Search

Traditional mathematical models used in designing next-generation communication systems often fall short due to inherent simplifications, narrow scope, and computational limitations. In recent years, the incorporation of deep learning (DL) methodologies into communication systems has made significant progress in system design and performance optimisation. Autoencoders (AEs) have become essential, enabling end-to-end learning that allows for the combined optimisation of transmitters and receivers. Consequently, AEs offer a data-driven methodology capable of bridging the gap between theoretical models and real-world complexities. The paper presents a comprehensive survey of the application of AEs within communication systems, with a particular focus on their architectures, associated challenges, and future directions. We examine 120 recent studies across wireless, optical, semantic, and quantum communication fields, categorising them according to transceiver design, channel modelling, digital signal processing, and computational complexity. This paper further examines the challenges encountered in the implementation of AEs, including the need for extensive training data, the risk of overfitting, and the requirement for differentiable channel models. Through data-driven approaches, AEs provide robust solutions for end-to-end system optimisation, surpassing traditional mathematical models confined by simplifying assumptions. This paper also summarises the computational complexity associated with AE-based systems by conducting an in-depth analysis employing the metric of floating-point operations per second (FLOPS). This analysis encompasses the evaluation of matrix multiplications, bias additions, and activation functions. This survey aims to establish a roadmap for future research, emphasising the transformative potential of AEs in the formulation of next-generation communication systems.

Synthetic data has gained attention for training large language models, but poor-quality data can harm performance (see, e.g., Shumailov et al. (2023); Seddik et al. (2024)). A potential solution is data pruning, which retains only high-quality data based on a score function (human or machine feedback). Previous work Feng et al. (2024) analyzed models trained on synthetic data as sample size increases. We extend this by using random matrix theory to derive the performance of a binary classifier trained on a mix of real and pruned synthetic data in a high dimensional setting. Our findings identify conditions where synthetic data could improve performance, focusing on the quality of the generative model and verification strategy. We also show a smooth phase transition in synthetic label noise, contrasting with prior sharp behavior in infinite sample limits. Experiments with toy models and large language models validate our theoretical results.

We demonstrate that preference optimization methods can effectively enhance LLM safety. Applying various alignment techniques to the Falcon 11B model using safety datasets, we achieve a significant boost in global safety score (from $57.64\%$ to $99.90\%$) as measured by LlamaGuard 3 8B, competing with state-of-the-art models. On toxicity benchmarks, average scores in adversarial settings dropped from over $0.6$ to less than $0.07$. However, this safety improvement comes at the cost of reduced general capabilities, particularly in math, suggesting a trade-off. We identify noise contrastive alignment (Safe-NCA) as an optimal method for balancing safety and performance. Our study ultimately shows that alignment techniques can be sufficient for building safe and robust models.

Anomaly detection in videos is challenging due to the complexity, noise, and diverse nature of activities such as violence, shoplifting, and vandalism. While deep learning (DL) has shown excellent performance in this area, existing approaches have struggled to apply DL models across different anomaly tasks without extensive retraining. This repeated retraining is time-consuming, computationally intensive, and unfair. To address this limitation, a new DL framework is introduced in this study, consisting of three key components: transfer learning to enhance feature generalization, model fusion to improve feature representation, and multi-task classification to generalize the classifier across multiple tasks without training from scratch when new task is introduced. The framework's main advantage is its ability to generalize without requiring retraining from scratch for each new task. Empirical evaluations demonstrate the framework's effectiveness, achieving an accuracy of 97.99% on the RLVS dataset (violence detection), 83.59% on the UCF dataset (shoplifting detection), and 88.37% across both datasets using a single classifier without retraining. Additionally, when tested on an unseen dataset, the framework achieved an accuracy of 87.25%. The study also utilizes two explainability tools to identify potential biases, ensuring robustness and fairness. This research represents the first successful resolution of the generalization issue in anomaly detection, marking a significant advancement in the field.

