Miracle-dz/UniFAR-FTUs huggingface dataset:
Extended codes and deep holes of MDS codes

For a given linear code $\C$ of length $n$ over $\gf(q)$ and a nonzero vector $\bu$ in $\gf(q)^n$, Sun, Ding and Chen defined an extended linear code $\overline{\C}(\bu)$ of $\C$, which is a generalisation of the classical extended code $\overline{\C}(-\bone)$ of $\C$ and called the second kind of an extended code of $\C$ (see arXiv:2307.04076 and arXiv:2307.08053). They developed some general theory of the extended codes $\overline{\C}(\bu)$ and studied the extended codes $\overline{\C}(\bu)$ of several families of linear codes, including cyclic codes, projective two-weight codes, nonbinary Hamming codes, and a family of reversible MDS cyclic codes. The objective of this paper is to investigate the extended codes $\overline{\C}(\bu)$ of MDS codes $\C$ over finite fields. The main result of this paper is that the extended code $\overline{\C}(\bu)$ of an MDS $[n,k]$ code $\C$ remains MDS if and only if the covering radius $\rho(\mathcal{C}^{\bot})=k$ and the vector $\bu$ is a deep hole of the dual code $\C^\perp$. As applications of this main result, the extended codes of the GRS codes and extended GRS codes are investigated and the covering radii of several families of MDS codes are determined.
$\Gamma$-Convergence for plane to wrinkles transition problem

We consider a variational problem modeling transition between flat and wrinkled region in a thin elastic sheet, and identify the $\Gamma$-limit as the sheet thickness goes to 0, thus extending the previous work of the first author [Bella, ARMA 2015]. The limiting problem is scalar and convex, but constrained and posed for measures. For the $\Gamma$-liminf inequality we first pass to quadratic variables so that the constraint becomes linear, and then obtain the lower bound using Reshetnyak's theorem. The construction of the recovery sequence for the $\Gamma$- limsup inequality relies on mollification of quadratic variables, and careful choice of multiple construction parameters. Eventually for the limiting problem we show existence of a minimizer and equipartition of the energy for each frequency.
Approximating the distribution of the $L_q$-norm of a random point in a $d$-dimensional cube

In this note, we assess the accuracy of CLT-based approximations for the volume of intersection of the $d$-dimensional cube $[-1,1]^d$ and an $L_q$-ball centred at the origin; this is clearly equivalent to approximating the distribution of the $L_q$-norm of a random point in a $d$-dimensional cube centered at 0. The approximations are CLT-based where to improve the normal approximation we use the first term in the Edgeworth expansion. We have included a section analysing the information obtained from ChatGPT in response to prompts regarding this theory; in our case, ChatGPT answers were not very helpful. Illustrations of the approximation formulae, as the radius of the ball increases, for different values of $d$ and $q$ are also given, alongside lines showing a Monte Carlo simulation of the intersection volume.
DMS*: Minimizing Makespan for Multi-Agent Combinatorial Path Finding

Multi-Agent Combinatorial Path Finding (MCPF) seeks collision-free paths for multiple agents from their initial to goal locations, while visiting a set of intermediate target locations in the middle of the paths. MCPF is challenging as it involves both planning collision-free paths for multiple agents and target sequencing, i.e., solving traveling salesman problems to assign targets to and find the visiting order for the agents. Recent work develops methods to address MCPF while minimizing the sum of individual arrival times at goals. Such a problem formulation may result in paths with different arrival times and lead to a long makespan, the maximum arrival time, among the agents. This paper proposes a min-max variant of MCPF, denoted as MCPF-max, that minimizes the makespan of the agents. While the existing methods (such as MS*) for MCPF can be adapted to solve MCPF-max, we further develop two new techniques based on MS* to defer the expensive target sequencing during planning to expedite the overall computation. We analyze the properties of the resulting algorithm Deferred MS* (DMS*), and test DMS* with up to 20 agents and 80 targets. We demonstrate the use of DMS* on differential-drive robots.
Physics-Aware Multifidelity Bayesian Optimization: a Generalized Formulation

The adoption of high-fidelity models for many-query optimization problems is majorly limited by the significant computational cost required for their evaluation at every query. Multifidelity Bayesian methods (MFBO) allow to include costly high-fidelity responses for a sub-selection of queries only, and use fast lower-fidelity models to accelerate the optimization process. State-of-the-art methods rely on a purely data-driven search and do not include explicit information about the physical context. This paper acknowledges that prior knowledge about the physical domains of engineering problems can be leveraged to accelerate these data-driven searches, and proposes a generalized formulation for MFBO to embed a form of domain awareness during the optimization procedure. In particular, we formalize a bias as a multifidelity acquisition function that captures the physical structure of the domain. This permits to partially alleviate the data-driven search from learning the domain properties on-the-fly, and sensitively enhances the management of multiple sources of information. The method allows to efficiently include high-fidelity simulations to guide the optimization search while containing the overall computational expense. Our physics-aware multifidelity Bayesian optimization is presented and illustrated for two classes of optimization problems frequently met in science and engineering, namely design optimization and health monitoring problems.
K\"ahler geometry of scalar flat metrics on Line bundles over polarized K\"ahler-Einstein manifolds

