781 results on '"Bell, Jason"'
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2. Consecutive Power Occurrences in Sturmian Words
- Author
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Bell, Jason, Schulz, Chris, and Shallit, Jeffrey
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Mathematics - Combinatorics ,Computer Science - Discrete Mathematics ,Computer Science - Formal Languages and Automata Theory ,Mathematics - Number Theory - Abstract
We show that every Sturmian word has the property that the distance between consecutive ending positions of cubes occurring in the word is always bounded by $10$ and this bound is optimal, extending a result of Rampersad, who proved that the bound $9$ holds for the Fibonacci word. We then give a general result showing that for every $e \in [1,(5+\sqrt{5})/2)$ there is a natural number $N$, depending only on $e$, such that every Sturmian word has the property that the distance between consecutive ending positions of $e$-powers occurring in the word is uniformly bounded by $N$.
- Published
- 2024
3. Noncommutative point spaces of symbolic dynamical systems
- Author
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Bell, Jason P. and Greenfeld, Be'eri
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Mathematics - Rings and Algebras ,14A22, 16S38, 37B10, 16D90 - Abstract
We study point modules of monomial algebras associated with symbolic dynamical systems, parametrized by proalgebraic varieties which 'linearize' the underlying dynamical systems. Faithful point modules correspond to transitive sub-systems, equivalently, to monomial algebras associated with infinite words. In particular, we prove that the space of point modules of every prime monomial algebra with Hilbert series $1/(1-t)^2$ -- which is thus thought of as a 'monomial $\mathbb{P}^1$' -- is isomorphic to a union of a classical projective line with a Cantor set. While there is a continuum of monomial $\mathbb{P}^1$'s with non-equivalent graded module categories, they all share isomorphic parametrizing spaces of point modules. In contrast, free algebras are geometrically rigid, and are characterized up to isomorphism from their spaces of point modules. Furthermore, we derive enumerative and ring-theoretic consequences from our analysis. In particular, we show that the formal power series counting the irreducible components of the moduli schemes of truncated point modules of finitely presented monomial algebras are rational functions, and classify isomorphisms and automorphisms of projectively simple monomial algebras.
- Published
- 2024
4. Fostering Recycling Participation in Wisconsin Households through Single-Stream Programs
- Author
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Bell, Jason, Huber, Joel, and Viscusi, W. Kip
- Published
- 2017
5. Filtered deformations of commutative algebras of Krull dimension two
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Bell, Jason
- Subjects
Mathematics - Rings and Algebras ,Mathematics - Quantum Algebra ,16S80, 16S38, 13A335 - Abstract
Let $F$ be an algebraically closed field of positive characteristic and let $R$ be a finitely generated $F$-algebra with a filtration with the property that the associated graded ring of $R$ is an integral domain of Krull dimension two. We show that under these conditions $R$ satisfies a polynomial identity, answering a question of Etingof in the affirmative in a special case., Comment: 9 pages
- Published
- 2023
6. Sparse regular subsets of the reals
- Author
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Bell, Jason and Gorman, Alexi Block
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Mathematics - Logic ,Computer Science - Formal Languages and Automata Theory ,03C64, 03D05, 28A80 - Abstract
This paper concerns the expansion of the real ordered additive group by a predicate for a subset of $[0,1]$ whose base-$r$ representations are recognized by a B\"uchi automaton. In the case that this predicate is closed, a dichotomy is established for when this expansion is interdefinable with the structure $(\mathbb{R},<,+,0,r^{-\mathbb{N}})$ for some $r \in \mathbb{N}_{>1}$. In the case that the closure of the predicate has Hausdorff dimension less than $1$, the dichotomy further characterizes these expansions of $(\mathbb{R},<,+,0,1)$ by when they have NIP and NTP$_2$, which is precisely when the closure of the predicate has Hausdorff dimension $0$., Comment: 25 pages
- Published
- 2023
7. Maximal dimensional subalgebras of general Cartan type Lie algebras
- Author
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Bell, Jason and Buzaglo, Lucas
- Subjects
Mathematics - Rings and Algebras ,Primary: 17B66, 17B35, 16P40. Secondary: 17B65, 17B68 - Abstract
Let $\Bbbk$ be a field of characteristic zero and let $\mathbb{W}_n = \operatorname{Der}(\Bbbk[x_1,\cdots,x_n])$ be the $n^{\text{th}}$ general Cartan type Lie algebra. In this paper, we study Lie subalgebras $L$ of $\mathbb{W}_n$ of maximal Gelfand--Kirillov (GK) dimension, that is, with $\operatorname{GKdim}(L) = n$. For $n = 1$, we completely classify such $L$, proving a conjecture of the second author. As a corollary, we obtain a new proof that $\mathbb{W}_1$ satisfies the Dixmier conjecture, in other words, $\operatorname{End}(\mathbb{W}_1) \setminus \{0\} = \operatorname{Aut}(\mathbb{W}_1)$, a result first shown by Du. For arbitrary $n$, we show that if $L$ is a GK-dimension $n$ subalgebra of $\mathbb{W}_n$, then $U(L)$ is not (left or right) noetherian., Comment: 16 pages. Comments welcome!