Adversarial attacks are a potential threat to machine learning models by causing incorrect predictions through imperceptible perturbations to the input data. While these attacks have been extensively studied in unstructured data like images, applying them to tabular data, poses new challenges. These challenges arise from the inherent heterogeneity and complex feature interdependencies in tabular data, which differ from the image data. To account for this distinction, it is necessary to establish tailored imperceptibility criteria specific to tabular data. However, there is currently a lack of standardised metrics for assessing the imperceptibility of adversarial attacks on tabular data. To address this gap, we propose a set of key properties and corresponding metrics designed to comprehensively characterise imperceptible adversarial attacks on tabular data. These are: proximity to the original input, sparsity of altered features, deviation from the original data distribution, sensitivity in perturbing features with narrow distribution, immutability of certain features that should remain unchanged, feasibility of specific feature values that should not go beyond valid practical ranges, and feature interdependencies capturing complex relationships between data attributes. We evaluate the imperceptibility of five adversarial attacks, including both bounded attacks and unbounded attacks, on tabular data using the proposed imperceptibility metrics. The results reveal a trade-off between the imperceptibility and effectiveness of these attacks. The study also identifies limitations in current attack algorithms, offering insights that can guide future research in the area. The findings gained from this empirical analysis provide valuable direction for enhancing the design of adversarial attack algorithms, thereby advancing adversarial machine learning on tabular data., Comment: 36 pages

The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the discretisation and proves the convergence of the approximate schemes using a compactness argument that works under natural assumptions on data. We also investigate, using a finite volume method, known as the hybrid mixed mimetic (HMM) approach, the effects of multiplicative noise on the dynamics of the travelling waves in the excitable media displayed by the model. Particularly, we consider how sufficiently high noise can cause waves to backfire or fail to propagate.

Deep learning has significantly advanced automatic medical diagnostics and released the occupation of human resources to reduce clinical pressure, yet the persistent challenge of data scarcity in this area hampers its further improvements and applications. To address this gap, we introduce a novel ensemble framework called `Efficient Transfer and Self-supervised Learning based Ensemble Framework' (ETSEF). ETSEF leverages features from multiple pre-trained deep learning models to efficiently learn powerful representations from a limited number of data samples. To the best of our knowledge, ETSEF is the first strategy that combines two pre-training methodologies (Transfer Learning and Self-supervised Learning) with ensemble learning approaches. Various data enhancement techniques, including data augmentation, feature fusion, feature selection, and decision fusion, have also been deployed to maximise the efficiency and robustness of the ETSEF model. Five independent medical imaging tasks, including endoscopy, breast cancer, monkeypox, brain tumour, and glaucoma detection, were tested to demonstrate ETSEF's effectiveness and robustness. Facing limited sample numbers and challenging medical tasks, ETSEF has proved its effectiveness by improving diagnostics accuracies from 10\% to 13.3\% when compared to strong ensemble baseline models and up to 14.4\% improvements compared with published state-of-the-art methods. Moreover, we emphasise the robustness and trustworthiness of the ETSEF method through various vision-explainable artificial intelligence techniques, including Grad-CAM, SHAP, and t-SNE. Compared to those large-scale deep learning models, ETSEF can be deployed flexibly and maintain superior performance for challenging medical imaging tasks, showing the potential to be applied to more areas that lack training data, Comment: 64 pages, 20 figures

Recently, transfer learning and self-supervised learning have gained significant attention within the medical field due to their ability to mitigate the challenges posed by limited data availability, improve model generalisation, and reduce computational expenses. Transfer learning and self-supervised learning hold immense potential for advancing medical research. However, it is crucial to recognise that transfer learning and self-supervised learning architectures exhibit distinct advantages and limitations, manifesting variations in accuracy, training speed, and robustness. This paper compares the performance and robustness of transfer learning and self-supervised learning in the medical field. Specifically, we pre-trained two models using the same source domain datasets with different pre-training methods and evaluated them on small-sized medical datasets to identify the factors influencing their final performance. We tested data with several common issues in medical domains, such as data imbalance, data scarcity, and domain mismatch, through comparison experiments to understand their impact on specific pre-trained models. Finally, we provide recommendations to help users apply transfer learning and self-supervised learning methods in medical areas, and build more convenient and efficient deployment strategies., Comment: 37 pages, 8 figures

