The Matrix Reproved (Verification Pearl)

International audienceIn this paper we describe a complete solution for the first challenge of the VerifyThis 2016 competition held at the 18th ETAPS Forum. We present the proof of two variants for the multiplication of matrices: a naive version using three nested loops and the Strassen's algorithm. The proofs are conducted using the Why3 platform for deductive program verification, and automated theorem provers to discharge proof obligations. In order to specify and prove the two multiplication algorithms , we develop a new Why3 theory of matrices and apply the proof by reflection methodology

Deductive Verification with the Help of Abstract Interpretation

Abstract interpretation is widely used in static analysis tools. However, to the best of our knowledge, it has not been extensively experimented in an interactive deductive verification context. This paper describes an analysis by abstract interpretation to infer loop invariants in the Why3 tool. The analysis takes advantage of the logic annotations present in the source code, including potential handwritten loop invariants. The inferred invariants are added to loops as if written by the user. They are checked by external provers and thus the analysis by abstract interpretation does not need to be trusted. Our analysis goes beyond numerical invariants. We describe two functors that add uninterpreted functions and quantifiers to a numerical abstract domain. The resulting domain is generic enough to reason about algebraic types, Booleans, or arrays. We show that it achieves a level of expressivity comparable to that of ad-hoc domains for arrays found in the literature

Comparison of the vocabularies of the Gregg shorthand dictionary and Horn-Peterson's basic vocabulary of business letters

This study is a comparative analysis of the vocabularies of Horn and Peterson's The Basic Vocabulary of Business Letters1 and the Gregg Shorthand Dictionary.2 Both books purport to present a list of words most frequently encountered by stenographers and students of shorthand. The, Basic Vocabulary of Business Letters, published "in answer to repeated requests for data on the words appearing most frequently in business letters,"3 is a frequency list specific to business writing. Although the book carries the copyright date of 1943, the vocabulary was compiled much earlier. The listings constitute a part of the data used in the preparation of the 10,000 words making up the ranked frequency list compiled by Ernest Horn and staff and published in 1926 under the title of A Basic Writing Vocabulary: 10,000 Words Lost Commonly Used in Writing. The introduction to that publication gives credit to Miss Cora Crowder for the contribution of her Master's study at the University of Minnesota concerning words found in business writing. With additional data from supplementary sources, the complete listing represents twenty-six classes of business, as follows 1. Miscellaneous 2. Florists 3. Automobile manufacturers and sales companie

Symplectic Topology of Projective Space: Lagrangians, Local Systems and Twistors

In this thesis we study monotone Lagrangian submanifolds of CPn . Our results are roughly of two types: identifying restrictions on the topology of such submanifolds and proving that certain Lagrangians cannot be displaced by a Hamiltonian isotopy. The main tool we use is Floer cohomology with high rank local systems. We describe this theory in detail, paying particular attention to how Maslov 2 discs can obstruct the differential. We also introduce some natural unobstructed subcomplexes. We apply this theory to study the topology of Lagrangians in projective space. We prove that a monotone Lagrangian in CPn with minimal Maslov number n + 1 must be homotopy equivalent to RPn (this is joint work with Jack Smith). We also show that, if a monotone Lagrangian in CP3 has minimal Maslov number 2, then it is diffeomorphic to a spherical space form, one of two possible Euclidean manifolds or a principal circle bundle over an orientable surface. To prove this, we use algebraic properties of lifted Floer cohomology and an observation about the degree of maps between Seifert fibred 3-manifolds which may be of independent interest. Finally, we study Lagrangians in CP(2n+1) which project to maximal totally complex subman- ifolds of HPn under the twistor fibration. By applying the above topological restrictions to such Lagrangians, we show that the only embedded maximal Kähler submanifold of HPn is the totally geodesic CPn and that an embedded, non-orientable, superminimal surface in S4 = HP1 is congruent to the Veronese RP2 . Lastly, we prove some non-displaceability results for such Lagrangians. In particular, we show that, when equipped with a specific rank 2 local system, the Chiang Lagrangian L∆ ⊆ CP3 becomes wide in characteristic 2, which is known to be impossible to achieve with rank 1 local systems. We deduce that L∆ and RP3 cannot be disjoined by a Hamiltonian isotopy

The Apothecary's Tales: a game of language in a language of games

A thesis submitted to the University of Bedfordshire, in partial fulfilment requirements for the degree of Doctor of Philosophy (Creative Writing)The thesis shows how the novel The Apothecary's Tales manipulates narrative frames to create a 'simulachron', an unreliable virtual world, which problematises the reader's conceptions of the past. The novel transgresses the generic rules of 'historical fiction' to create a quality of 'historicity' located in the affect of alterity. This is argued to be a somatic response to peril deferred. The novel seeks to evoke alterity by defamiliarising linguistic norms. It does this principally through the use of 'diachronic polysemia' (lexical 'false friends') and intertexts to syncopate the reader continually between the disparate sensibilities of the 1ih and 21 st centuries. These sensibilities are simulated in the novel by the imbedment of sociolects and 'hypomemes', the tacit thoughtways supposed peculiar to a given milieu. To self-authenticate its fictions, the novel employs the 'parafictive' devices of a testamentary found artifact, an unreliable narrator and editor, plausible sociologuemes (social conventions) and ideologuemes (ideologies that inform behaviour), along with a density of period minutiae putatively grounded in the record. Any truth effects achieved are then ludically subverted by a process of critique in which structural units of the novel systematically parody the other. The novel is patterned in the structure of a nested diptych, of expositions contra posed in a mutual commentary, which extends from the defining templates of plot and episode to the micro levels of morphemes in polysemic wordplay. The tropes of nested framing and repetition of form and syntagm are defined in the thesis, respectively, as encubi/atio and 'emblematic resonance'. It is argued that these tropes, encoded in a fictive discourse that defies closure, provide a simulation of hermetic form that -when mapped upon the aleatory life world -can be productive of aesthetic affect. The agonistic elements of plot and incident in the novel are figured within the tapas of theatre, foregrounded by the duplicitous self-fashioning of the characters, and by the continual metaleptic shifts or 'frame syncopation' of narrative viewpoint, both intra and extra-diegetic. Frame syncopation is used advisedly to dilemmatise significations at both the structural and syntagmatic levels. The thesis contends that such contrived collisions of narrative interpretation may be the dynamic of affectivity in all aesthetic discourse