- Published
- 2023
8. Machine learning : hands-on for developers and technical professionals.
- Author
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Bell, Jason
- Subjects
Algorithms ,Computers and IT ,Machine theory - Abstract
Summary: This book provides hands-on instruction and fully-coded working examples for the most common machine learning techniques used by developers and technical professionals. It contains a breakdown of each ML variant, explaining how it works and how it is used within certain industries, allowing readers to incorporate the presented techniques into their own work as they follow along. It is an accessible, comprehensive guide for the non-mathematician, providing clear guidance that allows readers to: learn the languages of machine learning including Hadoop, Mahout, and Weka; understand decision trees, Bayesian networks, and artificial neural networks; implement association rule, real time, and batch learning; develop a strategic plan for safe, effective, and efficient machine learning
- Published
- 2020
9. Invariant rational functions under rational transformations
- Author
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Bell, Jason, Moosa, Rahim, and Satriano, Matthew
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Mathematics - Algebraic Geometry ,Mathematics - Dynamical Systems ,Mathematics - Logic ,14E07, 12H10, 12L12 - Abstract
Let $X$ be an algebraic variety equipped with a dominant rational self-map $\phi:X\to X$. A new quantity measuring the interaction of $(X,\phi)$ with trivial dynamical systems is introduced; the stabilised algebraic dimension of $(X,\phi)$ captures the maximum number of new algebraically independent invariant rational functions on the cartesian product of $(X, \phi)$ and $(Y, \psi)$, as $(Y,\psi)$ ranges over all algebraic dynamical systems. It is shown that this birational invariant agrees with the maximum dimension of a dominant equivariant rational image $(X',\phi')$ where $\phi'$ is part of an algebraic group action on $X'$. As a consequence, it is deduced that if some cartesian power of $(X,\phi)$ admits a nonconstant invariant rational function, then already the second cartesian power does., Comment: 20 pages, to appear in Selecta
- Published
- 2023
10. D-finiteness, rationality, and height III: multivariate P\'olya-Carlson dichotomy
- Author
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Bell, Jason P., Chen, Shaoshi, Nguyen, Khoa D., and Zannier, Umberto
- Subjects
Mathematics - Number Theory - Abstract
We prove a result that can be seen as an analogue of the P\'olya-Carlson theorem for multivariate D-finite power series with coefficients in $\bar{\mathbb{Q}}$. In the special case that the coefficients are algebraic integers, our main result says that if $$F(x_1,\ldots ,x_m)=\sum f(n_1,\ldots ,n_m)x_1^{n_1}\cdots x_m^{n_m}$$ is a D-finite power series in $m$ variables with algebraic integer coefficients and if the logarithmic Weil height of $f(n_1,\ldots ,n_m)$ is $o(n_1+\cdots +n_m)$, then $F$ is a rational function and, up to scalar multiplication, every irreducible factor of the denominator of $F$ has the form $1-\zeta x_1^{q_1}\cdots x_m^{q_m}$ where $\zeta$ is a root of unity and $q_1,\ldots ,q_m$ are nonnegative integers, not all of which are zero.
