Related papers: Characterization of Fractal Basins Using Deep Conv…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account…

Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter \lambda of the system is modified. Complex patterns on the plane are visualised as a consequence of basins'…

We establish a correspondence between Pavlovian conditioning processes and fractals. The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level. In this way, one can represent a…

Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…

State-of-the-art deep neural networks have achieved impressive results on many image classification tasks. However, these same architectures have been shown to be unstable to small, well sought, perturbations of the images. Despite the…

We show that deep convolutional neural networks (CNN) can massively outperform traditional densely-connected neural networks (both deep or shallow) in predicting eigenvalue problems in mechanics. In this sense, we strike out in a new…

Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…

Field-scale properties of fractured rocks play crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion…

The wave properties of complex scattering systems that are large compared to the wavelength, and show chaos in the classical limit, are extremely sensitive to system details. A solution to the wave equation for a specific configuration can…

The increased presence of advanced sensors on the production floors has led to the collection of datasets that can provide significant insights into machine health. An important and reliable indicator of machine health, vibration signal…

Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper we establish some analysis for…

Neural networks predictions are unreliable when the input sample is out of the training distribution or corrupted by noise. Being able to detect such failures automatically is fundamental to integrate deep learning algorithms into robotics.…

Ball mills play a critical role in modern mining operations, making their bearing failures a significant concern due to the potential loss of production efficiency and economic consequences. This paper presents an anomaly detection method…

Deep neural networks have shown great achievements in solving complex problems. However, there are fundamental problems that limit their real world applications. Lack of measurable criteria for estimating uncertainty in the network outputs…

Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address…

In time-varying fading channels, channel coefficients are estimated using pilot symbols that are transmitted every coherence interval. For channels with high Doppler spread, the rapid channel variations over time will require considerable…

Convolutional Neural Networks (CNNs) are well established models capable of achieving state-of-the-art classification accuracy for various computer vision tasks. However, they are becoming increasingly larger, using millions of parameters,…

We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…

Sampling strategies are important for sparse imaging methodologies, especially those employing the discrete Fourier transform (DFT). Chaotic sensing is one such methodology that employs deterministic, fractal sampling in conjunction with…