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Higher-order interactions (HOIs) have the potential to greatly increase our understanding of ecological interaction networks beyond what is possible with established models that usually consider only pairwise interactions between organisms. While equilibrium values of such HOI-based models have been studied, the dynamics of these models and the stability of their equilibria remain underexplored. Here we present a novel investigation on the effect of the onset speed of a higher-order interaction. In particular, we study the stability of the equilibrium of all configurations of a three-species interaction network, including transitive as well as intransitive ones. We show that the HOI onset speed has a dramatic effect on the evolution and stability of the ecological network, with significant structural changes compared to commonly used HOI extensions or pairwise networks. Changes in the HOI onset speed from fast to slow can reverse the stability of the interaction network. The evolution of the system also affects the equilibrium that will be reached, influenced by the HOI onset speed. This implies that the HOI onset speed is an important determinant in the dynamics of ecological systems, and including it in models of ecological networks can improve our understanding thereof., Comment: Main: 9 pages, supplementary: 9 pages

A set of $2^n$ candidates is presented to a commission. At every round, each member of this commission votes by pairwise comparison, and one-half of the candidates is deleted from the tournament, the remaining ones proceeding to the next round until the $n$-th round (the final one) in which the final winner is declared. The candidates are arranged on a board in a given order, which is maintained among the remaining candidates at all rounds. A study of the size of the commission is carried out in order to obtain the desired result of any candidate being a possible winner. For $2^n$ candidates with $n \geq 3$, we identify a voting profile with $4n -3$ voters such that any candidate could win just by choosing a proper initial order of the candidates. Moreover, in the setting of a random number of voters, we obtain the same results, with high probability, when the expected number of voters is large., Comment: 14 pages

Texture, a significant visual attribute in images, has been extensively investigated across various image recognition applications. Convolutional Neural Networks (CNNs), which have been successful in many computer vision tasks, are currently among the best texture analysis approaches. On the other hand, Vision Transformers (ViTs) have been surpassing the performance of CNNs on tasks such as object recognition, causing a paradigm shift in the field. However, ViTs have so far not been scrutinized for texture recognition, hindering a proper appreciation of their potential in this specific setting. For this reason, this work explores various pre-trained ViT architectures when transferred to tasks that rely on textures. We review 21 different ViT variants and perform an extensive evaluation and comparison with CNNs and hand-engineered models on several tasks, such as assessing robustness to changes in texture rotation, scale, and illumination, and distinguishing color textures, material textures, and texture attributes. The goal is to understand the potential and differences among these models when directly applied to texture recognition, using pre-trained ViTs primarily for feature extraction and employing linear classifiers for evaluation. We also evaluate their efficiency, which is one of the main drawbacks in contrast to other methods. Our results show that ViTs generally outperform both CNNs and hand-engineered models, especially when using stronger pre-training and tasks involving in-the-wild textures (images from the internet). We highlight the following promising models: ViT-B with DINO pre-training, BeiTv2, and the Swin architecture, as well as the EfficientFormer as a low-cost alternative. In terms of efficiency, although having a higher number of GFLOPs and parameters, ViT-B and BeiT(v2) can achieve a lower feature extraction time on GPUs compared to ResNet50.

In recent years, we have seen many advancements in wood species identification. Methods like DNA analysis, Near Infrared (NIR) spectroscopy, and Direct Analysis in Real Time (DART) mass spectrometry complement the long-established wood anatomical assessment of cell and tissue morphology. However, most of these methods have some limitations such as high costs, the need for skilled experts for data interpretation, and the lack of good datasets for professional reference. Therefore, most of these methods, and certainly the wood anatomical assessment, may benefit from tools based on Artificial Intelligence. In this paper, we apply two transfer learning techniques with Convolutional Neural Networks (CNNs) to a multi-view Congolese wood species dataset including sections from different orientations and viewed at different microscopic magnifications. We explore two feature extraction methods in detail, namely Global Average Pooling (GAP) and Random Encoding of Aggregated Deep Activation Maps (RADAM), for efficient and accurate wood species identification. Our results indicate superior accuracy on diverse datasets and anatomical sections, surpassing the results of other methods. Our proposal represents a significant advancement in wood species identification, offering a robust tool to support the conservation of forest ecosystems and promote sustainable forestry practices., Comment: 33 pages, 7 tables, 9 figures

