Variations of Stack Sorting and Pattern Avoidance

University of Technology Sydney. Faculty of Science.Sorting is a process of arranging certain objects into an ordered sequence. Real world problems such as sorting using switchyard networks, genome arrangement, and delivery of network data packets can be realised as sorting problems. The study of these problems can be translated into the study of sorting permutations using a system of data structures which can store and output data. For instance, the sorting problem in certain switchyard networks can be formulated as the problem of sorting permutations using . The results of this thesis address the following research questions related to sorting permutations. Open research questions 1. In a sorting process with a finite stack followed by an infinite stack in series, what is the depth of the finite stack at which the basis becomes infinite? 2. Is there a pattern avoidance characterisation for k-pass pop stack sortable permutations? Apart from answering these questions, we develop a new notion of barred pattern avoidance to accommodate some of the limitations in the existing barred pattern avoidance definition. With the new notion of barred pattern avoidance, a proof can be established to answer question 2 above. The organisation of this thesis is as follows. Chapter 1 gives a detailed introduction to the research in permutation patterns and stack sorting. It includes some history and some major research outcomes. Moreover, several variations of sorting machines are described. Finally, a few types of non-classical patterns are explained. Chapter 2 answers the first question above. Based on some experimental data, a conjecture was made that the basis changes from finite to infinite when the depth of the finite stack is 3. We found an infinite antichain in the form of extendable sequence of numbers to prove the conjecture. Chapter 3 answers the second question and introduces a new notion of barred pattern avoidance to characterise permutations sortable by a k-pass pop-stack. Then, we finish the chapter by proving the number of forbidden patterns that the permutations sortable by k-pass pop-stack must avoid is finite. The set of forbidden patterns can be algorithmically constructed. Chapter 4 concludes the thesis with some directions for future research

Are You Being Rhetorical? An Open Corpus of Machine Annotated Rhetorical Moves

Writing analytics has emerged as a sub-field of learning analytics, with applications including the provision of formative feedback to students in developing their writing capacities. Rhetorical markers in writing have become a key feature in this feedback, with a number of tools being developed across research and teaching contexts. However, there is no shared corpus of texts annotated by these tools, nor is it clear how the tool annotations compare. Thus, resources are scarce for comparing tools for both tool development and pedagogic purposes. In this paper, we conduct such a comparison and introduce a sample corpus of texts representative of the particular genres, a subset of which has been annotated using three rhetorical analysis tools (one of which has two versions). This paper aims to provide both a description of the tools and a shared dataset in order to support extensions of existing analyses and tool design in support of writing skill development. We intend the description of these tools, which share a focus on rhetorical structures, alongside the corpus, to be a preliminary step to enable further research, with regard to both tool development and tool interaction

Mixed-Sandwich Cp*Cr Complexes Containing Poly(methimazolyl)borates (Cp* = C₅Me₅): Syntheses and Structural and Electrochemical Studies

Reaction of the scorpionate salts K­[HB­(mt)₃], Na­[H₂B­(mt)₂], and Li­[HB­(mt)₂(pz)] with [Cp*CrBr₂]₂ (<b>1</b>) gave the 15-electron Cr­(III) complexes [Cp*Cr­{κ³<i>-S</i>,<i>S′</i>,<i>S″</i>-HB­(mt)₃}]Br (<b>2</b>), [Cp*Cr­{κ²<i>-S</i>,<i>S′</i>-H₂B­(mt)₂}­Br] (<b>3</b>), and [Cp*Cr­{κ²<i>-S,S′</i>-HB­(mt)₂(pz)}­Br] (<b>4</b>) in moderate to high yields. These are the first examples of mixed-sandwich chromium­(III) complexes containing poly­(methimazolylborate) ligands. The tridentate coordination of the monoanionic ligands [H₂B­(mt)₂] in <b>3</b> and [HB­(mt)₂(pz)] in <b>4</b> can be effected by using a silver salt to remove the Br coligand, thus yielding the complexes [Cp*Cr­{κ³<i>-H</i>,<i>S</i>,<i>S′</i>-H₂B­(mt)₂}]­PF₆ (<b>6</b>) and [Cp*Cr­{κ³<i>-N</i>,<i>S</i>,<i>S′</i>-HB­(mt)₂(pz)}]­PF₆ (<b>7</b>). It was also found that, in the presence of acetonitrile, the reaction of <b>3</b> with AgPF₆ afforded [Cp*Cr­{κ²<i>-S</i>,<i>S′</i>-H₂B­(mt)₂}­(NCMe)]­PF₆ (<b>5</b>). The coordination geometries of all the complexes have been determined by X-ray diffraction analyses. Cyclic voltammetric studies of complexes <b>2</b>,<b> 4</b>, and <b>7</b> showed that the oxidation and reduction processes are chemically reversible and that the reduced and oxidized states of complexes <b>3</b>, <b>5</b>, and <b>6</b> are very short-lived

