arXiv subjects

Hao Wu

Publications and source records attributed to Hao Wu.

At least 793 records · Page 44Linked to original sources

arXiv2019

Cake Cutting on Graphs: A Discrete and Bounded Proportional Protocol

The classical cake cutting problem studies how to find fair allocations of a heterogeneous and divisible resource among multiple agents. Two of the most commonly studied fairness concepts in cake cutting are proportionality and envy-freeness. It is well known that a proportional allocation among $n$ agents can be found efficiently via simple protocols [16]. For envy-freeness, in a recent breakthrough, Aziz and Mackenzie [5] proposed a discrete and bounded envy-free protocol for any number of players. However, the protocol suffers from high multiple-exponential query complexity and it remains open to find simpler and more efficient envy-free protocols. In this paper we consider a variation of the cake cutting problem by assuming an underlying graph over the agents whose edges describe their acquaintance relationships, and agents evaluate their shares relatively to those of their neighbors. An allocation is called locally proportional if each agent thinks she receives at least the average value over her neighbors. Local proportionality generalizes proportionality and is in an interesting middle ground between proportionality and envy-freeness: its existence is guaranteed by that of an envy-free allocation, but no simple protocol is known to produce such a locally proportional allocation for general graphs. Previous works showed locally proportional protocols for special classes of graphs, and it is listed in both [1] and [8] as an open question to design simple locally proportional protocols for more general classes of graphs. In this paper we completely resolved this open question by presenting a discrete and bounded locally proportional protocol for any given graphs. Our protocol has a query complexity of only single exponential, which is significantly smaller than the six towers of $n$ query complexity of the envy-free protocol given in [5].

cs.DS↗

arXiv2019

Learning to Reconstruct and Understand Indoor Scenes from Sparse Views

This paper proposes a new method for simultaneous 3D reconstruction and semantic segmentation of indoor scenes. Unlike existing methods that require recording a video using a color camera and/or a depth camera, our method only needs a small number of (e.g., 3-5) color images from uncalibrated sparse views as input, which greatly simplifies data acquisition and extends applicable scenarios. Since different views have limited overlaps, our method allows a single image as input to discern the depth and semantic information of the scene. The key issue is how to recover relatively accurate depth from single images and reconstruct a 3D scene by fusing very few depth maps. To address this problem, we first design an iterative deep architecture, IterNet, that estimates depth and semantic segmentation alternately, so that they benefit each other. To deal with the little overlap and non-rigid transformation between views, we further propose a joint global and local registration method to reconstruct a 3D scene with semantic information from sparse views. We also make available a new indoor synthetic dataset simultaneously providing photorealistic high-resolution RGB images, accurate depth maps and pixel-level semantic labels for thousands of complex layouts, useful for training and evaluation. Experimental results on public datasets and our dataset demonstrate that our method achieves more accurate depth estimation, smaller semantic segmentation errors and better 3D reconstruction results, compared with state-of-the-art methods.

cs.CV↗

arXiv2019

Joint Reasoning for Temporal and Causal Relations

Understanding temporal and causal relations between events is a fundamental natural language understanding task. Because a cause must be before its effect in time, temporal and causal relations are closely related and one relation even dictates the other one in many cases. However, limited attention has been paid to studying these two relations jointly. This paper presents a joint inference framework for them using constrained conditional models (CCMs). Specifically, we formulate the joint problem as an integer linear programming (ILP) problem, enforcing constraints inherently in the nature of time and causality. We show that the joint inference framework results in statistically significant improvement in the extraction of both temporal and causal relations from text.

cs.CL↗

arXiv2019

Adaptive Learning Material Recommendation in Online Language Education

Recommending personalized learning materials for online language learning is challenging because we typically lack data about the student's ability and the relative difficulty of learning materials. This makes it hard to recommend appropriate content that matches the student's prior knowledge. In this paper, we propose a refined hierarchical knowledge structure to model vocabulary knowledge, which enables us to automatically organize the authentic and up-to-date learning materials collected from the internet. Based on this knowledge structure, we then introduce a hybrid approach to recommend learning materials that adapts to a student's language level. We evaluate our work with an online Japanese learning tool and the results suggest adding adaptivity into material recommendation significantly increases student engagement.

cs.IR↗

arXiv2019

Random products of matrices: a dynamical point of view

We study random products of matrices in SL_2(C) from the point of view of holomorphic dynamics. For non-elementary measures with finite first moment we obtain the exponential convergence towards the stationary measure in Sobolev norm. As a consequence we obtain the exponentially fast equidistribution of forward images of points towards the stationary measure. We also give a new proof of the Central Limit Theorem for the norm cocycle under a second moment condition, originally due to Benoist-Quint, and obtain some general regularity results for stationary measures.

math.CV↗

arXiv2019

UniVSE: Robust Visual Semantic Embeddings via Structured Semantic Representations

