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51. Intersections of orbits of self-maps with subgroups in semiabelian varieties

Author

Bell, Jason P. and Ghioca, Dragos

Subjects
Mathematics - Number Theory, Mathematics - Dynamical Systems, 14K12, 37P55
Abstract

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$, endowed with a rational self-map $\Phi$. Let $\alpha\in G(K)$ and let $\Gamma\subseteq G(K)$ be a finitely generated subgroup. We show that the set $\{n\in\mathbb{N}\colon \Phi^n(\alpha)\in \Gamma\}$ is a union of finitely many arithmetic progressions along with a set of Banach density equal to $0$. In addition, assuming $\Phi$ is regular, we prove that the set $S$ must be finite., Comment: 12 pages

Published
2022

52. Computing the linear hull: Deciding Deterministic? and Unambiguous? for weighted automata over fields

Author

Bell, Jason P. and Smertnig, Daniel

Subjects
Computer Science - Formal Languages and Automata Theory, Mathematics - Combinatorics
Abstract

The (left) linear hull of a weighted automaton over a field is a topological invariant. If the automaton is minimal, the linear hull can be used to determine whether or not the automaton is equivalent to a deterministic one. Furthermore, the linear hull can also be used to determine whether the minimal automaton is equivalent to an unambiguous one. We show how to compute the linear hull, and thus prove that it is decidable whether or not a given automaton over a number field is equivalent to a deterministic one. In this case we are also able to compute an equivalent deterministic automaton. We also show the analogous decidability and computability result for the unambiguous case. Our results resolve a problem posed in a 2006 survey by Lombardy and Sakarovitch., Comment: Completely restructured based on reviewer feedback

Published
2022

53. Rational self-maps with a regular iterate on a semiabelian variety

Author

Bell, Jason, Ghioca, Dragos, and Reichstein, Zinovy

Subjects
Mathematics - Number Theory, Mathematics - Algebraic Geometry, Mathematics - Dynamical Systems, 14K12, 37P55
Abstract

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$ of characteristic $0$. Let $\Phi\colon G\dashrightarrow G$ be a dominant rational self-map. Assume that an iterate $\Phi^m \colon G \to G$ is regular for some $m \geqslant 1$ and that there exists no non-constant homomorphism $\tau: G\to G_0$ of semiabelian varieties such that $\tau\circ \Phi^{m k}=\tau$ for some $k \geqslant 1$. We show that under these assumptions $\Phi$ itself must be a regular. We also prove a variant of this assertion in prime characteristic and present examples showing that our results are sharp., Comment: 15 pages

Published
2022

54. On noncommutative bounded factorization domains and prime rings

Author

Bell, Jason P., Brown, Ken, Nazemian, Zahra, and Smertnig, Daniel

Subjects
Mathematics - Rings and Algebras, Primary 16P40, Secondary 13F15, 16E65, 20M13
Abstract

A ring has bounded factorizations if every cancellative nonunit $a \in R$ can be written as a product of atoms and there is a bound $\lambda(a)$ on the lengths of such factorizations. The bounded factorization property is one of the most basic finiteness properties in the study of non-unique factorizations. Every commutative noetherian domain has bounded factorizations, but it is open whether such a result holds in the noncommutative setting. We provide sufficient conditions for a noncommutative noetherian prime ring to have bounded factorizations. Moreover, we construct a (noncommutative) finitely presented semigroup algebra that is an atomic domain but does not satisfy the ascending chain condition on principal right or left ideals (ACCP), whence it does not have bounded factorizations.

Published
2022

55. A general criterion for the P\'{o}lya-Carlson dichotomy and application

Author

Bell, Jason P., Gunn, Keira, Nguyen, Khoa D., and Saunders, J. C.

Subjects
Mathematics - Number Theory
Abstract

We prove a general criterion for an irrational power series $f(z)=\displaystyle\sum_{n=0}^{\infty}a_nz^n$ with coefficients in a number field $K$ to admit the unit circle as a natural boundary. As an application, let $F$ be a finite field, let $d$ be a positive integer, let $A\in M_d(F[t])$ be a $d\times d$-matrix with entries in $F[t]$, and let $\zeta_A(z)$ be the Artin-Mazur zeta function associated to the multiplication-by-$A$ map on the compact abelian group $F((1/t))^d/F[t]^d$. We provide a complete characterization of when $\zeta_A(z)$ is algebraic and prove that it admits the circle of convergence as a natural boundary in the transcendence case. This is in stark contrast to the case of linear endomorphisms on $\mathbb{R}^d/\mathbb{Z}^d$ in which Baake, Lau, and Paskunas prove that the zeta function is always rational. Some connections to earlier work of Bell, Byszewski, Cornelissen, Miles, Royals, and Ward are discussed. Our method uses a similar technique in recent work of Bell, Nguyen, and Zannier together with certain patching arguments involving linear recurrence sequences.

Published
2022

56. A fusion variant of the classical and dynamical Mordell-Lang conjectures in positive characteristic

Author

Bell, Jason and Ghioca, Dragos

Subjects
Mathematics - Number Theory, Mathematics - Dynamical Systems
Abstract

We study an open question at the interplay between the classical and the dynamical Mordell-Lang conjectures in positive characteristic. Let $K$ be an algebraically closed field of positive characteristic, let $G$ be a finitely generated subgroup of the multiplicative group of $K$, and let $X$ be a (irreducible) quasiprojective variety defined over $K$. We consider $K$-valued sequences of the form $a_n:=f(\varphi^n(x_0))$, where $\varphi\colon X\rightarrow X$ and $f\colon X\rightarrow\mathbb{P}^1$ are rational maps defined over $K$ and $x_0\in X$ is a point whose forward orbit avoids the indeterminacy loci of $\varphi$ and $f$. We show that the set of $n$ for which $a_n\in G$ is a finite union of arithmetic progressions along with a set of upper Banach density zero. In addition, we show that if $a_n\in G$ for every $n$ and the $\varphi$ orbit of $x$ is Zariski dense in $X$ then {there is} a multiplicative torus $\mathbb{G}_m^d$ and maps $\Psi:\mathbb{G}_m^d \to \mathbb{G}_m^d$ and $g:\mathbb{G}_m^d \to \mathbb{G}_m$ such that $a_n = g\circ \Psi^n(y)$ for some $y\in \mathbb{G}_m^d$. We then describe various applications of our results., Comment: 13 pages. arXiv admin note: text overlap with arXiv:2005.04281

Published
2022

57. D-finiteness, rationality, and height II: lower bounds over a set of positive density

Author

Bell, Jason P., Nguyen, Khoa D., and Zannier, Umberto

Subjects
Mathematics - Number Theory
Abstract

We consider D-finite power series $f(z)=\sum a_n z^n$ with coefficients in a number field $K$. We show that there is a dichotomy governing the behaviour of $h(a_n)$ as a function of $n$, where $h$ is the absolute logarithmic Weil height. As an immediate consequence of our results, we have that either $f(z)$ is rational or $h(a_n)>[K:\mathbb{Q}]^{-1}\cdot \log(n)+O(1)$ for $n$ in a set of positive upper density and this is best possible when $K=\mathbb{Q}$., Comment: Minor change in the proof of Proposition 4.1

Published
2022

58. A conjecture strengthening the Zariski dense orbit problem for birational maps of dynamical degree one

Author

Bell, Jason and Ghioca, Dragos

Subjects
Mathematics - Dynamical Systems, Mathematics - Number Theory, Mathematics - Rings and Algebras, 11G10, 14K12, 37P55, 16S38
Abstract

We formulate a strengthening of the Zariski dense orbit conjecture for birational maps of dynamical degree one. So, given a quasiprojective variety $X$ defined over an algebraically closed field $K$ of characteristic $0$, endowed with a birational self-map $\phi$ of dynamical degree $1$, we expect that either there exists a non-constant rational function $f:X\dashrightarrow \mathbb{P}^1$ such that $f\circ \phi=f$, or there exists a proper subvariety $Y\subset X$ with the property that for any invariant proper subvariety $Z\subset X$, we have that $Z\subseteq Y$. We prove our conjecture for automorphisms $\phi$ of dynamical degree $1$ of semiabelian varieties $X$. Also, we prove a related result for regular dominant self-maps $\phi$ of semiabelian varieties $X$: assuming $\phi$ does not preserve a non-constant rational function, we have that the dynamical degree of $\phi$ is larger than $1$ if and only if the union of all $\phi$-invariant proper subvarieties of $X$ is Zariski dense. We give applications of our results to representation theoretic questions about twisted homogeneous coordinate rings associated to abelian varieties., Comment: 13 pages

Published
2022

59. $p$-Adic interpolation of orbits under rational maps

Author

Bell, Jason P. and Zhong, Xiao

Subjects
Mathematics - Number Theory, Mathematics - Dynamical Systems, 37F10, 37P20, 37P55
Abstract

Let $L$ be a field of characteristic zero, let $h:\mathbb{P}^1\to \mathbb{P}^1$ be a rational map defined over $L$, and let $c\in \mathbb{P}^1(L)$. We show that there exists a finitely generated subfield $K$ of $L$ over which both $c$ and $h$ are defined along with an infinite set of inequivalent non-archimedean completions $K_{\mathfrak{p}}$ for which there exists a positive integer $a=a(\mathfrak{p})$ with the property that for $i\in \{0,\ldots ,a-1\}$ there exists a power series $g_i(t)\in K_{\mathfrak{p}}[[t]]$ that converges on the closed unit disc of $K_{\mathfrak{p}}$ such that $h^{an+i}(c)=g_i(n)$ for all sufficiently large $n$. As a consequence we show that the dynamical Mordell-Lang conjecture holds for split self-maps $(h,g)$ of $\mathbb{P}^1 \times X$ with $g$ \'etale., Comment: 12 pages

Published
2022

60. $D$-finite multivariate series with arithmetic restrictions on their coefficients

Author

Bell, Jason and Smertnig, Daniel

Subjects
Mathematics - Combinatorics
Abstract

A multivariate, formal power series over a field $K$ is a B\'ezivin series if all of its coefficients can be expressed as a sum of at most $r$ elements from a finitely generated subgroup $G \le K^*$; it is a P\'olya series if one can take $r=1$. We give explicit structural descriptions of $D$-finite B\'ezivin series and $D$-finite P\'olya series over fields of characteristic $0$, thus extending classical results of P\'olya and B\'ezivin to the multivariate setting.

