Perturbative Correlation Functions and Scattering Amplitudes in Planar N=4 Supersymmetric Yang-Mills

In this thesis, we study the integrands of a special four-point correlation function formed of protected half-BPS operators and scattering amplitudes in planar supersymmetric N=4 Yang-Mills. We use the "soft-collinear bootstrap" method to construct integrands of the aforementioned correlator and four-point scattering amplitudes to eight loops. Both have a unique representation in terms of (dual) conformal integrands with specified coefficients. The result is then extended to ten loops, by introducing two graphical relations, called the "triangle" and "pentagon" rules. These relations provide consistency conditions on the coefficients, and when combined with the "square" rule, prove sufficient to fix the answer to ten loops. We provide derivations for the graphical relations and illustrate their application with examples. The result exposes novel features seen for the first time at eight loops, that continue to be present through to ten loops. For example, the integrand includes terms that are finite even on-shell and terms that are divergent even off-shell (so-called "pseudoconformal" integrals). We then proceed to study the correlator/amplitude duality by taking six and seven adjacent points of the four-point correlator to be light-like separated. A conformal basis (with rational coefficients) is used to extract amplitude integrands for both six and seven particles up to two loops - more precisely, the complete one-loop amplitude and parity-even two-loop amplitude (at two loops, we use a refined prescriptive basis). We also construct an alternative six-point one-loop basis involving integrands with conformal cross-ratio coefficients, and reverse the duality to algebraically extract integrands from an ansatz, by introducing the Gram determinant. We expect the former approach to be applicable to n-points at arbitrary loop-order l, by going to one extra order of perturbation in the correlator (to determine all parity-odd l-loop ambiguities)

Using Color Thresholding and Contouring to Understand Coral Reef Biodiversity

This paper presents research outcomes of understanding coral reef biodiversity through the usage of various computer vision applications and techniques. It aims to help further analyze and understand the coral reef biodiversity through the usage of color thresholding and contouring onto images of the ARMS plates to extract groups of microorganisms based on color. The results are comparable to the manual markup tool developed to do the same tasks and shows that the manual process can be sped up using computer vision. The paper presents an automated way to extract groups of microorganisms based on color without the use of manual work

