Task Guided Compositional Representation Learning for ZDA

Zero-shot domain adaptation (ZDA) methods aim to transfer knowledge about a task learned in a source domain to a target domain, while data from target domain are not available. In this work, we address learning feature representations which are invariant to and shared among different domains considering task characteristics for ZDA. To this end, we propose a method for task-guided ZDA (TG-ZDA) which employs multi-branch deep neural networks to learn feature representations exploiting their domain invariance and shareability properties. The proposed TG-ZDA models can be trained end-to-end without requiring synthetic tasks and data generated from estimated representations of target domains. The proposed TG-ZDA has been examined using benchmark ZDA tasks on image classification datasets. Experimental results show that our proposed TG-ZDA outperforms state-of-the-art ZDA methods for different domains and tasks.

Rotational dynamics of bottom-heavy rods in turbulence from experiments and numerical simulations

We successfully perform the three-dimensional tracking in a turbulent fluid flow of small asymmetrical particles that are neutrally-buoyant and bottom-heavy, i.e., they have a non-homogeneous mass distribution along their symmetry axis. We experimentally show how a tiny mass inhomogeneity can affect the particle orientation along the preferred vertical direction and modify its tumbling rate. The experiment is complemented by a series of simulations based on realistic Navier-Stokes turbulence and on a point-like particle model that is capable to explore the full range of parameter space characterized by the gravitational torque stability number and by the particle aspect ratio. We propose a theoretical perturbative prediction valid in the high bottom-heaviness regime that agrees well with the observed preferential orientation and tumbling rate of the particles. We also show that the heavy-tail shape of the probability distribution function of the tumbling rate is weakly affected by the bottom-heaviness of the particles.

Multi-Pen Robust Robotic 3D Drawing Using Closed-Loop Planning

This paper develops a flexible and robust robotic system for autonomous drawing on 3D surfaces. The system takes 2D drawing strokes and a 3D target surface (mesh or point clouds) as input. It maps the 2D strokes onto the 3D surface and generates a robot motion to draw the mapped strokes using visual recognition, grasp pose reasoning, and motion planning. The system is flexible compared to conventional robotic drawing systems as we do not fix drawing tools to the end of a robot arm. Instead, a robot selects drawing tools using a vision system and holds drawing tools for painting using its hand. Meanwhile, with the flexibility, the system has high robustness thanks to the following crafts: First, a high-quality mapping method is developed to minimize deformation in the strokes. Second, visual detection is used to re-estimate the drawing tools pose before executing each drawing motion. Third, force control is employed to avoid noisy visual detection and calibration, and ensure a firm touch between the pen tip and a target surface. Fourth, error detection and recovery are implemented to deal with unexpected problems. The planning and executions are performed in a closed-loop manner until the strokes are successfully drawn. We evaluate the system and analyze the necessity of the various crafts using different real-word tasks. The results show that the proposed system is flexible and robust to generate a robot motion from picking and placing the pens to successfully drawing 3D strokes on given surfaces.

Multiple solutions of Kazdan-Warner equation on graphs in the negative case

Let $G=(V,E)$ be a finite connected graph, and let $kappa: Vrightarrow mathbb{R}$ be a function such that $int_Vkappa dmu<0$. We consider the following Kazdan-Warner equation on $G$:[Delta u+kappa-K_lambda e^{2u}=0,] where $K_lambda=K+lambda$ and $K: Vrightarrow mathbb{R}$ is a non-constant function satisfying $max_{xin V}K(x)=0$ and $lambdain mathbb{R}$. By a variational method, we prove that there exists a $lambda^*>0$ such that when $lambdain(-infty,lambda^*]$ the above equation has solutions, and has no solution when $lambdageq lambda^ast$. In particular, it has only one solution if $lambdaleq 0$; at least two distinct solutions if $0<lambda<lambda^*$; at least one solution if $lambda=lambda^ast$. This result complements earlier work of Grigoryan-Lin-Yang cite{GLY16}, and is viewed as a discrete analog of that of Ding-Liu cite{DL95} and Yang-Zhu cite{YZ19} on manifolds.

