Strongly Refuting Random CSPs Below the Spectral Threshold

Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be unsatisfiable with high probability. Strong refutation is the problem of certifying that no variable assignment satisfies more than a constant fraction of clauses; this is the natural algorithmic problem in the unsatisfiable regime (when $m/n = \omega(1)$). Intuitively, strong refutation should become easier as the clause density $m/n$ grows, because the contradictions introduced by the random clauses become more locally apparent. For CSPs such as $k$-SAT and $k$-XOR, there is a long-standing gap between the clause density at which efficient strong refutation algorithms are known, $m/n \ge \widetilde O(n^{k/2-1})$, and the clause density at which instances become unsatisfiable with high probability, $m/n = \omega (1)$. In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random $k$-XOR instances with clause density $m/n \ge \widetilde O(n^{(k/2-1)(1-\delta)})$ in time $\exp(\widetilde O(n^{\delta}))$ or in $\widetilde O(n^{\delta})$ rounds of the sum-of-squares hierarchy, for any $\delta \in [0,1)$ and any integer $k \ge 3$. Our algorithms provide a smooth transition between the clause density at which polynomial-time algorithms are known at $\delta = 0$, and brute-force refutation at the satisfiability threshold when $\delta = 1$. We also leverage our $k$-XOR results to obtain strong refutation algorithms for SAT (or any other Boolean CSP) at similar clause densities. Our algorithms match the known sum-of-squares lower bounds due to Grigoriev and Schonebeck, up to logarithmic factors. Additionally, we extend our techniques to give new results for certifying upper bounds on the injective tensor norm of random tensors

The Comic's Heartbeat: Framing Affective Structures in Comics History

This thesis proposed a structure-centered method for composing a critical history of comics. It examined the development building and breaking template--a rigid grid of panels depicting a narrative arc, which then leads to a panel depicting the arc's climax that breaks with that established structure--through four moments in the history of English-language comics. Rather than attempting a comprehensive overview of the building and breaking template, the thesis was a proof of concept for the application of recent advances in structure-oriented comics theory and in theories of affect--the pre-cognitive experience of emotion-- to specific comic structures. Examining the work of Bernard Krigstein, Art Spiegelman, David Mazzucchelli and Paul Karasik, and Joshua Cotter, the thesis placed these artists within a context of conditionality, dependent both upon the material circumstances of comics production and upon the unique semiotic and affective experiences of the comic's readers

Straightening Identities in the Onsager Algebra

The purpose of this work is to formulate and prove some straightening identities in the Onsager algebra. Our identities allow one to rewrite specific products of basis elements as linear combinations of products which are in a different order. Such identities could be helpful in understanding the representation theory of the Onsager algebra

Long-term impacts of wildfire and logging on forest soils

Soils are a fundamental component of terrestrial ecosystems, and play key roles in biogeochemical cycles and the ecology of microbial, plant and animal communities. Global increases in the intensity and frequency of ecological disturbances are driving major changes in the structure and function of forest ecosystems, yet little is known about the long-term impacts of disturbance on soils. Here we show that natural disturbance (fire) and human disturbances (clearcut logging and post-fire salvage logging) can significantly alter the composition of forest soils for far longer than previously recognized. Using extensive sampling across a multi-century chronosequence in some of the tallest and most carbon-dense forests worldwide (southern Australian, mountain ash (Eucalyptus regnans) forests), we provide compelling evidence that disturbance impacts on soils are evident up to least eight decades after disturbance, and potentially much longer. Relative to long-undisturbed forest (167 years old), sites subject to multiple fires, clearcut logging or salvage logging were characterized by soils with significantly lower values of a range of ecologically important measures at multiple depths, including available phosphorus and nitrate. Disturbance impacts on soils were most pronounced on sites subject to compounding perturbations, such as multiple fires and clearcut logging. Long-lasting impacts of disturbance on soil can have major ecological and functional implications.Thank you for the following groups for funding: the Paddy Pallin Foundation, Centre of Biodiversity Analysis, the Ecological Society of Australia and the Holsworth Wildlife Research Endowment fund

Multichip imager with improved optical performance near the butt region

A compound imager consists of two or more individual chips, each with at least one line array of sensors thereupon. Each chip has a glass support plate attached to the side from which light reaches the line arrays. The chips are butted together end-to-end to make large line arrays of sensors. Because of imperfections in cutting, the butted surfaces define a gap. Light entering in the region of the gap is either lost or falls on an individual imager other than the one for which it is intended. This results in vignetting and/or crosstalk near the butted region. The gap is filled with an epoxy resin or other similar material which, when hardened, has an index of referaction near that of the glass support plate

“If I am ready”: exploring the relationships between masculinities, pregnancy, and abortion among men in James Town, Ghana

The ability to exercise full sexual and reproductive health and rights is shaped by the contextual environment, meaning that women and pregnant people must navigate patriarchal norms when seeking care. Despite growing evidence that men are able to influence pregnancy outcomes, there remains a paucity of research on how and why men are able to involve themselves in pregnancy and abortion decision-making. This study interrogates the mechanisms that drive men’s involvement in pregnancies and abortions in James Town, Ghana. Data from a survey (n = 296) and in-depth interviews (n = 37) were collected between July 2020 and January 2021. The mixed-method analysis critically examined the relationship between men’s support for a pregnancy or abortion and their constructions of masculinities. Findings framed sex and reproduction as both a facilitator and a threat to men’s masculinity. Reproduction was an essential component of being a man. Men discussed the need to fulfil masculine ideals of being independent, provide financially, and be in an acceptable relationship in order to be ‘ready’ for fatherhood. However, men similarly operationalised the notion of ‘readiness’ as the driving force behind their involvement in abortion decision-making. As being a father without being ready could lead to social ostracism and derision, men discussed forcing their abortion desires onto their sexual partners and other pregnant people. Achieving masculine ideals, therefore, was a critical motivation for controlling women and pregnant people’s bodies. Understanding the role of masculinities is critical in acknowledging the contextual and environmental factors that women and pregnant people navigate, which contribute to continued reproductive injustices