- Published
- 2023
11. Duality of Lattices Associated to Left and Right Quotients
- Author
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Bell, Jason, Smertnig, Daniel, and Tamm, Hellis
- Subjects
Computer Science - Formal Languages and Automata Theory - Abstract
We associate lattices to the sets of unions and intersections of left and right quotients of a regular language. For both unions and intersections, we show that the lattices we produce using left and right quotients are dual to each other. We also give necessary and sufficient conditions for these lattices to have maximal possible complexity., Comment: In Proceedings AFL 2023, arXiv:2309.01126
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- 2023
- Full Text
- View/download PDF
12. Counting points by height in semigroup orbits
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Bell, Jason P., Hindes, Wade, and Zhong, Xiao
- Subjects
Mathematics - Number Theory ,Mathematics - Dynamical Systems - Abstract
We improve known estimates for the number of points of bounded height in semigroup orbits of polarized dynamical systems. In particular, we give exact asymptotics for generic semigroups acting on the projective line. The main new ingredient is the Wiener-Ikehara Tauberian theorem, which we use to count functions in semigroups of bounded degree.
- Published
- 2023
13. Quantitative estimates for the size of an intersection of sparse automatic sets
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Albayrak, Seda and Bell, Jason
- Subjects
Computer Science - Formal Languages and Automata Theory ,Mathematics - Number Theory ,68Q45, 11B85 - Abstract
A theorem of Cobham says that if $k$ and $\ell$ are two multiplicatively independent natural numbers then a subset of the natural numbers that is both $k$- and $\ell$-automatic is eventually periodic. A multidimensional extension was later given by Semenov. In this paper, we give a quantitative version of the Cobham-Semenov theorem for sparse automatic sets, showing that the intersection of a sparse $k$-automatic subset of $\mathbb{N}^d$ and a sparse $\ell$-automatic subset of $\mathbb{N}^d$ is finite with size that can be explicitly bounded in terms of data from the automata that accept these sets., Comment: 14 pages
- Published
- 2023
14. On the Task and Historical Position of the Logical Investigations
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Husserl, Edmund, Bonnemann, Catharina, and Bell, Jason
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- 2012
15. Investigating Husserl's Newly Discovered Manuscript, "On the Task and Historical Position of the Logical Investigations "
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Bell, Jason and Bonnemann, Catharina
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- 2012
16. Introduction: On the Discovery of Two Manuscripts by Edmund Husserl
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Bell, Jason
- Published
- 2012
17. The German Translation of Royce's Epistemology by Husserl's Student Winthrop Bell: A Neglected Bridge of Pragmatic-Phenomenological Interpretation?
- Author
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Bell, Jason M.
- Published
- 2011
18. Filtered deformations of commutative algebras of Krull dimension two
- Author
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Bell, Jason P.