In view of a better understanding of the geometry of scalar flat K\"ahler metrics, this paper studies two families of scalar flat K\"ahler metrics constructed in [10] by A. D. Hwang and M. A. Singer on $\mathbb C^{n+1}$ and on $\mathcal O(-k)$. For the metrics in both the families, we prove the existence of an asymptotic expansion for their $\epsilon$-functions and we show that they can be approximated by a sequence of projectively induced K\"ahler metrics. Further, we show that the metrics on $\mathbb C^{n+1}$ are not projectively induced, and that the Burns-Simanca metric is characterized among the scalar flat metrics on $\mathcal O(-k)$ to be the only projectively induced one as well as the only one whose second coefficient in the asymptotic expansion of the $\epsilon$-function vanishes.
Measurement of the depth-dependent local dynamics in thin polymer films through rejuvenation of ultrastable glasses

We measure the isothermal rejuvenation of stable glass films of poly(styrene) and poly(methylmethacrylate). We demonstrate that the propagation of the front responsible for the transformation to a supercooled-liquid state can serve as a highly localized probe of the local supercooled dynamics. We use this connection to probe the depth-dependent relaxation rate with nanometric precision for a series of polystyrene films over a range of temperatures near the bulk glass transition temperature. The analysis shows the spatial extent of enhanced surface mobility and reveals the existence of an unexpected large dynamical length scale in the system. The results are compared with the cooperative-string model for glassy dynamics. The data reveals that the film-thickness dependence of whole film properties arises only from the volume fraction of the near-surface region. While the dynamics at the middle of the samples shows the expected bulk-like temperature dependence, the near-surface region shows very little dependence on temperature.
NoiseCLR: A Contrastive Learning Approach for Unsupervised Discovery of Interpretable Directions in Diffusion Models

Generative models have been very popular in the recent years for their image generation capabilities. GAN-based models are highly regarded for their disentangled latent space, which is a key feature contributing to their success in controlled image editing. On the other hand, diffusion models have emerged as powerful tools for generating high-quality images. However, the latent space of diffusion models is not as thoroughly explored or understood. Existing methods that aim to explore the latent space of diffusion models usually relies on text prompts to pinpoint specific semantics. However, this approach may be restrictive in areas such as art, fashion, or specialized fields like medicine, where suitable text prompts might not be available or easy to conceive thus limiting the scope of existing work. In this paper, we propose an unsupervised method to discover latent semantics in text-to-image diffusion models without relying on text prompts. Our method takes a small set of unlabeled images from specific domains, such as faces or cats, and a pre-trained diffusion model, and discovers diverse semantics in unsupervised fashion using a contrastive learning objective. Moreover, the learned directions can be applied simultaneously, either within the same domain (such as various types of facial edits) or across different domains (such as applying cat and face edits within the same image) without interfering with each other. Our extensive experiments show that our method achieves highly disentangled edits, outperforming existing approaches in both diffusion-based and GAN-based latent space editing methods.
Adversarial Camera Patch: An Effective and Robust Physical-World Attack on Object Detectors

Physical adversarial attacks present a novel and growing challenge in cybersecurity, especially for systems reliant on physical inputs for Deep Neural Networks (DNNs), such as those found in Internet of Things (IoT) devices. They are vulnerable to physical adversarial attacks where real-world objects or environments are manipulated to mislead DNNs, thereby threatening the operational integrity and security of IoT devices. The camera-based attacks are one of the most practical adversarial attacks, which are easy to implement and more robust than all the other attack methods, and pose a big threat to the security of IoT. This paper proposes Adversarial Camera Patch (ADCP), a novel approach that employs a single-camera patch to launch robust physical adversarial attacks against object detectors. ADCP optimizes the physical parameters of the camera patch using Particle Swarm Optimization (PSO) to identify the most adversarial configuration. The optimized camera patch is then attached to the lens to generate stealthy and robust adversarial samples physically. The effectiveness of the proposed approach is validated through ablation experiments in a digital environment, with experimental results demonstrating its effectiveness even under worst-case scenarios (minimal width, maximum transparency). Notably, ADCP exhibits higher robustness in both digital and physical domains compared to the baseline. Given the simplicity, robustness, and stealthiness of ADCP, we advocate for attention towards the ADCP framework as it offers a means to achieve streamlined, robust, and stealthy physical attacks. Our adversarial attacks pose new challenges and requirements for cybersecurity.
AnyHome: Open-Vocabulary Generation of Structured and Textured 3D Homes

