arXiv subjects

Huy Nguyen

Publications and source records attributed to Huy Nguyen.

At least 91 records · Page 5Linked to original sources

arXiv2022

On Multimarginal Partial Optimal Transport: Equivalent Forms and Computational Complexity

We study the multi-marginal partial optimal transport (POT) problem between $m$ discrete (unbalanced) measures with at most $n$ supports. We first prove that we can obtain two equivalence forms of the multimarginal POT problem in terms of the multimarginal optimal transport problem via novel extensions of cost tensor. The first equivalence form is derived under the assumptions that the total masses of each measure are sufficiently close while the second equivalence form does not require any conditions on these masses but at the price of more sophisticated extended cost tensor. Our proof techniques for obtaining these equivalence forms rely on novel procedures of moving mass in graph theory to push transportation plan into appropriate regions. Finally, based on the equivalence forms, we develop optimization algorithm, named ApproxMPOT algorithm, that builds upon the Sinkhorn algorithm for solving the entropic regularized multimarginal optimal transport. We demonstrate that the ApproxMPOT algorithm can approximate the optimal value of multimarginal POT problem with a computational complexity upper bound of the order $\tilde{\mathcal{O}}(m^3(n+1)^{m}/ \varepsilon^2)$ where $\varepsilon > 0$ stands for the desired tolerance.

stat.ML↗

arXiv2022

Entropic Gromov-Wasserstein between Gaussian Distributions

We study the entropic Gromov-Wasserstein and its unbalanced version between (unbalanced) Gaussian distributions with different dimensions. When the metric is the inner product, which we refer to as inner product Gromov-Wasserstein (IGW), we demonstrate that the optimal transportation plans of entropic IGW and its unbalanced variant are (unbalanced) Gaussian distributions. Via an application of von Neumann's trace inequality, we obtain closed-form expressions for the entropic IGW between these Gaussian distributions. Finally, we consider an entropic inner product Gromov-Wasserstein barycenter of multiple Gaussian distributions. We prove that the barycenter is a Gaussian distribution when the entropic regularization parameter is small. We further derive a closed-form expression for the covariance matrix of the barycenter.

math.ST↗

arXiv2021

On Robust Optimal Transport: Computational Complexity and Barycenter Computation

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost of robust optimal transport in $\widetilde{\mathcal{O}}(\frac{n^2}{\varepsilon})$ time, in which $n$ is the number of supports of the probability distributions and $\varepsilon$ is the desired error. Furthermore, we investigate a fixed-support robust barycenter problem between $m$ discrete probability distributions with at most $n$ number of supports and develop an approximating algorithm based on iterative Bregman projections (IBP). For the specific case $m = 2$, we show that this algorithm can approximate the optimal barycenter value in $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon})$ time, thus being better than the previous complexity $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon^2})$ of the IBP algorithm for approximating the Wasserstein barycenter.

cs.LG↗

arXiv2020

Physical rendering of synthetic spaces for topological sound transport

Synthetic dimensions can be rendered in the physical space and this has been achieved with photonics and cold atomic gases, however, little to no work has been succeeded in acoustics because acoustic wave-guides cannot be weakly coupled in a continuous fashion. Here, we establish the theoretical principles and for the first time manufacture acoustic crystals composed of arrays of acoustic cavities strongly coupled through modulated channels to evidence one-dimensional (1D) and two-dimensional (2D) dynamic topological pumpings. In particular, the topological edge-bulkedge and corner-bulk-corner transport are physically illustrated in finite-sized acoustic structures. We delineate the generated 2D and four-dimensional (4D) quantum Hall effects by calculating first and second Chern numbers and demonstrating robustness against the geometrical imperfections. Synthetic dimensions could provide a powerful way for acoustic topological wave steering and open up a new platform to explore higher-order topological matter in dimensions four and higher.

cond-mat.mes-hall↗

arXiv2020

Multicomponent superfluidity in two-color QCD at finite density at next-to-leading order