Published
2022

61. Topological invariants for words of linear factor complexity

Author

Bell, Jason

Subjects
Computer Science - Formal Languages and Automata Theory, 68R15, 68Q45, 11B85
Abstract

Given a finite alphabet $\Sigma$ and a right-infinite word $w$ over the alphabet $\Sigma$, we construct a topological space ${\rm Rec}(w)$ consisting of all right-infinite recurrent words whose factors are all factors of $w$, where we work up to an equivalence in which two words are equivalent if they have the exact same set of factors (finite contiguous subwords). We show that ${\rm Rec}(w)$ can be endowed with a natural topology and we show that if $w$ is word of linear factor complexity then ${\rm Rec}(w)$ is a finite topological space. In addition, we note that there are examples which show that if $f:\mathbb{N}\to \mathbb{N}$ is a function that tends to infinity as $n\to \infty$ then there is a word whose factor complexity function is ${\rm O}(nf(n))$ such that ${\rm Rec}(w)$ is an infinite set. Finally, we pose a realization problem: which finite topological spaces can arise as ${\rm Rec}(w)$ for a word of linear factor complexity?, Comment: 14 pages

Published
2022

62. USING OBJECTIVE CHARACTERISTICS TO TARGET HOUSEHOLD RECYCLING POLICIES

Author

Huber, Joel, Viscusi, W. Kip, and Bell, Jason

Subjects
Raw materials -- Waste management, Recycling (Waste, etc.), Environmental issues, Law
Abstract

Household recycling is valuable because it reduces demand for virgin raw materials and lessens the cost of making products containing paper, metal, glass, or plastic. Effective recycling programs limit the [...]

Published
2023

64. Cogrowth Series for Free Products of Finite Groups

Author

Bell, Jason, Liu, Haggai, and Mishna, Marni

Subjects
Mathematics - Combinatorics, 05Exx
Abstract

Given a finitely generated group with generating set $S$, we study the cogrowth sequence, which is the number of words of length $n$ over the alphabet $S$ that are equal to one. This is related to the probability of return for walks the corresponding Cayley graph. Muller and Schupp proved the generating function of the sequence is algebraic when $G$ has a finite-index free subgroup (using a result of Dunwoody). In this work we make this result effective for free products of finite groups: we determine bounds for the degree and height of the minimal polynomial of the generating function, and determine the minimal polynomial explicitly for some families of free products. Using these results we are able to prove that a gap theorem holds: if $S$ is a finite symmetric generating set for a group $G$ and if $a_n$ denotes the number of words of length $n$ over the alphabet $S$ that are equal to $1$ then $\limsup_n a_n^{1/n}$ exists and is either $1$, $2$, or at least $2\sqrt{2}$., Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:1805.08118

Published
2021
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65. Automatic Sequences of Rank Two

Author

Bell, Jason and Shallit, Jeffrey

Subjects
Computer Science - Formal Languages and Automata Theory, Computer Science - Discrete Mathematics
Abstract

Given a right-infinite word $\bf x$ over a finite alphabet $A$, the rank of $\bf x$ is the size of the smallest set $S$ of words over $A$ such that $\bf x$ can be realized as an infinite concatenation of words in $S$. We show that the property of having rank two is decidable for the class of $k$-automatic words for each integer $k\ge 2$.

Published
2021

66. Birational maps with transcendental dynamical degree

Author

Bell, Jason, Diller, Jeffrey, Jonsson, Mattias, and Krieger, Holly

Subjects
Mathematics - Dynamical Systems, Mathematics - Algebraic Geometry, Mathematics - Number Theory, 32H50 (primary), 37F10, 11J81, 14E05 (secondary)
Abstract

We give examples of birational selfmaps of $\mathbb{P}^d, d \geq 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation., Comment: To appear in Proc. Lond. Math. Soc

Published
2021

68. Bacille Calmette-Guérin vaccination to prevent febrile and respiratory illness in adults (BRACE): secondary outcomes of a randomised controlled phase 3 trial