Higher spin gravity

Diese Dissertation ist den Quantenaspekten von Gravitationen höherer Spins (GRAHSs) und den ihnen zugrundeliegenden algebraischen Strukturen gewidmet. Theorien höherer Spins enthalten unendlichdimensionale Symmetrien, die mächtig genug sein sollten, um keine relevanten Gegenterme zuzulassen. Aus diesem Grund wird seit langem erwartet, dass GRAHSs endlich, oder zumindest renormierbar sind. Sobald gezeigt ist, dass diese Eigenschaft tatsächlich realisiert wird, macht sie Theorien höherer Spins zu interessanten Quantengravitationsmodellen. Wenn das keine-Gegenterme-Argument funktioniert, reduziert sich das Problem, eine quantenkonsistente Theorie höherer Spins zu konstruieren, bemerkenswerterweise auf das Problem, ein konsistentes klassisches Modell von GRAHS zu finden. Eine der interessantesten Klassen von GRAHSs ist die chirale GRAHS, die sowohl in der Minkowski- als auch in der AdS-Raumzeit existiert. Sie ist momentan die einzige Theorie mit propagierenden Feldern höherer Spins und einer recht einfachen Wirkung. Die Theorie ist auf perturbativer Ebene lokal. Die Wirkung der chiralen GRAHS ist in der Lichtkegel-Eichung bekannt und vermeidet alle Theoreme, welche die Existenz einer Theorie höherer Spins im flachen Raum verbieten. Wir studieren die Struktur der Quantenkorrekturen in der chiralen GRAHS im Minkowskiraum im Detail. Wir zeigen, dass aufgrund einer nichttrivialen Kürzung unter den Feynmandiagrammen dank einer spezifischen Form der Wechselwirkungen (dem Kopplungs-Verschwörungs-Mechanismus), alle Baumniveau-Amplituden verschwinden; wir analysieren im Detail zwei-, drei- und vier-Punkt Einschleifenamplituden und zeigen, dass diese UV-konvergent sind. Mit Hilfe von Unitaritätsschnitten berechnen wir die komplette n-Punkt Einschleifenamplitude und zeigen, dass sie aus drei Faktoren besteht: (i) der Einschleifenamplitude in QCD oder SDYM mit allen Helizitäten plus; (ii) einem bestimmten kinematischen Verzierungsfaktor für höhere Spins; (iii) einem rein numerischen Faktor der Gesamtanzahl der Freiheitsgrade. Im Kontext von AdS/KFT wird vermutet, dass GRAHSs dual zu recht einfachen konformen Feldtheorien (KFTs) sind: zu freien und kritischen Vektormodellen (Typ-A), freien Fermionen und Gross–Neveu-Modellen (Typ-B) und, allgemeiner, zu Chern–Simons-Materie- Theorien. Wir studieren im Detail die Vakuum-Einschleifenkorrekturen in verschiedenen Theorien höherer Spins in der anti-de Sitter (AdS) Raumzeit. Für die Typ-A-Theorie in AdSd+1 beweisen wir die Vermutung, dass die freie Energie für alle ganzzahligen Spins verschwindet und der freien Energie einer Kugel eines freien Skalarfeldes für alle geraden Spins gleicht. Wir erweitern dieses Resultat auf alle nicht-ganzzahligen Dimensionen und reproduzieren insbesondere die freie-Energie-Korrektur zur 4 − ε Wilson–Fisher KFT als einen Einschleifeneffekt in der Typ-A-Theorie auf AdS5−ε. Wir berechnen ebenfalls die Beiträge fermionischer Felder höherer Spins, die für supersymmetrische GRAHS relevant sind. Es wird gezeigt, dass diese exakt mit der Vorhersage der KFT übereinstimmen. Der Beitrag bestimmter Felder gemischter Symmetrie, die in Typ-B GRAHS vorkommen, wird ebenfalls berechnet. Der letztere Beitrag führt (in geraden Raumzeitdimensionen) auf eine Frage, die zu beantworten bleibt. Freie KFTs haben unendlichdimensionale globale Symmetrien, die in Algebras höherer Spins manifestiert sind. Die holographisch dualen GRAHSs sollten im Prinzip komplett durch diese Symmetrie bestimmt sein. Deshalb ist die einzige Information, die wir benötigen, um eine Theorie höherer Spins in AdS zu konstruieren, eine Algebra höherer Spins, die aus ihrer dualen freien KFT extrahiert werden kann. In dieser Dissertation rekonstruieren wir die Typ-A GRAHS in AdS5 auf der Ebene der formal konsistenten klassischen Bewegungsgleichungen (formale GRAHS).This dissertation is dedicated to the quantum aspects of higher spin gravities (HSGRAs) and to their underlining algebraic structures. Higher-spin theories are governed by infinite-dimensional symmetries called higher-spin symmetries. Higher-spin symmetry should be powerful enough to leave no room for any relevant counterterms. Therefore, higher spin gravities have long been expected to be finite or at least renormalizable. This feature, once shown to be realized, makes higher-spin theories interesting toy models of Quantum Gravity. Remarkably, if the no-counterterm argument works, the problem of constructing a quantum consistent higher-spin theory downgrades to a problem of finding a consistent classical model of higher-spin gravity. One of the most interesting classes of HSGRAs is chiral HSGRA, which exists both in Minkowski and AdS spacetime. It is the only theory at present with propagating massless higher spin fields and a rather simple action. The theory is perturbatively local. The action of the chiral theory is known in the light-cone gauge and and avoids all No-Go theorems that forbid the existence of higher-spin theories in flat space. We study in detail the structure of quantum corrections in the Minkowski Chiral HSGRA. We show that all tree-level amplitudes vanish, which is due to a nontrivial cancellation among all Feynman diagrams thanks to the specific form of the interactions (coupling conspiracy mechanism); we analyze in detail two-, three- and four-point one-loop amplitudes and show that they are UV-convergent. Using unitarity cuts we compute the complete one-loop n-point amplitude and show that it consists of three factors: (i) all-plus helicity one-loop amplitude in QCD or SDYM; (ii) a certain kinematical higher spin dressing factor; (iii) a purely numerical factor of the total number of degrees of freedom. In the context of AdS/CFT, HSGRAs are conjectured to be dual to rather simple conformal field theories (CFT): free and critical vector models (Type-A), free fermion and Gross-Neveu models (Type-B) and, more generally, to Chern-Simons Matter theories. We study in detail vacuum one-loop corrections in various higher-spin theories in anti-de Sitter (AdS) spacetime. For the Type-A theory in AdSd+1 we prove the conjecture that the free energy vanishes for all integer spins and is equal to the sphere free energy of one free scalar field for all even spins. We extend this result to non-integer dimension and, in particular, reproduce the free energy correction to the 4 − ε Wilson-Fisher CFT as a one-loop effect in the Type- A theory on AdS5−ε. We also compute the contribution of fermionic higher spin fields that are relevant for supersymmetric HSGRA. These are shown to match precisely with the prediction of the CFT. The contribution of certain mixed-symmetry fields that appear in Type-B HSGRA is also computed. The latter leads to a puzzle (in even spacetime dimension) that remains to be resolved. Free CFTs have infinite-dimensional global symmetries manifested in higher spin algebras. The holographic dual HSGRAs should, in principle, be completely determined by this higher spin symmetry. Therefore, to construct a higher-spin theory in AdS, the only initial data we need is a higher spin algebra extracted from its free CFT dual. In this thesis, we reconstructed the Type-A HSGRA in AdS5 at the level of formally consistent classical equations of motion (Formal HSGRA)