We propose Unified Visual-Semantic Embeddings (UniVSE) for learning a joint space of visual and textual concepts. The space unifies the concepts at different levels, including objects, attributes, relations, and full scenes. A contrastive learning approach is proposed for the fine-grained alignment from only image-caption pairs. Moreover, we present an effective approach for enforcing the coverage of semantic components that appear in the sentence. We demonstrate the robustness of Unified VSE in defending text-domain adversarial attacks on cross-modal retrieval tasks. Such robustness also empowers the use of visual cues to resolve word dependencies in novel sentences.

cs.CV↗

arXiv2019

Variational Selection of Features for Molecular Kinetics

The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long-time kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of twelve fast-folding protein simulations, and show that our procedure leads to more efficient model selection.

physics.bio-ph↗

arXiv2019

Experimental creation and annihilation of nonvolatile magnetic skyrmions using voltage control of magnetic anisotropy without an external magnetic field

In this work, we utilize voltage controlled magnetic anisotropy (VCMA) to manipulate magnetic skyrmions that are fixed in space. Memory devices based on this strategy can potentially be of smaller footprint and better energy efficiency than current-controlled motion-based skyrmionic devices. To demonstrate VCMA induced manipulation of skyrmions, we fabricate antiferromagnet/ferromagnet/oxide heterostructure films where skyrmions can be stabilized without any external magnetic field due to the presence of exchange bias. These isolated skyrmions were annihilated by applying a voltage pulse that increased PMA. On the other hand, decreasing PMA promoted formation of more skyrmions. Furthermore, skyrmions can be created from chiral domains by increasing PMA of the system. To corroborate our experimental observations, we performed micromagnetic simulation. The proposed method could potentially lead to novel skyrmion-based memory devices.

cond-mat.mes-hall↗

arXiv2019

A State-Failure--Network Method to Identify Critical Components in Power Systems

In order to mitigate cascading failure blackout risks in power systems, the critical components whose failures lead to high blackout risks should be identified. In this paper, such critical components are identified by the state-failure network (SF-network) formed by cascading failure chain and loss data, which can be gathered from either utilities or simulations. The failures along the chains are recombined in the SF-network, where each failure is allocated a value that can reveal the blackout risks after their occurrences. Thus, critical failures can be identified in the SF-network where the failures raise up blackout risks, and thus the critical components can be found based on their critical failure risks. The simulation results validate the effectiveness of the proposed method.

physics.soc-ph↗

arXiv2019

Identification of kinetic order parameters for non-equilibrium dynamics

A popular approach to analyze the dynamics of high-dimensional many-body systems, such as macromolecules, is to project the trajectories onto a space of slowly-varying collective variables, where subsequent analyses are made, such as clustering or estimation of free energy profiles or Markov state models (MSMs). However, existing "dynamical" dimension reduction methods, such as the time-lagged independent component analysis (TICA) are only valid if the dynamics obeys detailed balance (microscopic reversibility) and typically require long, equilibrated simulation trajectories. Here we develop a dimension reduction method for non-equilibrium dynamics based on the recently developed Variational Approach for Markov Processes (VAMP) by Wu and Noé. VAMP is illustrated by obtaining a low-dimensional description of a single file ion diffusion model and by identifying long-lived states from molecular dynamics simulations of the KcsA channel protein in an external electrochemical potential. This analysis provides detailed insights into the coupling of conformational dynamics, the configuration of the selectivity filter, and the conductance of the channel. We recommend VAMP as a replacement for the less general TICA method.

physics.chem-ph↗

arXiv2019

Delay and Power Tradeoff with Consideration of Caching Capabilities in Dense Wireless Networks

Enabling caching capabilities in dense small cell networks (DSCNs) has a direct impact on file delivery delay and power consumption. Most existing work studied these two performance metrics separately in cache-enabled DSCNs. However, file delivery delay and power consumption are coupled with each other and cannot be minimized simultaneously. In this paper, we investigate the optimal tradoff between these two performance metrics. Firstly, we formulate the joint file delivery delay and power consumption optimization (JDPO) problem where power control, user association and file placement are jointly considered. Then we convert it to a form that can be handled by Generalized Benders Decomposition (GDB). with GDB, we decompose the converted JDPO problem into two smaller problems, i.e., primal problem related to power control and master problem related to user association and file placement. An iterative algorithm is proposed and proved to be $ε$-optimal, in which the primal problem and master problem are solved iteratively to approach the optimal solution. To further reduce the complexity of the master problem, an accelerated algorithm based on semi-definite relaxation is proposed. Finally, the simulation results demonstrate that the proposed algorithm can approach the optimal tradeoff between file delivery delay and power consumption.

eess.SP↗

arXiv2019

Global and Local Multiple SLEs for $κ\leq 4$ and Connection Probabilities for Level Lines of GFF

This article pertains to the classification of multiple Schramm-Loewner evolutions (SLE). We construct the pure partition functions of multiple SLE$(κ)$ with $κ\in (0,4]$ and relate them to certain extremal multiple SLE measures, thus verifying a conjecture from [BBK05, KP16]. We prove that the two approaches to construct multiple SLEs - the global, configurational construction of [KL07, Law09a] and the local, growth process construction of [BBK05, Dub07, Gra07, KP16] - agree. The pure partition functions are closely related to crossing probabilities in critical statistical mechanics models. With explicit formulas in the special case of $κ= 4$, we show that these functions give the connection probabilities for the level lines of the Gaussian free field (GFF) with alternating boundary data. We also show that certain functions, known as conformal blocks, give rise to multiple SLE(4) that can be naturally coupled with the GFF with appropriate boundary data.