Author

Curtis, Nigel, Davidson, Andrew, Gardiner, Kaya, Gwee, Amanda, Jamieson, Tenaya, Messina, Nicole, Morawakage, Thilanka, Perlen, Susan, Perrett, Kirsten, Pittet, Laure, Sastry, Amber, Teo, Jia Wei, Orsini, Francesca, Lee, Katherine, Moore, Cecilia, Vidmar, Suzanna, PITTET, Laure, Ali, Rashida, Dunn, Ross, Edler, Peta, Gell, Grace, Goodall, Casey, Hall, Richard, Krastev, Ann, La, Nathan, McDonald, Ellie, McPhate, Nick, Nguyen, Thao, Ren, Jack, Stevens, Luke, Alamrousi, Ahmed, Bonnici, Rhian, Dang, Thanh, Germano, Susie, Hua, Jenny, McElroy, Rebecca, Razmovska, Monica, Reddiex, Scott, Wang, Xiaofang, Anderson, Jeremy, Azzopardi, Kristy, Bennett-Wood, Vicki, Czajko, Anna, Mazarakis, Nadia, McCafferty, Conor, Oppedisano, Frances, Ortika, Belinda, Pell, Casey, Spry, Leena, Toh, Ryan, Velagapudi, Sunitha, Vlahos, Amanda, Wee-Hee, Ashleigh, Ramos, Pedro, De La Cruz, Karina, Gamage, Dinusha, Karunanayake, Anushka, Mezzetti, Isabella, Ong, Benjamin, Singh, Ronita, Sooriyarachchi, Enoshini, Nicholson, Suellen, Cain, Natalie, Brizuela, Rianne, Huang, Han, Abruzzo, Veronica, Bealing, Morgan, Bimboese, Patricia, Bowes, Kirsty, Burrell, Emma, Chan, Joyce, Cushnahan, Jac, Elborough, Hannah, Elkington, Olivia, Fahey, Kieran, Fernandez, Monique, Flynn, Catherine, Fowler, Sarah, Andrit, Marie Gentile, Gladanac, Bojana, Hammond, Catherine, Ma, Norine, Macalister, Sam, Milojevic, Emmah, Mojeed, Jesutofunmi, Nguyen, Jill, O'Donnell, Liz, Olivier, Nadia, Ooi, Isabelle, Reynolds, Stephanie, Shen, Lisa, Sherry, Barb, Spotswood, Judith, Wedderburn, Jamie, Younes, Angela, Legge, Donna, Bell, Jason, Cheah, Jo, Cobbledick, Annie, Lim, Kee, Elia, Sonja, Addlem, Lynne, Bourke, Anna, Brophy, Clare, Henare, Nadine, Jenkins, Narelle, Machingaifa, Francesca, Miller, Skye, Mitchell, Kirsten, Pitkin, Sigrid, Wall, Kate, Villanueva, Paola, Crawford, Nigel, Norton, Wendy, Tan, Niki, Chengodu, Thilakavathi, Dawson, Diane, Gordon, Victoria, Korman, Tony, O'Bryan, Jess, Agius, Sophie, Bannister, Samantha, Bucholc, Jess, Burns, Alison, Camesella, Beatriz, Carlin, John, Ciaverella, Marianna, Curtis, Maxwell, Firth, Stephanie, Guo, Christina, Hannan, Matthew, Hill, Erin, Joshi, Sri, Lieschke, Katherine, Mathers, Megan, Odoi, Sasha, Rak, Ashleigh, Richards, Chris, Steve, Leah, Stewart, Carolyn, Sudbury, Eva, Thomson, Helen, Watts, Emma, Williams, Fiona, Young, Angela, Glenn, Penny, Kaynes, Andrew, De Floy, Amandine Philippart, Buchanan, Sandy, Sondag, Thijs, Xie, Ivy, Edmund, Harriet, Byrne, Bridie, Keeble, Tom, Ngien, Belle, Noonan, Fran, Wearing-Smith, Michelle, Clarke, Alison, Davies, Pemma, Eastwood, Oliver, Ellinghaus, Alric, Ghieh, Rachid, Hilton, Zahra, Jennings, Emma, Kakkos, Athina, Liang, Iris, Nicol, Katie, O'Callaghan, Sally, Osman, Helen, Rajaram, Gowri, Ratcliffe, Sophia, Rayner, Victoria, Salmon, Ashleigh, Scheppokat, Angela, Stevens, Aimee, Street, Rebekah, Toogood, Nicholas, Wood, Nicholas, Bahaduri, Twinkle, Baulman, Therese, Byrne, Jennifer, Carter, Candace, Corbett, Mary, Dao, Aiken, Desylva, Maria, Dunn, Andrew, Gardiner, Evangeline, Joyce, Rosemary, Kandasamy, Rama, Munns, Craig, Pelayo, Lisa, Sharma, Ketaki, Sterling, Katrina, Uren, Caitlin, Colaco, Clinton, Douglas, Mark, Hamilton, Kate, Bartlett, Adam, McMullan, Brendan, Palasanthiran, Pamela, Williams, Phoebe, Beardsley, Justin, Bergant, Nikki, Lagunday, Renier, Overton, Kristen, Post, Jeffrey, Al-Hindawi, Yasmeen, Barney, Sarah, Byrne, Anthony, Mead, Lee, Plit, Marshall, Lynn, David, Benson, Saoirse, Blake, Stephen, Botten, Rochelle, Chern, Tee Yee, Eden, Georgina, Griffith, Liddy, James, Jane, Lynn, Miriam, Markow, Angela, Sacca, Domenic, Stevens, Natalie, Wesselingh, Steve, Doran, Catriona, Barry, Simone, Sawka, Alice, Evans, Sue, Goodchild, Louise, Heath, Christine, Krieg, Meredith, Marshall, Helen, McMillan, Mark, Walker, Mary, Richmond, Peter, Amenyogbe, Nelly, Anthony, Christina, Arnold, Annabelle, Arrowsmith, Beth, Ben-Othman, Rym, Clark, Sharon, Dunnill, Jemma, Eiffler, Nat, Ewe, Krist, Finucane, Carolyn, Flynn, Lorraine, Gibson, Camille, Hartnell, Lucy, Hollams, Elysia, Hutton, Heidi, Jarvis, Lance, Jones, Jane, Jones, Jan, Jones, Karen, Kent, Jennifer, Kollmann, Tobias, Lalich, Debbie, Lee, Wenna, Lim, Rachel, McAlister, Sonia, McDonald, Fiona, Meehan, Andrea, Minhaj, Asma, Montgomery, Lisa, O'Donnell, Melissa, Ong, Jaslyn, Ong, Joanne, Parkin, Kimberley, Perez, Glady, Power, Catherine, Rezazadeh, Shadie, Richmond, Holly, Rogers, Sally, Schultz, Nikki, Shave, Margaret, Skut, Patrycja, Stiglmayer, Lisa, Truelove, Alexandra, Wadia, Ushma, Wallace, Rachael, Waring, Justin, England, Michelle, Latkovic, Erin, Manning, Laurens, Herrmann, Susan, Lucas, Michaela, Lacerda, Marcus, Andrade, Paulo Henrique, Barbosa, Fabiane Bianca, Barros, Dayanne, Brasil, Larissa, Capella, Ana Greyce, Castro, Ramon, Costa, Erlane, de Souza, Dilcimar, Dias, Maianne, Dias, José, Ferreira, Klenilson, Figueiredo, Paula, Freitas, Thamires, Furtado, Ana Carolina, Gama, Larissa, Godinho, Vanessa, Gouy, Cintia, Hinojosa, Daniele, Jardim, Bruno, Jardim, Tyane, Junior, Joel, Lima, Augustto, Maia, Bernardo, Marins, Adriana, Mazurega, Kelry, Medeiros, Tercilene, Melo, Rosangela, Moraes, Marinete, Nascimento, Elizandra, Neves, Juliana, Oliveira, Maria Gabriela, Oliveira, Thais, Oliveira, Ingrid, Otsuka, Arthur, Paes, Rayssa, Pereira, Handerson, Pereira, Gabrielle, Prado, Christiane, Queiroz, Evelyn, Rodrigues, Laleyska, Rodrigues, Bebeto, Sampaio, Vanderson, Santos, Anna Gabriela, Santos, Daniel, Santos, Tilza, Santos, Evelyn, Sartim, Ariandra, Silva, Ana Beatriz, Silva, Juliana, Silva, Emanuelle, Simão, Mariana, Soares, Caroline, Sousa, Antonny, Trindade, Alexandre, Val, Fernando, Vasconcelos, Adria, Vasconcelos, Heline, Croda, Julio, Abreu, Carolinne, Almeida, Katya Martinez, Bitencourt de Andrade, Camila, Campos Angelo, Jhenyfer Thalyta, Gonçalvez de Araújo Arcanjo, Ghislaine, Silva Menezes Arruda, Bianca Maria, Ayala, Wellyngthon Espindola, Refosco Barbosa, Adelita Agripina, Vieira Batista, Felipe Zampieri, de Morais Batista, Fabiani, de Jesus Costa, Miriam, Croda, Mariana Garcia, Alves da Cruz, Lais, Pereira Diogo, Roberta Carolina, Dutra Escobar, Rodrigo Cezar, Fernandes, Iara Rodrigues, Figueiredo, Leticia Ramires, Cavalcanti Gonçalves, Leandro Galdino, Lahdo, Sarita, Lencina, Joyce dos Santos, Teodoro de Lima, Guilherme, LEOPOLDINA MEIRELES, Bruna Tayara, Moreira, Debora Quadros, Silva Muranaka, Lilian Batista, de Oliveira, Adriely, Warszawski de Oliveira, Karla Regina, Vieira de Oliveira, Matheus, Dias de Oliveira, Roberto, Pereira, Andrea Antonia Souza de Almeida dos Reis, Puga, Marco, Ramos, Caroliny Veron, Souza da Rosa, Thaynara Haynara, Lopes dos Santos, Karla, Ribeiro dos Santos, Claudinalva, Leopoldina dos Santos, Dyenyffer Stéffany, Santos, Karina Marques, Pereira da Silva, Paulo César, Rocha da Silva, Paulo Victor, Silva, Débora dos Santos, Vieira da Silva, Patricia, Freitas da Rosa Soares, Bruno, Sperotto, Mariana Gazzoni, Tadokoro, Mariana Mayumi, Tsuha, Daniel, Ramos Vieira, Hugo Miguel, Pretti Dalcolmo, Margareth Maria, Lopes Alves da Paixão, Cíntia Maria, Corrêa E Castro, Gabriela, Collopy, Simone Silva, da Costa Silva, Renato, Almeida da Silveira, Samyra, Da-Cruz, Alda Maria, Maria da Silva Passos de Carvalho, Alessandra, de Cássia Batista, Rita, Silva De Freitas, Maria Luciana, Gerhardt de Oliveira Ferreira, Aline, Conceição de Souza, Ana Paula, Doblas, Paola Cerbino, Alcoforado da Silva dos Santos, Ayla, Cristine de Moraes dos Santos, Vanessa, Alves dos Santos Gomes, Dayane, Fortunato, Anderson Lage, Gomes-Silva, Adriano, Gonçalves, Monique Pinto, Garcia Meireless Junior, Paulo Leandro, Martins da Costa Carvalho, Estela, Motta, Fernando do Couto, Olivo de Mendonça, Ligia Maria, Pandine, Girlene dos Santos, Plácido Pereira, Rosa Maria, Maia, Ivan Ramos, Luiz da Rocha, Jorge, Paiva Romano, João Victor, Santos, Glauce dos, Fernandes da Silva, Erica, Mendonça Teixeira de Siqueira, Marilda Agudo, Prudêncio Soares, Ágatha Cristinne, Bonten, Marc, Arroyo, Sandra Franch, Besten, Henny Ophorst-den, Boon, Anna, Brakke, Karin M., Janssen, Axel, Koopmans, Marijke A.H., Lemmens, Toos, Leurink, Titia, Prat-Aymerich, Cristina, Septer-Bijleveld, Engelien, Stadhouders, Kimberly, Troeman, Darren, van der Waal, Marije, van Opdorp, Marjoleine, van Sluis, Nicolette, Wolters, Beatrijs, Kluytmans, Jan, Romme, Jannie, van den Bijllaardt, Wouter, van Mook, Linda, Rijen, M.M.L (Miranda) van, Filius, P.M.G., Gisolf, Jet, Greven, Frances, Huijbens, Danique, Hassing, Robert Jan, Pon, R.C., Preijers, Lieke, van Leusen, J.H., Verheij, Harald, Boersma, Wim, Brans, Evelien, Kloeg, Paul, Molenaar-Groot, Kitty, Nguyen, Nhat Khanh, Paternotte, Nienke, Rol, Anke, Stooper, Lida, Dijkstra, Helga, Eggenhuizen, Esther, Huijs, Lucas, Moorlag, Simone, Netea, Mihai, Pranger, Eva, Taks, Esther, Oever, Jaap ten, Heine, Rob ter, Blauwendraat, Kitty, Meek, Bob, Erkaya, Isil, Harbech, Houda, Roescher, Nienke, Peeters, Rifka, Riele, Menno te, Zhou, Carmen, Calbo, Esther, Marti, Cristina Badia, Palomares, Emma Triviño, Porcuna, Tomás Perez, Barriocanal, Anabel, Barriocanal, Ana Maria, Casas, Irma, Dominguez, Jose, Esteve, Maria, Lacoma, Alicia, Latorre, Irene, Molina, Gemma, Molina, Barbara, Rosell, Antoni, Vidal, Sandra, Barrera, Lydia, Bustos, Natalia, Calderón, Ines Portillo, Campos, David Gutierrez, Carretero, Jose Manuel, Castellano, Angel Dominguez, Compagnone, Renato, Ramirez de Arellano, Encarnacion, Serna, Almudena de la, del Toro Lopez, Maria Dolores, Clement Espindola, Marie-Alix, Martin Gutierrez, Ana Belen, Hernandez, Alvaro Pascual, Jiménez, Virginia Palomo, Moreno, Elisa, Navarrete, Nicolas, Paño, Teresa Rodriguez, Rodríguez-Baño, Jesús, Tristán, Enriqueta, Rios Villegas, Maria Jose, Garces, Atsegiñe Canga, Amo, Erika Castro, Guerrero, Raquel Coya, Goikoetxea, Josune, Jorge, Leticia, Perez, Cristina, Fariñas Álvarez, María Carmen, Cuadra, Manuel Gutierrez, Arnaiz de las Revillas Almajano, Francisco, Garcia, Pilar Bohedo, Poderos, Teresa Giménez, Rico, Claudia González, Sanchez, Blanca, Valero, Olga, Vega, Noelia, Campbell, John, Barnes, Anna, Catterick, Helen, Cranston, Tim, Dawe, Phoebe, Fletcher, Emily, Fouracre, Liam, Gifford, Alison, Gow, Neil, Kirkwood, John, Martin, Christopher, McAnew, Amy, Mitchell, Marcus, Newman, Georgina, O'Connell, Abby, Onysk, Jakob, Quinn, Lynne, Rhodes, Shelley, Stone, Samuel, Symons, Lorrie, Tripp, Harry, Watkins, Darcy, Whale, Bethany, Harding, Alex, Lockhart, Gemma, Sidaway-Lee, Kate, Hilton, Sam, Manton, Sarah, Webber-Rookes, Daniel, Winder, Rachel, Moore, James, Bateman, Freya, Gibbons, Michael, Knight, Bridget, Moss, Julie, Statton, Sarah, Studham, Josephine, Hall, Lydia, Moyle, Will, Venton, Tamsin, Pittet, Laure F., Messina, Nicole L., Croda, Mariana G., Dalcolmo, Margareth, Lacerda, Marcus V.G., Lynn, David J., Perrett, Kirsten P., Post, Jeffrey J., Richmond, Peter C., Rocha, Jorge L., Rodriguez-Baño, Jesus, Warris, Adilia, and Wood, Nicholas J.

Published
2024
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69. Specific and off-target immune responses following COVID-19 vaccination with ChAdOx1-S and BNT162b2 vaccines—an exploratory sub-study of the BRACE trial