We modify the axioms of triangulated categories to include both higher triangles and distinguished maps of higher triangles. The distinguished maps are specializations of Neeman's ``good'' maps of $2$-triangles. The axioms both simplify Neeman's axioms in his 1991 paper and generalize them to higher triangles in the way proposed by Balmer et al. We provide a geometric formulation via directed truncated simplices to enable a more concrete approach. The axioms are modelled by homotopy and derived categories. We look at a number of key theorems including the fact that sums of maps of $2$-triangles are distinguished if and only if the maps are distinguished and a strong version of the $3$x$3$ lemma. These illustrate some key proof methods. We also show that maps of faces of distinguished triangles are distinguished. We construct some useful distinguished $5$-triangles., Comment: 23 pages

Exact travelling wave solutions to the two-dimensional stochastic Allen-Cahn equation with multiplicative noise are obtained through the hyperbolic tangent (tanh) method. This technique limits the solutions to travelling wave profiles by representing them with a finite tanh power series. This study focuses on how multiplicative noise affects the dynamics of these travelling waves, in particular, occurring of wave propagation failure due to high levels of noise., Comment: Need to be revised in section of the derivation of exact travelling wave solutions

The recent advancement of Blockchain technology consolidates its status as a viable alternative for various domains. However, evaluating the performance of blockchain applications can be challenging due to the underlying infrastructure's complexity and distributed nature. Therefore, a reliable modelling approach is needed to boost Blockchain-based applications' development and evaluation. While simulation-based solutions have been researched, machine learning (ML) model-based techniques are rarely discussed in conjunction with evaluating blockchain application performance. Our novel research makes use of two ML model-based methods. Firstly, we train a $k$ nearest neighbour ($k$NN) and support vector machine (SVM) to predict blockchain performance using predetermined configuration parameters. Secondly, we employ the salp swarm optimization (SO) ML model which enables the investigation of optimal blockchain configurations for achieving the required performance level. We use rough set theory to enhance SO, hereafter called ISO, which we demonstrate to prove achieving an accurate recommendation of optimal parameter configurations; despite uncertainty. Finally, statistical comparisons indicate that our models have a competitive edge. The $k$NN model outperforms SVM by 5\% and the ISO also demonstrates a reduction of 4\% inaccuracy deviation compared to regular SO.

The impact of wettability on the co-moving velocity of two-fluid flow in porous media is analyzed herein. The co-moving velocity, developed by Roy et al. (2022), is a novel representation of the flow behavior of two fluids through porous media. Our study aims to better understand the behavior of the co-moving velocity by analyzing simulation data under various wetting conditions. The simulations were conducted using the Lattice-Boltzmann color-fluid model and evaluated the relative permeability for different wetting conditions on the same rock. The analysis of the simulation data followed the methodology proposed by Roy et al. (2022) to reconstruct a constitutive equation for the co-moving velocity. Surprisingly, it was found that the coefficients of the constitutive equation were nearly the same for all wetting conditions. Based on these results, a simple approach was proposed to reconstruct the oil phase relative permeability using only the co-moving velocity relationship and water phase relative permeability. This proposed method provides new insights into the dependency of relative permeability curves, which has implications for the history matching of production data and solving the associated inverse problem. The research findings contribute to a better understanding of the impact of wettability on fluid flow in porous media and provide a practical approach for estimating relative permeability based on the co-moving velocity relationship, which has never been shown before., Comment: 14 pages, 6 figures

Considerable recent work has focused on methods for analyzing experiments which exhibit treatment interference -- that is, when the treatment status of one unit may affect the response of another unit. Such settings are common in experiments on social networks. We consider a model of treatment interference -- the K-nearest neighbors interference model (KNNIM) -- for which the response of one unit depends not only on the treatment status given to that unit, but also the treatment status of its $K$ ``closest'' neighbors. We derive causal estimands under KNNIM in a way that allows us to identify how each of the $K$-nearest neighbors contributes to the indirect effect of treatment. We propose unbiased estimators for these estimands and derive conservative variance estimates for these unbiased estimators. We then consider extensions of these estimators under an assumption of no weak interaction between direct and indirect effects. We perform a simulation study to determine the efficacy of these estimators under different treatment interference scenarios. We apply our methodology to an experiment designed to assess the impact of a conflict-reducing program in middle schools in New Jersey, and we give evidence that the effect of treatment propagates primarily through a unit's closest connection.

