668 research outputs found
Mapping the Focal Points of WordPress: A Software and Critical Code Analysis
Programming languages or code can be examined through numerous analytical lenses. This project is a critical analysis of WordPress, a prevalent web content management system, applying four modes of inquiry. The project draws on theoretical perspectives and areas of study in media, software, platforms, code, language, and power structures. The applied research is based on Critical Code Studies, an interdisciplinary field of study that holds the potential as a theoretical lens and methodological toolkit to understand computational code beyond its function. The project begins with a critical code analysis of WordPress, examining its origins and source code and mapping selected vulnerabilities. An examination of the influence of digital and computational thinking follows this. The work also explores the intersection of code patching and vulnerability management and how code shapes our sense of control, trust, and empathy, ultimately arguing that a rhetorical-cultural lens can be used to better understand code\u27s controlling influence. Recurring themes throughout these analyses and observations are the connections to power and vulnerability in WordPress\u27 code and how cultural, processual, rhetorical, and ethical implications can be expressed through its code, creating a particular worldview. Code\u27s emergent properties help illustrate how human values and practices (e.g., empathy, aesthetics, language, and trust) become encoded in software design and how people perceive the software through its worldview. These connected analyses reveal cultural, processual, and vulnerability focal points and the influence these entanglements have concerning WordPress as code, software, and platform. WordPress is a complex sociotechnical platform worthy of further study, as is the interdisciplinary merging of theoretical perspectives and disciplines to critically examine code. Ultimately, this project helps further enrich the field by introducing focal points in code, examining sociocultural phenomena within the code, and offering techniques to apply critical code methods
Fundamental and Applied Problems of the String Theory Landscape
In this thesis we study quantum corrections to string-derived effective actions \textit{per se} as well as their implications for phenomenologically relevant setups like the \textit{Large Volume Scenario} (LVS) and the \textit{anti-D3-brane} uplift.
In the first part of this thesis, we improve the understanding of string loop corrections on general Calabi-Yau orientifolds from an effective field theory perspective by proposing a new classification scheme for quantum corrections. Thereby, we discover new features of string loop corrections, like for instance possible logarithmic effects in the Kahler and scalar potential, which are relevant for phenomenological applications like models of inflation.
In the next part of the thesis, we derive a simple and explicit formula, the \textit{LVS parametric tadpole constraint} (PTC),
that ensures that the anti-D3-brane uplifted LVS dS vacuum is protected against the most dangerous higher order corrections.
The main difficulty appears to be the small uplifting contribution which is necessary due to the exponentially large volume obtained via the LVS. This in turn requires a large negative contribution to the tadpole which is quantified in the PTC. As the negative contribution to the tadpole is limited in weakly coupled string theories, the PTC represents a concrete challenge for the LVS.
The last part of the thesis investigates the impact of corrections to the brane-flux annihilation process discovered by Kachru, Pearson, and Verlinde (KPV) on which the anti-D3-brane uplift is based. We find that corrections drastically alter the KPV analysis with the result that much more flux in the Klebanov-Strassler throat is required than previously assumed in order to control the leading corrections on the NS5-brane. The implication for the LVS with standard anti-D3-brane uplift can again be quantified by the PTC. Incorporating this new bound significantly increases the required negative contribution to the tadpole. In addition, we uncover a new uplifting mechanism not relying on large fluxes and hence deep warped throats, thereby sidestepping the main difficulties related to the PTC
On Hamilton cycles in graphs defined by intersecting set systems
In 1970 Lov\'asz conjectured that every connected vertex-transitive graph
admits a Hamilton cycle, apart from five exceptional graphs. This conjecture
has recently been settled for graphs defined by intersecting set systems, which
feature prominently throughout combinatorics. In this expository article, we
retrace these developments and give an overview of the many different
ingredients in the proofs
Homological algebra and moduli spaces in topological field theories
This is a survey of various types of Floer theories (both in symplectic
geometry and gauge theory) and relations among them.Comment: 56 pages 12 Figure
The spinor bundle on loop space
We give a construction of the spinor bundle of the loop space of a string
manifold together with its fusion product, inspired by ideas from Stolz and
Teichner. The spinor bundle is a super bimodule bundle for a bundle of Clifford
von Neumann algebras over the free path space, and the fusion product is
defined using Connes fusion of such bimodules. As the main result, we prove
that a spinor bundle with fusion product on a manifold X exists if and only X
is string.Comment: 86 pages; Some minor corrections; added 2 figures; divested material
on super bundle gerbes to Appendix
Torsion in cohomology and dimensional reduction
Conventional wisdom dictates that factors in the integral
cohomology group of a compact manifold cannot be
computed via smooth -forms. We revisit this lore in light of the dimensional
reduction of string theory on , endowed with a -structure metric that
leads to a supersymmetric EFT. If massive -form eigenmodes of the Laplacian
enter the EFT, then torsion cycles coupling to them will have a non-trivial
smeared delta form, that is an EFT long-wavelength description of -form
currents of the -cycles of . We conjecture that, whenever torsion
cycles are calibrated, their linking number can be computed via their smeared
delta forms. From the EFT viewpoint, a torsion factor in cohomology corresponds
to a gauge symmetry realised by a St\"uckelberg-like action, and
calibrated torsion cycles to BPS objects that source the massive fields
involved in it.Comment: 44 pages + appendice
Moduli Stabilization in String Theory
We give an overview of moduli stabilization in compactifications of string
theory. We summarize current methods for construction and analysis of vacua
with stabilized moduli, and we describe applications to cosmology and particle
physics. This is a contribution to the Handbook of Quantum Gravity.Comment: 74 pages. Invited chapter for the Handbook of Quantum Gravity (edited
by Cosimo Bambi, Leonardo Modesto, and Ilya Shapiro, Springer 2023
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Path properties of KPZ models
In this thesis we investigate large deviation and path properties of a few models within the Kardar-Parisi-Zhang (KPZ) universality class.
