Anomaly cancellation in the topological string

We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira-Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for open-closed topological B-model. At one loop this anomaly cancellation is analogous to the Green-Schwarz mechanism. As an application, we introduce a type I version of Kodaira-Spencer theory in complex dimensions 3 and 5. In complex dimension 5, we show that it can only be coupled consistently at the quantum level to holomorphic Chern-Simons theory with gauge group SO(32). This is analogous to the Green-Schwarz mechanism for the physical type I string. This coupled system is conjectured to be a supersymmetric localization of type I string theory. In complex dimension 3, the required gauge group is SO(8).Comment: 43 pages, 2 figures. Comments are welcom

Twisted supergravity and its quantization

Twisted supergravity is supergravity in a background where the bosonic ghost field takes a non-zero value. This is the supergravity counterpart of the familiar concept of twisting supersymmetric field theories. In this paper, we give conjectural descriptions of type IIA and IIB supergravity in $10$ dimensions. Our conjectural descriptions are in terms of the closed-string field theories associated to certain topological string theories, and we conjecture that these topological string theories are twists of the physical string theories. For type IIB, the results of arXiv:1505.6703 show that our candidate twisted supergravity theory admits a unique quantization in perturbation theory. This is despite the fact that the theories, like the original physical theories, are non-renormalizable. Although we do not prove our conjectures, we amass considerable evidence. We find that our candidates for the twisted supergravity theories contain the residual supersymmetry one would expect. We also prove (using heavily a result of Baulieu arXiv:1009.3893) the open string version of our conjecture: the theory living on a brane in the topological string theory is a twist of the maximally supersymmetric gauge theory living on the brane in the physical string theory.Comment: 72 page

Quantization of open-closed BCOV theory, I

This is the first in a series of papers which analyze the problem of quantizing the theory coupling Kodaira-Spencer gravity (or BCOV theory) on Calabi-Yau manifolds using the formalism for perturbative QFT developed by the first author. In this paper, we focus on flat space $\mathbb{C}^d$ for $d$ odd. We prove that there exists a unique quantization of the theory coupling BCOV theory and holomorphic Chern-Simons theory with gauge group the supergroup $GL(N \mid N)$. We deduce a canonically defined quantization of BCOV theory on its own. We also discuss some conjectural links between BCOV theory in various dimensions and twists of physical theories: in complex dimension $3$ we conjecture a relationship to twists of $(1,0)$ supersymmetric theories and in complex dimension $5$ to a twist of type IIB supergravity.Comment: 105 page

An end-to-end construction of doubly periodic minimal surfaces

Using Traizet's regeneration method, we prove that for each positive integer n there is a family of embedded, doubly periodic minimal surfaces with parallel ends in Euclidean space of genus 2n-1 and 4 ends in the quotient by the maximal group of translations. The genus 2n-1 family converges smoothly to 2n copies of Scherk's doubly periodic minimal surface. The only previously known doubly periodic minimal surfaces with parallel ends and genus greater than 3 limit in a foliation of Euclidean space by parallel planes

Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model

Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed that the B-model of mirror symmetry should be described by a quantum field theory on a Calabi-Yau variety, which they called the Kodaira-Spenser theory (we call it the BCOV theory). This is the first of three papers in which we construct and analyze the quantum BCOV theory. In this paper, we construct the classical field theory on a Calabi-Yau variety of arbitrary dimension; define what it means to give a quantization; analyze the relation Givental's symplectic formalism for Gromov-Witten theory; prove uniqueness of the quantization on an elliptic curve; and prove the Virasoro constraints on an elliptic curve. The second paper (arXiv:1112.4063) proves that the partition function of the quantum BCOV theory on the elliptic curve is equivalent to the Gromov-Witten theory of the mirror elliptic curve. The third paper, in progress, constructs the quantum BCOV theory on a general Calabi-Yau.Comment: 75 page