In this paper, we study two-color, two-flavor QCD using chiral perturbation theory at next-to-leading order when the diquark chemical potential ($μ_{B}$) is equal to the isospin chemical potential ($μ_{I}$). For chemical potentials larger than the physical pion mass, the system is in a multicomponent superfluid phase with both pions and diquarks. We construct the one-loop effective potential using $χ$PT in the presence of an external multicomponent superfluid source and use the effective potential to calculate the chiral condensate, the multicomponent superfluid condensate and the (multicomponent) superfluid density. We also find the critical chemical potential and the order of the phase transition from the normal phase to the multicomponent condensed phase at next-to-leading order. The phase transition remains second order (as at tree-level) and the critical chemical potential is equal to the one-loop renormalized diquark (or pion) mass.

hep-ph↗

arXiv2020

Channel-Coupling Fano Resonance and Acoustic Metadamping

Fano resonance featuring asymmetric spectral profiles originates from the interference of local resonances and background continuum. Its narrow-band nature looks seemingly adverse to broadband noise cancellation purposes. In this study, we report theoretically on an intriguing acoustic metamaterial capable of generating multiple Fano-like resonances to realize a broadband sound barrier with satisfactory transmission loss performance. Our proposed design involves an effective channel characterized by effective parameters and short channels filled with air. The effective channel support both monopolar and dipolar modes which interact with the continuum state admitted by the short channels to generate a pair of Fano-like resonances. Due to the destructive interference of sound waves, the two resonances result in transmission loss overall exceeding 10 dB over a broad range 0.6-1.1 kHz. In order to further optimize the overall performance, we introduce metadamping by integrating additional viscous foams in the proposed unit cell. Furthermore, for future experimental tests, the dampened design is decoded into a real space-coiling cell which exhibits identical functionality and is assembled into a partition wall to ensure transmission loss over 10 dB across the range 0.32-4 Hz. Lastly, acoustic negative refraction is accessible by deploying two coupled space-coiling channels in a similar fashion. We believe this work paves the way for realizing effective broadband sound insulation devices with efficient ventilation.

physics.app-ph↗

arXiv2020

EPEM: Efficient Parameter Estimation for Multiple Class Monotone Missing Data

The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations through the data before yielding convergence. Moreover, those approaches may introduce extra noises and biases to the subsequent modeling. In this work, we derive exact formulas and propose a novel algorithm to compute the maximum likelihood estimators (MLEs) of a multiple class, monotone missing dataset when all the covariance matrices of all categories are assumed to be equal, namely EPEM. We then illustrate an application of our proposed methods in Linear Discriminant Analysis (LDA). As the computation is exact, our EPEM algorithm does not require multiple iterations through the data as other imputation approaches, thus promising to handle much less time-consuming than other methods. This effectiveness was validated by empirical results when EPEM reduced the error rates significantly and required a short computation time compared to several imputation-based approaches. We also release all codes and data of our experiments in one GitHub repository to contribute to the research community related to this problem.

cs.LG↗

arXiv2020

Differentially private $k$-means clustering via exponential mechanism and max cover

We introduce a new $(ε_p, δ_p)$-differentially private algorithm for the $k$-means clustering problem. Given a dataset in Euclidean space, the $k$-means clustering problem requires one to find $k$ points in that space such that the sum of squares of Euclidean distances between each data point and its closest respective point among the $k$ returned is minimised. Although there exist privacy-preserving methods with good theoretical guarantees to solve this problem [Balcan et al., 2017; Kaplan and Stemmer, 2018], in practice it is seen that it is the additive error which dictates the practical performance of these methods. By reducing the problem to a sequence of instances of maximum coverage on a grid, we are able to derive a new method that achieves lower additive error then previous works. For input datasets with cardinality $n$ and diameter $Δ$, our algorithm has an $O(Δ^2 (k \log^2 n \log(1/δ_p)/ε_p + k\sqrt{d \log(1/δ_p)}/ε_p))$ additive error whilst maintaining constant multiplicative error. We conclude with some experiments and find an improvement over previously implemented work for this problem.

