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Osteosarcoma, the most common primary bone cancer, often requires accurate necrosis assessment from whole slide images (WSIs) for effective treatment planning and prognosis. However, manual assessments are subjective and prone to variability. In response, we introduce FDDM, a novel framework bridging the gap between patch classification and region-based segmentation. FDDM operates in two stages: patch-based classification, followed by region-based refinement, enabling cross-patch information intergation. Leveraging a newly curated dataset of osteosarcoma images, FDDM demonstrates superior segmentation performance, achieving up to a 10% improvement mIOU and a 32.12% enhancement in necrosis rate estimation over state-of-the-art methods. This framework sets a new benchmark in osteosarcoma assessment, highlighting the potential of foundation models and diffusion-based refinements in complex medical imaging tasks., Comment: Accepted for presentation at the 2025 IEEE International Symposium on Biomedical Imaging (ISBI 2025)

We prove that a random Cayley graph on a group of order $N$ has clique number $O(\log N \log \log N)$ with high probability. This bound is best possible up to the constant factor for certain groups, including~$\mathbb{F}_2^n$, and improves the longstanding upper bound of $O(\log^2 N)$ due to Alon. Our proof does not make use of the underlying group structure and is purely combinatorial, with the key result being an essentially best possible upper bound for the number of subsets of given order that contain at most a given number of colors in a properly edge-colored complete graph. As a further application of this result, we study a conjecture of Alon stating that every group of order $N$ has a Cayley graph whose clique number and independence number are both $O(\log N)$, proving the conjecture for all abelian groups of order $N$ for almost all $N$. For finite vector spaces of order $N$ with characteristic congruent to $1 \pmod 4$, we prove the existence of a self-complementary Cayley graph on the vector space whose clique number and independence number are both at most $(2+o(1))\log N$. This matches the lower bound for Ramsey numbers coming from random graphs and solves, in a strong form, a problem of Alon and Orlitsky motivated by information theory.

Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal solutions of the corresponding Morozov or Tikhonov regularized optimization problems. In this paper, we propose new characterizations for stable recovery in finite-dimensional spaces, uncovering the role of nonsmooth second-order information. These insights enable a deeper understanding of stable recovery and their practical implications. As a consequence, we apply our theory to derive new sufficient conditions for stable recovery of the analysis group sparsity problems, including the group sparsity and isotropic total variation problems. Numerical experiments on these two problems give favorable results about using our conditions to test stable recovery., Comment: 29 pages, 4 figures

Expectation thresholds arise from a class of integer linear programs (LPs) that are fundamental to the study of thresholds in large random systems. An avenue towards estimating expectation thresholds comes from the fractional relaxation of these integer LPs, which yield the fractional expectation thresholds. Regarding the gap between the integer LPs and their fractional relaxations, Talagrand made a bold conjecture, that the integral and fractional expectation thresholds are within a constant factor of each other. In other words, any small fractional solution can be ``rounded''. In this paper, we prove a strong upper bound on the expectation threshold starting from a fractional solution supported on sets with small size. In particular, this resolves Talagrand's conjecture for fractional solutions supported on sets with bounded size. Our key input for rounding the fractional solutions is a sharp version of Talagrand's selector process conjecture that is of independent interest.

Positron Emission Tomography (PET) and Computed Tomography (CT) are essential for diagnosing, staging, and monitoring various diseases, particularly cancer. Despite their importance, the use of PET/CT systems is limited by the necessity for radioactive materials, the scarcity of PET scanners, and the high cost associated with PET imaging. In contrast, CT scanners are more widely available and significantly less expensive. In response to these challenges, our study addresses the issue of generating PET images from CT images, aiming to reduce both the medical examination cost and the associated health risks for patients. Our contributions are twofold: First, we introduce a conditional diffusion model named CPDM, which, to our knowledge, is one of the initial attempts to employ a diffusion model for translating from CT to PET images. Second, we provide the largest CT-PET dataset to date, comprising 2,028,628 paired CT-PET images, which facilitates the training and evaluation of CT-to-PET translation models. For the CPDM model, we incorporate domain knowledge to develop two conditional maps: the Attention map and the Attenuation map. The former helps the diffusion process focus on areas of interest, while the latter improves PET data correction and ensures accurate diagnostic information. Experimental evaluations across various benchmarks demonstrate that CPDM surpasses existing methods in generating high-quality PET images in terms of multiple metrics. The source code and data samples are available at https://github.com/thanhhff/CPDM., Comment: IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) 2025