Advances in bioinformatics are primarily due to new algorithms for processing diverse biological data sources. While sophisticated alignment algorithms have been pivotal in analyzing biological sequences, deep learning has substantially transformed bioinformatics, addressing sequence, structure, and functional analyses. However, these methods are incredibly data-hungry, compute-intensive and hard to interpret. Hyperdimensional computing (HDC) has recently emerged as an intriguing alternative. The key idea is that random vectors of high dimensionality can represent concepts such as sequence identity or phylogeny. These vectors can then be combined using simple operators for learning, reasoning or querying by exploiting the peculiar properties of high-dimensional spaces. Our work reviews and explores the potential of HDC for bioinformatics, emphasizing its efficiency, interpretability, and adeptness in handling multimodal and structured data. HDC holds a lot of potential for various omics data searching, biosignal analysis and health applications.

Microbial communities play a key role in biological wastewater treatment processes. Activated sludge settling characteristics, for example, are affected by microbial community composition, varying by changes in operating conditions and influent characteristics of wastewater treatment plants (WWTPs). Timely assessment and prediction of changes in microbial composition leading to settling problems, such as filamentous bulking (FB), can prevent operational challenges, reductions in treatment efficiency, and adverse environmental impacts. This study presents an innovative computer vision-based approach to assess activated sludge-settling characteristics based on the morphological properties of flocs and filaments in microscopy images. Implementing the transfer learning of deep convolutional neural network (CNN) models, this approach aims to overcome the limitations of existing quantitative image analysis techniques. The offline microscopy image dataset was collected over two years, with weekly sampling at a full-scale industrial WWTP in Belgium. Multiple data augmentation techniques were employed to enhance the generalizability of the CNN models. Various CNN architectures, including Inception v3, ResNet18, ResNet152, ConvNeXt-nano, and ConvNeXt-S, were tested to evaluate their performance in predicting sludge settling characteristics. The sludge volume index was used as the final prediction variable, but the method can easily be adjusted to predict any other settling metric of choice. The results showed that the suggested CNN-based approach provides less labour-intensive, objective, and consistent assessments, while transfer learning notably minimises the training phase, resulting in a generalizable system that can be employed in real-time applications., Comment: 34 Pages, 8 figures

Hyperdimensional computing (HDC) is an increasingly popular computing paradigm with immense potential for future intelligent applications. Although the main ideas already took form in the 1990s, HDC recently gained significant attention, especially in the field of machine learning and data science. Next to efficiency, interoperability and explainability, HDC offers attractive properties for generalization as it can be seen as an attempt to combine connectionist ideas from neural networks with symbolic aspects. In recent work, we introduced the hyperdimensional transform, revealing deep theoretical foundations for representing functions and distributions as high-dimensional holographic vectors. Here, we present the power of the hyperdimensional transform to a broad data science audience. We use the hyperdimensional transform as a theoretical basis and provide insight into state-of-the-art HDC approaches for machine learning. We show how existing algorithms can be modified and how this transform can lead to a novel, well-founded toolbox. Next to the standard regression and classification tasks of machine learning, our discussion includes various aspects of statistical modelling, such as representation, learning and deconvolving distributions, sampling, Bayesian inference, and uncertainty estimation.

Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable functions into noise-robust, holographic, high-dimensional representations called hyperdimensional vectors. The central idea is to approximate a function by a linear combination of random functions. We formally introduce a set of stochastic, orthogonal basis functions and define the hyperdimensional transform and its inverse. We discuss general transform-related properties such as its uniqueness, approximation properties of the inverse transform, and the representation of integrals and derivatives. The hyperdimensional transform offers a powerful, flexible framework that connects closely with other integral transforms, such as the Fourier, Laplace, and fuzzy transforms. Moreover, it provides theoretical foundations and new insights for the field of hyperdimensional computing, a computing paradigm that is rapidly gaining attention for efficient and explainable machine learning algorithms, with potential applications in statistical modelling and machine learning. In addition, we provide straightforward and easily understandable code, which can function as a tutorial and allows for the reproduction of the demonstrated examples, from computing the transform to solving differential equations.

