Bounding the Locating-Total Domination Number of a Tree in Terms of Its Annihilation Number

Suppose G = (V,E) is a graph with no isolated vertex. A subset S of V is called a locating-total dominating set of G if every vertex in V is adjacent to a vertex in S, and for every pair of distinct vertices u and v in V −S, we have N(u) ∩ S ≠ N(v) ∩ S. The locating-total domination number of G, denoted by γLt(G), is the minimum cardinality of a locating-total dominating set of G. The annihilation number of G, denoted by a(G), is the largest integer k such that the sum of the first k terms of the nondecreasing degree sequence of G is at most the number of edges in G. In this paper, we show that for any tree of order n ≥ 2, γLt(T) ≤ a(T) + 1 and we characterize the trees achieving this bound

The roles of random boundary conditions in spin systems

Random boundary conditions are one of the simplest realizations of quenched disorder. They have been used as an illustration of various conceptual issues in the theory of disordered spin systems. Here we review some of these result

"Lawless wingd & unconfind": aesthetics and the possibility of justice in early British romantic-era literature

This dissertation seeks to remedy the gap in the scholarship pertaining to the intersection of justice and aesthetics in 1790s British literature. While many critics have considered the literature of this period within the historical context of the French Revolution and its tumultuous aftermath, few have questioned how contemporary writers use specific aesthetic categories to argue for egalitarian social change. My inquiry, however, is not limited to a discussion of the overlap between aesthetics and justice in early British Romantic-era literature. In addition to examining how Helen Maria Williams, Mary Wollstonecraft, William Godwin, and William Blake radically rewrite sensibility and the sublime to articulate the possibility of justice, I also argue that these writers radically rethink subjectivity and demonstrate a parallel between formal aesthetic features and phenomenological identity structures. Thus, this dissertation is an overture into the possibility of justice vis-à-vis aesthetic expression of, as Wollstonecraft conflates the term, "sublime sensibility" about human suffering under inequitable laws and social customs. This aesthetic expression condemns the economic, physical, and emotional dislocation individuals endure, but it also harbors significant implications for how we understand the individual. Conflating the traditionally segregated categories of sensibility and the sublime, these writers also challenge the notion of a unitary self and articulate instead the existence of the subject as multiple, the "I" as "we," the "I" as, in Emmanuel Levinas's term, "being-for-the-other" or, in my phrasing, "communal subjectivity." Just as community in the form of egalitarian justice is essential to the aesthetic constructions of sensibility and the sublime of Williams, Wollstonecraft, Godwin, and Blake, so too is community at the heart of subjectivity as announced by these writers. Williams, Wollstonecraft, Godwin, and Blake deconstruct the traditional paradigms and uses of sensibility and the sublime, liberating them from aesthetic categories and resituating them onto sites of human egalitarian struggle. These writers articulate a possibility of justice beyond the written laws and social customs that aim to enforce compliance. The possibility of justice, for these writers, must be found beyond the call or command of the law, beyond, as Derrida describes it, the "force of law"; the possibility of justice, for these writers, is aesthetic(s)

DRAMATIC FORMS AND IDENTITY-FORMATION IN THE WORKS OF WILLIAM BLAKE

This study investigates the dramatic nature of William Blake’s multimedia art (poetry, painting, engraving) and the resulting implications for identity. Although he wrote little conventional drama, his illuminated works resonate with theatre and performance. The recent surge of Romantic scholarship devoted to theatricality and dramatic stagings offers new perspectives for understanding Blake’s art form and his conception of identity and identity-formation. The initial chapters of this project explore the way the dynamism between word and image in his works not only creates a distinctly dramatic genre but also encourages a specifically theatrical audience, one which is called on to act. Chapter one situates Blake in the theatre discourses of his time and interprets the illuminated works as a dramatic form that unsettles the binaries of mind/body, interior/exterior, reading/performance. The second chapter examines the opposing tendencies toward immersion and distancing in his works by drawing on contemporary media theory, Brecht’s alienation-effect, and medieval presence; Blake provokes a twofold process of alienation that leads to a self-conscious entrance into his works. Subsequent chapters examine individual and communal identity in light of Blake’s dramatic elements and contemporary theories of performativity, subjectivity, and identity-construction. Chapter three rereads The Book ofUrizen as a melodrama—a major dramatic form in the Romantic period—that locates the source of the fall in a kind of Althusserian interpellation, wherein individuals misrecognize themselves and are misrecognized as independent and isolated identities rather than as interrelated and dependent ones. The final chapter explores Milton and its depiction of inspiration and self-annihilation and the emerging tension between essentialist and constructivist notions of identity through the lens of theories of performativity, action, and performance. By viewing the illuminated works as dramatic performances and by analyzing them in relation to theatre and performativity, this study shows how Blake fits an alternative view of Romanticism, one that foregrounds vision, exteriority, and community. Moreover, it argues that Blake’s works uphold a model of identity based on action and an integration of mind and body, the imagination and the senses, and singularity and multiplicit