Inspired by cognitive theories, we introduce AnyHome, a framework that translates any text into well-structured and textured indoor scenes at a house-scale. By prompting Large Language Models (LLMs) with designed templates, our approach converts provided textual narratives into amodal structured representations. These representations guarantee consistent and realistic spatial layouts by directing the synthesis of a geometry mesh within defined constraints. A Score Distillation Sampling process is then employed to refine the geometry, followed by an egocentric inpainting process that adds lifelike textures to it. AnyHome stands out with its editability, customizability, diversity, and realism. The structured representations for scenes allow for extensive editing at varying levels of granularity. Capable of interpreting texts ranging from simple labels to detailed narratives, AnyHome generates detailed geometries and textures that outperform existing methods in both quantitative and qualitative measures.
Modeling Homophily in Exponential-Family Random Graph Models for Bipartite Networks

Homophily, the tendency of individuals who are alike to form ties with one another, is an important concept in the study of social networks. Yet accounting for homophily effects is complicated in the context of bipartite networks where ties connect individuals not with one another but rather with a separate set of nodes, which might also be individuals but which are often an entirely different type of objects. As a result, much work on the effect of homophily in a bipartite network proceeds by first eliminating the bipartite structure, collapsing a two-mode network to a one-mode network and thereby ignoring potentially meaningful structure in the data. We introduce a set of methods to model homophily on bipartite networks without losing information in this way, then we demonstrate that these methods allow for substantively interesting findings in management science not possible using standard techniques. These methods are implemented in the widely-used ergm package for R.
Generative AI for Physical Layer Communications: A Survey

The recent evolution of generative artificial intelligence (GAI) leads to the emergence of groundbreaking applications such as ChatGPT, which not only enhances the efficiency of digital content production, such as text, audio, video, or even network traffic data, but also enriches its diversity. Beyond digital content creation, GAI's capability in analyzing complex data distributions offers great potential for wireless communications, particularly amidst a rapid expansion of new physical layer communication technologies. For example, the diffusion model can learn input signal distributions and use them to improve the channel estimation accuracy, while the variational autoencoder can model channel distribution and infer latent variables for blind channel equalization. Therefore, this paper presents a comprehensive investigation of GAI's applications for communications at the physical layer, ranging from traditional issues, including signal classification, channel estimation, and equalization, to emerging topics, such as intelligent reflecting surfaces and joint source channel coding. We also compare GAI-enabled physical layer communications with those supported by traditional AI, highlighting GAI's inherent capabilities and unique contributions in these areas. Finally, the paper discusses open issues and proposes several future research directions, laying a foundation for further exploration and advancement of GAI in physical layer communications.
VGF: Value-Guided Fuzzing - Fuzzing Hardware as Hardware

As the complexity of logic designs increase, new avenues for testing digital hardware becomes necessary. Fuzz Testing (fuzzing) has recently received attention as a potential candidate for input vector generation on hardware designs. Using this technique, a fuzzer is used to generate an input to a logic design. Using a simulation engine, the logic design is given the generated stimulus and some metric of feedback is given to the fuzzer to aid in the input mutation. However, much like software fuzzing, hardware fuzzing uses code coverage as a metric to find new possible fuzzing paths. Unfortunately, as we show in this work, this coverage metric falls short of generic on some hardware designs where designers have taken a more direct approach at expressing a particular microarchitecture, or implementation, of the desired hardware. With this work, we introduce a new coverage metric which employs not code coverage, but state coverage internal to a design. By observing changes in signals within the logic circuit under testing, we are able to explore the state space of the design and provide feedback to a fuzzer engine for input generation. Our approach, Value-Guided Fuzzing (VGF), provides a generic metric of coverage which can be applied to any design regardless of its implementation. In this paper, we introduce our state-based VGF metric as well as a sample implementation which can be used with any VPI, DPI, VHPI, or FLI compliant simulator, making it completely HDL agnostic. We demonstrate the generality of VGF and show how our sample implementation is capable of finding bugs considerably faster than previous approaches.
Local Randomized Neural Networks with Hybridized Discontinuous Petrov-Galerkin Methods for Stokes-Darcy Flows