A set of integers $A$ is non-averaging if there is no element $a$ in $A$ which can be written as an average of a subset of $A$ not containing $a$. We show that the largest non-averaging subset of $\{1, \ldots, n\}$ has size $n^{1/4+o(1)}$, thus solving the Erd\H{o}s-Straus problem. We also determine the largest size of a non-averaging set in a $d$-dimensional box for any fixed $d$. Our main tool includes the structure theorem for the set of subset sums due to Conlon, Fox and the first author, together with a result about the structure of a point set in nearly convex position., Comment: 16 pages

We study the number of monochromatic solutions to linear equations in a $2$-coloring of $\{1,\ldots,n\}$. We show that any nontrivial linear equation has a constant fraction of solutions that are monochromatic in any $2$-coloring of $\{1,\ldots,n\}$. We further study commonness of four-term equations and disprove a conjecture of Costello and Elvin by showing that, unlike over $\mathbb{F}_p$, the four-term equation $x_1 + 2x_2 - x_3 - 2x_4 = 0$ is uncommon over $\{1,\ldots,n\}$., Comment: 12 pages

Combining ideas of Pham, Sah, Sawhney, and Simkin on spread perfect matchings in super-regular bipartite graphs with an algorithmic blow-up lemma, we prove a spread version of the blow-up lemma. Intuitively, this means that there exists a probability measure over copies of a desired spanning graph $H$ in a given system of super-regular pairs which does not heavily pin down any subset of vertices. This allows one to complement the use of the blow-up lemma with the recently resolved Kahn-Kalai conjecture. As an application, we prove an approximate version of a conjecture of B\"ottcher, Parczyk, Sgueglia, and Skokan on the threshold for appearance of powers of Hamilton cycles in perturbed random graphs., Comment: 12 pages

Federated Learning (FL) is a method for training machine learning models using distributed data sources. It ensures privacy by allowing clients to collaboratively learn a shared global model while storing their data locally. However, a significant challenge arises when dealing with missing modalities in clients' datasets, where certain features or modalities are unavailable or incomplete, leading to heterogeneous data distribution. While previous studies have addressed the issue of complete-modality missing, they fail to tackle partial-modality missing on account of severe heterogeneity among clients at an instance level, where the pattern of missing data can vary significantly from one sample to another. To tackle this challenge, this study proposes a novel framework named FedMAC, designed to address multi-modality missing under conditions of partial-modality missing in FL. Additionally, to avoid trivial aggregation of multi-modal features, we introduce contrastive-based regularization to impose additional constraints on the latent representation space. The experimental results demonstrate the effectiveness of FedMAC across various client configurations with statistical heterogeneity, outperforming baseline methods by up to 26% in severe missing scenarios, highlighting its potential as a solution for the challenge of partially missing modalities in federated systems., Comment: The 22nd International Symposium on Network Computing and Applications (NCA 2024)

We present a short and simple proof of the celebrated hypergraph container theorem of Balogh--Morris--Samotij and Saxton--Thomason. On a high level, our argument utilises the idea of iteratively taking vertices of largest degree from an independent set and constructing a hypergraph of lower uniformity which preserves independent sets and inherits edge distribution. The original algorithms for constructing containers also remove in each step vertices of high degree which are not in the independent set. Our modified algorithm postpones this until the end, which surprisingly results in a significantly simplified analysis., Comment: 4 pages

A family of $r$ distinct sets $\{A_1,\ldots, A_r\}$ is an $r$-sunflower if for all $1 \leqslant i < j \leqslant r$ and $1 \leqslant i' < j' \leqslant r$, we have $A_i \cap A_j = A_{i'} \cap A_{j'}$. Erd\H{o}s and Rado conjectured in 1960 that every family $\mathcal{H}$ of $\ell$-element sets of size at least $K(r)^\ell$ contains an $r$-sunflower, where $K(r)$ is some function that depends only on $r$. We prove that if $\mathcal{H}$ is a family of $\ell$-element sets of VC-dimension at most $d$ and $|\mathcal{H}| > (C r (\log d+\log^\ast \ell))^\ell$ for some absolute constant $C > 0$, then $\mathcal{H}$ contains an $r$-sunflower. This improves a recent result of Fox, Pach, and Suk. When $d=1$, we obtain a sharp bound, namely that $|\mathcal{H}| > (r-1)^\ell$ is sufficient. Along the way, we establish a strengthening of the Kahn-Kalai conjecture for set families of bounded VC-dimension, which is of independent interest., Comment: 14 pages

