We study some versions of the cylindrical Hardy identities and inequalities in the style of Badia... more We study some versions of the cylindrical Hardy identities and inequalities in the style of Badiale-Tarantello [2]. We show that the best constants of the cylindrical Hardy inequalities can be improved when we consider functions on half-spaces. For more information see https://ejde.math.txstate.edu/Volumes/2020/75/abstr.html
Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it... more Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality. The value of sliced Wasserstein distance is the average of transportation cost between one-dimensional representations (projections) of original measures that are obtained by Radon Transform (RT). Despite its efficiency in the number of supports, estimating the sliced Wasserstein requires a relatively large number of projections in high-dimensional settings. Therefore, for applications where the number of supports is relatively small compared with the dimension, e.g., several deep learning applications where the mini-batch approaches are utilized, the complexities from matrix multiplication of Radon Transform become the main computational bottleneck. To address this issue, we propose to derive projections by linearly and randomly combining a smaller number of projections which are named bottleneck projections. We explain the usage of these projections by introducing Hierarchical Radon Transform (HRT) which is constructed by applying Radon Transform variants recursively. We then formulate the approach into a new metric between measures, named Hierarchical Sliced Wasserstein (HSW) distance. By proving the injectivity of HRT, we derive the metricity of HSW. Moreover, we investigate the theoretical properties of HSW including its connection to SW variants and its computational and sample complexities. Finally, we compare the computational cost and generative quality of HSW with the conventional SW on the task of deep generative modeling using various benchmark datasets including CIFAR10, CelebA, and Tiny ImageNet 1 .
Ksii Transactions on Internet and Information Systems, Dec 29, 2013
This version includes new figures and additional analysis compared to state-of-the-art methods as... more This version includes new figures and additional analysis compared to state-of-the-art methods as well as complete editing in English.
We propose a novel hashing-based matching scheme, called Locally Optimized Hashing (LOH), based o... more We propose a novel hashing-based matching scheme, called Locally Optimized Hashing (LOH), based on a state-of-the-art quantization algorithm that can be used for efficient, large-scale search, recommendation, clustering, and deduplication. We show that matching with LOH only requires set intersections and summations to compute and so is easily implemented in generic distributed computing systems. We further show application of LOH to: a) large-scale search tasks where performance is on par with other state-of-the-art hashing approaches; b) large-scale recommendation where queries consisting of thousands of images can be used to generate accurate recommendations from collections of hundreds of millions of images; and c) efficient clustering with a graph-based algorithm that can be scaled to massive collections in a distributed environment or can be used for deduplication for small collections, like search results, performing better than traditional hashing approaches while only requiring a few milliseconds to run. In this paper we experiment on datasets of up to 100 million images, but in practice our system can scale to larger collections and can be used for other types of data that have a vector representation in a Euclidean space.
We study classic streaming and sparse recovery problems using deterministic linear sketches, incl... more We study classic streaming and sparse recovery problems using deterministic linear sketches, including ℓ1/ℓ1 and ℓ∞/ℓ1 sparse recovery problems (the latter also being known as ℓ1-heavy hitters), norm estimation, and approximate inner product. We focus on devising a fixed matrix A ∈ R m×n and a deterministic recovery/estimation procedure which work for all possible input vectors simultaneously. Our results improve upon existing work, the following being our main contributions: • A proof that ℓ∞/ℓ1 sparse recovery and inner product estimation are equivalent, and that incoherent matrices can be used to solve both problems. Our upper bound for the number of measurements is m = O(ε -2 min{log n, (log n/ log(1/ε)) 2 }). We can also obtain fast sketching and recovery algorithms by making use of the Fast Johnson-Lindenstrauss transform. Both our running times and number of measurements improve upon previous work. We can also obtain better error guarantees than previous work in terms of a smaller tail of the input vector. • A new lower bound for the number of linear measurements required to solve ℓ1/ℓ1 sparse recovery. We show Ω(k/ε 2 + k log(n/k)/ε) measurements are required to recover an x ′ with x -x ′ 1 ≤ (1 + ε) x tail(k) 1, where x tail(k) is x projected onto all but its largest k coordinates in magnitude. • A tight bound of m = Θ(ε -2 log(ε 2 n)) on the number of measurements required to solve deterministic norm estimation, i.e., to recover x 2 ± ε x 1. For all the problems we study, tight bounds are already known for the randomized complexity from previous work, except in the case of ℓ1/ℓ1 sparse recovery, where a nearly tight bound is known. Our work thus aims to study the deterministic complexities of these problems.