This paper introduces a new numerical approach that integrates local randomized neural networks (LRNNs) and the hybridized discontinuous Petrov-Galerkin (HDPG) method for solving coupled fluid flow problems. The proposed method partitions the domain of interest into several subdomains and constructs an LRNN on each subdomain. Then, the HDPG scheme is used to couple the LRNNs to approximate the unknown functions. We develop LRNN-HDPG methods based on velocity-stress formulation to solve two types of problems: Stokes-Darcy problems and Brinkman equations, which model the flow in porous media and free flow. We devise a simple and effective way to deal with the interface conditions in the Stokes-Darcy problems without adding extra terms to the numerical scheme. We conduct extensive numerical experiments to demonstrate the stability, efficiency, and robustness of the proposed method. The numerical results show that the LRNN-HDPG method can achieve high accuracy with a small number of degrees of freedom.
Open WDVV Equations and Frobenius Structures for Toric Calabi-Yau 3-Folds

Let $X$ be a toric Calabi-Yau 3-fold and let $L\subset X$ be an Aganagic-Vafa outer brane. We prove two versions of open WDVV equations for the open Gromov-Witten theory of $(X,L)$. The first version of the open WDVV equation leads to the construction of a semi-simple (formal) Frobenius manifold and the second version leads to the construction of a (formal) $F$-manifold.
Beyond Gradient and Priors in Privacy Attacks: Leveraging Pooler Layer Inputs of Language Models in Federated Learning

Language models trained via federated learning (FL) demonstrate impressive capabilities in handling complex tasks while protecting user privacy. Recent studies indicate that leveraging gradient information and prior knowledge can potentially reveal training samples within FL setting. However, these investigations have overlooked the potential privacy risks tied to the intrinsic architecture of the models. This paper presents a two-stage privacy attack strategy that targets the vulnerabilities in the architecture of contemporary language models, significantly enhancing attack performance by initially recovering certain feature directions as additional supervisory signals. Our comparative experiments demonstrate superior attack performance across various datasets and scenarios, highlighting the privacy leakage risk associated with the increasingly complex architectures of language models. We call for the community to recognize and address these potential privacy risks in designing large language models.
DeconV: Probabilistic Cell Type Deconvolution from Bulk RNA-sequencing Data

Bulk RNA-Seq remains a widely adopted technique to profile gene expression, primarily due to the persistent challenges associated with achieving single-cell resolution. However, a key challenge is accurately estimating the proportions of different cell types within these bulk samples. To address this issue, we introduce DeconV, a probabilistic framework for cell-type deconvolution that uses scRNA-Seq data as a reference. This approach aims to mitigate some of the limitations in existing methods by incorporating statistical frameworks developed for scRNA-Seq, thereby simplifying issues related to reference preprocessing such as normalization and marker gene selection. We benchmarked DeconV against established methods, including MuSiC, CIBERSORTx, and Scaden. Our results show that DeconV performs comparably in terms of accuracy to the best-performing method, Scaden, but provides additional interpretability by offering confidence intervals for its predictions. Furthermore, the modular design of DeconV allows for the investigation of discrepancies between bulk-sequenced samples and artificially generated pseudo-bulk samples.
A Fluorescence-Based Sensor for Calibrated Measurement of Protein Kinase Stability in Live Cells

Oncogenic mutations can destabilize signaling proteins, resulting in increased or unregulated activity. Thus, there is considerable interest in mapping the relationship between mutations and the stability of proteins, to better understand the consequences of oncogenic mutations and potentially inform the development of new therapeutics. Here, we develop a tool to study protein-kinase stability in live mammalian cells and the effects of the HSP90 chaperone system on the stability of these kinases. We monitor the fluorescence of kinases fused to a fluorescent protein relative to that of a co-expressed reference fluorescent protein. We used this tool to study the dependence of Src- and Raf-family kinases on the HSP90 system. We demonstrate that this sensor reports on destabilization induced by oncogenic mutations in these kinases. We also show that Src-homology 2 (SH2) and Src-homology 3 (SH3) domains, which are required for autoinhibition of Src-family kinases, stabilize these kinase domains in the cell. Our expression-calibrated sensor enables the facile characterization of the effects of mutations and small-molecule drugs on protein-kinase stability.
Disinfection By-Products in Swimming Pool Water: Formation, Modeling, and Control

Disinfection is practiced to minimize the occurrence and growth of microbial pathogens and thus ensure the hygienic safety of swimming pool water. However, potentially hazardous disinfection by-products (DBPs) are formed from the reaction between disinfectants and DBP precursors. This chapter discusses the formation of these DBPs in swimming pool water and modeling approaches for quantification of their levels given estimates of anthropogenic contaminant input in swimming pools. Promising DBP control technologies are also discussed. Overview of the three key aspects related to swimming pool water help readers to better understand the profile of DBPs and their control in swimming pool water.