Heat transfer enhancement in Rayleigh-Benard convection using a single passive barrier

In this numerical study on Rayleigh-Benard convection we seek to improve the heat transfer by passive means. To this end we introduce a single tilted conductive barrier centered in an aspect ratio one cell, breaking the symmetry of the geometry and to channel the ascending hot and descending cold plumes. We study the global and local heat transfer and the flow organization for Rayleigh numbers $10^5 leq Ra leq 10^9$ for a fixed Prandtl number of $Pr=4.3$. We find that the global heat transfer can be enhanced up to $18%$, and locally around $800%$. The averaged Reynolds number is always decreased when a barrier is introduced, even for those cases where the global heat transfer is increased. We map the entire parameter space spanned by the orientation and the size of a single barrier for $Ra=10^8$.

Translate the Facial Regions You Like Using Region-Wise Normalization

Though GAN (Generative Adversarial Networks) based technique has greatly advanced the performance of image synthesis and face translation, only few works available in literature provide region based style encoding and translation. We propose in this paper a region-wise normalization framework, for region level face translation. While per-region style is encoded using available approach, we build a so called RIN (region-wise normalization) block to individually inject the styles into per-region feature maps and then fuse them for following convolution and upsampling. Both shape and texture of different regions can thus be translated to various target styles. A region matching loss has also been proposed to significantly reduce the inference between regions during the translation process. Extensive experiments on three publicly available datasets, i.e. Morph, RaFD and CelebAMask-HQ, suggest that our approach demonstrate a large improvement over state-of-the-art methods like StarGAN, SEAN and FUNIT. Our approach has further advantages in precise control of the regions to be translated. As a result, region level expression changes and step by step make up can be achieved. The video demo is available at https://youtu.be/ceRqsbzXAfk.

Selected topics on reaction-diffusion-advection models from spatial ecology

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented.

Stacked invasion waves in a competition-diffusion model with three species

We investigate the spreading properties of a three-species competition-diffusion system, which is non-cooperative. We apply the Hamilton-Jacobi approach, due to Freidlin, Evans and Souganidis, to establish upper and lower estimates of spreading speed of the slowest species, in terms of the spreading speed of two faster species, and show that the estimates are sharp in some situations. The spreading speed will first be characterized as the free boundary point of the viscosity solution for certain variational inequality cast in the space of speeds. Its exact formulas will then be derived by solving the variational inequality explicitly. To the best of our knowledge, this is the first theoretical result on three-species competition system in unbounded domains.

Multi-task Batch Reinforcement Learning with Metric Learning

We tackle the Multi-task Batch Reinforcement Learning problem. Given multiple datasets collected from different tasks, we train a multi-task policy to perform well in unseen tasks sampled from the same distribution. The task identities of the unseen tasks are not provided. To perform well, the policy must infer the task identity from collected transitions by modelling its dependency on states, actions and rewards. Because the different datasets may have state-action distributions with large divergence, the task inference module can learn to ignore the rewards and spuriously correlate $textit{only}$ state-action pairs to the task identity, leading to poor test time performance. To robustify task inference, we propose a novel application of the triplet loss. To mine hard negative examples, we relabel the transitions from the training tasks by approximating their reward functions. When we allow further training on the unseen tasks, using the trained policy as an initialization leads to significantly faster convergence compared to randomly initialized policies (up to $80%$ improvement and across 5 different Mujoco task distributions). We name our method $textbf{MBML}$ ($textbf{M}text{ulti-task}$ $textbf{B}text{atch}$ RL with $textbf{M}text{etric}$ $textbf{L}text{earning}$).

Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data

This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial data are exponential decaying. By establishing a comparison principle for Hamilton-Jacobi equations, we are able to apply the Hamilton-Jacobi approach for Fisher-KPP equation due to Freidlin, Evans and Souganidis. As a result, the exact formulas of spreading speeds and their dependence on initial data are derived. Our results indicate that sometimes the spreading speed of the slower species is nonlocally determined. Connections of our results with the traveling profile due to Tang and Fife, as well as the more recent spreading result of Girardin and Lam, will be discussed.