International Journal of Advanced Computer Science and Applications, 2023
This paper introduces a real-time workflow for implementing neural networks in the context of aut... more This paper introduces a real-time workflow for implementing neural networks in the context of autonomous driving. The UNet architecture is specifically selected for road segmentation due to its strong performance and low complexity. To further improve the model's capabilities, Local Binary Convolution (LBC) is incorporated into the skip connections, enhancing feature extraction, and elevating the Intersection over Union (IoU) metric. The performance evaluation of the model focuses on road detection, utilizing the IOU metric. Two datasets are used for training and validation: the widely used KITTI dataset and a custom dataset collected within the ROS2 environment. Simulation validation is performed on both datasets to assess the performance of our model. The evaluation of our model on the KITTI dataset demonstrates an impressive IoU score of 97.90% for road segmentation. Moreover, when evaluated on our custom dataset, our model achieves an IoU score of 98.88%, which is comparable to the performance of conventional UNet models. Our proposed method to reconstruct the model structure and provide input feature extraction can effectively improve the performance of existing lane road segmentation methods.
HAL (Le Centre pour la Communication Scientifique Directe), 2011
In this paper, we study the div-curl-grad operators and some elliptic problems in the whole space... more In this paper, we study the div-curl-grad operators and some elliptic problems in the whole space R n and in the half-space R n + , with n ≥ 2. We consider data in weighted Sobolev spaces and in L 1 .
We prove that the limit of any weakly convergent sequence of Leray-Hopf solutions of dissipative ... more 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.
bioRxiv (Cold Spring Harbor Laboratory), May 5, 2022
Annotating cell types using single-cell transcriptome data usually requires binarizing the expres... more Annotating cell types using single-cell transcriptome data usually requires binarizing the expression data to distinguish between the background noise vs. real expression or low expression vs. high expression cases. A common approach is choosing a "reasonable" cutoff value, but it remains unclear how to choose it. In this work, we describe a simple yet effective approach for finding this threshold value.
Creating large, good quality labeled data has become one of the major bottlenecks for developing ... more Creating large, good quality labeled data has become one of the major bottlenecks for developing machine learning applications. Multiple techniques have been developed to either decrease the dependence of labeled data (zero/few-shot learning, weak supervision) or to improve the efficiency of labeling process (active learning). Among those, Weak Supervision has been shown to reduce labeling costs by employing hand crafted labeling functions designed by domain experts. We propose AutoWSa novel framework for increasing the efficiency of weak supervision process while decreasing the dependency on domain experts. Our method requires a small set of labeled examples per label class and automatically creates a set of labeling functions to assign noisy labels to numerous unlabeled data. Noisy labels can then be aggregated into probabilistic labels used by a downstream discriminative classifier. Our framework is fully automatic and requires no hyper-parameter specification by users. We compare our approach with different state-of-the-art work on weak supervision and noisy training. Experimental results show that our method outperforms competitive baselines.
Precisely tracking uncertainties is crucial for robots to successfully and safely operate in unst... more 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.