cs.DS↗

arXiv2020

Differentially Private Decomposable Submodular Maximization

We study the problem of differentially private constrained maximization of decomposable submodular functions. A submodular function is decomposable if it takes the form of a sum of submodular functions. The special case of maximizing a monotone, decomposable submodular function under cardinality constraints is known as the Combinatorial Public Projects (CPP) problem [Papadimitriou et al., 2008]. Previous work by Gupta et al. [2010] gave a differentially private algorithm for the CPP problem. We extend this work by designing differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints, with competitive utility guarantees. We complement our theoretical bounds with experiments demonstrating empirical performance, which improves over the differentially private algorithms for the general case of submodular maximization and is close to the performance of non-private algorithms.

cs.LG↗

arXiv2020

Development of a Robotic System for Automated Decaking of 3D-Printed Parts

With the rapid rise of 3D-printing as a competitive mass manufacturing method, manual "decaking" - i.e. removing the residual powder that sticks to a 3D-printed part - has become a significant bottleneck. Here, we introduce, for the first time to our knowledge, a robotic system for automated decaking of 3D-printed parts. Combining Deep Learning for 3D perception, smart mechanical design, motion planning, and force control for industrial robots, we developed a system that can automatically decake parts in a fast and efficient way. Through a series of decaking experiments performed on parts printed by a Multi Jet Fusion printer, we demonstrated the feasibility of robotic decaking for 3D-printing-based mass manufacturing.

cs.RO↗

arXiv2019

Ge virtual substrates for high efficiency III-V solar cells: applications, potential and challenges

Virtual substrates based on thin Ge layers on Si by direct deposition have achieved high quality recently. Their application to high efficiency III-V solar cells is analyzed in this work. Replacing traditional Ge substrates with Ge/Si virtual substrates in standard lattice-matched and upright metamorphic GaInP/Ga(In)As/Ge solar cells is feasible according to our calculations using realistic parameters of state-of-the-art Ge solar cells but with thin bases (< 5um). The first experimental steps are tackled by implementing Ge single-junction and full GaInP/Ga(In)As/Ge triple-junction solar cells on medium quality Ge/Si virtual substrates with 5um thick Ge layers. The results show that the photocurrent in the Ge bottom cell is barely enough to achieve current matching with the upper subcells, but the overall performance is poor due to low voltages in the junctions. Moreover, observed cracks in the triple-junction structure point to the need to reduce the thickness of the Ge + III-V structure or using other advanced approaches to mitigate the thermal expansion coefficient mismatch effects, such as using embedded porous silicon. Next experimental work will pursue this objective and use more advanced Ge/Si virtual substrates available with lower threading dislocation densities and different Ge thicknesses.

physics.app-ph↗

arXiv2019

A probabilistic framework for tracking uncertainties in robotic manipulation

Precisely tracking uncertainties is crucial for robots to successfully and safely operate in unstructured and dynamic environments. We present a probabilistic framework to precisely keep track of uncertainties throughout the entire manipulation process. In agreement with common manipulation pipelines, we decompose the process into two subsequent stages, namely perception and physical interaction. Each stage is associated with different sources and types of uncertainties, requiring different techniques. We discuss which representation of uncertainties is the most appropriate for each stage (e.g. as probability distributions in SE(3) during perception, as weighted particles during physical interactions), how to convert from one representation to another, and how to initialize or update the uncertainties at each step of the process (camera calibration, image processing, pushing, grasping, etc.). Finally, we demonstrate the benefit of this fine-grained knowledge of uncertainties in an actual assembly task.

cs.RO↗

arXiv2018

Learning Embeddings for Product Visual Search with Triplet Loss and Online Sampling