Author

Curtis, Nigel, Davidson, Andrew, Gardiner, Kaya, Gwee, Amanda, Jamieson, Tenaya, Messina, Nicole, Morawakage, Thilanka, Perlen, Susan, Perrett, Kirsten, Pittet, Laure, Sastry, Amber, Teo, Jia Wei, Orsini, Francesca, Lee, Katherine, Moore, Cecilia, Vidmar, Suzanna, Ali, Rashida, Dunn, Ross, Edler, Peta, Gell, Grace, Goodall, Casey, Hall, Richard, Krastev, Ann, La, Nathan, McDonald, Ellie, McPhate, Nick, Nguyen, Thao, Ren, Jack, Stevens, Luke, Alamrousi, Ahmed, Bonnici, Rhian, Dang, Thanh, Germano, Susie, Hua, Jenny, McElroy, Rebecca, Razmovska, Monica, Reddiex, Scott, Wang, Xiaofang, Anderson, Jeremy, Azzopardi, Kristy, Bennett-Wood, Vicki, Czajko, Anna, Mazarakis, Nadia, McCafferty, Conor, Oppedisano, Frances, Ortika, Belinda, Pell, Casey, Spry, Leena, Toh, Ryan, Velagapudi, Sunitha, Vlahos, Amanda, Wee-Hee, Ashleigh, Ramos, Pedro, De La Cruz, Karina, Gamage, Dinusha, Karunanayake, Anushka, Mezzetti, Isabella, Ong, Benjamin, Singh, Ronita, Sooriyarachchi, Enoshini, Nicholson, Suellen, Cain, Natalie, Brizuela, Rianne, Huang, Han, Abruzzo, Veronica, Bealing, Morgan, Bimboese, Patricia, Bowes, Kirsty, Burrell, Emma, Chan, Joyce, Cushnahan, Jac, Elborough, Hannah, Elkington, Olivia, Fahey, Kieran, Fernandez, Monique, Flynn, Catherine, Fowler, Sarah, Andrit, Marie Gentile, Gladanac, Bojana, Hammond, Catherine, Ma, Norine, Macalister, Sam, Milojevic, Emmah, Mojeed, Jesutofunmi, Nguyen, Jill, O’Donnell, Liz, Olivier, Nadia, Ooi, Isabelle, Reynolds, Stephanie, Shen, Lisa, Sherry, Barb, Spotswood, Judith, Wedderburn, Jamie, Younes, Angela, Legge, Donna, Bell, Jason, Cheah, Jo, Cobbledick, Annie, Lim, Kee, Elia, Sonja, Addlem, Lynne, Bourke, Anna, Brophy, Clare, Henare, Nadine, Jenkins, Narelle, Machingaifa, Francesca, Miller, Skye, Mitchell, Kirsten, Pitkin, Sigrid, Wall, Kate, Villanueva, Paola, Crawford, Nigel, Norton, Wendy, Tan, Niki, Chengodu, Thilakavathi, Dawson, Diane, Gordon, Victoria, Korman, Tony, O’Bryan, Jess, Agius, Sophie, Bannister, Samantha, Bucholc, Jess, Burns, Alison, Camesella, Beatriz, Carlin, John, Ciaverella, Marianna, Curtis, Maxwell, Firth, Stephanie, Guo, Christina, Hannan, Matthew, Hill, Erin, Joshi, Sri, Lieschke, Katherine, Mathers, Megan, Odoi, Sasha, Rak, Ashleigh, Richards, Chris, Steve, Leah, Stewart, Carolyn, Sudbury, Eva, Thomson, Helen, Watts, Emma, Williams, Fiona, Young, Angela, Glenn, Penny, Kaynes, Andrew, De Floy, Amandine Philippart, Buchanan, Sandy, Sondag, Thijs, Xie, Ivy, Edmund, Harriet, Byrne, Bridie, Keeble, Tom, Ngien, Belle, Noonan, Fran, Wearing-Smith, Michelle, Clarke, Alison, Davies, Pemma, Eastwood, Oliver, Ellinghaus, Alric, Ghieh, Rachid, Hilton, Zahra, Jennings, Emma, Kakkos, Athina, Liang, Iris, Nicol, Katie, O’Callaghan, Sally, Osman, Helen, Rajaram, Gowri, Ratcliffe, Sophia, Rayner, Victoria, Salmon, Ashleigh, Scheppokat, Angela, Stevens, Aimee, Street, Rebekah, Toogood, Nicholas, Wood, Nicholas, Bahaduri, Twinkle, Baulman, Therese, Byrne, Jennifer, Carter, Candace, Corbett, Mary, Dao, Aiken, Desylva, Maria, Dunn, Andrew, Gardiner, Evangeline, Joyce, Rosemary, Kandasamy, Rama, Munns, Craig, Pelayo, Lisa, Sharma, Ketaki, Sterling, Katrina, Uren, Caitlin, Colaco, Clinton, Douglas, Mark, Hamilton, Kate, Bartlett, Adam, McMullan, Brendan, Palasanthiran, Pamela, Williams, Phoebe, Beardsley, Justin, Bergant, Nikki, Lagunday, Renier, Overton, Kristen, Post, Jeffrey, Al-Hindawi, Yasmeen, Barney, Sarah, Byrne, Anthony, Mead, Lee, Plit, Marshall, Lynn, David, Benson, Saoirse, Blake, Stephen, Botten, Rochelle, Chern, Tee Yee, Eden, Georgina, Griffith, Liddy, James, Jane, Lynn, Miriam, Markow, Angela, Sacca, Domenic, Stevens, Natalie, Wesselingh, Steve, Doran, Catriona, Barry, Simone, Sawka, Alice, Evans, Sue, Goodchild, Louise, Heath, Christine, Krieg, Meredith, Marshall, Helen, McMillan, Mark, Walker, Mary, Richmond, Peter, Amenyogbe, Nelly, Anthony, Christina, Arnold, Annabelle, Arrowsmith, Beth, Ben-Othman, Rym, Clark, Sharon, Dunnill, Jemma, Eiffler, Nat, Ewe, Krist, Finucane, Carolyn, Flynn, Lorraine, Gibson, Camille, Hartnell, Lucy, Hollams, Elysia, Hutton, Heidi, Jarvis, Lance, Jones, Jane, Jones, Jan, Jones, Karen, Kent, Jennifer, Kollmann, Tobias, Lalich, Debbie, Lee, Wenna, Lim, Rachel, McAlister, Sonia, McDonald, Fiona, Meehan, Andrea, Minhaj, Asma, Montgomery, Lisa, O’Donnell, Melissa, Ong, Jaslyn, Ong, Joanne, Parkin, Kimberley, Perez, Glady, Power, Catherine, Rezazadeh, Shadie, Richmond, Holly, Rogers, Sally, Schultz, Nikki, Shave, Margaret, Skut, Patrycja, Stiglmayer, Lisa, Truelove, Alexandra, Wadia, Ushma, Wallace, Rachael, Waring, Justin, England, Michelle, Latkovic, Erin, Manning, Laurens, Herrmann, Susan, Lucas, Michaela, Lacerda, Marcus, Andrade, Paulo Henrique, Barbosa, Fabiane Bianca, Barros, Dayanne, Brasil, Larissa, Capella, Ana Greyce, Castro, Ramon, Costa, Erlane, de Souza, Dilcimar, Dias, Maianne, Dias, José, Ferreira, Klenilson, Figueiredo, Paula, Freitas, Thamires, Furtado, Ana Carolina, Gama, Larissa, Godinho, Vanessa, Gouy, Cintia, Hinojosa, Daniele, Jardim, Bruno, Jardim, Tyane, Junior, Joel, Lima, Augustto, Maia, Bernardo, Marins, Adriana, Mazurega, Kelry, Medeiros, Tercilene, Melo, Rosangela, Moraes, Marinete, Nascimento, Elizandra, Neves, Juliana, Oliveira, Maria Gabriela, Oliveira, Thais, Oliveira, Ingrid, Otsuka, Arthur, Paes, Rayssa, Pereira, Handerson, Pereira, Gabrielle, Prado, Christiane, Queiroz, Evelyn, Rodrigues, Laleyska, Rodrigues, Bebeto, Sampaio, Vanderson, Santos, Anna Gabriela, Santos, Daniel, Santos, Tilza, Santos, Evelyn, Sartim, Ariandra, Silva, Ana Beatriz, Silva, Juliana, Silva, Emanuelle, Simão, Mariana, Soares, Caroline, Sousa, Antonny, Trindade, Alexandre, Val, Fernando, Vasconcelos, Adria, Vasconcelos, Heline, Croda, Julio, Abreu, Carolinne, Almeida, Katya Martinez, Bitencourt de Andrade, Camila, Campos Angelo, Jhenyfer Thalyta, Gonçalvez de Araújo Arcanjo, Ghislaine, Silva Menezes Arruda, Bianca Maria, Ayala, Wellyngthon Espindola, Refosco Barbosa, Adelita Agripina, Vieira Batista, Felipe Zampieri, de Morais Batista, Fabiani, de Jesus Costa, Miriam, Croda, Mariana Garcia, Alves da Cruz, Lais, Pereira Diogo, Roberta Carolina, Dutra Escobar, Rodrigo Cezar, Fernandes, Iara Rodrigues, Figueiredo, Leticia Ramires, Cavalcanti Gonçalves, Leandro Galdino, Lahdo, Sarita, Lencina, Joyce dos Santos, Teodoro de Lima, Guilherme, Matos, Larissa Santos, Leopoldina Meireles, Bruna Tayara, Moreira, Debora Quadros, Silva Muranaka, Lilian Batista, de Oliveira, Adriely, Warszawski de Oliveira, Karla Regina, Vieira de Oliveira, Matheus, Dias de Oliveira, Roberto, Souza de Almeida dos Reis Pereira, Andrea Antonia, Puga, Marco, Ramos, Caroliny Veron, Souza da Rosa, Thaynara Haynara, Lopes dos Santos, Karla, Ribeiro dos Santos, Claudinalva, Leopoldina dos Santos, Dyenyffer Stéffany, Santos, Karina Marques, Pereira da Silva, Paulo César, Rocha da Silva, Paulo Victor, Silva, Débora dos Santos, Vieira da Silva, Patricia, Freitas da Rosa Soares, Bruno, Sperotto, Mariana Gazzoni, Tadokoro, Mariana Mayumi, Tsuha, Daniel, Ramos Vieira, Hugo Miguel, Pretti Dalcolmo, Margareth Maria, Lopes Alves da Paixão, Cíntia Maria, Corrêa E Castro, Gabriela, Collopy, Simone Silva, da Costa Silva, Renato, Almeida da Silveira, Samyra, Da-Cruz, Alda Maria, Maria da Silva Passos de Carvalho, Alessandra, de Cássia Batista, Rita, Silva De Freitas, Maria Luciana, Gerhardt de Oliveira Ferreira, Aline, Conceição de Souza, Ana Paula, Doblas, Paola Cerbino, Alcoforado da Silva dos Santos, Ayla, Cristine de Moraes dos Santos, Vanessa, Alves dos Santos Gomes, Dayane, Fortunato, Anderson Lage, Gomes-Silva, Adriano, Gonçalves, Monique Pinto, Garcia Meireless Junior, Paulo Leandro, Martins da Costa Carvalho, Estela, Motta, Fernando do Couto, Olivo de Mendonça, Ligia Maria, Pandine, Girlene dos Santos, Plácido Pereira, Rosa Maria, Maia, Ivan Ramos, Luiz da Rocha, Jorge, Paiva Romano, João Victor, Santos, Glauce dos, Fernandes da Silva, Erica, Mendonça Teixeira de Siqueira, Marilda Agudo, Prudêncio Soares, Ágatha Cristinne, Bonten, Marc, Arroyo, Sandra Franch, Besten, Henny Ophorst-den, Boon, Anna, Brakke, Karin M., Janssen, Axel, Koopmans, Marijke A.H., Lemmens, Toos, Leurink, Titia, Prat-Aymerich, Cristina, Septer-Bijleveld, Engelien, Stadhouders, Kimberly, Troeman, Darren, van der Waal, Marije, van Opdorp, Marjoleine, van Sluis, Nicolette, Wolters, Beatrijs, Kluytmans, Jan, Romme, Jannie, van den Bijllaardt, Wouter, van Mook, Linda, Rijen, M.M.L (Miranda) van, Filius, Margreet, Gisolf, Jet, Greven, Frances, Huijbens, Danique, Hassing, Robert Jan, Pon, Roos, Preijers, Lieke, van Leusen, Joke, Verheij, Harald, Boersma, Wim, Brans, Evelien, Kloeg, Paul, Molenaar-Groot, Kitty, Nguyen, Nhat Khanh, Paternotte, Nienke, Rol, Anke, Stooper, Lida, Dijkstra, Helga, Eggenhuizen, Esther, Huijs, Lucas, Moorlag, Simone, Netea, Mihai, Pranger, Eva, Taks, Esther, Oever, Jaap ten, Heine, Rob ter, Blauwendraat, Kitty, Meek, Bob, Erkaya, Isil, Harbech, Houda, Roescher, Nienke, Peeters, Rifka, Riele, Menno te, Zhou, Carmen, Calbo, Esther, Marti, Cristina Badia, Palomares, Emma Triviño, Porcuna, Tomás Perez, Barriocanal, Anabel, Barriocanal, Ana Maria, Casas, Irma, Dominguez, Jose, Esteve, Maria, Lacoma, Alicia, Latorre, Irene, Molina, Gemma, Molina, Barbara, Rosell, Antoni, Vidal, Sandra, Barrera, Lydia, Bustos, Natalia, Calderón, Ines Portillo, Campos, David Gutierrez, Carretero, Jose Manuel, Castellano, Angel Dominguez, Compagnone, Renato, Ramirez de Arellano, Encarnacion, Serna, Almudena de la, Dolores del Toro Lopez, Maria, Clement Espindola, Marie-Alix, Martin Gutierrez, Ana Belen, Hernandez, Alvaro Pascual, Jiménez, Virginia Palomo, Moreno, Elisa, Navarrete, Nicolas, Paño, Teresa Rodriguez, Rodríguez-Baño, Jesús, Tristán, Enriqueta, Rios Villegas, Maria Jose, Garces, Atsegiñe Canga, Amo, Erika Castro, Guerrero, Raquel Coya, Goikoetxea, Josune, Jorge, Leticia, Perez, Cristina, Fariñas Álvarez, María Carmen, Cuadra, Manuel Gutierrez, Arnaiz de las Revillas Almajano, Francisco, Garcia, Pilar Bohedo, Poderos, Teresa Giménez, Rico, Claudia González, Sanchez, Blanca, Valero, Olga, Vega, Noelia, Campbell, John, Barnes, Anna, Catterick, Helen, Cranston, Tim, Dawe, Phoebe, Fletcher, Emily, Fouracre, Liam, Gifford, Alison, Kirkwood, John, Martin, Christopher, McAnew, Amy, Mitchell, Marcus, Newman, Georgina, O’Connell, Abby, Onysk, Jakob, Quinn, Lynne, Rhodes, Shelley, Stone, Samuel, Symons, Lorrie, Tripp, Harry, Warris, Adilia, Watkins, Darcy, Whale, Bethany, Harding, Alex, Lockhart, Gemma, Sidaway-Lee, Kate, Hilton, Sam, Manton, Sarah, Webber-Rookes, Daniel, Winder, Rachel, Moore, James, Bateman, Freya, Gibbons, Michael, Knight, Bridget, Moss, Julie, Statton, Sarah, Studham, Josephine, Hall, Lydia, Moyle, Will, Venton, Tamsin, Messina, Nicole L., Grubor-Bauk, Branka, Lynn, David J., Perrett, Kirsten P., Pittet, Laure F., Rudraraju, Rajeev, Stevens, Natalie E., and Subbarao, Kanta