We study the maximum likelihood estimation (MLE) in the multivariate deviated model where the dat... more We study the maximum likelihood estimation (MLE) in the multivariate deviated model where the data are generated from the density function and (µ * , Σ * ) are unknown parameters to estimate. The main challenges in deriving the convergence rate of the MLE mainly come from two issues: (1) The interaction between the function h 0 and the density function f ; (2) The deviated proportion λ * can go to the extreme points of [0, 1] as the sample size tends to infinity. To address these challenges, we develop the distinguishability condition to capture the linear independent relation between the function h 0 and the density function f . We then provide comprehensive convergence rates of the MLE via the vanishing rate of λ * to zero as well as the distinguishability of two functions h 0 and f .
The efficiency droop characteristics of single quantum well (SQW) InGaN/GaN light-emitting diodes... more The efficiency droop characteristics of single quantum well (SQW) InGaN/GaN light-emitting diodes (LEDs) including the phase-space filling (PSF) effect are predicted by a three-dimensional (3-D) numerical simulation. The carrier transport is based on the solution of the 3-D non-linear Poisson and drift-diffusion equations for both holes and electrons. A modified formulation of the Shockley-Reed-Hall (SRH) coefficient is proposed to describe the SRH carrier lifetime behavior, which increases at a low excitation level and decreases at a higher one. The current crowding causes a non-uniform distribution of the carrier concentration in the active layer that leads to the inversion of the local internal quantum efficiency (IQE) under the n-pad region when the injection current density increases from low to high levels. To further understand the correlation of the efficiency droop with the PSF effect, we systematically investigate carrier transport in the SQW InGaN/GaN LEDs and how the different PSF effect coefficients affect the current-voltage curve and IQE. The lumped IQE found in this study agrees well with previous experimental measurements. Moreover, the PSF effect has a strong impact on the IQE behavior including its peak and droop in efficiency.
Predicting fund performance is beneficial to both investors and fund managers, and yet is a chall... more Predicting fund performance is beneficial to both investors and fund managers, and yet is a challenging task. In this paper, we have tested whether deep learning models can predict fund performance more accurately than traditional statistical techniques. Fund performance is typically evaluated by the Sharpe ratio, which represents the risk-adjusted performance to ensure meaningful comparability across funds. We calculated the annualised Sharpe ratios based on the monthly returns time series data for more than 600 open-end mutual funds investing in listed large-cap equities in the United States. We find that long short-term memory (LSTM) and gated recurrent units (GRUs) deep learning methods, both trained with modern Bayesian optimization, provide higher accuracy in forecasting funds' Sharpe ratios than traditional statistical ones. An ensemble method, which combines forecasts from LSTM and GRUs, achieves the best performance of all models. There is evidence to say that deep learning and ensembling offer promising solutions in addressing the challenge of fund performance forecasting.
Person re-ID matches persons across multiple nonoverlapping cameras. Despite the increasing deplo... more Person re-ID matches persons across multiple nonoverlapping cameras. Despite the increasing deployment of airborne platforms in surveillance, current existing person re-ID benchmarks' focus is on ground-ground matching and very limited efforts on aerial-aerial matching. We propose a new benchmark dataset -AG-ReID, which performs person re-ID matching in a new setting: across aerial and ground cameras. Our dataset contains 21,983 images of 388 identities and 15 soft attributes for each identity. The data was collected by a UAV flying at altitudes between 15 to 45 meters and a ground-based CCTV camera on a university campus. Our dataset presents a novel elevated-viewpoint challenge for person re-ID due to the significant difference in person appearance across these cameras. We propose an explainable algorithm to guide the person re-ID model's training with soft attributes to address this challenge. Experiments demonstrate the efficacy of our method on the aerial-ground person re-ID task. The dataset will be published and the baseline codes will be open-sourced at to facilitate research in this area.
