Effects of interaction in BEC

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.Includes bibliographical references (p. 150-167).This thesis discusses a series of studies that investigate the effects of interaction - essentially the s-wave scattering - in the various properties of Bose-Einstein condensates (BEC). The phonon wavefunction in a BEC was measured using Bragg spectroscopy and compared with the well-known Bogoliubov theory. Phonons were first excited in a BEC of 3 x 107 condensed 23Na atoms via small-angle two-photon Bragg scattering. Large angle Bragg scattering was then used to probe the momentum distribution. We found reasonable agreement with the theory. With the same technique of Bragg diffraction, we studied the four-wave mixing process for matter waves. The BEC was split into two strong source waves and a weak seed wave. The s-wave scattering coherently mixed pairs of atoms from the sources into the seed and its conjugate wave, creating a pair-correlated atomic beams with "squeezed" number difference. A Feshbach resonance was used to produce ultracold Na2 molecules with initial phase-space density in excess of 20. Starting from an atomic BEC, a magnetic field ramp shifted a bound state from above the threshold of the unbound continuum to below, creating a molecular population with almost zero center-of-mass motion.(cont.) A reverse field ramp dissociated the cold molecules into free atom pairs carrying kinetic energy dependent on the ramp speed. This dependence provided a measure of the coupling strength between the bound state and the continuum. Condensates were loaded into optical lattices formed with retro-reflected single frequency lasers. Quantum phase transition from the superfluid state to Mott-insulator state was observed in a three dimensional lattice. The increased interaction and flattened dispersion relation led to strongly enhanced quantum depletion in the superfluid state.by Kaiwen Xu.Ph.D

Statistically Significant Concept-based Explanation of Image Classifiers via Model Knockoffs

A concept-based classifier can explain the decision process of a deep learning model by human-understandable concepts in image classification problems. However, sometimes concept-based explanations may cause false positives, which misregards unrelated concepts as important for the prediction task. Our goal is to find the statistically significant concept for classification to prevent misinterpretation. In this study, we propose a method using a deep learning model to learn the image concept and then using the Knockoff samples to select the important concepts for prediction by controlling the False Discovery Rate (FDR) under a certain value. We evaluate the proposed method in our synthetic and real data experiments. Also, it shows that our method can control the FDR properly while selecting highly interpretable concepts to improve the trustworthiness of the model.Comment: Accepted to IJCAI'2

DiffMorpher: Unleashing the Capability of Diffusion Models for Image Morphing

Diffusion models have achieved remarkable image generation quality surpassing previous generative models. However, a notable limitation of diffusion models, in comparison to GANs, is their difficulty in smoothly interpolating between two image samples, due to their highly unstructured latent space. Such a smooth interpolation is intriguing as it naturally serves as a solution for the image morphing task with many applications. In this work, we present DiffMorpher, the first approach enabling smooth and natural image interpolation using diffusion models. Our key idea is to capture the semantics of the two images by fitting two LoRAs to them respectively, and interpolate between both the LoRA parameters and the latent noises to ensure a smooth semantic transition, where correspondence automatically emerges without the need for annotation. In addition, we propose an attention interpolation and injection technique and a new sampling schedule to further enhance the smoothness between consecutive images. Extensive experiments demonstrate that DiffMorpher achieves starkly better image morphing effects than previous methods across a variety of object categories, bridging a critical functional gap that distinguished diffusion models from GANs

Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesis

In text-to-speech (TTS) synthesis, diffusion models have achieved promising generation quality. However, because of the pre-defined data-to-noise diffusion process, their prior distribution is restricted to a noisy representation, which provides little information of the generation target. In this work, we present a novel TTS system, Bridge-TTS, making the first attempt to substitute the noisy Gaussian prior in established diffusion-based TTS methods with a clean and deterministic one, which provides strong structural information of the target. Specifically, we leverage the latent representation obtained from text input as our prior, and build a fully tractable Schrodinger bridge between it and the ground-truth mel-spectrogram, leading to a data-to-data process. Moreover, the tractability and flexibility of our formulation allow us to empirically study the design spaces such as noise schedules, as well as to develop stochastic and deterministic samplers. Experimental results on the LJ-Speech dataset illustrate the effectiveness of our method in terms of both synthesis quality and sampling efficiency, significantly outperforming our diffusion counterpart Grad-TTS in 50-step/1000-step synthesis and strong fast TTS models in few-step scenarios. Project page: https://bridge-tts.github.io

Notch2 controls hepatocyte-derived cholangiocarcinoma formation in mice.