Our recent intensive study has found that physics-informed neural networks (PINN) tend to be local approximators after training. This observation leads to this novel physics-informed radial basis network (PIRBN), which can maintain the local property throughout the entire training process. Compared to deep neural networks, a PIRBN comprises of only one hidden layer and a radial basis "activation" function. Under appropriate conditions, we demonstrated that the training of PIRBNs using gradient descendent methods can converge to Gaussian processes. Besides, we studied the training dynamics of PIRBN via the neural tangent kernel (NTK) theory. In addition, comprehensive investigations regarding the initialisation strategies of PIRBN were conducted. Based on numerical examples, PIRBN has been demonstrated to be more effective and efficient than PINN in solving PDEs with high-frequency features and ill-posed computational domains. Moreover, the existing PINN numerical techniques, such as adaptive learning, decomposition and different types of loss functions, are applicable to PIRBN. The programs that can regenerate all numerical results can be found at https://github.com/JinshuaiBai/PIRBN., Comment: 48 pages, 26 figures

Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications, such as structural risk estimation and medical diagnosis. This presents a significant barrier to the practical implementation of DL in these fields. Physics-guided deep learning (PGDL) is a novel type of DL that can integrate physics laws to train neural networks. This can be applied to any systems that are controlled or governed by physics laws, such as mechanics, finance and medical applications. It has been demonstrated that, with the additional information provided by physics laws, PGDL achieves great accuracy and generalisation in the presence of data scarcity. This review provides a detailed examination of PGDL and offers a structured overview of its use in addressing data scarcity across various fields, including physics, engineering and medical applications. Moreover, the review identifies the current limitations and opportunities for PGDL in relation to data scarcity and offers a thorough discussion on the future prospects of PGDL., Comment: 26 Pages, 4 figures, 2 tables, 116 references. This work is going to submit to Nature Machine Intelligence

Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. In this work, we present a detailed introduction to programming PINN-based computational solid mechanics. Besides, two prevailingly used physics-informed loss functions for PINN-based computational solid mechanics are summarised. Moreover, numerical examples ranging from 1D to 3D solid problems are presented to show the performance of PINN-based computational solid mechanics. The programs are built via Python coding language and TensorFlow library with step-by-step explanations. It is worth highlighting that PINN-based computational mechanics is easy to implement and can be extended for more challenging applications. This work aims to help the researchers who are interested in the PINN-based solid mechanics solver to have a clear insight into this emerging area. The programs for all the numerical examples presented in this work are available on https://github.com/JinshuaiBai/PINN_Comp_Mech., Comment: 32 pages, 20 figures are include in this manuscript

Recently, distributed ledger technologies like blockchain have been proliferating and have attracted interest from the academic community, government, and industry. A wide range of blockchain solutions has been introduced, such as Bitcoin, Ethereum, and Hyperledger technologies in the literature. However, tools for evaluating these solutions and their applications are still lacking, limiting the exploration of their potentiality and associated challenges/limitations. That is, experimenting with real blockchain networks usually requires a solid budget; and thus, sophisticated blockchain simulators can facilitate designing and evaluating solutions before the actual implementation stage. The quality of such simulators depends on several factors such as usability, reliability, provided capabilities, and supported features. This paper aims to provide a systemic mapping review of blockchain simulators focusing on these quality factors. This paper also sheds light on the configuration parameters (inputs) and produced metrics (outputs) supported by each simulator. Furthermore, it investigates which metrics supported by each simulator are scientifically validated/evaluated. Moreover, code quality comparison is carried out to assess the source code of the covered simulators. The results reveal that no simulator fully covers the wide operational range of features and capabilities of existing blockchain technologies. However, several promising efforts exist in the domain of blockchain simulation with interesting and useful features. Finally, we discuss the subject of blockchain simulation and provide our insight into the matter.

Based on the phenomenological extension of Darcy's law, two-fluid flow is dependent on a relative permeability function of saturation only that is process/path dependent with an underlying dependency on pore structure. For applications, fuel cells to underground $CO_2$ storage, it is imperative to determine the effective phase permeability relationships where the traditional approach is based on the inverse modelling of time-consuming experiments. The underlying reason is that the fundamental upscaling step from pore to Darcy scale, which links the pore structure of the porous medium to the continuum hydraulic conductivities, is not solved. Herein, we develop an Artificial Neural Network (ANN) that relies on fundamental geometrical relationships to determine the mechanical energy dissipation during creeping immiscible two-fluid flow. The developed ANN is based on a prescribed set of state variables based on physical insights that predicts the effective permeability of 4,500 unseen pore-scale geometrical states with $R^2 = 0.98$., Comment: 6 Pages, 2 Figures, and Supporting Material

We propose a model of treatment interference where the response of a unit depends only on its treatment status and the statuses of units within its K-neighborhood. Current methods for detecting interference include carefully designed randomized experiments and conditional randomization tests on a set of focal units. We give guidance on how to choose focal units under this model of interference. We then conduct a simulation study to evaluate the efficacy of existing methods for detecting network interference. We show that this choice of focal units leads to powerful tests of treatment interference which outperform current experimental methods.