The KPZ equation is the central object in the KPZ universality class. It is a stochastic PDE describing various objects in statistical mechanics such as random interface growth, directed polymers, interacting particle systems. In the first project we study one point upper tail large deviations of the KPZ equation (t,x) started from narrow wedge initial data. We obtain precise expression of the upper tail LDP in the long time regime for the KPZ equation. We then extend our techniques and methods to obtain upper tail LDP for the asymmetric exclusion process model, which is a prelimit of the KPZ equation.
In the next direction, we investigate temporal path properties of the KPZ equation. We show that the upper and lower law of iterated logarithms for the rescaled KPZ temporal process occurs at a scale (log log )²/³ and (log log )¹/³ respectively. We also compute the exact Hausdorff dimension of the upper level sets of the solution, i.e., the set of times when the rescaled solution exceeds (log log )²/³. This has relevance from the point of view of fractal geometry of the KPZ equation.
We next study superdiffusivity and localization features of the (1+1)-dimensional continuum directed random polymer whose free energy is given by the KPZ equation. We show that for a point-to-point polymer of length and any ⋲ (0,1), the point on the path which is distance away from the origin stays within a (1) stochastic window around a random point _, that depends on the environment. This provides an affirmative case of the folklore `favorite region' conjecture. Furthermore, the quenched density of the point when centered around _, converges in law to an explicit random density function as → ∞ without any scaling. The limiting random density is proportional to ^{-(x)} where (x) is a two-sided 3D Bessel process with diffusion coefficient 2. Our proof techniques also allow us to prove properties of the KPZ equation such as ergodicity and limiting Bessel behaviors around the maximum. In a follow up project, we show that the annealed law of polymer of length , upon ²/³ superdiffusive scaling, is tight (as → ∞) in the space of ([0,1]) valued random variables. On the other hand, as → 0, under diffusive scaling, we show that the annealed law of the polymer converges to Brownian bridge.
In the final part of this thesis, we focus on an integrable discrete half-space variant of the CDRP, called half-space log-gamma polymer.We consider the point-to-point log-gamma polymer of length 2 in a half-space with i.i.d.Gamma⁻¹(2) distributed bulk weights and i.i.d. Gamma⁻¹(+) distributed boundary weights for > 0 and > -. We establish the KPZ exponents (1/3 fluctuation and 2/3 transversal) for this model when ≥ 0. In particular, in this regime, we show that after appropriate centering, the free energy process with spatial coordinate scaled by ²/³ and fluctuations scaled by ¹/³ is tight.
The primary technical contribution of our work is to construct the half-space log-gamma Gibbsian line ensemble and develop a toolbox for extracting tightness and absolute continuity results from minimal information about the top curve of such half-space line ensembles. This is the first study of half-space line ensembles. The ≥ 0 regime correspond to a polymer measure which is not pinned at the boundary. In a companion work, we investigate the < 0 setting. We show that in this case, the endpoint of the point-to-line polymer stays within (1) window of the diagonal. We also show that the limiting quenched endpoint distribution of the polymer around the diagonal is given by a random probability mass function proportional to the exponential of a random walk with log-gamma type increments
Crystals for shifted key polynomials
This article continues our study of - and -key polynomials, which are
(non-symmetric) "partial" Schur - and -functions as well as "shifted"
versions of key polynomials. Our main results provide a crystal interpretation
of - and -key polynomials, namely, as the characters of certain connected
subcrystals of normal crystals associated to the queer Lie superalgebra
. In the -key case, the ambient normal crystals are the
-crystals studied by Grantcharov et al., while in the -key
case, these are replaced by the extended -crystals recently
introduced by the first author and Tong. Using these constructions, we propose
a crystal-theoretic lift of several conjectures about the decomposition of
involution Schubert polynomials into - and -key polynomials. We verify
these generalized conjectures in a few special cases. Along the way, we
establish some miscellaneous results about normal -crystals and
Demazure -crystals.Comment: 60 pages, 6 figure
Coulomb and Higgs Phases of -manifolds
Ricci flat manifolds of special holonomy are a rich framework as models of
the extra dimensions in string/-theory. At special points in vacuum moduli
space, special kinds of singularities occur and demand a physical
interpretation. In this paper we show that the topologically distinct
-holonomy manifolds arising from desingularisations of codimension four
orbifold singularities due to Joyce and Karigiannis correspond physically to
Coulomb and Higgs phases of four dimensional gauge theories. The results
suggest generalisations of the Joyce-Karigiannis construction to arbitrary
ADE-singularities and higher order twists which we explore in detail in
explicitly solvable local models. These models allow us to derive an
isomorphism between moduli spaces of Ricci flat metrics on these non-compact
-manifolds and flat ADE-connections on compact flat 3-manifolds which we
establish explicitly for .Comment: 22 page
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