ vanishes at precisely those $\\alpha$ such that $f^c(\\alpha)$\nhas period exactly $d$ under iteration of $f(x)$. We show that the shifted\ndynatom…
View article: HIGH-SENSITIVITY FRANCK-CONDON FACTOR MEASUREMENTS ENABLED BY OPTICAL CYCLING
HIGH-SENSITIVITY FRANCK-CONDON FACTOR MEASUREMENTS ENABLED BY OPTICAL CYCLING Open
Recent experiments have successfully laser cooled a variety of molecules, including diatomic, linear triatomic, and symmetric top species [1-3]. Laser cooling and trapping can require repeatedly scattering more than 10,000 photons per mole…
View article: Multivariate Polynomial Values in Difference Sets
Multivariate Polynomial Values in Difference Sets Open
For $\ell\geq 2$ and $h\in \mathbb{Z}[x_1,\dots,x_{\ell}]$ of degree $k\geq 2$, we show that every set $A\subseteq \{1,2,\dots,N\}$ lacking nonzero differences in $h(\mathbb{Z}^{\ell})$ satisfies $|A|\ll_h Ne^{-c(\log N)^μ}$, where $c=c(h)…
View article: Preperiodic points for quadratic polynomials over cyclotomic quadratic fields
Preperiodic points for quadratic polynomials over cyclotomic quadratic fields Open
Given a number field $K$ and a polynomial $f(z) \in K[z]$ of degree at least 2, one can construct a finite directed graph $G(f,K)$ whose vertices are the $K$-rational preperiodic points for $f$, with an edge $α\to β$ if and only if $f(α) =…
View article: The relative age effect in European elite soccer: A practical guide to Poisson regression modelling
The relative age effect in European elite soccer: A practical guide to Poisson regression modelling Open
Many disciplines of scholarship are interested in the Relative Age Effect (RAE), whereby age-banding confers advantages on older members of the cohort over younger ones. Most research does not test this relationship in a manner consistent …
View article: Finite index theorems for iterated Galois groups of unicritical\n polynomials
Finite index theorems for iterated Galois groups of unicritical\n polynomials Open
Let $K$ be the function field of a smooth, irreducible curve defined over\n$\\overline{\\mathbb{Q}}$. Let $f\\in K[x]$ be of the form $f(x)=x^q+c$ where $q =\np^{r}, r \\ge 1,$ is a power of the prime number $p$, and let $\\beta\\in\n\\ove…
View article: A Uniform Field-of-Definition/Field-of-Moduli Bound for Dynamical Systems on $\mathbf{P}^N$
A Uniform Field-of-Definition/Field-of-Moduli Bound for Dynamical Systems on $\mathbf{P}^N$ Open
Let $f:\mathbb{P}^N\to\mathbb{P}^N$ be an endomorphism of degree $d\ge2$ defined over $\overline{\mathbb{Q}}$ or $\overline{\mathbb{Q}}_p$, and let $K$ be the field of moduli of $f$. We prove that there is a field of definition $L$ for $f$…
View article: Relative age effect in elite soccer: More early-born players, but no better valued, and no paragon clubs or countries
Relative age effect in elite soccer: More early-born players, but no better valued, and no paragon clubs or countries Open
The paper analyses two datasets of elite soccer players (top 1000 professionals and UEFA Under-19 Youth League). In both, we find a Relative Age Effect (RAE) for frequency, but not for value. That is, while there are more players born at t…
View article: Reduction of dynatomic curves
Reduction of dynatomic curves Open
In this paper, we make partial progress on a function field version of the dynamical uniform boundedness conjecture for certain one-dimensional families ${\mathcal{F}}$ of polynomial maps, such as the family $f_{c}(x)=x^{m}+c$ , where $m\g…
View article: Dynamical modular curves for quadratic polynomial maps
Dynamical modular curves for quadratic polynomial maps Open
Motivated by the dynamical uniform boundedness conjecture of Morton and Silverman, specifically in the case of quadratic polynomials, we give a formal construction of a certain class of dynamical analogues of classical modular curves. The …
View article: Tails of the Travelling Gaussian model and the relative age effect: Tales of age discrimination and wasted talent
Tails of the Travelling Gaussian model and the relative age effect: Tales of age discrimination and wasted talent Open
The Relative Age Effect (RAE) documents the inherent disadvantages of being younger rather than older in an age-banded cohort, typically a school- or competition-year, to the detriment of career-progression, earnings and wellbeing into adu…
View article: Configuration of the Crucial Set for a Quadratic Rational Map
Configuration of the Crucial Set for a Quadratic Rational Map Open
Let $K$ be a complete, algebraically closed non-archimedean valued field, and let $φ(z) \in K(z)$ have degree two. We describe the crucial set of $φ$ in terms of the multipliers of $φ$ at the classical fixed points, and use this to show th…
View article: Preperiodic portraits for unicritical polynomials
Preperiodic portraits for unicritical polynomials Open
Let $K$ be an algebraically closed field of characteristic zero, and for $c \in K$ and an integer $d \ge 2$, define $f_{d,c}(z) := z^d + c \in K[z]$. We consider the following question: If we fix $x \in K$ and integers $M \ge 0$, $N \ge 1$…
View article: Fault Detection using Random Forest Similarity Distance
Fault Detection using Random Forest Similarity Distance Open
To maintain the pace of development set by Moore's law, semiconductor manufactures continue to shrink and redesign transistor architectures delivering better device performance. This has led to an increase in the complexity of the manufact…