Fine Computability of Probability Distribution Functions and Computability of Probability Distributions on the Real Line

　We continue our work in [9] on an effective relationship between the sequence of probability distributions and the corresponding sequence of probability distribution functions. In order to deal with discontinuous distribution functions, we define the notion of Fine topology on the whole real line, and show that, when a probability distribution is associated with a Fine continuous distribution function, the computability of the former and the sequential computability of the latter can be effectively mutually translatable under a certain condition. The effectivity of the translations is secured by the treatment of the sequences of the objects in concern. The equivalences of effective convergences will also be proved

Computability of Probability Distributions and Distribution Functions

We define the computability of probability distributions on the real line as well as that of distribution functions. Mutual relationships between the computability notion of a probability distribution and that of the corresponding distribution function are discussed. It is carried out through attempts to effectivize some classical fundamental theorems concerning probability distributions. We then define the effective convergence of probability distributions as an effectivization of the classical vague convergence. For distribution functions, computability and effective convergence are naturally defined as real functions. A weaker effective convergence is also defined as an effectivization of pointwise convergence

Probabilistic Analysis of Slide-Rocking Structures Under Earthquake Loads

Estimates of rare seismic hazard are essential for the resilience of critical infrastructure and facilities. However, these estimates are highly uncertain at long return periods due to the lack of observed earthquake records. Several ground motion prediction equations have been proposed to close this gap and estimate rare seismic demands; however, these models were developed based on more moderate earthquake records and can yield physically unrealizable ground motions when extrapolated to long return periods. For this reason, seismologists have proposed using precariously balanced rocks (PBRs) as a way to constrain rare seismic hazard. PBRs are a type of fragile geologic structure whose upright existence indicates that a seismic event powerful enough to cause the structure to overturn has not yet occurred. PBRs are individual or stacks of freestanding rocks that tend to respond in rigid body modes, such as rocking and sliding, when subjected to earthquake loads. The behavior of these freestanding structures is very sensitive to small changes in geometry, position, and ground motion characteristics. As a result, reliable probabilistic relationships for the seismic response of freestanding structures are lacking. To this end, this thesis aims to rigorously evaluate and identify a robust probabilistic relationship between the intensity of a ground motion and the dynamic behavior of freestanding structures, including both rocking and sliding demands, such that PBRs can be used to constrain seismic hazard. The dynamic response of freestanding structures is modeled analytically via two-dimensional equations of motion. Various ground motion intensity measures are evaluated in both scalar and vector forms to identify an optimal predictor of structural response. After thorough analysis, a vector combination of Cumulative Absolute Velocity and Response Spectrum Intensity is selected. This relationship is then used in a case study to demonstrate the applicability of the vector intensity measure in a PBR analysis and comparison with current seismic hazard in the New Madrid Seismic Zone. Advisor: Christine E. Wittic

Failurists: When Things Go Awry

Failure is a popular topic of research. It has long been a source of study in fields such as sociology and anthropology, science and technology studies (STS), privacy and surveillance, cultural, feminist and media studies, art, theatre, film, and political science. When things go awry, breakdown, or rupture they can lead to valuable insights into the mundane mechanisms of social worlds. Yet, while failure is a familiar topic of research, failure in and as a tactic of research is far less visible, valued, and explored within academia. In this book the authors reflect upon the role of creative interventions as a critical mode for methods, research techniques, fieldwork, and knowledge transmission or impact. Here, failure is considered a productive part of engaging with and in the field. It is about acknowledging the ‘mess’ of the social and how we need methods, modes of attunement, and knowledge translation that address this complexity in nuanced ways. In this collection, interdisciplinary researchers and practitioners share their practices, insights, and challenges around rethinking failure beyond normalized tropes. Across four sections — Section I: Digitality, Archives, and Design; Section II: Care/Activism; Section III: Creative Critical Interventions; and Section IV: Play and the Senses — the contributors bring different subjectivities, relationalities, and positionalities — rhythms reflecting the numerous material, social, and digital encounters. Each subtheme is an invitation to probe certain areas of failure in all its complexity; an invitation to sit with someone’s own lived experience of failure and how it manifests in research practice and theory. What does failure mean? What does it do? What does putting failure under the microscope do to our assumptions around ontology and epistemologies? How can it be deployed to challenge norms in a time of great uncertainty, crisis, and anxiety? And what are some of the ways resilience and failure are interrelated

Coloring in the void: Absurdity and contemporary art

Boo Boo Bird is a song, or a poem perhaps, or a song and a poem, by the Scottish poet, songwriter and humorist Ivor Cutler. This wistful ballad describes the plight and flight of a mythical bird, the Boo Boo bird. What we discover through the song is that the Boo Boo bird has no defining features, in fact — it has no features at all. The Boo Boo bird is invisible and recognized only by its call: ‘boo boo, boo boo’. The repetition of the word is important, and the absurdity of the invisible bird is amplified by its childish double name; boo boo, like an infant’s first attempts at vocalization, or that informal way of referring to a failure, a mistake, a booboo. There is something haunting about the way Cutler sings to this impossible creature and it is this element which makes the work so compelling; that it can be simultaneously ridiculous and also very moving.1 It straddles a certain border between irony and sincerity. And it is this border, or rather the oscillation between the states of irony and sincerity and between falling and failing, that features in the works discussed within this chapter, tracing a line between things and what is at the outermost edge of things, namely, the void