Conditional video diffusion models (CDM) have shown promising results for video synthesis, potentially enabling the generation of realistic echocardiograms to address the problem of data scarcity. However, current CDMs require a paired segmentation map and echocardiogram dataset. We present a new method called Free-Echo for generating realistic echocardiograms from a single end-diastolic segmentation map without additional training data. Our method is based on the 3D-Unet with Temporal Attention Layers model and is conditioned on the segmentation map using a training-free conditioning method based on SDEdit. We evaluate our model on two public echocardiogram datasets, CAMUS and EchoNet-Dynamic. We show that our model can generate plausible echocardiograms that are spatially aligned with the input segmentation map, achieving performance comparable to training-based CDMs. Our work opens up new possibilities for generating echocardiograms from a single segmentation map, which can be used for data augmentation, domain adaptation, and other applications in medical imaging. Our code is available at \url{https://github.com/gungui98/echo-free}, Comment: Accepted to MICCAI 2024

Purpose: This study focuses on the development of automated text generation from radiology images, termed diagnostic captioning, to assist medical professionals in reducing clinical errors and improving productivity. The aim is to provide tools that enhance report quality and efficiency, which can significantly impact both clinical practice and deep learning research in the biomedical field. Methods: In our participation in the ImageCLEFmedical2024 Caption evaluation campaign, we explored caption prediction tasks using advanced Transformer-based models. We developed methods incorporating Transformer encoder-decoder and Query Transformer architectures. These models were trained and evaluated to generate diagnostic captions from radiology images. Results: Experimental evaluations demonstrated the effectiveness of our models, with the VisionDiagnostor-BioBART model achieving the highest BERTScore of 0.6267. This performance contributed to our team, DarkCow, achieving third place on the leaderboard. Conclusion: Our diagnostic captioning models show great promise in aiding medical professionals by generating high-quality reports efficiently. This approach can facilitate better data processing and performance optimization in medical imaging departments, ultimately benefiting healthcare delivery.

There are various desired capabilities to create aerial forest-traversing robots capable of monitoring both biological and abiotic data. The features range from multi-functionality, robustness, and adaptability. These robots have to weather turbulent winds and various obstacles such as forest flora and wildlife thus amplifying the complexity of operating in such uncertain environments. The key for successful data collection is the flexibility to intermittently move from tree-to-tree, in order to perch at vantage locations for elongated time. This effort to perch not only reduces the disturbance caused by multi-rotor systems during data collection, but also allows the system to rest and recharge for longer outdoor missions. Current systems feature the addition of perching modules that increase the aerial robots' weight and reduce the drone's overall endurance. Thus in our work, the key questions currently studied are: "How do we develop a single robot capable of metamorphosing its body for multi-modal flight and dynamic perching?", "How do we detect and land on perchable objects robustly and dynamically?", and "What important spatial-temporal data is important for us to collect?", Comment: RSS Pioneers 2024 Research Statement

We present an explicit subset $A\subseteq \mathbb{N} = \{0,1,\ldots\}$ such that $A + A = \mathbb{N}$ and for all $\varepsilon > 0$, \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\in A^2\big\}\big|}{N^{\varepsilon}} = 0.\] This answers a question of Erd\H{o}s., Comment: 5 pages

We initiate the systematic study of the following Tur\'an-type question. Suppose $\Gamma$ is a graph with $n$ vertices such that the edge density between any pair of subsets of vertices of size at least $t$ is at most $1 - c$, for some $t$ and $c > 0$. What is the largest number of edges in a subgraph $G \subseteq \Gamma$ which does not contain a fixed graph $H$ as an induced subgraph or, more generally, which belongs to a hereditary property $\mathcal{P}$? This provides a common generalization of two recently studied cases, namely $\Gamma$ being a (pseudo-)random graph and a graph without a large complete bipartite subgraph. We focus on the interesting case where $H$ is a bipartite graph. We determine the answer up to a constant factor with respect to $n$ and $t$, for certain bipartite $H$ and for $\Gamma$ either a dense random graph or a Paley graph with a square number of vertices. In particular, our bounds match if $H$ is a tree, or if one part of $H$ has $d$ vertices complete to the other part, all other vertices in that part have degree at most $d$, and the other part has sufficiently many vertices. As applications of the latter result, we answer a question of Alon, Krivelevich, and Samotij on the largest subgraph with a hereditary property which misses a bipartite graph, and determine up to a constant factor the largest number of edges in a string subgraph of $\Gamma$. The proofs are based on a variant of the dependent random choice and a novel approach for finding induced copies by inductively defining probability distributions supported on induced copies of smaller subgraphs., Comment: 20 pages

Optical Character Recognition - Visual Question Answering (OCR-VQA) is the task of answering text information contained in images that have just been significantly developed in the English language in recent years. However, there are limited studies of this task in low-resource languages such as Vietnamese. To this end, we introduce a novel dataset, ViOCRVQA (Vietnamese Optical Character Recognition - Visual Question Answering dataset), consisting of 28,000+ images and 120,000+ question-answer pairs. In this dataset, all the images contain text and questions about the information relevant to the text in the images. We deploy ideas from state-of-the-art methods proposed for English to conduct experiments on our dataset, revealing the challenges and difficulties inherent in a Vietnamese dataset. Furthermore, we introduce a novel approach, called VisionReader, which achieved 0.4116 in EM and 0.6990 in the F1-score on the test set. Through the results, we found that the OCR system plays a very important role in VQA models on the ViOCRVQA dataset. In addition, the objects in the image also play a role in improving model performance. We open access to our dataset at link (https://github.com/qhnhynmm/ViOCRVQA.git) for further research in OCR-VQA task in Vietnamese.