Published
2024
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70. On Dynamical Cancellation

Author

Bell, Jason P., Matsuzawa, Yohsuke, and Satriano, Matthew

Subjects
Mathematics - Algebraic Geometry, Mathematics - Dynamical Systems, Mathematics - Number Theory, 37P55, 14G05
Abstract

Let $X$ be a projective variety and let $f$ be a dominant endomorphism of $X$, both of which are defined over a number field $K$. We consider a question of the second author, Meng, Shibata, and Zhang, which asks whether the tower of $K$-points $Y(K)\subseteq (f^{-1}(Y))(K)\subseteq (f^{-2}(Y))(K)\subseteq \cdots$ eventually stabilizes, where $Y\subset X$ is a subvariety invariant under $f$. We show this question has an affirmative answer when the map $f$ is \'etale. We also look at a related problem of showing that there is some integer $s_0$, depending only on $X$ and $K$, such that whenever $x, y \in X(K)$ have the property that $f^{s}(x) = f^{s}(y)$ for some $s \geq 0$, we necessarily have $f^{s_{0}}(x) = f^{s_{0}}(y)$. We prove this holds for \'etale morphisms of projective varieties, as well as self-morphisms of smooth projective curves. We also prove a more general cancellation theorem for polynomial maps on $\mathbb{P}^1$ where we allow for composition by multiple different maps $f_1,\dots,f_r$., Comment: 27 pages

Published
2021

72. A Tits alternative for rational functions

Author

Bell, Jason P., Huang, Keping, Peng, Wayne, and Tucker, Thomas J.

Subjects
Mathematics - Number Theory, Mathematics - Algebraic Geometry, Mathematics - Group Theory, Primary: 20M05. Secondary: 14H37, 20D15
Abstract

We prove an analog of the Tits alternative for rational functions. In particular, we show that if $S$ is a finitely generated semigroup of rational functions over the complex numbers, then either $S$ has polynomially bounded growth or $S$ contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field that do not have the same set of preperiodic points, then the semigroup generated by f and g contains a nonabelian free semigroup., Comment: 16 pages

Published
2021

73. Lie complexity of words

Author

Bell, Jason P. and Shallit, Jeffrey

Subjects
Computer Science - Formal Languages and Automata Theory, Computer Science - Discrete Mathematics, Mathematics - Combinatorics, 68R15, 11B85
Abstract

Given a finite alphabet $\Sigma$ and a right-infinite word $\bf w$ over $\Sigma$, we define the Lie complexity function $L_{\bf w}:\mathbb{N}\to \mathbb{N}$, whose value at $n$ is the number of conjugacy classes (under cyclic shift) of length-$n$ factors $x$ of $\bf w$ with the property that every element of the conjugacy class appears in $\bf w$. We show that the Lie complexity function is uniformly bounded for words with linear factor complexity, and as a result we show that words of linear factor complexity have at most finitely many primitive factors $y$ with the property that $y^n$ is again a factor for every $n$. We then look at automatic sequences and show that the Lie complexity function of a $k$-automatic sequence is again $k$-automatic., Comment: 13 pages

Published
2021

74. Affine representability and decision procedures for commutativity theorems for rings and algebras

Author

Bell, Jason P. and Danchev, Peter V.

Subjects
Mathematics - Rings and Algebras, 16R10, 16R30, 16R60
Abstract

We consider applications of a finitary version of the Affine Representability theorem, which follows from recent work of Belov-Kanel, Rowen, and Vishne. Using this result we are able to show that when given a finite set of polynomial identities, there is an algorithm that terminates after a finite number of steps which decides whether these identities force a ring to be commutative. We then revisit old commutativity theorems of Jacobson and Herstein in light of this algorithm and obtain general results in this vein. In addition, we completely characterize the homogeneous multilinear identities that imply the commutativity of a ring., Comment: 30 pages, to appear in Israel J. Math. Proposition 5.2 added in this version; title changed from earlier version; Acknowledgment updated

Published
2020

75. Effective isotrivial Mordell-Lang in positive characteristic

Author

Bell, Jason, Ghioca, Dragos, and Moosa, Rahim

Subjects
Mathematics - Number Theory, Mathematics - Algebraic Geometry
Abstract

The isotrivial Mordell-Lang theorem of Moosa and Scanlon describes the set $X\cap\Gamma$ when $X$ is a subvariety of a semiabelian variety $G$ over a finite field $\mathbb{F}_q$ and $\Gamma$ is a finitely generated subgroup of $G$ that is invariant under the $q$-power Frobenius endomorphism $F$. That description is here made effective, and extended to arbitrary commutative algebraic groups $G$ and arbitrary finitely generated $\mathbb{Z}[F]$-submodules $\Gamma$. The approach is to use finite automata to give a concrete description of $X\cap \Gamma$. These methods and results have new applications even when specialised to the case when $G$ is an abelian variety over a finite field, $X\subseteq G$ a subvariety defined over a function field $K$, and $\Gamma=G(K)$. As an application of the automata-theoretic approach, a dichotomy theorem is established for the growth of the number of points in $X(K)$ of bounded height. As an application of the effective description of $X\cap\Gamma$, decision procedures are given for the following three diophantine problems: Is $X(K)$ nonempty? Is it infinite? Does it contain an infinite coset?

Published
2020

76. Autistic Traits Are Associated with Less Precise Perceptual Integration of Face Identity

Author

Turbett, Kaitlyn, Jeffery, Linda, Bell, Jason, Burton, Jessamy, and Palermo, Romina

Abstract

Face recognition difficulties are common in autism and could be a consequence of perceptual atypicalities that disrupt the ability to integrate current and prior information. We tested this theory by measuring the strength of serial dependence for faces (i.e. how likely is it that current perception of a face is biased towards a previously seen face) across the broader autism phenotype. Though serial dependence was not weaker in individuals with more autistic traits, more autistic traits were associated with greater integration of less similar faces. These results suggest that serial dependence is less specialised, and may not operate optimally, in individuals with more autistic traits and could therefore be a contributing factor to autism-linked face recognition difficulties.

Published
2022
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77. A serial mediation model of attentional engagement with thin bodies on body dissatisfaction: The role of appearance comparisons and rumination

Author

Dondzilo, Laura, Basanovic, Julian, Grafton, Ben, Bell, Jason, Turnbull, Georgia, and MacLeod, Colin

Subjects
Body image -- Research, Eating disorders -- Risk factors, Psychological research, Engagement (Philosophy) -- Health aspects -- Psychological aspects, Rumination (Psychology) -- Research, Attentional bias -- Research, Psychology and mental health
Abstract

The present study examined the associations among biased attentional responding to thin-ideal bodies, appearance comparisons, eating disorder-specific rumination, and body dissatisfaction. Sixty-seven females completed an attentional task capable of independently assessing biased attentional engagement with, and biased attentional disengagement from, images of thin-ideal bodies relative to images of non-thin bodies. Self-report measures of the other relevant constructs were also taken. Results revealed that a heightened tendency to engage in appearance comparisons was predicted by increased attentional engagement with thin-ideal bodies but not by impaired attentional disengagement from thin-ideal bodies. Moreover, a serial mediation analysis revealed that increased attentional engagement with thin-ideal bodies was associated with greater appearance comparison, which in turn was associated with greater eating disorder-specific rumination and consequently greater body dissatisfaction. The current findings suggest that increased attentional engagement with thin-ideal bodies might represent a pathway to body dissatisfaction, mediated by greater appearance comparison and eating-disorder specific rumination., Author(s): Laura Dondzilo [sup.1] [sup.2] , Julian Basanovic [sup.1] [sup.2] , Ben Grafton [sup.1] [sup.2] , Jason Bell [sup.2] , Georgia Turnbull [sup.2] , Colin MacLeod [sup.1] [sup.2] Author Affiliations: [...]

