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Description
Computable properties of quantum states are given a dual gravitational interpretation via the AdS/CFT correspondence. For holographic states, boundary entanglement entropy is dual to the area of bulk geodesics, known as Ryu-Takayanagi surfaces. Furthermore, the viability of states to admit a holographic dual at all is constrained by their entanglement structure. Entanglement therefore defines a coarse classification of states in the Hilbert space. Similarly, how a state transforms under a group of operators also provides a classification on the Hilbert space. Certain states, e.g. stabilizer states, are invariant under large sets of operations, and consequently can be simulated on a classical computer. Cayley graphs offer a useful representation for a group of operators, where vertices represent group elements and edges represent group generators. In this representation, the orbit of a state under action of the group can also be represented as a ``reachability graph'', defined as a quotient of the group Cayley graph. Reachability graphs can be dressed to encode entanglement information, making them a useful tool for studying entanglement dynamics under quantum operations. Further quotienting a reachability graph by group elements that fix a chosen state property, e.g. entanglement entropy, builds a ``contracted graph''. Contracted graphs provide explicit bounds on state parameter evolution under quantum circuits. In this work, an upper bound on entropy vector evolution under Clifford group action is presented. Another important property of quantum systems is magic, which quantifies the difficulty of classically simulating a quantum state. Magic and entanglement are intimately related, but the two are not equivalent measures of complexity. Nonetheless, entanglement and magic play complementary roles when describing emergent gravitational phenomena in AdS/CFT. This manuscript describes the interplay between entanglement and magic, and offers a holographic interpretation for magic as cosmic brane back-reaction.
ContributorsMunizzi, William Richard (Author) / Keeler, Cynthia (Thesis advisor) / Parikh, Maulik (Committee member) / Baumgart, Matthew (Committee member) / Schmidt, Kevin (Committee member) / Arizona State University (Publisher)
Created2024
Description
The deficiency of American primary and secondary schools as compared to schools worldwide has long been documented. The Teaching Gap highlights exactly where our problems might lie, and lays out a plan for how to deal with it. Progress would be slow, but tangible. Our country, however, seems to prefer vast and immediate overhauls that have historically failed (see: New math, etc.). If we had implemented the changes in The Teaching Gap in the decade in which it was written, we would be seeing results by now. Instead, every change we make gets reverted. The Common Core State Standards will prove over the next few years to be either another one of these attempts or a large step in the right direction. It might finally be the latter, as its creation was informed by practices that work best in every state in the US, as well as high- performing countries around the world.
ContributorsMcKee, Emily (Author) / Sande, V. Carla (Thesis director) / Ashbrook, Mark (Committee member) / Schroeder, Darcy (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Identifying associations between genotypes and gene expression levels using next-generation technology has enabled systematic interrogation of regulatory variation underlying complex phenotypes. Understanding the source of expression variation has important implications for disease susceptibility, phenotypic diversity, and adaptation (Main, 2009). Interest in the existence of allele-specific expression in autosomal genes evolved with the increased awareness of the important role that variation in non-coding DNA sequences can play in determining phenotypic diversity, and the essential role parent-of-origin expression has in early development (Knight, 2004). As new implications of high-throughput sequencing are conceived, it is becoming increasingly important to develop statistical methods tailored to large and formidably complex data sets in order to maximize the biological insights derived from next-generation sequencing experiments. Here, a Bayesian hierarchical probability model based on the beta-binomial distribution is proposed as a possible approach for quantifying allele-specific expression from whole genome (WGS) and whole transcriptome (RNA-seq) data. Pipeline for the analysis of WGS and RNA-seq data sets from ten samples was developed and implemented, while allele-specific expression (ASE) was quantified from both haplotypes using individuals heterozygous at the tested variants utilizing the described methodology. Both computational and statistical framework applied accurately quantified ASE, achieving high reproducibility of already described allele-specific genes in the literature. In conclusion, described methodology provides a solid starting point for quantifying allele specific expression across whole genomes.
ContributorsMalenica, Ivana (Author) / Craig, David (Thesis director) / Rosenberg, Michael (Committee member) / Szelinger, Szabolcs (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12