math.PR↗

arXiv2019

Convergence to equilibrium for a bulk--surface Allen--Cahn system coupled through a Robin boundary condition

We consider a coupled bulk--surface Allen--Cahn system affixed with a Robin-type boundary condition between the bulk and surface variables. This system can also be viewed as a relaxation to a bulk--surface Allen--Cahn system with non-trivial transmission conditions. Assuming that the nonlinearities are real analytic, we prove the convergence of every global strong solution to a single equilibrium as time tends to infinity. Furthermore, we obtain an estimate on the rate of convergence. The proof relies on an extended Lojasiewicz--Simon type inequality for the bulk--surface coupled system. Compared with previous works, new difficulties arise as in our system the surface variable is no longer the trace of the bulk variable, but now they are coupled through a nonlinear Robin boundary condition.

math.AP↗

arXiv2019

Soft Label Memorization-Generalization for Natural Language Inference

Often when multiple labels are obtained for a training example it is assumed that there is an element of noise that must be accounted for. It has been shown that this disagreement can be considered signal instead of noise. In this work we investigate using soft labels for training data to improve generalization in machine learning models. However, using soft labels for training Deep Neural Networks (DNNs) is not practical due to the costs involved in obtaining multiple labels for large data sets. We propose soft label memorization-generalization (SLMG), a fine-tuning approach to using soft labels for training DNNs. We assume that differences in labels provided by human annotators represent ambiguity about the true label instead of noise. Experiments with SLMG demonstrate improved generalization performance on the Natural Language Inference (NLI) task. Our experiments show that by injecting a small percentage of soft label training data (0.03% of training set size) we can improve generalization performance over several baselines.

cs.CL↗

arXiv2019

An Energetic Variational Approach for the Cahn--Hilliard Equation with Dynamic Boundary Condition: Model Derivation and Mathematical Analysis

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range interactions of the material with the solid wall. Our first aim in this paper is to propose a new class of dynamic boundary conditions for the Cahn--Hilliard equation in a rather general setting. The derivation is based on an energetic variational approach that combines the least action principle and Onsager's principle of maximum energy dissipation. One feature of our model is that it naturally fulfills three important physical constraints such as conservation of mass, dissipation of energy and force balance relations. Next, we provide a comprehensive analysis of the resulting system of partial differential equations. Under suitable assumptions, we prove the existence and uniqueness of global weak/strong solutions to the initial boundary value problem with or without surface diffusion. Furthermore, we establish the uniqueness of asymptotic limit as $t\to+\infty$ and characterize the stability of local energy minimizers for the system.

math.AP↗

arXiv2019

Long-time Dynamics and Optimal Control of a Diffuse Interface Model for Tumor Growth

We investigate the long-time dynamics and optimal control problem of a diffuse interface model that describes the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type equation for the tumor cell fraction and a reaction-diffusion equation for the nutrient. The possible medication that serves to eliminate tumor cells is in terms of drugs and is introduced into the system through the nutrient. In this setting, the control variable acts as an external source in the nutrient equation. First, we consider the problem of `long-time treatment' under a suitable given source and prove the convergence of any global solution to a single equilibrium as $t\to+\infty$. Then we consider the `finite-time treatment' of a tumor, which corresponds to an optimal control problem. Here we also allow the objective cost functional to depend on a free time variable, which represents the unknown treatment time to be optimized. We prove the existence of an optimal control and obtain first order necessary optimality conditions for both the drug concentration and the treatment time. One of the main aim of the control problem is to realize in the best possible way a desired final distribution of the tumor cells, which is expressed by the target function $ϕ_Ω$. By establishing the Lyapunov stability of certain equilibria of the state system (without external source), we see that $ϕ_Ω$ can be taken as a stable configuration, so that the tumor will not grow again once the finite-time treatment is completed.

math.AP↗

arXiv2019

Deep Generative Markov State Models

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.

stat.ML↗

arXiv2019

Cherenkov Radiation Induced by Megavolt X-Ray Beams in the Second Near-Infrared Window

Although the Cherenkov light contains mostly short-wavelength components, it is beneficial in the aspect of imaging to visualize it in the second near-infrared (NIR-II) window. In this study, Cherenkov imaging was performed within the NIR-II range on megavolt X-ray beams delivered by a medical linear accelerator. A shielding system was used to reduce the noises of the NIR-II image, enabling high quality signal acquisition. It was demonstrated that the NIR-II Cherenkov imaging is potentially a tool for radiotherapy dosimetry, and correlates well with different parameters. The NIR-II Cherenkov imaging is less susceptible to scattering, while more susceptible to absorption, compared with the visible-near-infrared imaging. Finally, a mouse was used to demonstrate this technology on animals. These results indicate the potentials to apply NIR-II Cherenkov imaging in the practice of radiotherapy.

physics.med-ph↗