Answering a question of Erd\H{o}s and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive integers each at most $n$ is $2^{(c_x + o(1))n}$ for an explicit constant $c_x$ increasing with $x$., Comment: 8 pages

We consider the problem of algorithmically sampling from the Gibbs measure of a mixed $p$-spin spherical spin glass. We give a polynomial-time algorithm that samples from the Gibbs measure up to vanishing total variation error, for any model whose mixture satisfies $$\xi''(s) < \frac{1}{(1-s)^2}, \qquad \forall s\in [0,1).$$ This includes the pure $p$-spin glasses above a critical temperature that is within an absolute ($p$-independent) constant of the so-called shattering phase transition. Our algorithm follows the algorithmic stochastic localization approach introduced in (Alaoui, Montanari, Sellke, 20022). A key step of this approach is to estimate the mean of a sequence of tilted measures. We produce an improved estimator for this task by identifying a suitable correction to the TAP fixed point selected by approximate message passing (AMP). As a consequence, we improve the algorithm's guarantee over previous work, from normalized Wasserstein to total variation error. In particular, the new algorithm and analysis opens the way to perform inference about one-dimensional projections of the measure., Comment: 107 pages

Visual Question Answering (VQA) is a complicated task that requires the capability of simultaneously processing natural language and images. Initially, this task was researched, focusing on methods to help machines understand objects and scene contexts in images. However, some text appearing in the image that carries explicit information about the full content of the image is not mentioned. Along with the continuous development of the AI era, there have been many studies on the reading comprehension ability of VQA models in the world. As a developing country, conditions are still limited, and this task is still open in Vietnam. Therefore, we introduce the first large-scale dataset in Vietnamese specializing in the ability to understand text appearing in images, we call it ViTextVQA (\textbf{Vi}etnamese \textbf{Text}-based \textbf{V}isual \textbf{Q}uestion \textbf{A}nswering dataset) which contains \textbf{over 16,000} images and \textbf{over 50,000} questions with answers. Through meticulous experiments with various state-of-the-art models, we uncover the significance of the order in which tokens in OCR text are processed and selected to formulate answers. This finding helped us significantly improve the performance of the baseline models on the ViTextVQA dataset. Our dataset is available at this \href{https://github.com/minhquan6203/ViTextVQA-Dataset}{link} for research purposes., Comment: Preprint submitted to IJCV

In this work, we provide data stream algorithms that compute optimal splits in decision tree learning. In particular, given a data stream of observations $x_i$ and their labels $y_i$, the goal is to find the optimal split $j$ that divides the data into two sets such that the mean squared error (for regression) or misclassification rate and Gini impurity (for classification) is minimized. We provide several fast streaming algorithms that use sublinear space and a small number of passes for these problems. These algorithms can also be extended to the massively parallel computation model. Our work, while not directly comparable, complements the seminal work of Domingos-Hulten (KDD 2000) and Hulten-Spencer-Domingos (KDD 2001).

It is well-known that polynomial versions of theorems of R\"odl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical Erd\H{o}s-Hajnal conjecture. In this note, we prove that these three conjectures are in fact equivalent, extending several previous particular results in this direction by Fox, Nguyen, Scott and Seymour; Nguyen, Scott and Seymour and Gishboliner and Shapira. We deduce that the family of string graphs satisfies the polynomial R\"odl conjecture. We also derive analogous results for hypergraphs, tournaments, ordered graphs, and colored graphs., Comment: Added a section showing analogs of our results in the setting of tournaments, ordered graphs, hypergraphs and colored graphs

We prove that every partially ordered set on $n$ elements contains $k$ subsets $A_{1},A_{2},\dots,A_{k}$ such that either each of these subsets has size $\Omega(n/k^{5})$ and, for every $i_{\ell}a_{2}>_{\ell}\dots>_{\ell}a_{k}$ for any $(a_1,a_2,\dots,a_k) \in A_1\times A_2\times \dots \times A_k$, or $a_i$ is incomparable with $a_j$ for any $i\ne j$, $a_i\in A_i$ and $a_j\in A_j$. This improves on a 2009 result of Pach and the first author motivated by problems in discrete geometry.