Published
2023
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78. AGENT A12 BRITAIN'S MAN IN BERLIN: Read how a dashing intellectual from Nova Scotia became a spy who warned the world of Nazi Germany's plans for a race war

Author

Bell, Jason

Subjects
Radicals -- Planning, Natural resources -- Germany -- Canada -- France -- United Kingdom, Company business planning, History
Abstract

Of the many important figures that had the bravery and conviction to stand up against Nazi Germany, one has remained unnoticed in war history until now. Recently declassified papers reveal [...]

Published
2023

79. On the importance of being primitive

Author

Bell, Jason P.

Subjects
Mathematics - Rings and Algebras, 16D60, 16A20, 16A32
Abstract

We give a brief survey of primitivity in ring theory and in particular look at characterizations of primitive ideals in the prime spectrum for various classes of rings., Comment: 18 pages, survey paper

Published
2020

80. Mahler's and Koksma's classifications in fields of power series

Author

Bell, Jason and Bugeaud, Yann

Subjects
Mathematics - Number Theory, 11J61, 11J04, 11J81
Abstract

Let $q$ a prime power and ${\mathbb F}_q$ the finite field of $q$ elements. We study the analogues of Mahler's and Koksma's classifications of complex numbers for power series in ${\mathbb F}_q((T^{-1}))$. Among other results, we establish that both classifications coincide, thereby answering a question of Ooto.

Published
2020

81. Rational dynamical systems, $S$-units, and $D$-finite power series

Author

Bell, Jason P., Chen, Shaoshi, and Hossain, Ehsaan

Subjects
Mathematics - Number Theory, Mathematics - Combinatorics
Abstract

Let $K$ be an algebraically closed field of characteristic zero and let $G$ be a finitely generated subgroup of the multiplicative group of $K$. We consider $K$-valued sequences of the form $a_n:=f(\varphi^n(x_0))$, where $\varphi\colon X\to X$ and $f\colon X\to\mathbb{P}^1$ are rational maps defined over $K$ and $x_0\in X$ is a point whose forward orbit avoids the indeterminacy loci of $\varphi$ and $f$. Many classical sequences from number theory and algebraic combinatorics fall under this dynamical framework, and we show that the set of $n$ for which $a_n\in G$ is a finite union of arithmetic progressions along with a set of Banach density zero. In addition, we show that if $a_n\in G$ for every $n$ and $X$ is irreducible and the $\varphi$ orbit of $x$ is Zariski dense in $X$ then there are a multiplicative torus $\mathbb{G}_m^d$ and maps $\Psi:\mathbb{G}_m^d \to \mathbb{G}_m^d$ and $g:\mathbb{G}_m^d \to \mathbb{G}_m$ such that $a_n = g\circ \Psi^n(y)$ for some $y\in \mathbb{G}_m^d$. We then obtain results about the coefficients of $D$-finite power series using these facts., Comment: 29 pages

Published
2020
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82. A height gap theorem for coefficients of Mahler functions

Author

Adamczewski, Boris, Bell, Jason, and Smertnig, Daniel

Subjects
Mathematics - Number Theory
Abstract

We study the asymptotic growth of coefficients of Mahler power series with algebraic coefficients, as measured by their logarithmic Weil height. We show that there are five different growth behaviors, all of which being reached. Thus, there are \emph{gaps} in the possible growths. In proving this height gap theorem, we obtain that a $k$-Mahler function is $k$-regular if and only if its coefficients have height in $O(\log n)$. Furthermore, we deduce that, over an arbitrary ground field of characteristic zero, a $k$-Mahler function is $k$-automatic if and only if its coefficients belong to a finite set. As a by-product of our results, we also recover a conjecture of Becker which was recently settled by Bell, Chyzak, Coons, and Dumas.

Published
2020

83. Height Gap Conjectures, $D$-Finiteness, and Weak Dynamical Mordell-Lang

Author

Bell, Jason P., Hu, Fei, and Satriano, Matthew

Subjects
Mathematics - Number Theory, Mathematics - Algebraic Geometry, Mathematics - Dynamical Systems
Abstract

In previous work, the first author, Ghioca, and the third author introduced a broad dynamical framework giving rise to many classical sequences from number theory and algebraic combinatorics. Specifically, these are sequences of the form $f(\Phi^n(x))$, where $\Phi\colon X\to X$ and $f\colon X\to\mathbb{P}^1$ are rational maps defined over $\overline{\mathbb{Q}}$ and $x\in X(\overline{\mathbb{Q}})$ is a point whose forward orbit avoids the indeterminacy loci of $\Phi$ and $f$. They conjectured that if the sequence is infinite, then $\limsup \frac{h(f(\Phi^n(x)))}{\log n} > 0$. They also made a corresponding conjecture for $\liminf$ and showed that it implies the Dynamical Mordell-Lang Conjecture. In this paper, we prove the $\limsup$ conjecture as well as the $\liminf$ conjecture away from a set of density $0$. As applications, we prove results concerning the growth rate of coefficients of $D$-finite power series as well as the Dynamical Mordell-Lang Conjecture up to a set of density $0$.

Published
2020
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84. The upper density of an automatic set is rational

Author

Bell, Jason P.

Subjects
Computer Science - Formal Languages and Automata Theory, 11B85, 68Q45
Abstract

Given a natural number $k\ge 2$ and a $k$-automatic set $S$ of natural numbers, we show that the lower density and upper density of $S$ are recursively computable rational numbers and we provide an algorithm for computing these quantities. In addition, we show that for every natural number $k\ge 2$ and every pair of rational numbers $(\alpha,\beta)$ with $0<\alpha<\beta<1$ or with $(\alpha,\beta)\in \{(0,0),(1,1)\}$ there is a $k$-automatic subset of the natural numbers whose lower density and upper density are $\alpha$ and $\beta$ respectively, and we show that these are precisely the values that can occur as the lower and upper densities of an automatic set., Comment: 16 pages. This version corrects the proof of Lemma 3.1 in addition to making other changes

Published
2020

85. An analogue of Ruzsa's conjecture for polynomials over finite fields

Author

Bell, Jason P. and Nguyen, Khoa D.

Subjects
Mathematics - Number Theory, 11T55
Abstract

In 1971, Ruzsa conjectured that if $f:\ \mathbb{N}\rightarrow\mathbb{Z}$ with $f(n+k)\equiv f(n)$ mod $k$ for every $n,k\in\mathbb{N}$ and $f(n)=O(\theta^n)$ with $\theta

Published
2019

86. Bacillus Calmette-Guérin vaccination for protection against recurrent herpes labialis: a nested randomised controlled trial