Developing innovative informatics approaches aimed to enhance fetal monitoring is a burgeoning field of study in reproductive medicine. Several reviews have been conducted regarding Artificial intelligence (AI) techniques to improve pregnancy outcomes. They are limited by focusing on specific data such as mother's care during pregnancy. This systematic survey aims to explore how artificial intelligence (AI) can assist with fetal growth monitoring via Ultrasound (US) image. We used eight medical and computer science bibliographic databases, including PubMed, Embase, PsycINFO, ScienceDirect, IEEE explore, ACM Library, Google Scholar, and the Web of Science. We retrieved studies published between 2010 to 2021. Data extracted from studies were synthesized using a narrative approach. Out of 1269 retrieved studies, we included 107 distinct studies from queries that were relevant to the topic in the survey. We found that 2D ultrasound images were more popular (n=88) than 3D and 4D ultrasound images (n=19). Classification is the most used method (n=42), followed by segmentation (n=31), classification integrated with segmentation (n=16) and other miscellaneous such as object-detection, regression and reinforcement learning (n=18). The most common areas within the pregnancy domain were the fetus head (n=43), then fetus body (n=31), fetus heart (n=13), fetus abdomen (n=10), and lastly the fetus face (n=10). In the most recent studies, deep learning techniques were primarily used (n=81), followed by machine learning (n=16), artificial neural network (n=7), and reinforcement learning (n=2). AI techniques played a crucial role in predicting fetal diseases and identifying fetus anatomy structures during pregnancy. More research is required to validate this technology from a physician's perspective, such as pilot studies and randomized controlled trials on AI and its applications in a hospital setting., Comment: 25 pages, 4 figures, submitted to Artificial Intelligence in Medicine

We consider a biochemical model that consists of a system of partial differential equations based on reaction terms and subject to non--homogeneous Dirichlet boundary conditions. The model is discretised using the gradient discretisation method (GDM) which is a framework covering a large class of conforming and non conforming schemes. Under classical regularity assumptions on the exact solutions, the GDM enables us to establish the existence of the model solutions in a weak sense, and strong convergence for the approximate solution and its approximate gradient. Numerical test employing a finite volume method is presented to demonstrate the behaviour of the solutions to the model.

Deep Learning (DL) requires a large amount of training data to provide quality outcomes. However, the field of medical imaging suffers from the lack of sufficient data for properly training DL models because medical images require manual labelling carried out by clinical experts thus the process is time-consuming, expensive, and error-prone. Recently, transfer learning (TL) was introduced to reduce the need for the annotation procedure by means of transferring the knowledge performed by a previous task and then fine-tuning the result using a relatively small dataset. Nowadays, multiple classification methods from medical imaging make use of TL from general-purpose pre-trained models, e.g., ImageNet, which has been proven to be ineffective due to the mismatch between the features learned from natural images (ImageNet) and those more specific from medical images especially medical gray images such as X-rays. ImageNet does not have grayscale images such as MRI, CT, and X-ray. In this paper, we propose a novel DL model to be used for addressing classification tasks of medical imaging, called MedNet. To do so, we aim to issue two versions of MedNet. The first one is Gray-MedNet which will be trained on 3M publicly available gray-scale medical images including MRI, CT, X-ray, ultrasound, and PET. The second version is Color-MedNet which will be trained on 3M publicly available color medical images including histopathology, taken images, and many others. To validate the effectiveness MedNet, both versions will be fine-tuned to train on the target tasks of a more reduced set of medical images. MedNet performs as the pre-trained model to tackle any real-world application from medical imaging and achieve the level of generalization needed for dealing with medical imaging tasks, e.g. classification. MedNet would serve the research community as a baseline for future research., Comment: 6 Pages

A gradient discretisation method (GDM), Gradient schemes, Convergence analysis, Existence of weak solutions, Anisotropic reaction diffusion models, Dirichlet and Neumann boundary conditions, Non conforming finite element methods, Finite volume schemes, Hybrid mixed mimetic (HMM) method, Crouzeix--Raviart scheme, Brain tumour dynamics, Fractional anisotropy.