Deep neural networks are often applied to medical images to automate the problem of medical diagn... more Deep neural networks are often applied to medical images to automate the problem of medical diagnosis. However, a more clinically relevant question that practitioners usually face is how to predict the future trajectory of a disease. Current methods for prognosis or disease trajectory forecasting often require domain knowledge and are complicated to apply. In this paper, we formulate the prognosis prediction problem as a one-to-many prediction problem. Inspired by a clinical decision-making process with two agents -a radiologist and a general practitioner -we predict prognosis with two transformer-based components that share information with each other. The first transformer in this framework aims to analyze the imaging data, and the second one leverages its internal states as inputs, also fusing them with auxiliary clinical data. The temporal nature of the problem is modeled within the transformer states, allowing us to treat the forecasting problem as a multi-task classification, for which we propose a novel loss. We show the effectiveness of our approach in predicting the development of structural knee osteoarthritis changes and forecasting Alzheimer's disease clinical status directly from raw multi-modal data. The proposed method outperforms multiple state-of-the-art baselines with respect to performance and calibration, both of which are needed for realworld applications. An open-source implementation of our method is made publicly available at .
This paper tackles the challenge of forensic medical image matching (FMIM) using deep neural netw... more This paper tackles the challenge of forensic medical image matching (FMIM) using deep neural networks (DNNs). FMIM is a particular case of content-based image retrieval (CBIR). The main challenge in FMIM compared to the general case of CBIR, is that the subject to whom a query image belongs may be affected by aging and progressive degenerative disorders, making it difficult to match data on a subject level. CBIR with DNNs is generally solved by minimizing a ranking loss, such as Triplet loss (TL), computed on image representations extracted by a DNN from the original data. TL, in particular, operates on triplets: anchor, positive (similar to anchor) and negative (dissimilar to anchor). Although TL has been shown to perform well in many CBIR tasks, it still has limitations, which we identify and analyze in this work. In this paper, we introduce (i) the AdaTriplet loss -an extension of TL whose gradients adapt to different difficulty levels of negative samples, and (ii) the AutoMargin method -a technique to adjust hyperparameters of margin-based losses such as TL and our proposed loss dynamically. Our results are evaluated on two large-scale benchmarks for FMIM based on the Osteoarthritis Initiative and Chest X-ray-14 datasets. The codes allowing replication of this study have been made publicly available at .
A challenge in digital learning games is assessing students’ learning behaviors, which are often ... more A challenge in digital learning games is assessing students’ learning behaviors, which are often intertwined with game behaviors. How do we know whether students have learned enough or needed more practice at the end of their game play? To answer this question, we performed post hoc analyses on a prior study of the game Decimal Point, which teaches decimal numbers and decimal operations to middle school students. Using Bayesian Knowledge Tracing, we found that students had the most difficulty with mastering the number line and sorting skills, but also tended to overpractice the skills they had previously mastered. In addition, using students’ survey responses and in-game measurements, we identified the best feature sets to predict test scores and self-reported enjoyment. Analyzing these features and their connections with learning outcomes and enjoyment yielded useful insights into areas of improvement for the game. We conclude by highlighting the need for combining traditional test...
Proline has been reported to play an important role in helping plants cope with several stresses,... more Proline has been reported to play an important role in helping plants cope with several stresses, including salinity. This study investigates the relationship between proline accumulation and salt tolerance in an accession of Australian wild rice Oryza australiensis Domin using morphological, physiological, and molecular assessments. Seedlings of O. australiensis wild rice accession JC 2304 and two other cultivated rice Oryza sativa L. cultivars, Nipponbare (salt-sensitive), and Pokkali (salt-tolerant), were screened at 150 mM NaCl for 14 days. The results showed that O. australiensis was able to rapidly accumulate free proline and lower osmotic potential at a very early stage of salt stress compared to cultivated rice. The qRT-PCR result revealed that O. australiensis wild rice JC 2304 activated proline synthesis genes OsP5CS1, OsP5CS2, and OsP5CR and depressed the expression of proline degradation gene OsProDH as early as 1 h after exposure to salinity stress. Wild rice O. austral...
The problem of monotone missing data has been broadly studied during the last two decades and has... more 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.
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