Author

Curtis, Nigel, Davidson, Andrew, Gardiner, Kaya, Gwee, Amanda, Jamieson, Tenaya, Messina, Nicole, Morawakage, Thilanka, Perlen, Susan, Perrett, Kirsten, Pittet, Laure, Sastry, Amber, Teo, Jia Wei, Orsini, Francesca, Lee, Katherine, Moore, Cecilia, Vidmar, Suzanna, Ali, Rashida, Dunn, Ross, Edler, Peta, Gell, Grace, Goodall, Casey, Hall, Richard, Krastev, Ann, La, Nathan, McDonald, Ellie, McPhate, Nick, Nguyen, Thao, Ren, Jack, Stevens, Luke, Alamrousi, Ahmed, Bonnici, Rhian, Dang, Thanh, Germano, Susie, Hua, Jenny, McElroy, Rebecca, Razmovska, Monica, Reddiex, Scott, Wang, Xiaofang, Anderson, Jeremy, Azzopardi, Kristy, Bennett-Wood, Vicki, Czajko, Anna, Mazarakis, Nadia, McCafferty, Conor, Oppedisano, Frances, Ortika, Belinda, Pell, Casey, Spry, Leena, Toh, Ryan, Velagapudi, Sunitha, Vlahos, Amanda, Wee-Hee, Ashleigh, Ramos, Pedro, De La Cruz, Karina, Gamage, Dinusha, Karunanayake, Anushka, Mezzetti, Isabella, Ong, Benjamin, Singh, Ronita, Sooriyarachchi, Enoshini, Nicholson, Suellen, Cain, Natalie, Brizuela, Rianne, Huang, Han, Abruzzo, Veronica, Bealing, Morgan, Bimboese, Patricia, Bowes, Kirsty, Burrell, Emma, Chan, Joyce, Cushnahan, Jac, Elborough, Hannah, Elkington, Olivia, Fahey, Kieran, Fernandez, Monique, Flynn, Catherine, Fowler, Sarah, Andrit, Marie Gentile, Gladanac, Bojana, Hammond, Catherine, Ma, Norine, Macalister, Sam, Milojevic, Emmah, Mojeed, Jesutofunmi, Nguyen, Jill, O'Donnell, Liz, Olivier, Nadia, Ooi, Isabelle, Reynolds, Stephanie, Shen, Lisa, Sherry, Barb, Spotswood, Judith, Wedderburn, Jamie, Younes, Angela, Legge, Donna, Bell, Jason, Cheah, Jo, Cobbledick, Annie, Lim, Kee, Elia, Sonja, Addlem, Lynne, Bourke, Anna, Brophy, Clare, Henare, Nadine, Jenkins, Narelle, Machingaifa, Francesca, Miller, Skye, Mitchell, Kirsten, Pitkin, Sigrid, Wall, Kate, Villanueva, Paola, Crawford, Nigel, Norton, Wendy, Tan, Niki, Chengodu, Thilakavathi, Dawson, Diane, Gordon, Victoria, Korman, Tony, O'Bryan, Jess, Agius, Sophie, Bannister, Samantha, Bucholc, Jess, Burns, Alison, Camesella, Beatriz, Carlin, John, Ciaverella, Marianna, Curtis, Maxwell, Firth, Stephanie, Guo, Christina, Hannan, Matthew, Hill, Erin, Joshi, Sri, Lieschke, Katherine, Mathers, Megan, Odoi, Sasha, Rak, Ashleigh, Richards, Chris, Steve, Leah, Stewart, Carolyn, Sudbury, Eva, Thomson, Helen, Watts, Emma, Williams, Fiona, Young, Angela, Glenn, Penny, Kaynes, Andrew, Philippart De Floy, Amandine, Buchanan, Sandy, Sondag, Thijs, Xie, Ivy, Edmund, Harriet, Byrne, Bridie, Keeble, Tom, Ngien, Belle, Noonan, Fran, Wearing-Smith, Michelle, Clarke, Alison, Davies, Pemma, Eastwood, Oliver, Ellinghaus, Alric, Ghieh, Rachid, Hilton, Zahra, Jennings, Emma, Kakkos, Athina, Liang, Iris, Nicol, Katie, O'Callaghan, Sally, Osman, Helen, Rajaram, Gowri, Ratcliffe, Sophia, Rayner, Victoria, Salmon, Ashleigh, Scheppokat, Angela, Stevens, Aimee, Street, Rebekah, Toogood, Nicholas, Wood, Nicholas, Bahaduri, Twinkle, Baulman, Therese, Byrne, Jennifer, Carter, Candace, Corbett, Mary, Dao, Aiken, Desylva, Maria, Dunn, Andrew, Gardiner, Evangeline, Joyce, Rosemary, Kandasamy, Rama, Munns, Craig, Pelayo, Lisa, Sharma, Ketaki, Sterling, Katrina, Uren, Caitlin, Colaco, Clinton, Douglas, Mark, Hamilton, Kate, Bartlett, Adam, McMullan, Brendan, Palasanthiran, Pamela, Williams, Phoebe, Beardsley, Justin, Bergant, Nikki, Lagunday, Renier, Overton, Kristen, Post, Jeffrey, Al-Hindawi, Yasmeen, Barney, Sarah, Byrne, Anthony, Mead, Lee, Plit, Marshall, Lynn, David, Benson, Saoirse, Blake, Stephen, Botten, Rochelle, Chern, Tee Yee, Eden, Georgina, Griffith, Liddy, James, Jane, Lynn, Miriam, Markow, Angela, Sacca, Domenic, Stevens, Natalie, Wesselingh, Steve, Doran, Catriona, Barry, Simone, Sawka, Alice, Evans, Sue, Goodchild, Louise, Heath, Christine, Krieg, Meredith, Marshall, Helen, McMillan, Mark, Walker, Mary, Richmond, Peter, Amenyogbe, Nelly, Anthony, Christina, Arnold, Annabelle, Arrowsmith, Beth, Ben-Othman, Rym, Clark, Sharon, Dunnill, Jemma, Eiffler, Nat, Ewe, Krist, Finucane, Carolyn, Flynn, Lorraine, Gibson, Camille, Hartnell, Lucy, Hollams, Elysia, Hutton, Heidi, Jarvis, Lance, Jones, Jane, Jones, Jan, Jones, Karen, Kent, Jennifer, Kollmann, Tobias, Lalich, Debbie, Lee, Wenna, Lim, Rachel, McAlister, Sonia, McDonald, Fiona, Meehan, Andrea, Minhaj, Asma, Montgomery, Lisa, O'Donnell, Melissa, Ong, Jaslyn, Ong, Joanne, Parkin, Kimberley, Perez, Glady, Power, Catherine, Rezazadeh, Shadie, Richmond, Holly, Rogers, Sally, Schultz, Nikki, Shave, Margaret, Skut, Patrycja, Stiglmayer, Lisa, Truelove, Alexandra, Wadia, Ushma, Wallace, Rachael, Waring, Justin, England, Michelle, Latkovic, Erin, Manning, Laurens, Herrmann, Susan, Lucas, Michaela, Lacerda, Marcus, Andrade, Paulo Henrique, Barbosa, Fabiane Bianca, Barros, Dayanne, Brasil, Larissa, Capella, Ana Greyce, Castro, Ramon, Costa, Erlane, de Souza, Dilcimar, Dias, Maianne, Dias, José, Ferreira, Klenilson, Figueiredo, Paula, Freitas, Thamires, Furtado, Ana Carolina, Gama, Larissa, Godinho, Vanessa, Gouy, Cintia, Hinojosa, Daniele, Jardim, Bruno, Jardim, Tyane, Junior, Joel, Lima, Augustto, Maia, Bernardo, Marins, Adriana, Mazurega, Kelry, Medeiros, Tercilene, Melo, Rosangela, Moraes, Marinete, Nascimento, Elizandra, Neves, Juliana, Oliveira, Maria Gabriela, Oliveira, Thais, Oliveira, Ingrid, Otsuka, Arthur, Paes, Rayssa, Pereira, Handerson, Pereira, Gabrielle, Prado, Christiane, Queiroz, Evelyn, Rodrigues, Laleyska, Rodrigues, Bebeto, Sampaio, Vanderson, Santos, Anna Gabriela, Santos, Daniel, Santos, Tilza, Santos, Evelyn, Sartim, Ariandra, Silva, Ana Beatriz, Silva, Juliana, Silva, Emanuelle, Simão, Mariana, Soares, Caroline, Sousa, Antonny, Trindade, Alexandre, Val, Fernando, Vasconcelos, Adria, Vasconcelos, Heline, Croda, Julio, Abreu, Carolinne, Almeida, Katya Martinez, Bitencourt de Andrade, Camila, Campos Angelo, Jhenyfer Thalyta, Gonçalvez de Araújo Arcanjo, Ghislaine, Silva Menezes Arruda, Bianca Maria, Ayala, Wellyngthon Espindola, Refosco Barbosa, Adelita Agripina, Vieira Batista, Felipe Zampieri, de Morais Batista, Fabiani, de Jesus Costa, Miriam, Croda, Mariana Garcia, Alves da Cruz, Lais, Pereira Diogo, Roberta Carolina, Dutra Escobar, Rodrigo Cezar, Fernandes, Iara Rodrigues, Figueiredo, Leticia Ramires, Cavalcanti Gonçalves, Leandro Galdino, Lahdo, Sarita, Lencina, Joyce dos Santos, Teodoro de Lima, Guilherme, Matos, Larissa Santos, Leopoldina Meireles, Bruna Tayara, Moreira, Debora Quadros, Silva Muranaka, Lilian Batista, de Oliveira, Adriely, Warszawski de Oliveira, Karla Regina, Vieira de Oliveira, Matheus, Dias de Oliveira, Roberto, Souza de Almeida dos Reis Pereira, Andrea Antonia, Puga, Marco, Ramos, Caroliny Veron, Souza da Rosa, Thaynara Haynara, Lopes dos Santos, Karla, Ribeiro dos Santos, Claudinalva, Leopoldina dos Santos, Dyenyffer Stéffany, Santos, Karina Marques, Pereira da Silva, Paulo César, Rocha da Silva, Paulo Victor, Silva, Débora dos Santos, Vieira da Silva, Patricia, Freitas da Rosa Soares, Bruno, Sperotto, Mariana Gazzoni, Tadokoro, Mariana Mayumi, Tsuha, Daniel, Ramos Vieira, Hugo Miguel, Pretti Dalcolmo, Margareth Maria, Lopes Alves da Paixão, Cíntia Maria, Corrêa E Castro, Gabriela, Collopy, Simone Silva, da Costa Silva, Renato, Almeida da Silveira, Samyra, Da-Cruz, Alda Maria, Maria da Silva Passos de Carvalho, Alessandra, de Cássia Batista, Rita, Silva De Freitas, Maria Luciana, Gerhardt de Oliveira Ferreira, Aline, Conceição de Souza, Ana Paula, Doblas, Paola Cerbino, Alcoforado da Silva dos Santos, Ayla, Cristine de Moraes dos Santos, Vanessa, Alves dos Santos Gomes, Dayane, Fortunato, Anderson Lage, Gomes-Silva, Adriano, Gonçalves, Monique Pinto, Garcia Meireless Junior, Paulo Leandro, Martins da Costa Carvalho, Estela, Motta, Fernando do Couto, Olivo de Mendonça, Ligia Maria, Pandine, Girlene dos Santos, Plácido Pereira, Rosa Maria, Maia, Ivan Ramos, Luiz da Rocha, Jorge, Paiva Romano, João Victor, Santos, Glauce dos, Fernandes da Silva, Erica, Mendonça Teixeira de Siqueira, Marilda Agudo, Prudêncio Soares, Ágatha Cristinne, Bonten, Marc, Arroyo, Sandra Franch, Besten, Henny Ophorst-den, Boon, Anna, Brakke, Karin M., Janssen, Axel, Koopmans, Marijke A.H., Lemmens, Toos, Leurink, Titia, Prat-Aymerich, Cristina, Septer-Bijleveld, Engelien, Stadhouders, Kimberly, Troeman, Darren, van der Waal, Marije, van Opdorp, Marjoleine, van Sluis, Nicolette, Wolters, Beatrijs, Kluytmans, Jan, Romme, Jannie, van den Bijllaardt, Wouter, van Mook, Linda, Rijen, M.M.L (Miranda) van, Filius, P.M.G., Gisolf, Jet, Greven, Frances, Huijbens, Danique, Hassing, Robert Jan, Pon, R.C., Preijers, Lieke, van Leusen, J.H., Verheij, Harald, Boersma, Wim, Brans, Evelien, Kloeg, Paul, Molenaar-Groot, Kitty, Nguyen, Nhat Khanh, Paternotte, Nienke, Rol, Anke, Stooper, Lida, Dijkstra, Helga, Eggenhuizen, Esther, Huijs, Lucas, Moorlag, Simone, Netea, Mihai, Pranger, Eva, Taks, Esther, Oever, Jaap ten, Heine, Rob ter, Blauwendraat, Kitty, Meek, Bob, Erkaya, Isil, Harbech, Houda, Roescher, Nienke, Peeters, Rifka, Riele, Menno te, Zhou, Carmen, Calbo, Esther, Marti, Cristina Badia, Palomares, Emma Triviño, Porcuna, Tomás Perez, Barriocanal, Anabel, Barriocanal, Ana Maria, Casas, Irma, Dominguez, Jose, Esteve, Maria, Lacoma, Alicia, Latorre, Irene, Molina, Gemma, Molina, Barbara, Rosell, Antoni, Vidal, Sandra, Barrera, Lydia, Bustos, Natalia, Calderón, Ines Portillo, Campos, David Gutierrez, Carretero, Jose Manuel, Castellano, Angel Dominguez, Compagnone, Renato, Ramirez de Arellano, Encarnacion, Serna, Almudena de la, Dolores del Toro Lopez, Maria, Clement Espindola, Marie-Alix, Martin Gutierrez, Ana Belen, Hernandez, Alvaro Pascual, Jiménez, Virginia Palomo, Moreno, Elisa, Navarrete, Nicolas, Paño, Teresa Rodriguez, Rodríguez-Baño, Jesús, Tristán, Enriqueta, Rios Villegas, Maria Jose, Garces, Atsegiñe Canga, Amo, Erika Castro, Guerrero, Raquel Coya, Goikoetxea, Josune, Jorge, Leticia, Perez, Cristina, Fariñas Álvarez, María Carmen, Cuadra, Manuel Gutierrez, Arnaiz de las Revillas Almajano, Francisco, Garcia, Pilar Bohedo, Poderos, Teresa Giménez, Rico, Claudia González, Sanchez, Blanca, Valero, Olga, Vega, Noelia, Campbell, John, Barnes, Anna, Catterick, Helen, Cranston, Tim, Dawe, Phoebe, Fletcher, Emily, Fouracre, Liam, Gifford, Alison, Kirkwood, John, Martin, Christopher, McAnew, Amy, Mitchell, Marcus, Newman, Georgina, O'Connell, Abby, Onysk, Jakob, Quinn, Lynne, Rhodes, Shelley, Stone, Samuel, Symons, Lorrie, Tripp, Harry, Warris, Adilia, Watkins, Darcy, Whale, Bethany, Harding, Alex, Lockhart, Gemma, Sidaway-Lee, Kate, Hilton, Sam, Manton, Sarah, Webber-Rookes, Daniel, Winder, Rachel, Moore, James, Bateman, Freya, Gibbons, Michael, Knight, Bridget, Moss, Julie, Statton, Sarah, Studham, Josephine, Hall, Lydia, Moyle, Will, Venton, Tamsin, Pittet, Laure F., Moore, Cecilia L., Dalcolmo, Margareth, Douglas, Mark W., Lacerda, Marcus V.G., Lynn, David J., de Oliveira, Roberto D., Perrett, Kirsten P., Richmond, Peter C., Rocha, Jorge L., Rodriguez-Baño, Jesus, Wood, Nicholas J., and Messina, Nicole L.