Within cloud-based internet of things (IoT) applications, typically cloud providers employ Service Level Agreements (SLAs) to ensure the quality of their provisioned services. Similar to any other contractual method, an SLA is not immune to breaches. Ideally, an SLA stipulates consequences (e.g. penalties) imposed on cloud providers when they fail to conform to SLA terms. The current practice assumes trust in service providers to acknowledge SLA breach incidents and executing associated consequences. Recently, the Blockchain paradigm has introduced compelling capabilities that may enable us to address SLA enforcement more elegantly. This paper proposes and implements a blockchain-based approach for assessing SLA compliance and enforcing consequences. It employs a diagnostic accuracy method for validating the dependability of the proposed solution. The paper also benchmarks Hyperledger Fabric to investigate its feasibility as an underlying blockchain infrastructure concerning latency and transaction success/fail rates.

Applying the gradient discretisation method (GDM), the paper develops a comprehensive numerical analysis for the reaction diffusion model. Using only three properties, this analysis provides convergence results for several conforming and non-conforming numerical schemes that align with the GDM. As an application of this analysis, the hybrid mimetic mixed (HMM) method for the reaction diffusion model is designed and its convergence established. Numerical experiments using the HMM method are presented to facilitate study of the creation of spiral waves in the Barkley model and the ways in which the waves behave when interacting with the boundaries of their generating medium

Smartphones and tablets have become ubiquitous in our daily lives. Smartphones, in particular, have become more than personal assistants. These devices have provided new avenues for consumers to play, work, and socialize whenever and wherever they want. Smartphones are small in size, so they are easy to handle and to stow and carry in users' pockets or purses. However, mobile devices are also susceptible to various problems. One of the greatest concerns is the possibility of breach in security and privacy if the device is seized by an outside party. It is possible that threats can come from friends as well as strangers. Due to the size of smart devices, they can be easily lost and may expose details of users' private lives. In addition, this might enable pervasive observation or imitation of one's movements and activities, such as sending messages to contacts, accessing private communication, shopping with a credit card, and relaying information about where one has been. This paper highlights the potential risks that occur when smartphones are stolen or seized, discusses the concept of continuous authentication, and analyzes current approaches and mechanisms of behavioral biometrics with respect to methodology, associated datasets and evaluation approaches.

The conventional authentication technologies, like RFID tags and authentication cards/badges, suffer from different weaknesses, therefore a prompt replacement to use biometric method of authentication should be applied instead. Biometrics, such as fingerprints, voices, and ECG signals, are unique human characters that can be used for authentication processing. In this work, we present an IoT real-time authentication system based on using extracted ECG features to identify the unknown persons. The Discrete Cosine Transform (DCT) is used as an ECG feature extraction, where it has better characteristics for real-time system implementations. There are a substantial number of researches with a high accuracy of authentication, but most of them ignore the real-time capability of authenticating individuals. With the accuracy rate of 97.78% at around 1.21 seconds of processing time, the proposed system is more suitable for use in many applications that require fast and reliable authentication processing demands., Comment: 6 pages, 8 figures, IoT, Authentication, ECG, DCT

The aim of this paper is to describe a Matlab toolbox, called $\mu$-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in $\mu$-diff are based on the Fourier series expansions of the four basic integral operators arising in scattering theory. Based on these expressions, an efficient spectrally accurate finite-dimensional solution of multiple scattering problems can be simply obtained for complex media even when many scatterers are considered as well as large frequencies. The solution of the global linear system to solve can use either direct solvers or preconditioned iterative Krylov subspace solvers for block Toeplitz matrices. Based on this approach, this paper explains how the code is built and organized. Some complete numerical examples of applications (direct and inverse scattering) are provided to show that $\mu$-diff is a flexible, efficient and robust toolbox for solving some complex multiple scattering problems., Comment: 27 pages, 15 figures, associated code available online at http://mu-diff.math.cnrs.fr