- Published
- 2024
- Full Text
- View/download PDF
19. D-finiteness, rationality, and height III: multivariate Pólya–Carlson dichotomy
- Author
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Bell, Jason P., Chen, Shaoshi, Nguyen, Khoa D., and Zannier, Umberto
- Published
- 2024
- Full Text
- View/download PDF
20. Assembly mechanism and cryoEM structure of RecA recombination nucleofilaments from Streptococcus pneumoniae
- Author
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Hertzog, Maud, Perry, Thomas Noé, Dupaigne, Pauline, Serres, Sandra, Morales, Violette, Soulet, Anne-Lise, Bell, Jason C, Margeat, Emmanuel, Kowalczykowski, Stephen C, Le Cam, Eric, Fronzes, Rémi, and Polard, Patrice
- Subjects
Biochemistry and Cell Biology ,Bioinformatics and Computational Biology ,Biological Sciences ,Lung ,Pneumonia ,Pneumonia & Influenza ,1.1 Normal biological development and functioning ,Underpinning research ,Generic health relevance ,Infection ,Adenosine Triphosphate ,DNA ,DNA ,Single-Stranded ,Escherichia coli ,Rec A Recombinases ,Streptococcus pneumoniae ,Cryoelectron Microscopy ,Environmental Sciences ,Information and Computing Sciences ,Developmental Biology ,Biological sciences ,Chemical sciences ,Environmental sciences - Abstract
RecA-mediated homologous recombination (HR) is a key mechanism for genome maintenance and plasticity in bacteria. It proceeds through RecA assembly into a dynamic filament on ssDNA, the presynaptic filament, which mediates DNA homology search and ordered DNA strand exchange. Here, we combined structural, single molecule and biochemical approaches to characterize the ATP-dependent assembly mechanism of the presynaptic filament of RecA from Streptococcus pneumoniae (SpRecA), in comparison to the Escherichia coli RecA (EcRecA) paradigm. EcRecA polymerization on ssDNA is assisted by the Single-Stranded DNA Binding (SSB) protein, which unwinds ssDNA secondary structures that block EcRecA nucleofilament growth. We report by direct microscopic analysis of SpRecA filamentation on ssDNA that neither of the two paralogous pneumococcal SSBs could assist the extension of SpRecA nucleopolymers. Instead, we found that the conserved RadA helicase promotes SpRecA nucleofilamentation in an ATP-dependent manner. This allowed us to solve the atomic structure of such a long native SpRecA nucleopolymer by cryoEM stabilized with ATPγS. It was found to be equivalent to the crystal structure of the EcRecA filament with a marked difference in how RecA mediates nucleotide orientation in the stretched ssDNA. Then, our results show that SpRecA and EcRecA HR activities are different, in correlation with their distinct ATP-dependent ssDNA binding modes.
- Published
- 2023
21. BRCA2 chaperones RAD51 to single molecules of RPA-coated ssDNA
- Author
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Bell, Jason C, Dombrowski, Christopher C, Plank, Jody L, Jensen, Ryan B, and Kowalczykowski, Stephen C
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Biological Sciences ,Biomedical and Clinical Sciences ,Oncology and Carcinogenesis ,Genetics ,Breast Cancer ,Cancer ,Biotechnology ,2.1 Biological and endogenous factors ,Aetiology ,Humans ,BRCA2 Protein ,DNA ,DNA ,Single-Stranded ,Genes ,BRCA2 ,Homologous Recombination ,Protein Binding ,Rad51 Recombinase ,Replication Protein A ,DNA recombination ,DNA repair ,breast cancer ,RAD51 ,single-molecule visualization - Abstract
Mutations in the breast cancer susceptibility gene, BRCA2, greatly increase an individual's lifetime risk of developing breast and ovarian cancers. BRCA2 suppresses tumor formation by potentiating DNA repair via homologous recombination. Central to recombination is the assembly of a RAD51 nucleoprotein filament, which forms on single-stranded DNA (ssDNA) generated at or near the site of chromosomal damage. However, replication protein-A (RPA) rapidly binds to and continuously sequesters this ssDNA, imposing a kinetic barrier to RAD51 filament assembly that suppresses unregulated recombination. Recombination mediator proteins-of which BRCA2 is the defining member in humans-alleviate this kinetic barrier to catalyze RAD51 filament formation. We combined microfluidics, microscopy, and micromanipulation to directly measure both the binding of full-length BRCA2 to-and the assembly of RAD51 filaments on-a region of RPA-coated ssDNA within individual DNA molecules designed to mimic a resected DNA lesion common in replication-coupled recombinational repair. We demonstrate that a dimer of RAD51 is minimally required for spontaneous nucleation; however, growth self-terminates below the diffraction limit. BRCA2 accelerates nucleation of RAD51 to a rate that approaches the rapid association of RAD51 to naked ssDNA, thereby overcoming the kinetic block imposed by RPA. Furthermore, BRCA2 eliminates the need for the rate-limiting nucleation of RAD51 by chaperoning a short preassembled RAD51 filament onto the ssDNA complexed with RPA. Therefore, BRCA2 regulates recombination by initiating RAD51 filament formation.