Conformal prediction, and split conformal prediction as a specific implementation, offer a distribution-free approach to estimating prediction intervals with statistical guarantees. Recent work has shown that split conformal prediction can produce state-of-the-art prediction intervals when focusing on marginal coverage, i.e. on a calibration dataset the method produces on average prediction intervals that contain the ground truth with a predefined coverage level. However, such intervals are often not adaptive, which can be problematic for regression problems with heteroskedastic noise. This paper tries to shed new light on how prediction intervals can be constructed, using methods such as normalized and Mondrian conformal prediction, in such a way that they adapt to the heteroskedasticity of the underlying process. Theoretical and experimental results are presented in which these methods are compared in a systematic way. In particular, it is shown how the conditional validity of a chosen conformal predictor can be related to (implicit) assumptions about the data-generating distribution., Comment: 36 pages

Texture analysis is a classical yet challenging task in computer vision for which deep neural networks are actively being applied. Most approaches are based on building feature aggregation modules around a pre-trained backbone and then fine-tuning the new architecture on specific texture recognition tasks. Here we propose a new method named \textbf{R}andom encoding of \textbf{A}ggregated \textbf{D}eep \textbf{A}ctivation \textbf{M}aps (RADAM) which extracts rich texture representations without ever changing the backbone. The technique consists of encoding the output at different depths of a pre-trained deep convolutional network using a Randomized Autoencoder (RAE). The RAE is trained locally to each image using a closed-form solution, and its decoder weights are used to compose a 1-dimensional texture representation that is fed into a linear SVM. This means that no fine-tuning or backpropagation is needed. We explore RADAM on several texture benchmarks and achieve state-of-the-art results with different computational budgets. Our results suggest that pre-trained backbones may not require additional fine-tuning for texture recognition if their learned representations are better encoded., Comment: 17 pages, 3 figures, submitted to peer-review journal

In this paper, we introduce the notion of a t-norm on bounded pseudo-ordered sets and in particular on bounded trellises (also known as weakly associative lattices), and provide some basic examples. The impact of abandoning transitivity is considerable: on a proper bounded trellis, the meet operation is not a t-norm, and there might actually exist no or even multiple maximal t-norms. We provide a first generic construction method that allows to extend a t-norm on an interior range of a given $\meet$-semi-trellis to the entire $\meet$-semi-trellis. Also, we discuss at length an instantiation of this method based on a particular interior range, namely a finite sub-trellis of the set of right-transitive elements of a given trellis. We pay specific attention to bounded pseudo-chains and modular trellises., Comment: 37 pages, 8 figure. To appear in an Elsevier Journal

As a result of the ever increasing complexity of configuring and fine-tuning machine learning models, the field of automated machine learning (AutoML) has emerged over the past decade. However, software implementations like Auto-WEKA and Auto-sklearn typically focus on classical machine learning (ML) tasks such as classification and regression. Our work can be seen as the first attempt at offering a single AutoML framework for most problem settings that fall under the umbrella of multi-target prediction, which includes popular ML settings such as multi-label classification, multivariate regression, multi-task learning, dyadic prediction, matrix completion, and zero-shot learning. Automated problem selection and model configuration are achieved by extending DeepMTP, a general deep learning framework for MTP problem settings, with popular hyperparameter optimization (HPO) methods. Our extensive benchmarking across different datasets and MTP problem settings identifies cases where specific HPO methods outperform others., Comment: 17 pages, 4 figures, 1 table

The deep learning literature is continuously updated with new architectures and training techniques. However, weight initialization is overlooked by most recent research, despite some intriguing findings regarding random weights. On the other hand, recent works have been approaching Network Science to understand the structure and dynamics of Artificial Neural Networks (ANNs) after training. Therefore, in this work, we analyze the centrality of neurons in randomly initialized networks. We show that a higher neuronal strength variance may decrease performance, while a lower neuronal strength variance usually improves it. A new method is then proposed to rewire neuronal connections according to a preferential attachment (PA) rule based on their strength, which significantly reduces the strength variance of layers initialized by common methods. In this sense, PA rewiring only reorganizes connections, while preserving the magnitude and distribution of the weights. We show through an extensive statistical analysis in image classification that performance is improved in most cases, both during training and testing, when using both simple and complex architectures and learning schedules. Our results show that, aside from the magnitude, the organization of the weights is also relevant for better initialization of deep ANNs., Comment: 17 pages, 5 figures, under peer-review