In this technical report, we present VinaLLaMA, an open-weight, state-of-the-art (SOTA) Large Language Model for the Vietnamese language, built upon LLaMA-2 with an additional 800 billion trained tokens. VinaLLaMA not only demonstrates fluency in Vietnamese but also exhibits a profound understanding of Vietnamese culture, making it a truly indigenous model. VinaLLaMA-7B-chat, trained on 1 million high-quality synthetic samples, achieves SOTA results on key benchmarks, including VLSP, VMLU, and Vicuna Benchmark Vietnamese, marking a significant advancement in the Vietnamese AI landscape and offering a versatile resource for various applications., Comment: VinaLLaMA Technical Report - 13 pages

We show that for every positive integer $k$ there are positive constants $C$ and $c$ such that if $A$ is a subset of $\{1, 2, \dots, n\}$ of size at least $C n^{1/k}$, then, for some $d \leq k-1$, the set of subset sums of $A$ contains a homogeneous $d$-dimensional generalized arithmetic progression of size at least $c|A|^{d+1}$. This strengthens a result of Szemer\'edi and Vu, who proved a similar statement without the homogeneity condition. As an application, we make progress on the Erd\H{o}s--Straus non-averaging sets problem, showing that every subset $A$ of $\{1, 2, \dots, n\}$ of size at least $n^{\sqrt{2} - 1 + o(1)}$ contains an element which is the average of two or more other elements of $A$. This gives the first polynomial improvement on a result of Erd\H{o}s and S\'ark\"ozy from 1990., Comment: 34 pages

Automated visual inspection of on-and offshore wind turbines using aerial robots provides several benefits, namely, a safe working environment by circumventing the need for workers to be suspended high above the ground, reduced inspection time, preventive maintenance, and access to hard-to-reach areas. A novel nonlinear model predictive control (NMPC) framework alongside a global wind turbine path planner is proposed to achieve distance-optimal coverage for wind turbine inspection. Unlike traditional MPC formulations, visual tracking NMPC (VT-NMPC) is designed to track an inspection surface, instead of a position and heading trajectory, thereby circumventing the need to provide an accurate predefined trajectory for the drone. An additional capability of the proposed VT-NMPC method is that by incorporating inspection requirements as visual tracking costs to minimize, it naturally achieves the inspection task successfully while respecting the physical constraints of the drone. Multiple simulation runs and real-world tests demonstrate the efficiency and efficacy of the proposed automated inspection framework, which outperforms the traditional MPC designs, by providing full coverage of the target wind turbine blades as well as its robustness to changing wind conditions. The implementation codes are open-sourced., Comment: 8 pages, accepted for publication at ICAR conference

We study Glauber dynamics for sampling from discrete distributions $\mu$ on the hypercube $\{\pm 1\}^n$. Recently, techniques based on spectral independence have successfully yielded optimal $O(n)$ relaxation times for a host of different distributions $\mu$. We show that spectral independence is universal: a relaxation time of $O(n)$ implies spectral independence. We then study a notion of tractability for $\mu$, defined in terms of smoothness of the multilinear extension of its Hamiltonian -- $\log \mu$ -- over $[-1,+1]^n$. We show that Glauber dynamics has relaxation time $O(n)$ for such $\mu$, and using the universality of spectral independence, we conclude that these distributions are also fractionally log-concave and consequently satisfy modified log-Sobolev inequalities. We sharpen our estimates and obtain approximate tensorization of entropy and the optimal $\widetilde{O}(n)$ mixing time for random Hamiltonians, i.e. the classically studied mixed $p$-spin model at sufficiently high temperature. These results have significant downstream consequences for concentration of measure, statistical testing, and learning.

In this work, we investigate the time series representation learning problem using self-supervised techniques. Contrastive learning is well-known in this area as it is a powerful method for extracting information from the series and generating task-appropriate representations. Despite its proficiency in capturing time series characteristics, these techniques often overlook a critical factor - the inherent noise in this type of data, a consideration usually emphasized in general time series analysis. Moreover, there is a notable absence of attention to developing efficient yet lightweight encoder architectures, with an undue focus on delivering contrastive losses. Our work address these gaps by proposing an innovative training strategy that promotes consistent representation learning, accounting for the presence of noise-prone signals in natural time series. Furthermore, we propose an encoder architecture that incorporates dilated convolution within the Inception block, resulting in a scalable and robust network with a wide receptive field. Experimental findings underscore the effectiveness of our method, consistently outperforming state-of-the-art approaches across various tasks, including forecasting, classification, and abnormality detection. Notably, our method attains the top rank in over two-thirds of the classification UCR datasets, utilizing only 40% of the parameters compared to the second-best approach. Our source code for CoInception framework is accessible at https://github.com/anhduy0911/CoInception.

