Related papers: Zigzags in Turing machines
We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
We consider learning nonholonomic dynamical systems while discovering the constraints, and describe in detail the case of the rolling disk. A nonholonomic system is a system subject to nonholonomic constraints. Unlike holonomic constraints,…
We investigate the dynamics of substitution subshifts and their associated tiling spaces. For a given subshift, the associated tiling spaces are all homeomorphic, but their dynamical properties may differ. We give criteria for such a tiling…
The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher…
In this paper, we modify some previous definitions of fuzzy Turing machines to define the notions of accepting and rejecting degrees of inputs, computationally. We use a BFS-based search method and obtain an upper level bound to guarantee…
The problem of learning a manifold structure on a dataset is framed in terms of a generative model, to which we use ideas behind autoencoders (namely adversarial/Wasserstein autoencoders) to fit deep neural networks. From a machine learning…
We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a softmax classification network acts on an input topological…
Drifting is a complicated task for autonomous vehicle control. Most traditional methods in this area are based on motion equations derived by the understanding of vehicle dynamics, which is difficult to be modeled precisely. We propose a…
In the pursuit of autonomous learning systems, the foundational assumption of stationarity, the premise that data distributions and model behaviors remain constant, is fundamentally untenable. Historically, the research community has…
Convolutional neural networks (CNNs) evaluate short-range correlations in input images which progress along the layers, whereas vision transformer (ViT) architectures evaluate long-range correlations, using repeated transformer encoders…
Human learning relies on specialization -- distinct cognitive mechanisms working together to enable rapid learning. In contrast, most modern neural networks rely on a single mechanism: gradient descent over an objective function. This…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic…
Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…
Head-mounted device-based human-computer interaction often requires egocentric recognition of hand gestures and fingertips detection. In this paper, a unified approach of egocentric hand gesture recognition and fingertip detection is…
Tactical driving decision making is crucial for autonomous driving systems and has attracted considerable interest in recent years. In this paper, we propose several practical components that can speed up deep reinforcement learning…
We investigate the sensorimotor loop of simple robots simulated within the LPZRobots environment from the point of view of dynamical systems theory. For a robot with a cylindrical shaped body and an actuator controlled by a single…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…