The Lynching of Cleo Wright

On January 20, 1942, black oil mill worker Cleo Wright assaulted a white woman in her home and nearly killed the first police officer who tried to arrest him. An angry mob then hauled Wright out of jail and dragged him through the streets of Sikeston, Missouri, before burning him alive. Wright\u27s death was, unfortunately, not unique in American history, but what his death meant in the larger context of life in the United States in the twentieth-century is an important and compelling story. After the lynching, the U.S. Justice Department was forced to become involved in civil rights concerns for the first time, provoking a national reaction to violence on the home front at a time when the country was battling for democracy in Europe. Dominic Capeci unravels the tragic story of Wright\u27s life on several stages, showing how these acts of violence were indicative not only of racial tension but the clash of the traditional and the modern brought about by the war. Capeci draws from a wide range of archival sources and personal interviews with the participants and spectators to draw vivid portraits of Wright, his victims, law-enforcement officials, and members of the lynch mob. He places Wright in the larger context of southern racial violence and shows the significance of his death in local, state, and national history during the most important crisis of the twentieth-century. Winner of the 1999 Missouri History Award given by the State Historical Society of Missouri. A painstaking and valuable study of these tragic events that confirms and extends the findings of other recent scholars of lynching. —American Historical Review A creatively conceptualized anatomy of a lynching. Capeci places the lynching of Cleo Wright within the context of the city of Sikeston, the state of Missouri, and the nation. —Arvarh E. Strickland Capeci touches on the social forces behind the attack and the reactions that followed. —Booklist Capeci\u27s account of a lynching in the small city of Sikeston, Missouri, in 1942 adds to a growing list of investigations into the relationship between mob justice and race relations. —Choice Capeci skillfully dissects the thoughts and actions of supporters and white opponents of the mob. —Georgia Historical Quarterly A meticulous and dynamic examination of a pivotal incident during the age of lynching. —Journal of American History For the first time, the U.S. Justice Department intervened in a lynching, although it failed to secure any indictments. —Library Journal A cogent guide and a milepost for understanding the history of lynching in Missouri. —Missouri Historical Review His extensive research, including interviews with survivors, is evident in his intricate and engrossing perspective, especially when describing the lynching and the bloodshed that led to it. —Publishers Weekly A valuable complement to broader-gauged scholarship, because Capeci constructed it so patiently and assiduously. —Reviews in American History Concludes that the Sikeston event contributed more to the subsequent history of civil rights and race relations than any other in the state. . . . A fascinating book packed with surprises. —Richard S. Kirkendall Illustrates the national significance of Cleo Wright’s murder. —Southern Historianhttps://uknowledge.uky.edu/upk_united_states_history/1094/thumbnail.jp

Arnold conjecture over integers

For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti number over Q and torsions of all characteristic. The proof is based on constructing a Hamiltonian Floer theory over the Novikov ring with integer coefficients, which generalizes our earlier work for constructing integer-valued Gromov-Witten type invariants. In the course of the construction, we build a Hamiltonian Floer flow category with compatible smooth global Kuranishi charts. This generalizes a recent work of Abouzaid-McLean-Smith, which might be of independent interest.Comment: 168 pages, 2 figures. Comments welcome

In the Labyrinths of Deceit: Culture, Modernity and Disidentity in the Nineteenth Century

This thesis examines the nature of identity and the problems implicit in attempts to affirm it within the context of nineteenth century modernity. By exploring a number of texts from Romanticism to the fin de siecle, it can be. seen that autonomous and coherent identity is not a stable entity. Drawing upon Rene Descartes'work on constructions of selfhood as a starting point, these ideas can be detected in an assessment of identity's alter ego - the disidentical self which is characterised by masks, disguises, madness, pathological behaviour, criminality and addiction. Examples of such paradigms for disidentity can be found in a variety of cultural texts and genres throughout the century, from the self-consciously 'high' poetry of Matthew Arnold, Alfred Tennyson and Gerard Manley Hopkins to the popular Gothic novels of Robert Louis Stevenson, Oscar Wilde and Bram Stoker. These metaphorisations of a crisis for identity in the nineteenth century are reflected in the analyses of insanity by physicians such as W.A.F. Browne and Henry Maudsley, prominent cultural critics such as Arthur Hallam and Amold, and the degeneration theorists of the late nineteenth century. Much of the project is shaped by Karl Marx and Friedrich Engels' assessment of modernity found in The Communist Manifesto, in particular their descriptions of nineteenth century socio-cultural topographies as fluid and vaporous. Stable identity is effectively threatened from a plethora of directions, including the Orient, criminality, sexual deviancy, scientific discovery and accelerated social change. Taking into consideration the many different ways in which identity can be problematised in the nineteenth century, three important sites of disidentification have been chosen for the purposes of this argument. Chapter one examines the split-personality, chapter two religious madness, and chapter three addiction. Each chapter demonstrates that within the conditions of nineteenth century modernity, the fragility and consequent fragmentation of individual identity is evoked in many different manifestations