Related papers: An absorbing set for the Chialvo map

For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed…

Encoding a sequence of observations is an essential task with many applications. The encoding can become highly efficient when the observations are generated by a dynamical system. A dynamical system imposes regularities on the observations…

We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…

Recent work has observed an intriguing ''Neural Collapse'' phenomenon in well-trained neural networks, where the last-layer representations of training samples with the same label collapse into each other. This appears to suggest that the…

Schizophrenia is a severe mental health condition that requires a long and complicated diagnostic process. However, early diagnosis is vital to control symptoms. Deep learning has recently become a popular way to analyse and interpret…

Making an informed, correct and quick decision can be life-saving. It's crucial for animals during an escape behaviour or for autonomous cars during driving. The decision can be complex and may involve an assessment of the amount of threats…

Despite much effort, deep neural networks remain highly susceptible to tiny input perturbations and even for MNIST, one of the most common toy datasets in computer vision, no neural network model exists for which adversarial perturbations…

Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…

Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…

Deep learning models are used in critical applications, in which mistakes can have serious consequences. Therefore, it is crucial to understand how and why models generate predictions. This understanding provides useful information to check…

Neurons can code for multiple variables simultaneously and neuroscientists are often interested in classifying neurons based on their receptive field properties. Statistical models provide powerful tools for determining the factors…

Deep neural networks (DNNs) are vulnerable to adversarial examples where inputs with imperceptible perturbations mislead DNNs to incorrect results. Despite the potential risk they bring, adversarial examples are also valuable for providing…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

Absorbing boundaries are frequently employed in real-time propagation of the Schr\"odinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an…

In this paper, we address the problem of computing the maximal admissible robust positive invariant (MARPI) set for discrete-time linear time-varying systems with parametric uncertainties and additive disturbances. The system state and…

Learning and inferring features that generate sensory input is a task continuously performed by cortex. In recent years, novel algorithms and learning rules have been proposed that allow neural network models to learn such features from…

The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high-dimensional inputs/outputs (I/O), conventional approaches usually use a low-dimensional manifold to…

This paper proposes a new paradigm for learning a set of independent logical rules in disjunctive normal form as an interpretable model for classification. We consider the problem of learning an interpretable decision rule set as training a…

Cell segmentation is a critical step for quantitative single-cell analysis in microscopy images. Existing cell segmentation methods are often tailored to specific modalities or require manual interventions to specify hyper-parameters in…

When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…