In this paper, we propose learning an embedding function for content-based image retrieval within the e-commerce domain using the triplet loss and an online sampling method that constructs triplets from within a minibatch. We compare our method to several strong baselines as well as recent works on the DeepFashion and Stanford Online Product datasets. Our approach significantly outperforms the state-of-the-art on the DeepFashion dataset. With a modification to favor sampling minibatches from a single product category, the same approach demonstrates competitive results when compared to the state-of-the-art for the Stanford Online Products dataset.

cs.CV↗

arXiv2018

Inviscid limit for SQG in bounded domains

We prove that the limit of any weakly convergent sequence of Leray-Hopf solutions of dissipative SQG equations is a weak solution of the inviscid SQG equation in bounded domains.

math.AP↗

arXiv2017

Touch-based object localization in cluttered environments

Touch-based object localization is an important component of autonomous robotic systems that are to perform dexterous tasks in real-world environments. When the objects to locate are placed within clutters, this touch-based procedure tends to generate outlier measurements which, in turn, can lead to a significant loss in localization precision. Our first contribution is to address this problem by applying the RANdom SAmple Consensus (RANSAC) method to a Bayesian estimation framework. As RANSAC requires repeatedly applying the (computationally intensive) Bayesian updating step, it is crucial to improve that step in order to achieve practical running times. Our second contribution is therefore a fast method to find the most probable object face that corresponds to a given touch measurement, which yields a significant acceleration of the Bayesian updating step. Experiments show that our overall algorithm provides accurate localization in practical times, even when the measurements are corrupted by outliers.

cs.RO↗

arXiv2017

On singularity formation in a Hele-Shaw model

We discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in \cite{CDGKSZ93} and widely studied since. The model consists of a single one dimensional evolution equation for the thickness $2h = 2h(x,t)$ of a thin neck of fluid, \[ \partial_t h + \partial_x( h \, \partial_x^3 h) = 0\, , \] for $x\in (-1,1)$ and $t\ge 0$. The boundary conditions fix the neck height and the pressure jump: \[ h(\pm 1,t) = 1, \qquad \partial_{x}^2 h(\pm 1,t) = P>0. \] We prove that starting from smooth and positive $h$, as long as $h(x,t) >0$, for $x\in [-1,1], \; t\in [0,T]$, no singularity can arise in the solution up to time $T$. As a consequence, we prove for any $P>2$ and any smooth and positive initial datum that the solution pinches off in either finite or infinite time, i.e., $\inf_{[-1,1]\times[0,T_*)} h = 0$, for some $T_* \in (0,\infty]$. These facts have been long anticipated on the basis of numerical and theoretical studies.

math.AP↗

arXiv2017

A Deep Neural Architecture for Sentence-level Sentiment Classification in Twitter Social Networking

This paper introduces a novel deep learning framework including a lexicon-based approach for sentence-level prediction of sentiment label distribution. We propose to first apply semantic rules and then use a Deep Convolutional Neural Network (DeepCNN) for character-level embeddings in order to increase information for word-level embedding. After that, a Bidirectional Long Short-Term Memory Network (Bi-LSTM) produces a sentence-wide feature representation from the word-level embedding. We evaluate our approach on three Twitter sentiment classification datasets. Experimental results show that our model can improve the classification accuracy of sentence-level sentiment analysis in Twitter social networking.

cs.CL↗

arXiv2017

On the covariance of X in AX = XB

Hand-eye calibration, which consists in identifying the rigid- body transformation between a camera mounted on the robot end-effector and the end-effector itself, is a fundamental problem in robot vision. Mathematically, this problem can be formulated as: solve for X in AX = XB. In this paper, we provide a rigorous derivation of the covariance of the solution X, when A and B are randomly perturbed matrices. This fine-grained information is critical for applications that require a high degree of perception precision. Our approach consists in applying covariance propagation methods in SE(3). Experiments involving synthetic and real calibration data confirm that our approach can predict the covariance of the hand-eye transformation with excellent precision.

cs.RO↗