Air entrainment by a plunging jet under intermittent vortex conditions

This fluid dynamic video entry to the 2011 APS-DFD Gallery of Fluid Motion details the transient evolution of the free surface surrounding the impact region of a low-viscosity laminar liquid jet as it enters a quiescent pool. The close-up images depict the destabilization and breakup of the annular air gap and the subsequent entrainment of bubbles into the bulk liquid.Comment: 2 page abstract description, two video files (HQ = 1280x720, LQ = 640x360

Quantum spin transport and dynamics through a novel F/N junction

We study the spin transport in the low temperature regime (often referred to as the precession-dominated regime) between a ferromagnetic Fermi liquid (FFL) and a normal metal metallic Fermi liquid (NFL), also known as the F/N junction, which is considered as one of the most basic spintronic devices. In particular, we explore the propagation of spin waves and transport of magnetization through the interface of the F/N junction where nonequilibrium spin polarization is created on the normal metal side of the junction by electrical spin injection. We calculate the probable spin wave modes in the precession-dominated regime on both sides of the junction especially on the NFL side where the system is out of equilibrium. Proper boundary conditions at the interface are introduced to establish the transport of the spin properties through the F/N junction. A possible transmission conduction electron spin resonance (CESR) experiment is suggested on the F/N junction to see if the predicted spin wave modes could indeed propagate through the junction. Potential applications based on this novel spin transport feature of the F/N junction are proposed in the end.Comment: 7 pages, 2 figure

Latent Gaussian Mixture Models for Nationwide Kidney Transplant Center Evaluation

Five year post-transplant survival rate is an important indicator on quality of care delivered by kidney transplant centers in the United States. To provide a fair assessment of each transplant center, an effect that represents the center-specific care quality, along with patient level risk factors, is often included in the risk adjustment model. In the past, the center effects have been modeled as either fixed effects or Gaussian random effects, with various pros and cons. Our numerical analyses reveal that the distributional assumptions do impact the prediction of center effects especially when the effect is extreme. To bridge the gap between these two approaches, we propose to model the transplant center effect as a latent random variable with a finite Gaussian mixture distribution. Such latent Gaussian mixture models provide a convenient framework to study the heterogeneity among the transplant centers. To overcome the weak identifiability issues, we propose to estimate the latent Gaussian mixture model using a penalized likelihood approach, and develop sequential locally restricted likelihood ratio tests to determine the number of components in the Gaussian mixture distribution. The fitted mixture model provides a convenient means of controlling the false discovery rate when screening for underperforming or outperforming transplant centers. The performance of the methods is verified by simulations and by the analysis of the motivating data example

Training Neural Networks by Using Power Linear Units (PoLUs)

In this paper, we introduce "Power Linear Unit" (PoLU) which increases the nonlinearity capacity of a neural network and thus helps improving its performance. PoLU adopts several advantages of previously proposed activation functions. First, the output of PoLU for positive inputs is designed to be identity to avoid the gradient vanishing problem. Second, PoLU has a non-zero output for negative inputs such that the output mean of the units is close to zero, hence reducing the bias shift effect. Thirdly, there is a saturation on the negative part of PoLU, which makes it more noise-robust for negative inputs. Furthermore, we prove that PoLU is able to map more portions of every layer's input to the same space by using the power function and thus increases the number of response regions of the neural network. We use image classification for comparing our proposed activation function with others. In the experiments, MNIST, CIFAR-10, CIFAR-100, Street View House Numbers (SVHN) and ImageNet are used as benchmark datasets. The neural networks we implemented include widely-used ELU-Network, ResNet-50, and VGG16, plus a couple of shallow networks. Experimental results show that our proposed activation function outperforms other state-of-the-art models with most networks

The Gauss-Bonnet Formula for Harmonic Surfaces

We consider harmonic immersions in $\R^{\N}$ of compact Riemann surfaces with finitely many punctures where the harmonic coordinate functions are given as real parts of meromorphic functions. We prove that such surfaces have finite total Gauss curvature. The contribution of each end is a multiple of $2\pi$, determined by the maximal pole order of the meromorphic functions. This generalizes the well known Gackstatter-Jorge-Meeks formula for minimal surfaces. The situation is complicated as the ends are generally not conformally equivalent to punctured disks, nor does the surface have limit tangent planes.Comment: 30 pages, 4 figure