Over the last few decades, various methods have been proposed for estimating prediction intervals in regression settings, including Bayesian methods, ensemble methods, direct interval estimation methods and conformal prediction methods. An important issue is the calibration of these methods: the generated prediction intervals should have a predefined coverage level, without being overly conservative. In this work, we review the above four classes of methods from a conceptual and experimental point of view. Results on benchmark data sets from various domains highlight large fluctuations in performance from one data set to another. These observations can be attributed to the violation of certain assumptions that are inherent to some classes of methods. We illustrate how conformal prediction can be used as a general calibration procedure for methods that deliver poor results without a calibration step., Comment: Minor correction (bibliography and typo in Fig. 3). Thanks to Dr. Mar\'ia Moreno de Castro for spotting this typo

Multi-target prediction (MTP) serves as an umbrella term for machine learning tasks that concern the simultaneous prediction of multiple target variables. Classical instantiations are multi-label classification, multivariate regression, multi-task learning, dyadic prediction, zero-shot learning, network inference, and matrix completion. Despite the significant similarities, all these domains have evolved separately into distinct research areas over the last two decades. This led to the development of a plethora of highly-engineered methods, and created a substantially-high entrance barrier for machine learning practitioners that are not experts in the field. In this work we present a generic deep learning methodology that can be used for a wide range of multi-target prediction problems. We introduce a flexible multi-branch neural network architecture, partially configured via a questionnaire that helps end-users to select a suitable MTP problem setting for their needs. Experimental results for a wide range of domains illustrate that the proposed methodology manifests a competitive performance compared to methods from specific MTP domains.

The ordinal sum construction provides a very effective way to generate a new triangular norm on the real unit interval from existing ones. One of the most prominent theorems concerning the ordinal sum of triangular norms on the real unit interval states that a triangular norm is continuous if and only if it is uniquely representable as an ordinal sum of continuous Archimedean triangular norms. However, the ordinal sum of triangular norms on subintervals of a bounded lattice is not always a triangular norm (even if only one summand is involved), if one just extends the ordinal sum construction to a bounded lattice in a na\"{\i}ve way. In the present paper, appropriately dealing with those elements that are incomparable with the endpoints of the given subintervals, we propose an alternative definition of ordinal sum of countably many (finite or countably infinite) triangular norms on subintervals of a complete lattice, where the endpoints of the subintervals constitute a chain. The completeness requirement for the lattice is not needed when considering finitely many triangular norms. The newly proposed ordinal sum is shown to be always a triangular norm. Several illustrative examples are given.

In this work, we analysed the satellite-based responses of sea surface temperature (SST) and chlorophyll-a (chl-a) concentration in the waters of the Exclusive Economic Zone (EEZ) of Cuba to hurricanes that crossed the EEZ between 1998 and 2016. We considered two spatial scales to capture the spatially heterogeneous nature of the effects of hurricanes. A first more fine-grained one where we considered 120 km radius disks centered at every consecutive hurricane position within the EEZ (scale 1) and a second more coarse grained one enclosing the entire EEZ (scale 2). We conclude that the hurricanes induced a weak cooling since 75 and 85% of the SST anomalies at scale 1 and 2, respectively, were smaller than -1{\deg}C. The cooling was mainly caused by the wind, inducing mixing and/or upwelling of subsurface cool waters. The maximum chl-a responses were recorded in the first and second post-storm weeks, with 60% ranging between -0.01 and 0.04 mg m$^{-3}$ at scale 1, and between -0.07 and 0.02 mg m$^{-3}$ at scale 2. During those post-storm weeks SST and chl-a anomalies were 18 and 44% higher at scale 1 than at scale 2, respectively. We argue that the transport of chl-a from the deep chlorophyll maximum and/or the rich coastal waters are the dominant mechanisms determining the post-storm chl-a response in the EEZ. We also found that the magnitude of the Island Mass Effect in the EEZ after the passage of the hurricanes was 89% higher than before its passage., Comment: 33 pages, 14 figures. Submitted to Remote Sensing of Environment

This paper concerns $d$-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or density-conserving cellular automata, are of particular interest to mathematicians, computer scientists and physicists, as they can serve as models of physical phenomena obeying some conservation law. We propose a new approach to study such cellular automata that works in any dimension $d$ and for any set of states $Q$. Essentially, the local rule of a cellular automaton is decomposed into two parts: a split function and a perturbation. This decomposition is unique and, moreover, the set of all possible split functions has a very simple structure, while the set of all perturbations forms a linear space and is therefore very easy to describe in terms of its basis. We show how this approach allows to find all number-conserving cellular automata in many cases of $d$ and $Q$. In particular, we find all three-dimensional number-conserving CAs with three states, which until now was beyond the capabilities of computers.