For positive integers $n,r,s$ with $r > s$, the set-coloring Ramsey number $R(n;r,s)$ is the minimum $N$ such that if every edge of the complete graph $K_N$ receives a set of $s$ colors from a palette of $r$ colors, then there is a subset of $n$ vertices where all of the edges between them receive a common color. If $n$ is fixed and $\frac{s}{r}$ is less than and bounded away from $1-\frac{1}{n-1}$, then $R(n;r,s)$ is known to grow exponentially in $r$, while if $\frac{s}{r}$ is greater than and bounded away from $1-\frac{1}{n-1}$, then $R(n;r,s)$ is bounded. Here we prove bounds for $R(n;r,s)$ in the intermediate range where $\frac{s}{r}$ is close to $1 - \frac{1}{n-1}$ by establishing a connection to the maximum size of error-correcting codes near the zero-rate threshold.

Let $G$ be a graph on $n$ vertices of maximum degree $\Delta$. We show that, for any $\delta > 0$, the down-up walk on independent sets of size $k \leq (1-\delta)\alpha_c(\Delta)n$ mixes in time $O_{\Delta,\delta}(k\log{n})$, thereby resolving a conjecture of Davies and Perkins in an optimal form. Here, $\alpha_{c}(\Delta)n$ is the NP-hardness threshold for the problem of counting independent sets of a given size in a graph on $n$ vertices of maximum degree $\Delta$. Our mixing time has optimal dependence on $k,n$ for the entire range of $k$; previously, even polynomial mixing was not known. In fact, for $k = \Omega_{\Delta}(n)$ in this range, we establish a log-Sobolev inequality with optimal constant $\Omega_{\Delta,\delta}(1/n)$. At the heart of our proof are three new ingredients, which may be of independent interest. The first is a method for lifting $\ell_\infty$-independence from a suitable distribution on the discrete cube -- in this case, the hard-core model -- to the slice by proving stability of an Edgeworth expansion using a multivariate zero-free region for the base distribution. The second is a generalization of the Lee-Yau induction to prove log-Sobolev inequalities for distributions on the slice with considerably less symmetry than the uniform distribution. The third is a sharp decomposition-type result which provides a lossless comparison between the Dirichlet form of the original Markov chain and that of the so-called projected chain in the presence of a contractive coupling., Comment: 25 pages; comments welcome!

Federated learning (FL) enables multiple clients to train a model without compromising sensitive data. The decentralized nature of FL makes it susceptible to adversarial attacks, especially backdoor insertion during training. Recently, the edge-case backdoor attack employing the tail of the data distribution has been proposed as a powerful one, raising questions about the shortfall in current defenses' robustness guarantees. Specifically, most existing defenses cannot eliminate edge-case backdoor attacks or suffer from a trade-off between backdoor-defending effectiveness and overall performance on the primary task. To tackle this challenge, we propose FedGrad, a novel backdoor-resistant defense for FL that is resistant to cutting-edge backdoor attacks, including the edge-case attack, and performs effectively under heterogeneous client data and a large number of compromised clients. FedGrad is designed as a two-layer filtering mechanism that thoroughly analyzes the ultimate layer's gradient to identify suspicious local updates and remove them from the aggregation process. We evaluate FedGrad under different attack scenarios and show that it significantly outperforms state-of-the-art defense mechanisms. Notably, FedGrad can almost 100% correctly detect the malicious participants, thus providing a significant reduction in the backdoor effect (e.g., backdoor accuracy is less than 8%) while not reducing the main accuracy on the primary task., Comment: Accepted for presentation at the International Joint Conference on Neural Networks (IJCNN 2023)

Due to the significant resemblance in visual appearance, pill misuse is prevalent and has become a critical issue, responsible for one-third of all deaths worldwide. Pill identification, thus, is a crucial concern needed to be investigated thoroughly. Recently, several attempts have been made to exploit deep learning to tackle the pill identification problem. However, most published works consider only single-pill identification and fail to distinguish hard samples with identical appearances. Also, most existing pill image datasets only feature single pill images captured in carefully controlled environments under ideal lighting conditions and clean backgrounds. In this work, we are the first to tackle the multi-pill detection problem in real-world settings, aiming at localizing and identifying pills captured by users in a pill intake. Moreover, we also introduce a multi-pill image dataset taken in unconstrained conditions. To handle hard samples, we propose a novel method for constructing heterogeneous a priori graphs incorporating three forms of inter-pill relationships, including co-occurrence likelihood, relative size, and visual semantic correlation. We then offer a framework for integrating a priori with pills' visual features to enhance detection accuracy. Our experimental results have proved the robustness, reliability, and explainability of the proposed framework. Experimentally, it outperforms all detection benchmarks in terms of all evaluation metrics. Specifically, our proposed framework improves COCO mAP metrics by 9.4% over Faster R-CNN and 12.0% compared to vanilla YOLOv5. Our study opens up new opportunities for protecting patients from medication errors using an AI-based pill identification solution., Comment: Under review by Plos ONE journal