- Published
- 2023
22. Counterexamples to a Conjecture of Dombi in Additive Number Theory
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Bell, Jason P. and Shallit, Jeffrey
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Mathematics - Number Theory ,Computer Science - Discrete Mathematics ,Computer Science - Formal Languages and Automata Theory ,Mathematics - Combinatorics - Abstract
We disprove a 2002 conjecture of Dombi from additive number theory. More precisely, we find examples of sets $A \subset \mathbb{N}$ with the property that $\mathbb{N} \setminus A$ is infinite, but the sequence $n \rightarrow |\{ (a,b,c) \, : \, n=a+b+c \text{ and } a,b,c \in A \}|$, counting the number of $3$-compositions using elements of $A$ only, is strictly increasing., Comment: additional author added; largely rewritten with different example
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- 2022
23. PI Degree and Irreducible Representations of Quantum Determinantal Rings and their Associated Quantum Schubert Varieties
- Author
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Bell, Jason P., Launois, Stéphane, and Rogers, Alexandra
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Mathematics - Quantum Algebra ,Mathematics - Combinatorics ,Mathematics - Rings and Algebras ,Mathematics - Representation Theory - Abstract
We study quantum determinantal rings at roots of unity and calculate the PI degree using results of Lenagan-Rigal and Haynal to reduce the problem to finding properties of their associated matrices. These matrices, in turn, correspond to Cauchon-Le diagrams from which we can calculate the required matrix properties. In particular, we show that any matrix corresponding to an $m\times n$ diagram has invariant factors which are powers of 2. Our calculations allow us to state an explicit expression for the PI degree of quantum determinantal rings when the deformation parameter $q$ is a primitive $\ell^{\text{th}}$ root of unity with $\ell$ odd. Using this newly calculated PI degree we present a method to construct an irreducible representation of maximal dimension. Building on these results, we use the strong connection between quantum determinantal rings and certain quantum Schubert varieties through noncommutative dehomogenisation to obtain expressions for the PI degree of such quantum Schubert varieties under the same conditions on $q$., Comment: 36 pages
- Published
- 2022
24. Amenability of monomial algebras, minimal subshifts and free subalgebras
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Bell, Jason P. and Greenfeld, Be'eri
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Mathematics - Rings and Algebras ,Mathematics - Dynamical Systems ,Mathematics - Functional Analysis - Abstract
We give a combinatorial characterization of amenability of monomial algebras and prove the existence of monomial Folner sequences, answering a question due to Ceccherini-Silberstein and Samet-Vaillant. We then use our characterization to prove that over projectively simple monomial algebras, every module is exhaustively amenable; we conclude that convolution algebras of minimal subshifts admit the same property. We deduce that any minimal subshift of positive entropy gives rise to a graded algebra which does not satisfy an extension of Vershik's conjecture on amenable groups, proposed by Bartholdi. Finally, we show that non-amenable monomial algebras must contain noncommutative free subalgebras. Examples are given to emphasize the sharpness and necessity of the assumptions in our results., Comment: Accepted to IMRN
- Published
- 2022
25. A differential analogue of the wild automorphism conjecture
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Bell, Jason, Ingalls, Colin, Moosa, Rahim, and Satriano, Matthew
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Mathematics - Algebraic Geometry ,Mathematics - Logic ,Mathematics - Rings and Algebras ,12H05, 03C98, 32M25, 13N15, 11J95 - Abstract
A differential analogue of the conjecture of Reichstein, Rogalski, and Zhang in algebraic dynamics is here established: if $X$ is a projective variety over an algebraically closed field of characteristic zero which admits a global algebraic vector field $v:X\to TX$ such that $(X,v)$ has no proper invariant subvarieties then $X$ is an abelian variety. Vector fields on abelian varieties with this property are also examined., Comment: 7 pages
- Published
- 2022
26. Ore extensions of commutative rings and the Dixmier-Moeglin equivalence
- Author
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Bell, Jason P., Burkhardt, Léon, and Priebe, Nicholas
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Mathematics - Rings and Algebras ,16D60, 16A20, 16A3 - Abstract
We consider Ore extensions of the form $T:=R[x;\sigma,\delta]$ with $R$ a commutative integral domain that is finitely generated over a field $k$. We show that if $T$ has Gelfand-Kirillov dimension less than four then a prime ideal $P\in {\rm Spec}(T)$ is primitive if and only if $\{P\}$ is locally closed in ${\rm Spec}(T)$, if and only if the Goldie ring of quotients of $T/P$ has centre that is an algebraic extension of $k$. We also show that there are examples for which these equivalences do not all hold for $T$ of integer Gelfand-Kirillov dimension greater than or equal to $4$., Comment: 13 pages
- Published
- 2022
27. Intersections of orbits of self-maps with subgroups in semiabelian varieties
- Author
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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
28. Computing the linear hull: Deciding Deterministic? and Unambiguous? for weighted automata over fields
- Author
