17 results on '"Joanna B. Fawcett"'
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2. On k-connected-homogeneous graphs.
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Alice Devillers, Joanna B. Fawcett, Cheryl E. Praeger, and Jin-Xin Zhou
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- 2020
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3. Locally triangular graphs and rectagraphs with symmetry.
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John Bamberg, Alice Devillers, Joanna B. Fawcett, and Cheryl E. Praeger
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- 2015
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4. Information transmission, holographic defect detection and signal permutation in active flow networks.
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Francis G. Woodhouse, Joanna B. Fawcett, and Jörn Dunkel
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- 2017
5. Partial linear spaces with a rank 3 affine primitive group of automorphisms
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Alice Devillers, Joanna B. Fawcett, John Bamberg, and Cheryl E. Praeger
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Rank (linear algebra) ,Group (mathematics) ,General Mathematics ,Linear space ,010102 general mathematics ,51E30, 05E18, 20B15, 05B25, 20B25 ,Group Theory (math.GR) ,0102 computer and information sciences ,Permutation group ,Automorphism ,01 natural sciences ,Combinatorics ,010201 computation theory & mathematics ,Ordered pair ,Line (geometry) ,FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Affine transformation ,0101 mathematics ,Mathematics - Group Theory ,Mathematics - Abstract
A partial linear space is a pair $(\mathcal{P},\mathcal{L})$ where $\mathcal{P}$ is a non-empty set of points and $\mathcal{L}$ is a collection of subsets of $\mathcal{P}$ called lines such that any two distinct points are contained in at most one line, and every line contains at least two points. A partial linear space is proper when it is not a linear space or a graph. A group of automorphisms $G$ of a proper partial linear space acts transitively on ordered pairs of distinct collinear points and ordered pairs of distinct non-collinear points precisely when $G$ is transitive of rank 3 on points. In this paper, we classify the finite proper partial linear spaces that admit rank 3 affine primitive automorphism groups, except for certain families of small groups, including subgroups of $A\Gamma L_1(q)$. Up to these exceptions, this completes the classification of the finite proper partial linear spaces admitting rank 3 primitive automorphism groups. We also provide a more detailed version of the classification of the rank 3 affine primitive permutation groups, which may be of independent interest., Comment: In this version, we have removed the assumption $V\leq H$ from 18.1 (old 13.2) and we have a new elementary proof of 10.10 (old 13.1). We have also reorganised some of the sections and made minor revisions throughout. 69 pages, 1 figure
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- 2021
6. Information transmission and signal permutation in active flow networks
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Francis G Woodhouse, Joanna B Fawcett, and Jörn Dunkel
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flow networks ,information transmission ,permutation groups ,active suspensions ,autonomous microfluidics ,Science ,Physics ,QC1-999 - Abstract
Recent experiments show that both natural and artificial microswimmers in narrow channel-like geometries will self-organise to form steady, directed flows. This suggests that networks of flowing active matter could function as novel autonomous microfluidic devices. However, little is known about how information propagates through these far-from-equilibrium systems. Through a mathematical analogy with spin-ice vertex models, we investigate here the input–output characteristics of generic incompressible active flow networks (AFNs). Our analysis shows that information transport through an AFN is inherently different from conventional pressure or voltage driven networks. Active flows on hexagonal arrays preserve input information over longer distances than their passive counterparts and are highly sensitive to bulk topological defects, whose presence can be inferred from marginal input–output distributions alone. This sensitivity further allows controlled permutations on parallel inputs, revealing an unexpected link between active matter and group theory that can guide new microfluidic mixing strategies facilitated by active matter and aid the design of generic autonomous information transport networks.
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- 2018
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7. Intermediate Trees.