Mixed-Sandwich (Cp*/(HMB))Ru Complexes Containing Bis(methimazolyl)(pyrazolyl)borate (Cp* = η⁵-C₅Me₅, HMB = η⁶-C₆Me₆)

Reaction of the scorpionate salt Li­[HB­(mt)₂(pz)] (mt = <i>N</i>-methyl-2-mercaptoimidazol-1-yl, pz = pyrazolyl) with the organometallic complexes [Cp*RuOMe]₂ (Cp* = η⁵-C₅Me₅) (<b>1</b>) and [(HMB)­RuCl₂]₂ (HMB = η⁶-C₆Me₆) (<b>2</b>) gave the 18-electron Ru­(II) complexes [Cp*Ru­(κ³<i>-H,S,S′</i>)<i>-</i>{HB­(mt)₂(pz)}] (<b>3</b>) and [(HMB)­Ru­(κ³<i>-H,S,S′</i>)<i>-</i>{HB­(mt)₂(pz)}]­(<b>4B</b>)­PF₆ in moderate yields. In the absence of the PF₆^– anion, [(HMB)­Ru­(κ²-<i>S</i>,<i>S</i>′-{HB­(mt)₂(pz)})­(Cl)] [<b>4C</b>] was isolated as a coproduct with (<b>4B</b>)­Cl. These complexes are the first examples of organoruthenium­(II) complexes containing bis­(methimazolyl)­(pyrazolyl)­borate ligands. Isomers of <b>4B</b> were observed in solution, and the isomerization process was studied using variable-temperature ¹H NMR spectroscopy. The reactivity of <b>3</b> toward O₂ and CO was investigated, and in the process we isolated the first Ru­(IV) peroxo complex containing a poly­(methimazolyl)­borate ligand, [Cp*Ru­(κ²-<i>S</i>,<i>S</i>′-{HB­(mt)₂(pz)})­(η²-O₂)] (<b>5</b>), and a CO adduct, [Cp*Ru­(κ²-<i>S</i>,<i>S</i>′-{HB­(mt)₂(pz)})­(CO)] (<b>6</b>), respectively. The oxidation process was reversible, but treatment of <b>5</b> with CO converted it irreversibly to <b>6</b>. All the new compounds were fully characterized, including by X-ray diffraction analyses. Cyclic voltammetric studies were also conducted for complexes <b>3</b>, <b>5</b>, and <b>6</b>

Mixed-Sandwich Cp*Cr Complexes Containing Poly(methimazolyl)borates (Cp* = C₅Me₅): Syntheses and Structural and Electrochemical Studies

Reaction of the scorpionate salts K­[HB­(mt)₃], Na­[H₂B­(mt)₂], and Li­[HB­(mt)₂(pz)] with [Cp*CrBr₂]₂ (<b>1</b>) gave the 15-electron Cr­(III) complexes [Cp*Cr­{κ³<i>-S</i>,<i>S′</i>,<i>S″</i>-HB­(mt)₃}]Br (<b>2</b>), [Cp*Cr­{κ²<i>-S</i>,<i>S′</i>-H₂B­(mt)₂}­Br] (<b>3</b>), and [Cp*Cr­{κ²<i>-S,S′</i>-HB­(mt)₂(pz)}­Br] (<b>4</b>) in moderate to high yields. These are the first examples of mixed-sandwich chromium­(III) complexes containing poly­(methimazolylborate) ligands. The tridentate coordination of the monoanionic ligands [H₂B­(mt)₂] in <b>3</b> and [HB­(mt)₂(pz)] in <b>4</b> can be effected by using a silver salt to remove the Br coligand, thus yielding the complexes [Cp*Cr­{κ³<i>-H</i>,<i>S</i>,<i>S′</i>-H₂B­(mt)₂}]­PF₆ (<b>6</b>) and [Cp*Cr­{κ³<i>-N</i>,<i>S</i>,<i>S′</i>-HB­(mt)₂(pz)}]­PF₆ (<b>7</b>). It was also found that, in the presence of acetonitrile, the reaction of <b>3</b> with AgPF₆ afforded [Cp*Cr­{κ²<i>-S</i>,<i>S′</i>-H₂B­(mt)₂}­(NCMe)]­PF₆ (<b>5</b>). The coordination geometries of all the complexes have been determined by X-ray diffraction analyses. Cyclic voltammetric studies of complexes <b>2</b>,<b> 4</b>, and <b>7</b> showed that the oxidation and reduction processes are chemically reversible and that the reduced and oxidized states of complexes <b>3</b>, <b>5</b>, and <b>6</b> are very short-lived

