On the Central Charge of Spacetime Current Algebras and Correlators in String Theory on AdS3

Spacetime Virasoro and affine Lie algebras for strings propagating in AdS3 are known to all orders in $\alpha'$. The central extension of such algebras is a string vertex, whose expectation value can depend on the number of long strings present in the background but should be otherwise state-independent. In hep-th/0106004, on the other hand, a state-dependent expectation value was found. Another puzzling feature of the theory is lack of cluster decomposition property in certain connected correlators. This note shows that both problems can be removed by defining the free energy of the spacetime boundary conformal field theory as the Legendre transform of the formula proposed in the literature. This corresponds to pass from a canonical ensemble, where the number of fundamental strings that create the background can fluctuate, to a microcanonical one, where it is fixed.Comment: 10 pages, one minor correction, version published in JHE

On a Canonical Quantization of 3D Anti de Sitter Pure Gravity

We perform a canonical quantization of pure gravity on AdS3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,R)xSL(2,R). We first quantize the theory canonically on an asymptotically AdS space --which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kaehler quantization of Teichmuller space. After explicitly computing the Kaehler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,R) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS3.Comment: 61 pages, 7 figures. Minor misprints corrected, text in sections 1.3 and 5.4 clarified; version accepted for publication in JHEP. The first version was released jointly with arXiv:1508.04079 [hep-th

An Urban-Conscious Rapid Wind Downscaling Model for Early Design Stages

Assessments of urban contexts using existing microclimate models mostly fall short, when considering topographies along with complex layouts of buildings and streets, regardless of their significant influences on building performances and outdoor environments. The challenge exists mainly due to modelâ??s inherent complexities and the associated high computational costs. This becomes especially challenging at early design stages when time, expertise, and computational resources are limited, even though the opportunities for performance enhancement are greater than at later stages. This dissertation develops a wind downscaling model that can rapidly assess urban contexts to relate climate data in a large spatial resolution for a smaller-scale site. Surrounding slopes and terrains, up to a few kilometers in diameter, are considered to predict wind pressure on the volumetric boundary of a neighborhood and local wind speed. The new model strives for prediction accuracy and computational efficiency by employing the capacities of a computational fluid dynamics (CFD) simulation and of an existing mathematical method. The proposed model is composed of three parts: pressure database, speed database, and interpolation. The databases store wind data for existing urban contexts that are generated with CFD simulations. Using the databases, the interpolation approximates the pressure outcomes for a new urban context; thus, real-time CFD runs can be avoided for the model users. Independent development of data for pressure and speed facilitates the flexibility and expandability of the model. The proposed model showed an acceptable prediction accuracy, with average errors of less than 10%, compared to the full-scale CFD simulation for the same territorial scope. An exceptional computational efficiency is also shown, with a runtime in 0.308 seconds, which is 16568 times faster than the CFD simulation. This rate allows creation of a yearlong prediction in a few tens of minutes with a personal desktop computer. For non-experts, the pertinence of the model is enhanced with a limited number of parameters, making it easily adaptable during early design stages of buildings and urban design scales. Geometric sensitivities are embedded for incremental study, which is crucial to finding optimal solutions, toward more efficient, yet healthier, urban environments

Asymptotic Symmetries of Colored Gravity in Three Dimensions

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the $SU(N)$-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with $SU(N,N)\times SU(N,N)$ gauge group, the theory contains graviton, $SU(N)$ Chern-Simons gauge fields and massless spin-two multiplets in the $SU(N)$ adjoint representation, thus extending diffeomorphism to colored, nonabelian counterpart. We identify the asymptotic symmetry as Poisson algebra of generators associated with the residual global symmetries of the nonabelian diffeomorphism set by appropriately chosen boundary conditions. The resulting asymptotic symmetry algebra is a nonlinear extension of Virasoro algeba and $\widehat{\mathfrak{su}(N)}$ Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.Comment: 22 pages, published version in JHE

Biomechanically-Regularized Deformable Image Registration for Head and Neck Adaptive Radiation Therapy

Radiation treatment (RT), one of the best treatments available for head and neck (HN) cancer, may fail to accurately target tumors and spare surrounding healthy tissue that change in shape and location during 5-7 weeks of RT. This anatomical change can be monitored by calculating deformation maps from planning computed tomography (CT) image (taken prior to the start of RT) to treatment CT images (taken at every treatment fractions for patient setup) via deformable image registration (DIR). In response to the deformations estimated by DIR, initial radiation treatment plan established on the planning CT can be adjusted to deliver sufficient radiation dose to the tumors while sparing healthy tissue. However, since DIR is formulated as an optimization problem to find a deformation map that simply maximizes a similarity metric between two images, it may result in physically unreasonable deformations, such as bone warping. Moreover, DIR accuracy of HN soft tissue region is limited and parameter-dependent as reported in previous studies. Finally, previous studies have evaluated DIR accuracy with a limited number of landmarks, with which accuracy of volumetric deformation cannot be rigorously evaluated. The objective of this dissertation is 1) to improve registration accuracy of HN CT images by introducing penalty terms (from biomechanical principles) into B-spline DIR, in which deformation is represented using a linear combinations of B-spline functions, and 2) to develop an improved evaluation method for DIR accuracy based on finite element model (FE) model of HN region. First, a penalty for prevent the bone warping was developed to preserve inter-voxel distances within each of rigid regions. Second, a penalty that prevents resultant deformations from violating the static equilibrium equations of linear elastic material was used for the B-spline DIR of muscle in HN region. Third, a FE HN model was developed to generate deformation maps similar to those seen in patients that can be used as ground-truth for the evaluation of registration accuracy. The outcome of the dissertation would support research/development in RT of HN cancer by enabling the accurate estimation of deformations of healthy tissue surrounding tumor and the rigorous assessment of registration accuracy.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113532/1/jihun_1.pd

SNU_IDS at SemEval-2018 Task 12: Sentence Encoder with Contextualized Vectors for Argument Reasoning Comprehension

We present a novel neural architecture for the Argument Reasoning Comprehension task of SemEval 2018. It is a simple neural network consisting of three parts, collectively judging whether the logic built on a set of given sentences (a claim, reason, and warrant) is plausible or not. The model utilizes contextualized word vectors pre-trained on large machine translation (MT) datasets as a form of transfer learning, which can help to mitigate the lack of training data. Quantitative analysis shows that simply leveraging LSTMs trained on MT datasets outperforms several baselines and non-transferred models, achieving accuracies of about 70% on the development set and about 60% on the test set.Comment: SemEval 201

Slopes of smooth curves on Fano manifolds

Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds of dimension $n\geq 3$ with respect to smooth curves. The question turns out to be easy for curves of genus $\geq 1$ and the interest lies in the case of smooth rational curves. Our main result classifies completely the cases when a polarized Fano manifold $(X, -K_X)$ is not slope stable with respect to a smooth curve. Our result also states that a Fano threefold $X$ with Picard number 1 is slope stable with respect to every smooth curve unless $X$ is the projective space.Comment: 13 pages, Theorems in the original version were modified. This paper will be published in the Bulletin of the London Mathematical Societ