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Kathie Cameron and Joanna B. Fawcett
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- 2009
8. Information transmission and signal permutation in active flow networks
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Joanna B. Fawcett, Francis G. Woodhouse, Jörn Dunkel, Woodhouse, Francis Gordon [0000-0002-5305-5510], Apollo - University of Cambridge Repository, Massachusetts Institute of Technology. Department of Mathematics, and Dunkel, Joern
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FOS: Computer and information sciences ,MOTION ,Computer science ,Fluids & Plasmas ,permutation groups ,Physics, Multidisciplinary ,Microfluidics ,flow networks ,Computer Science - Emerging Technologies ,General Physics and Astronomy ,FOS: Physical sciences ,02 engineering and technology ,Condensed Matter - Soft Condensed Matter ,COMPUTATION ,Topology ,01 natural sciences ,Topological defect ,Permutation ,SYSTEMS ,0103 physical sciences ,LOGIC ,Physics - Biological Physics ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Science & Technology ,02 Physical Sciences ,Statistical Mechanics (cond-mat.stat-mech) ,Physics ,ORDER ,information transmission ,active suspensions ,021001 nanoscience & nanotechnology ,autonomous microfluidics ,Active matter ,Vertex (geometry) ,MODEL ,Emerging Technologies (cs.ET) ,Biological Physics (physics.bio-ph) ,Physical Sciences ,Compressibility ,Soft Condensed Matter (cond-mat.soft) ,0210 nano-technology ,MATTER ,Group theory ,Voltage - Abstract
Recent experiments show that both natural and artificial microswimmers in narrow channel-like geometries will self-organise to form steady, directed flows. This suggests that networks of flowing active matter could function as novel autonomous microfluidic devices. However, little is known about how information propagates through these far-from-equilibrium systems. Through a mathematical analogy with spin-ice vertex models, we inves tigate here the input-output characteristics of generic incompressible active flow networks (AFNs). Our analysis shows that information transport through an AFN is inherently different from conventional pressure or voltage driven networks. Active flows on hexagonal arrays preserve input information over longer distances than their passive counterparts and are highly sensitive to bulk topological defects, whose presence can be inferred from marginal input-output distributions alone. This sensitivity further allows controlled permutations on parallel inputs, revealing an unexpected link between active matter and group theory that can guide new microfluidic mixing strategies facilitated by active matter and aid the design of generic autonomous information transport networks., National Science Foundation (U.S.) (Grant CBET-1510768)
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- 2019
9. Regular orbits of symmetric and alternating groups
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Jan Saxl, Eamonn A. O'Brien, and Joanna B. Fawcett
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Algebra and Number Theory ,Covering group ,010102 general mathematics ,Primitive permutation group ,Alternating group ,010103 numerical & computational mathematics ,Group Theory (math.GR) ,Permutation group ,16. Peace & justice ,01 natural sciences ,Covering groups of the alternating and symmetric groups ,Combinatorics ,Base (group theory) ,Symmetric group ,FOS: Mathematics ,Order (group theory) ,0101 mathematics ,Representation Theory (math.RT) ,Mathematics - Group Theory ,Mathematics - Representation Theory ,Mathematics - Abstract
Given a finite group $G$ and a faithful irreducible $FG$-module $V$ where $F$ has prime order, does $G$ have a regular orbit on $V$? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. In this paper, we classify the pairs $(G,V)$ for which $G$ has a regular orbit on $V$ where $G$ is a covering group of a symmetric or alternating group and $V$ is a faithful irreducible $FG$-module such that the order of $F$ is prime and divides the order of $G$., 26 pages
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- 2018
10. Stochastic cycle selection in active flow networks
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Jörn Dunkel, Aden Forrow, Joanna B. Fawcett, Francis G. Woodhouse, Woodhouse, Francis Gordon [0000-0002-5305-5510], and Apollo - University of Cambridge Repository
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topology ,FOS: Physical sciences ,Bronchial mucus ,Condensed Matter - Soft Condensed Matter ,Biology ,Topology ,Transition rate matrix ,Network topology ,01 natural sciences ,010305 fluids & plasmas ,Physical Phenomena ,MD Multidisciplinary ,0103 physical sciences ,active transport ,Physics - Biological Physics ,010306 general physics ,Topology (chemistry) ,Stochastic Processes ,Multidisciplinary ,business.industry ,Stochastic process ,stochastic dynamics ,Graph theory ,Biological Sciences ,Models, Theoretical ,Range (mathematics) ,Flow (mathematics) ,Biological Physics (physics.bio-ph) ,networks ,Soft Condensed Matter (cond-mat.soft) ,Artificial intelligence ,business - Abstract
Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such non-equilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of non-biological far-from-equilibrium networks, including actively controlled information flows, and establishes a new correspondence between active flow networks and generalized ice-type models., 7 pages, 4 figures; SI text available at article on pnas.org
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- 2016
11. Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5
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Joanna B. Fawcett, Gordon F. Royle, Cheryl E. Praeger, Cai Heng Li, Gabriel Verret, and Michael Giudici
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Vertex (graph theory) ,Discrete mathematics ,010102 general mathematics ,Valency ,0102 computer and information sciences ,Group Theory (math.GR) ,Permutation group ,01 natural sciences ,Theoretical Computer Science ,0101 Pure Mathematics ,Computation Theory & Mathematics ,Combinatorics ,Maximal subgroup ,Corollary ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Simple group ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,0101 mathematics ,Mathematics - Group Theory ,Mathematics - Abstract
We classify finite primitive permutation groups having a suborbit of length 5. As a corollary, we obtain a classification of finite vertex-primitive graphs of valency 5. In the process, we also classify finite almost simple groups that have a maximal subgroup isomorphic to Alt ( 5 ) or Sym ( 5 ) .