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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
29. Rational self-maps with a regular iterate on a semiabelian variety
- Author
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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
30. On noncommutative bounded factorization domains and prime rings
- Author
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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
31. A general criterion for the P\'{o}lya-Carlson dichotomy and application
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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
32. A fusion variant of the classical and dynamical Mordell-Lang conjectures in positive characteristic
- Author
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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
33. D-finiteness, rationality, and height II: lower bounds over a set of positive density
- Author
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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
34. A conjecture strengthening the Zariski dense orbit problem for birational maps of dynamical degree one
- Author
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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
35. $p$-Adic interpolation of orbits under rational maps
- Author
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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
36. $D$-finite multivariate series with arithmetic restrictions on their coefficients
- Author
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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
37. Topological invariants for words of linear factor complexity
- Author
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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
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- 2022
38. Cogrowth Series for Free Products of Finite Groups
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Bell, Jason, Liu, Haggai, and Mishna, Marni
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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
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- 2021
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39. Automatic Sequences of Rank Two
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Bell, Jason and Shallit, Jeffrey
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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 $k\ge 2$.
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- 2021
40. Birational maps with transcendental dynamical degree
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Bell, Jason, Diller, Jeffrey, Jonsson, Mattias, and Krieger, Holly
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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
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- 2021
41. Development and testing of a versatile genome editing application reporter (V-GEAR) system
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Kleinboehl, Evan W., Laoharawee, Kanut, Lahr, Walker S., Jensen, Jacob D., Peterson, Joseph J., Bell, Jason B., Webber, Beau R., and Moriarity, Branden S.
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- 2024
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42. Bacille Calmette-Guérin vaccination to prevent febrile and respiratory illness in adults (BRACE): secondary outcomes of a randomised controlled phase 3 trial
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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.
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- 2024
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43. Specific and off-target immune responses following COVID-19 vaccination with ChAdOx1-S and BNT162b2 vaccines—an exploratory sub-study of the BRACE trial
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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
- Full Text
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44. On Dynamical Cancellation
- Author
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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
45. Sharing imagery and analysis tools in a simulated submarine control room
- Author
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Michailovs, Stephanie, Howard, Zachary, Pond, Stephen, Fitzgerald, Madison, Visser, Troy A.W., Bell, Jason, Pinniger, Gavin, Irons, Jessica, Schmitt, Megan, Stoker, Matthew, Huf, Sam, and Loft, Shayne
- Published
- 2024
- Full Text
- View/download PDF
46. A Tits alternative for rational functions
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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
47. Lie complexity of words
- Author
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Bell, Jason P. and Shallit, Jeffrey
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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
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- 2021
48. Affine representability and decision procedures for commutativity theorems for rings and algebras
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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
49. Effective isotrivial Mordell-Lang in positive characteristic
- Author
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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?
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- 2020
50. 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
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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
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