Cardiovascular disease remains a significant problem in modern society. Among non-invasive techniques, the electrocardiogram (ECG) is one of the most reliable methods for detecting abnormalities in cardiac activities. However, ECG interpretation requires expert knowledge and it is time-consuming. Developing a novel method to detect the disease early could prevent death and complication. The paper presents novel various approaches for classifying cardiac diseases from ECG recordings. The first approach suggests the Poincare representation of ECG signal and deep-learning-based image classifiers (ResNet50 and DenseNet121 were learned over Poincare diagrams), which showed decent performance in predicting AF (atrial fibrillation) but not other types of arrhythmia. XGBoost, a gradient-boosting model, showed an acceptable performance in long-term data but had a long inference time due to highly-consuming calculation within the pre-processing phase. Finally, the 1D convolutional model, specifically the 1D ResNet, showed the best results in both studied CinC 2017 and CinC 2020 datasets, reaching the F1 score of 85% and 71%, respectively, and that was superior to the first-ranking solution of each challenge. The paper also investigated efficiency metrics such as power consumption and equivalent CO2 emissions, with one-dimensional models like 1D CNN and 1D ResNet being the most energy efficient. Model interpretation analysis showed that the DenseNet detected AF using heart rate variability while the 1DResNet assessed AF pattern in raw ECG signals., Comment: 12 pages, 6 figures, 6 tables

Federated learning (FL) is recently surging as a promising decentralized deep learning (DL) framework that enables DL-based approaches trained collaboratively across clients without sharing private data. However, in the context of the central party being active and dishonest, the data of individual clients might be perfectly reconstructed, leading to the high possibility of sensitive information being leaked. Moreover, FL also suffers from the nonindependent and identically distributed (non-IID) data among clients, resulting in the degradation in the inference performance on local clients' data. In this paper, we propose a novel framework, namely Personalized Privacy-Preserving Federated Learning (PPPFL), with a concentration on cross-silo FL to overcome these challenges. Specifically, we introduce a stabilized variant of the Model-Agnostic Meta-Learning (MAML) algorithm to collaboratively train a global initialization from clients' synthetic data generated by Differential Private Generative Adversarial Networks (DP-GANs). After reaching convergence, the global initialization will be locally adapted by the clients to their private data. Through extensive experiments, we empirically show that our proposed framework outperforms multiple FL baselines on different datasets, including MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100.

Federated learning enables edge devices to train a global model collaboratively without exposing their data. Despite achieving outstanding advantages in computing efficiency and privacy protection, federated learning faces a significant challenge when dealing with non-IID data, i.e., data generated by clients that are typically not independent and identically distributed. In this paper, we tackle a new type of Non-IID data, called cluster-skewed non-IID, discovered in actual data sets. The cluster-skewed non-IID is a phenomenon in which clients can be grouped into clusters with similar data distributions. By performing an in-depth analysis of the behavior of a classification model's penultimate layer, we introduce a metric that quantifies the similarity between two clients' data distributions without violating their privacy. We then propose an aggregation scheme that guarantees equality between clusters. In addition, we offer a novel local training regularization based on the knowledge-distillation technique that reduces the overfitting problem at clients and dramatically boosts the training scheme's performance. We theoretically prove the superiority of the proposed aggregation over the benchmark FedAvg. Extensive experimental results on both standard public datasets and our in-house real-world dataset demonstrate that the proposed approach improves accuracy by up to 16% compared to the FedAvg algorithm., Comment: Accepted for presentation at the 23rd International Symposium on Cluster, Cloud and Internet Computing (CCGrid 2023)

We show that the threshold for the binomial random $3$-partite, $3$-uniform hypergraph $G^{3}((n,n,n),p)$ to contain a Latin square is $\Theta(\log{n}/n)$. We also prove analogous results for Steiner triple systems and proper list edge-colorings of the complete (bipartite) graph with random lists. Our results answer several related questions of Johansson, Luria-Simkin, Casselgren-H\"aggkvist, Simkin, and Kang-Kelly-K\"uhn-Methuku-Osthus., Comment: 10 pages. Simplified proof; results unchanged