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- 2016
12. Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples
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Joanna B. Fawcett and Cheryl E. Praeger
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Conjecture ,Group (mathematics) ,General Mathematics ,010102 general mathematics ,General linear group ,0102 computer and information sciences ,Group Theory (math.GR) ,Permutation group ,16. Peace & justice ,01 natural sciences ,Linear subspace ,Base (group theory) ,Combinatorics ,Mathematics::Group Theory ,010201 computation theory & mathematics ,Symmetric group ,15A04, 20B15 ,FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,0101 mathematics ,Tuple ,Mathematics::Representation Theory ,Mathematics - Group Theory ,Mathematics - Abstract
For a subgroup $L$ of the symmetric group $S_\ell$, we determine the minimal base size of $GL_d(q)\wr L$ acting on $V_d(q)^\ell$ as an imprimitive linear group. This is achieved by computing the number of orbits of $GL_d(q)$ on spanning $m$-tuples, which turns out to be the number of $d$-dimensional subspaces of $V_m(q)$. We then use these results to prove that for certain families of subgroups $L$, the affine groups whose stabilisers are large subgroups of $GL_d(q)\wr L$ satisfy a conjecture of Pyber concerning bases., 8 pages
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- 2016
13. Bruck nets and partial Sherk planes
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Joanna B. Fawcett, John Bamberg, and Jesse Lansdown
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Pure mathematics ,51E14, 51E05, 51E15, 51F05 ,Plane (geometry) ,General Mathematics ,0101 Pure Mathematics ,Orthogonality ,Affine plane (incidence geometry) ,FOS: Mathematics ,Finite geometry ,Order (group theory) ,Mathematics - Combinatorics ,Degree (angle) ,Combinatorics (math.CO) ,Affine transformation ,Incidence (geometry) ,Mathematics - Abstract
In Bachmann's Aufbau der Geometrie aus dem Spiegelungsbegriff (1959), it was shown that a finite metric plane is a Desarguesian affine plane of odd order equipped with a perpendicularity relation on lines, and conversely. Sherk (1967) generalised this result to characterise the finite affine planes of odd order by removing the 'three reflections axioms' from a metric plane. We show that one can obtain a larger class of natural finite geometries, the so-called Bruck nets of even degree, by weakening Sherk's axioms to allow non-collinear points., We have removed the condition from our main theorem that there is a constant number of lines on any point. Instead, we have replaced it with the much weaker condition that there is a line all of whose points are thick (incident with more than 2 lines)
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- 2016
14. Locally triangular graphs and normal quotients of the $n$-cube
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Joanna B. Fawcett
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Vertex (graph theory) ,Algebra and Number Theory ,010102 general mathematics ,Minimum distance ,Group Theory (math.GR) ,0102 computer and information sciences ,Automorphism ,01 natural sciences ,Graph ,Combinatorics ,05C25, 05C75, 05E18, 20B25 ,Quadrangle ,010201 computation theory & mathematics ,FOS: Mathematics ,Bipartite graph ,Discrete Mathematics and Combinatorics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,0101 mathematics ,Mathematics - Group Theory ,Quotient ,Binary linear codes ,Mathematics - Abstract
For an integer $n\geq 2$, the triangular graph has vertex set the $2$-subsets of $\{1,\ldots,n\}$ and edge set the pairs of $2$-subsets intersecting at one point. Such graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every $2$-path lies in a unique quadrangle. We refine this result and provide a characterisation of connected locally triangular graphs as halved graphs of normal quotients of $n$-cubes. To do so, we study a parameter that generalises the concept of minimum distance for a binary linear code to arbitrary automorphism groups of the $n$-cube., 9 pages
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- 2015
15. Locally triangular graphs and rectagraphs with symmetry
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Cheryl E. Praeger, Joanna B. Fawcett, John Bamberg, and Alice Devillers