Mixed-Sandwich (Cp*/(HMB))Ru Complexes Containing Bis(methimazolyl)(pyrazolyl)borate (Cp* = η⁵-C₅Me₅, HMB = η⁶-C₆Me₆)

Reaction of the scorpionate salt Li­[HB­(mt)₂(pz)] (mt = <i>N</i>-methyl-2-mercaptoimidazol-1-yl, pz = pyrazolyl) with the organometallic complexes [Cp*RuOMe]₂ (Cp* = η⁵-C₅Me₅) (<b>1</b>) and [(HMB)­RuCl₂]₂ (HMB = η⁶-C₆Me₆) (<b>2</b>) gave the 18-electron Ru­(II) complexes [Cp*Ru­(κ³<i>-H,S,S′</i>)<i>-</i>{HB­(mt)₂(pz)}] (<b>3</b>) and [(HMB)­Ru­(κ³<i>-H,S,S′</i>)<i>-</i>{HB­(mt)₂(pz)}]­(<b>4B</b>)­PF₆ in moderate yields. In the absence of the PF₆^– anion, [(HMB)­Ru­(κ²-<i>S</i>,<i>S</i>′-{HB­(mt)₂(pz)})­(Cl)] [<b>4C</b>] was isolated as a coproduct with (<b>4B</b>)­Cl. These complexes are the first examples of organoruthenium­(II) complexes containing bis­(methimazolyl)­(pyrazolyl)­borate ligands. Isomers of <b>4B</b> were observed in solution, and the isomerization process was studied using variable-temperature ¹H NMR spectroscopy. The reactivity of <b>3</b> toward O₂ and CO was investigated, and in the process we isolated the first Ru­(IV) peroxo complex containing a poly­(methimazolyl)­borate ligand, [Cp*Ru­(κ²-<i>S</i>,<i>S</i>′-{HB­(mt)₂(pz)})­(η²-O₂)] (<b>5</b>), and a CO adduct, [Cp*Ru­(κ²-<i>S</i>,<i>S</i>′-{HB­(mt)₂(pz)})­(CO)] (<b>6</b>), respectively. The oxidation process was reversible, but treatment of <b>5</b> with CO converted it irreversibly to <b>6</b>. All the new compounds were fully characterized, including by X-ray diffraction analyses. Cyclic voltammetric studies were also conducted for complexes <b>3</b>, <b>5</b>, and <b>6</b>

Are you being rhetorical? A description of rhetorical move annotation tools and open corpus of sample machine-annotated rhetorical moves

Writing analytics has emerged as a sub-field of learning analytics, with applications including the provision of formative feedback to students in developing their writing capacities. Rhetorical markers in writing have become a key feature in this feedback, with a number of tools being developed across research and teaching contexts. However, there is no shared corpus of texts annotated by these tools, nor is it clear how the tool annotations compare. Thus, resources are scarce for comparing tools for both tool development and pedagogic purposes. In this paper, we conduct such a comparison and introduce a sample corpus of texts representative of the particular genres, a subset of which has been annotated using three rhetorical analysis tools (one of which has two versions). This paper aims to provide both a description of the tools and a shared dataset in order to support extensions of existing analyses and tool design in support of writing skill development. We intend the description of these tools, which share a focus on rhetorical structures, alongside the corpus, to be a preliminary step to enable further research, with regard to both tool development and tool interaction.</p

Are You Being Rhetorical? An Open Corpus of Machine Annotated Rhetorical Moves

Writing analytics has emerged as a sub-field of learning analytics, with applications including the provision of formative feedback to students in developing their writing capacities. Rhetorical markers in writing have become a key feature in this feedback, with a number of tools being developed across research and teaching contexts. However, there is no shared corpus of texts annotated by these tools, nor is it clear how the tool annotations compare. Thus, resources are scarce for comparing tools for both tool development and pedagogic purposes. In this paper, we conduct such a comparison and introduce a sample corpus of texts representative of the particular genres, a subset of which has been annotated using three rhetorical analysis tools (one of which has two versions). This paper aims to provide both a description of the tools and a shared dataset in order to support extensions of existing analyses and tool design in support of writing skill development. We intend the description of these tools, which share a focus on rhetorical structures, alongside the corpus, to be a preliminary step to enable further research, with regard to both tool development and tool interaction.This article is published as Knight, S., Abel, S., Shibani, A., Goh, Y. K., Conijn, R., Gibson, A., Vajjala, S., Cotos, E., Sándor, Ágnes, & Buckingham Shum, S. (2020). Are You Being Rhetorical? An Open Corpus of Machine Annotated Rhetorical Moves. Journal of Learning Analytics, 7(3), 138-154. https://doi.org/10.18608/jla.2020.73.10. </p