For a subset $A$ of an abelian group $G$, given its size $|A|$, its doubling $\kappa=|A+A|/|A|$, and a parameter $s$ which is small compared to $|A|$, we study the size of the largest sumset $A+A'$ that can be guaranteed for a subset $A'$ of $A$ of size at most $s$. We show that a subset $A'\subseteq A$ of size at most $s$ can be found so that $|A+A'| = \Omega(\min(\kappa^{1/3},s)|A|)$. Thus a sumset significantly larger than the Cauchy--Davenport bound can be guaranteed by a bounded size subset assuming that the doubling $\kappa$ is large. Building up on the same ideas, we resolve a conjecture of Bollob\'as, Leader and Tiba that for subsets $A,B$ of $\mathbb{Z}_p$ of size at most $\alpha p$ for an appropriate constant $\alpha>0$, one only needs three elements $b_1,b_2,b_3\in B$ to guarantee $|A+\{b_1,b_2,b_3\}|\ge |A|+|B|-1$. Allowing the use of larger subsets $A'$, we show that for sets $A$ of bounded doubling, one only needs a subset $A'$ with $o(|A|)$ elements to guarantee that $A+A'=A+A$. We also address another conjecture and a question raised by Bollob\'as, Leader and Tiba on high-dimensional analogs and sets whose sumset cannot be saturated by a bounded size subset.

Consider a host hypergraph $G$ which contains a spanning structure due to minimum degree considerations. We collect three results proving that if the edges of $G$ are sampled at the appropriate rate then the spanning structure still appears with high probability in the sampled hypergraph. We prove such results for perfect matchings in hypergraphs above Dirac thresholds, for $K_r$-factors in graphs satisfying the Hajnal--Szemer\'edi minimum degree condition, and for bounded-degree spanning trees. In each case our proof is based on constructing a spread measure and then applying recent results on the (fractional) Kahn--Kalai conjecture connecting the existence of such measures with probabilistic thresholds. For our second result we give a shorter and more general proof of a recent theorem of Allen, B\"ottcher, Corsten, Davies, Jenssen, Morris, Roberts, and Skokan which handles the $r=3$ case with different techniques. In particular, we answer a question of theirs with regards to the number of $K_r$-factors in graphs satisfying the Hajnal--Szemer\'edi minimum degree condition., Comment: 41 pages. Corrected an error in the proof of Theorem 1.5 and improved exposition

Medication mistaking is one of the risks that can result in unpredictable consequences for patients. To mitigate this risk, we develop an automatic system that correctly identifies pill-prescription from mobile images. Specifically, we define a so-called pill-prescription matching task, which attempts to match the images of the pills taken with the pills' names in the prescription. We then propose PIMA, a novel approach using Graph Neural Network (GNN) and contrastive learning to address the targeted problem. In particular, GNN is used to learn the spatial correlation between the text boxes in the prescription and thereby highlight the text boxes carrying the pill names. In addition, contrastive learning is employed to facilitate the modeling of cross-modal similarity between textual representations of pill names and visual representations of pill images. We conducted extensive experiments and demonstrated that PIMA outperforms baseline models on a real-world dataset of pill and prescription images that we constructed. Specifically, PIMA improves the accuracy from 19.09% to 46.95% compared to other baselines. We believe our work can open up new opportunities to build new clinical applications and improve medication safety and patient care., Comment: Accepted for publication and presentation at the 19th Pacific Rim International Conference on Artificial Intelligence (PRICAI 2022)

Sleep apnea (SA) is a type of sleep disorder characterized by snoring and chronic sleeplessness, which can lead to serious conditions such as high blood pressure, heart failure, and cardiomyopathy (enlargement of the muscle tissue of the heart). The electrocardiogram (ECG) plays a critical role in identifying SA since it might reveal abnormal cardiac activity. Recent research on ECG-based SA detection has focused on feature engineering techniques that extract specific characteristics from multiple-lead ECG signals and use them as classification model inputs. In this study, a novel method of feature extraction based on the detection of S peaks is proposed to enhance the detection of adjacent SA segments using a single-lead ECG. In particular, ECG features collected from a single lead (V2) are used to identify SA episodes. On the extracted features, a CNN model is trained to detect SA. Experimental results demonstrate that the proposed method detects SA from single-lead ECG data is more accurate than existing state-of-the-art methods, with 91.13% classification accuracy, 92.58% sensitivity, and 88.75% specificity. Moreover, the further usage of features associated with the S peaks enhances the classification accuracy by 0.85%. Our findings indicate that the proposed machine learning system has the potential to be an effective method for detecting SA episodes., Comment: This work has been accepted for publication by the Asia Pacific Signal and Information Processing Association Annual Summit and Conference 2022 (APSIPA ASC 2022)