‘The painting can be fake, but not the feeling’: an overview of the Vietnamese market through the lens of fake, forgery and copy paintings

A work of Vietnamese art crossed a million-dollar mark in the international art market in early 2017. The event was reluctantly seen as a sign of maturity from the Vietnamese art amidst the many existing problems. Even though the Vietnamese media has discussed the issues enthusiastically, there is a lack of literature from the Vietnamese academics examining the subject, and even rarer in from the market perspective. This paper aims to contribute an insightful perspective on the Vietnamese art market, and hesitantly the Vietnamese art as well, through the lens of fake, forgery and copy artworks. 35 cases of fake, forgery and copy paintings were found on the news and from the experts' wisdom. Through the examples, we argue that the Vietnamese art market is a temporary reaction to the immaturely rising of the Vietnamese art and the economy. Therefore, the art market is unable to function healthily unless the Vietnamese art and the economy developed

Persistent-Transient Duality: A Multi-mechanism Approach for Modeling Human-Object Interaction

Humans are highly adaptable, swiftly switching between different modes to progressively handle different tasks, situations and contexts. In Human-object interaction (HOI) activities, these modes can be attributed to two mechanisms: (1) the large-scale consistent plan for the whole activity and (2) the small-scale children interactive actions that start and end along the timeline. While neuroscience and cognitive science have confirmed this multi-mechanism nature of human behavior, machine modeling approaches for human motion are trailing behind. While attempted to use gradually morphing structures (e.g., graph attention networks) to model the dynamic HOI patterns, they miss the expeditious and discrete mode-switching nature of the human motion. To bridge that gap, this work proposes to model two concurrent mechanisms that jointly control human motion: the Persistent process that runs continually on the global scale, and the Transient sub-processes that operate intermittently on the local context of the human while interacting with objects. These two mechanisms form an interactive Persistent-Transient Duality that synergistically governs the activity sequences. We model this conceptual duality by a parent-child neural network of Persistent and Transient channels with a dedicated neural module for dynamic mechanism switching. The framework is trialed on HOI motion forecasting. On two rich datasets and a wide variety of settings, the model consistently delivers superior performances, proving its suitability for the challenge.Comment: Accepted at ICCV 202

The debates and the long-awaited reform

Trung Tran, Phuong-Thao T. Trinh, Thu-Trang Vuong, Hiep-Hung Pham (2019). Chapter 1. The debates and the long-awaited reform. In Quan-Hoang Vuong, Trung Tran (Eds.), The Vietnamese Social Sciences at a Fork in the Road (pp. 17–32). Warsaw, Poland: De Gruyter / Sciendo. DOI:10.2478/9783110686081-006 Online ISBN: 9783110686081 © 2019 De Gruyter / Sciend

To Know, To Love and To Heal: PhotoStory and Duo-Ethnography as Approaches to Enhancing Social Justice and Self-Actualization in High School Classrooms

This article explores using PhotoStory to promote social justice in the classroom. Interweaving Photovoice (Wang & Burris, 1997) with story-sharing results in PhotoStory, a unique teaching and learning approach that can empower voices of marginalized high school students. Through PhotoStory, we explore possibilities for self-actualization in high schools, where a primary pedagogical goal is to disrupt inequitable social orders and change oppressive behaviors and perceptions. Coming to critical consciousness for both teachers and students is vital, leading to engagement in dialogical pedagogy (Mthethwa-Sommers, 2014). As bell hooks (1994) asserts, oppression emanates in and through differences in relation to sex/gender, class and race. Similarly, Freire (1970) highlights the critical role of literacy skills to equip those who are oppressed to speak truth to power. Contextualized by habitus (Bourdieu, 1986), creators of PhotoStory documentaries come to understand their own and others’ lived experiences, enhancing individual and collective empathy, and promoting healing, offering holistic ways to connect through culturally responsive learning, and flipped and flattened pedagogies. By applying duoethnography (Sawyer & Norris, 2013), three authors, two graduate students and one professor discuss and critique this art-based pedagogical method via experiences of utilizing PhotoStory as an experiential teaching and learning tool. Although the scholars are different in relation to age, status, gender and sexual identities, they are committed to exploring an ethic of care and pedagogical self-actualization that serves our need “to know, to love, and to heal”