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Vertex (graph theory) ,Discrete mathematics ,Neighbourhood (graph theory) ,20B25, 05C75, 05E18, 05E20 ,Group Theory (math.GR) ,1-planar graph ,Theoretical Computer Science ,Combinatorics ,Indifference graph ,Computational Theory and Mathematics ,Chordal graph ,Covering graph ,Triangle-free graph ,Bipartite graph ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Mathematics - Group Theory ,Mathematics - Abstract
Locally triangular graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every $2$-arc lies in a unique quadrangle. A graph $\Gamma$ is locally rank 3 if there exists $G\leq \mathrm{Aut}(\Gamma)$ such that for each vertex $u$, the permutation group induced by the vertex stabiliser $G_u$ on the neighbourhood $\Gamma(u)$ is transitive of rank 3. One natural place to seek locally rank 3 graphs is among the locally triangular graphs, where every induced neighbourhood graph is isomorphic to a triangular graph $T_n$. This is because the graph $T_n$, which has vertex set the $2$-subsets of $\{1,\ldots,n\}$ and edge set the pairs of $2$-subsets intersecting at one point, admits a rank 3 group of automorphisms. In this paper, we classify the locally $4$-homogeneous rectagraphs under some additional structural assumptions. We then use this result to classify the connected locally triangular graphs that are also locally rank 3., Comment: 21 pages
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- 2014
16. Regular orbits of sporadic simple groups
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Joanna B. Fawcett, Robert A. Wilson, Jürgen Müller, Eamonn A. O'Brien, and Commission of the European Communities
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BASE SIZES ,General Mathematics ,20C20, 20C34, 20C40, 20B15 ,Group Theory (math.GR) ,FINITE ,Type (model theory) ,01 natural sciences ,Base size ,0101 Pure Mathematics ,Base (group theory) ,Combinatorics ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,Representation Theory (math.RT) ,Mathematics ,Finite group ,Science & Technology ,Algebra and Number Theory ,Covering group ,Primitive affine group ,010102 general mathematics ,Permutation group ,Sporadic simple group ,Almost simple group ,Simple group ,Physical Sciences ,Regular orbit ,010307 mathematical physics ,Affine transformation ,Mathematics - Group Theory ,Mathematics - Representation Theory - Abstract
Given a finite group $G$ and a faithful irreducible $FG$-module $V$ where $F$ has prime order, does $G$ have a regular orbit on $V$? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. Let $G$ be a covering group of an almost simple group whose socle $T$ is sporadic, and let $V$ be a faithful irreducible $FG$-module where $F$ has prime order dividing $|G|$. We classify the pairs $(G,V)$ for which $G$ has no regular orbit on $V$, and determine the minimal base size of $G$ in its action on $V$. To obtain this classification, for each non-trivial $g\in G/Z(G)$, we compute the minimal number of $T$-conjugates of $g$ generating $\langle T,g\rangle$., 17 pages, shortened proof plus new result (Theorem 1.3)
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17. The base size of a primitive diagonal group
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Joanna B. Fawcett
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Discrete mathematics ,Algebra and Number Theory ,Diagonal actions ,Group (mathematics) ,010102 general mathematics ,Finite permutation groups ,Outer automorphism group ,Alternating group ,Primitive permutation group ,Group Theory (math.GR) ,Permutation group ,01 natural sciences ,Base size ,Combinatorics ,Base (group theory) ,Primitive groups ,Symmetric group ,0103 physical sciences ,FOS: Mathematics ,20B15 ,010307 mathematical physics ,Identity component ,0101 mathematics ,Mathematics - Group Theory ,Mathematics - Abstract
A base B for a finite permutation group G acting on a set X is a subset of X with the property that only the identity of G can fix every point of B. We prove that a primitive diagonal group G has a base of size 2 unless the top group of G is the alternating or symmetric group acting naturally, in which case a tight bound for the minimal base size of G is given. This bound also satisfies a well-known conjecture of Pyber. Moreover, we prove that if the top group of G does not contain the alternating group, then the proportion of pairs of points that are bases for G tends to 1 as |G| tends to infinity. A similar result for the case when the degree of the top group is fixed is given., Comment: 24 pages
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