Liver cancer comprises a group of malignant tumors, among which hepatocellular carcinoma (HCC) and intrahepatic cholangiocarcinoma (ICC) are the most common. ICC is especially pernicious and associated with poor clinical outcome. Studies have shown that a subset of human ICCs may originate from mature hepatocytes. However, the mechanisms driving the trans-differentiation of hepatocytes into malignant cholangiocytes remain poorly defined. We adopted lineage tracing techniques and an established murine hepatocyte-derived ICC model by hydrodynamic injection of activated forms of AKT (myr-AKT) and Yap (YapS127A) proto-oncogenes. Wild-type, Notch1 flox/flox , and Notch2 flox/flox mice were used to investigate the role of canonical Notch signaling and Notch receptors in AKT/Yap-driven ICC formation. Human ICC and HCC cell lines were transfected with siRNA against Notch2 to determine whether Notch2 regulates biliary marker expression in liver tumor cells. We found that AKT/Yap-induced ICC formation is hepatocyte derived and this process is strictly dependent on the canonical Notch signaling pathway in vivo. Deletion of Notch2 in AKT/Yap-induced tumors switched the phenotype from ICC to hepatocellular adenoma-like lesions, while inactivation of Notch1 in hepatocytes did not result in significant histomorphological changes. Finally, in vitro studies revealed that Notch2 silencing in ICC and HCC cell lines down-regulates the expression of Sox9 and EpCAM biliary markers. Notch2 is the major determinant of hepatocyte-derived ICC formation in mice

Learning to Branch in Combinatorial Optimization with Graph Pointer Networks

Branch-and-bound is a typical way to solve combinatorial optimization problems. This paper proposes a graph pointer network model for learning the variable selection policy in the branch-and-bound. We extract the graph features, global features and historical features to represent the solver state. The proposed model, which combines the graph neural network and the pointer mechanism, can effectively map from the solver state to the branching variable decisions. The model is trained to imitate the classic strong branching expert rule by a designed top-k Kullback-Leibler divergence loss function. Experiments on a series of benchmark problems demonstrate that the proposed approach significantly outperforms the widely used expert-designed branching rules. Our approach also outperforms the state-of-the-art machine-learning-based branch-and-bound methods in terms of solving speed and search tree size on all the test instances. In addition, the model can generalize to unseen instances and scale to larger instances

Equirectangular image construction method for standard CNNs for Semantic Segmentation

360{\deg} spherical images have advantages of wide view field, and are typically projected on a planar plane for processing, which is known as equirectangular image. The object shape in equirectangular images can be distorted and lack translation invariance. In addition, there are few publicly dataset of equirectangular images with labels, which presents a challenge for standard CNNs models to process equirectangular images effectively. To tackle this problem, we propose a methodology for converting a perspective image into equirectangular image. The inverse transformation of the spherical center projection and the equidistant cylindrical projection are employed. This enables the standard CNNs to learn the distortion features at different positions in the equirectangular image and thereby gain the ability to semantically the equirectangular image. The parameter, {\phi}, which determines the projection position of the perspective image, has been analyzed using various datasets and models, such as UNet, UNet++, SegNet, PSPNet, and DeepLab v3+. The experiments demonstrate that an optimal value of {\phi} for effective semantic segmentation of equirectangular images is 6{\pi}/16 for standard CNNs. Compared with the other three types of methods (supervised learning, unsupervised learning and data augmentation), the method proposed in this paper has the best average IoU value of 43.76%. This value is 23.85%, 10.7% and 17.23% higher than those of other three methods, respectively