Published
2023
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88. Noncommutative analogues of a cancellation theorem of Abhyankar, Eakin, and Heinzer

Author

Bell, Jason P., Hamidizadeh, Maryam, Huang, Hongdi, and Venegas, Helbert

Subjects
Mathematics - Rings and Algebras, 16P99, 16W99
Abstract

Let $k$ be a field and let $A$ be a finitely generated $k$-algebra. The algebra $A$ is said to be cancellative if whenever $B$ is another $k$-algebra with the property that $A[x]\cong B[x]$ then we necessarily have $A\cong B$. An important result of Abhyankar, Eakin, and Heinzer shows that if $A$ is a finitely generated commutative integral domain of Krull dimension one then it is cancellative. We consider the question of cancellation for finitely generated not-necessarily-commutative domains of Gelfand-Kirillov dimension one, and show that such algebras are necessarily cancellative when the characteristic of the base field is zero. In particular, this recovers the cancellation result of Abhyankar, Eakin, and Heinzer in characteristic zero when one restricts to the commutative case. We also provide examples that show affine domains of Gelfand-Kirillov dimension one need not be cancellative when the base field has positive characteristic, giving a counterexample to a conjecture of Tang, the fourth-named author, and Zhang. In addition, we prove a skew analogue of the result of Abhyankar-Eakin-Heinzer, in which one works with skew polynomial extensions as opposed to ordinary polynomial rings., Comment: 19 pages

Published
2019

89. A refinement of Christol's theorem for algebraic power series

Author

Albayrak, Seda and Bell, Jason P.

Subjects
Mathematics - Number Theory, Mathematics - Combinatorics, 11B85, 12J25, 13J05
Abstract

A famous result of Christol gives that a power series $F(t)=\sum_{n\ge 0} f(n)t^n$ with coefficients in a finite field $\mathbb{F}_q$ of characteristic $p$ is algebraic over the field of rational functions in $t$ if and only if there is a finite-state automaton accepting the base-$p$ digits of $n$ as input and giving $f(n)$ as output for every $n\ge 0$. An extension of Christol's theorem, giving a complete description of the algebraic closure of $\mathbb{F}_q(t)$, was later given by Kedlaya. When one looks at the support of an algebraic power series, that is the set of $n$ for which $f(n)\neq 0$, a well-known dichotomy for sets generated by finite-state automata shows that the support set is either sparse---with the number of $n\le x$ for which $f(n)\neq 0$ bounded by a polynomial in $\log(x)$---or it is reasonably large in the sense that the number of $n\le x$ with $f(n)\neq 0$ grows faster than $x^{\alpha}$ for some positive $\alpha$. The collection of algebraic power series with sparse supports forms a ring and we give a purely algebraic characterization of this ring in terms of Artin-Schreier extensions and we extend this to the context of Kedlaya's work on generalized power series., Comment: 21 pages; statement of main theorem updated slightly

Published
2019

90. On the growth of algebras, semigroups, and hereditary languages

Author

Bell, Jason and Zelmanov, Efim

Subjects
Mathematics - Rings and Algebras, Mathematics - Group Theory, 16P90, 20M25
Abstract

We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras., Comment: 14 pages

Published
2019

91. A transcendental dynamical degree

Author

Bell, Jason P., Diller, Jeffrey, and Jonsson, Mattias

Subjects
Mathematics - Dynamical Systems, Mathematics - Algebraic Geometry, Mathematics - Number Theory, 32H50 (primary), 37F10, 11J81, 14E05 (secondary)
Abstract

We give an example of a dominant rational selfmap of the projective plane whose dynamical degree is a transcendental number., Comment: 26 pages. Exposition has been changed after receiving a careful referee report. To appear in Acta Math

Published
2019

92. Dynamical Uniform Bounds for Fibers and a Gap Conjecture

Author

Bell, Jason, Ghioca, Dragos, and Satriano, Matthew

Subjects
Mathematics - Number Theory, Mathematics - Algebraic Geometry, Mathematics - Dynamical Systems
Abstract

We prove a uniform version of the Dynamical Mordell-Lang Conjecture for \'etale maps; also, we obtain a gap result for the growth rate of heights of points in an orbit along an arbitrary endomorphism of a quasiprojective variety defined over a number field. More precisely, for our first result, we assume $X$ is a quasi-projective variety defined over a field $K$ of characteristic $0$, endowed with the action of an \'etale endomorphism $\Phi$, and $f\colon X\to Y$ is a morphism with $Y$ a quasi-projective variety defined over $K$. Then for any $x\in X(K)$, if for each $y\in Y(K)$, the set $S_y:=\{n\in \mathbb{N}\colon f(\Phi^n(x))=y\}$ is finite, then there exists a positive integer $N$ such that $\#S_y\le N$ for each $y\in Y(K)$. For our second result, we let $K$ be a number field, $f:X\dashrightarrow \mathbb{P}^1$ is a rational map, and $\Phi$ is an arbitrary endomorphism of $X$. If $\mathcal{O}_\Phi(x)$ denotes the forward orbit of $x$ under the action of $\Phi$, then either $f(\mathcal{O}_\Phi(x))$ is finite, or $\limsup_{n\to\infty} h(f(\Phi^n(x)))/\log(n)>0$, where $h(\cdot)$ represents the usual logarithmic Weil height for algebraic points.

Published
2019

93. Noncommutative rational P\'olya series

Author

Bell, Jason and Smertnig, Daniel

Subjects
Mathematics - Combinatorics, Mathematics - Number Theory, Primary 68Q45, 68Q70, Secondary 11B37
Abstract

A (noncommutative) P\'olya series over a field $K$ is a formal power series whose nonzero coefficients are contained in a finitely generated subgroup of $K^\times$. We show that rational P\'olya series are unambiguous rational series, proving a 40 year old conjecture of Reutenauer. The proof combines methods from noncommutative algebra, automata theory, and number theory (specifically, unit equations). As a corollary, a rational series is a P\'olya series if and only if it is Hadamard sub-invertible. Phrased differently, we show that every weighted finite automaton taking values in a finitely generated subgroup of a field (and zero) is equivalent to an unambiguous weighted finite automaton., Comment: 35 pages; added several examples

Published
2019

94. D-finiteness, rationality, and height

Author

Bell, Jason P., Nguyen, Khoa D., and Zannier, Umberto

Subjects
Mathematics - Number Theory, Primary: 11D61, 11G50. Secondary: 13F25
Abstract

Motivated by a result of van der Poorten and Shparlinski for univariate power series, Bell and Chen prove that if a multivariate power series over a field of characteristic 0 is D-finite and its coefficients belong to a finite set then it is a rational function. We extend and strengthen their results to certain power series whose coefficients may form an infinite set. We also prove that if the coefficients of a univariate D-finite power series `look like' the coefficients of a rational function then the power series is rational. Our work relies on the theory of Weil heights, the Manin-Mumford theorem for tori, an application of the Subspace Theorem, and various combinatorial arguments involving heights, power series, and linear recurrence sequences., Comment: 18 pages, comments are welcome

Published
2019

95. Promoting circular-orderability to left-orderability

Author

Bell, Jason, Clay, Adam, and Ghaswala, Tyrone

Subjects
Mathematics - Group Theory, Mathematics - Dynamical Systems, Mathematics - Geometric Topology, 20F60 (Primary) 37E10, 57M27 (Secondary)
Abstract

Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group $G$ is left-orderable if and only if $G \times \mathbb{Z}/n\mathbb{Z}$ is circularly-orderable for all $n > 1$. This implies that every circularly-orderable group which is not left-orderable gives rise to a collection of positive integers that exactly encode the obstruction to left-orderability, which we call the obstruction spectrum. We precisely describe the behaviour of the obstruction spectrum with respect to torsion, and show that this same behaviour can be mirrored by torsion-free groups, whose obstruction spectra are in general more complex., Comment: Revised version. A new section has been added to include a new result shown to us by Dave Morris. Changes have been made to improve the readability and to streamline some of the proofs. To appear in Annales de l'institut Fourier

Published
2019

99. Invariant hypersurfaces

Author

Bell, Jason, Moosa, Rahim, and Topaz, Adam

Subjects
Mathematics - Algebraic Geometry, Mathematics - Logic, Primary 14E99, Secondary 12H05 and 12H10
Abstract

The following theorem, which includes as very special cases results of Jouanolou and Hrushovski on algebraic $D$-varieties on the one hand, and of Cantat on rational dynamics on the other, is established: Working over a field of characteristic zero, suppose $\phi_1,\phi_2: Z \to X$ are dominant rational maps from a (possibly nonreduced) irreducible scheme $Z$ of finite-type to an algebraic variety $X$, with the property that there are infinitely many hypersurfaces on $X$ whose scheme-theoretic inverse images under $\phi_1$ and $\phi_2$ agree. Then there is a nonconstant rational function $g$ on $X$ such that $g\phi_1=g\phi_2$. In the case when $Z$ is also reduced the scheme-theoretic inverse image can be replaced by the proper transform. A partial result is obtained in positive characteristic. Applications include an extension of the Jouanolou-Hrushovski theorem to generalised algebraic $\mathcal D$-varieties and of Cantat's theorem to self-correspondences., Comment: Final version following minor changes suggested by the referee

Published
2018
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100. On free subgroups in division rings

Author

Bell, Jason P. and Goncalves, Jairo

Subjects
Mathematics - Rings and Algebras, 12E15, 16K40, 20E05
Abstract

Let $K$ be a field and let $\sigma$ be an automorphism and let $\delta$ be a $\sigma$-derivation of $K$. Then we show that the multiplicative group of nonzero elements of the division ring $D=K(x;\sigma,\delta)$ contains a free non-cyclic subgroup unless $D$ is commutative, answering a special case of a conjecture of Lichtman. As an application, we show that division algebras formed by taking the Goldie ring of quotients of group algebras of torsion-free non-abelian solvable-by-finite groups always contain free non-cyclic subgroups., Comment: nine pages

Published
2018

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