相关论文: Developing Mathematics for Insight into Sensorimot…

Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear waves-settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to…

Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off…

We present an approach to sensorimotor control in immersive environments. Our approach utilizes a high-dimensional sensory stream and a lower-dimensional measurement stream. The cotemporal structure of these streams provides a rich…

Rapid development of social robots stimulates active research in human motion modeling, interpretation and prediction, proactive collision avoidance, human-robot interaction and co-habitation in shared spaces. Modern approaches to this end…

Despite the recent success of neural network models in mimicking animal performance on visual perceptual tasks, critics worry that these models fail to illuminate brain function. We take it that a central approach to explanation in systems…

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…

Organogenesis is a tightly regulated process that has been studied experimentally for decades. Computational models can help to integrate available knowledge and to better understand the underlying regulatory logic. We are currently…

Multimodal neuroimaging grants a powerful in vivo window into the structure and function of the human brain. Recent methodological and conceptual advances have enabled investigations of the interplay between large-scale spatial trends, or…

The neural networks of the brain are capable of learning statistical input regularities on the basis of synaptic learning, functional integration into increasingly larger, interconnected neural assemblies, and self organization. This self…

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of…

It is not surprising that the idea of efficient maintenance algorithms (originally motivated by strict emission regulations, and now driven by safety issues, logistics and customer satisfaction) has culminated in the so-called…

Human-centred systems require an understanding of human actions in the physical world. Temporally extended sequences of actions are intentional and structured, yet existing methods for recognising what actions are performed often do not…

The acceleration race of digital computing technologies seems to be steering toward impasses -- technological, economical and environmental -- a condition that has spurred research efforts in alternative, "neuromorphic" (brain-like)…

Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…

Emotions are a central key for understanding human beings and of fundamental importance regarding their impact in human and animal behaviors. They have been for a long time a subject of study for various scholars including in particular…

Mathematical modeling has broad applications in neuroscience whether modeling the dynamics of a single synapse or an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better…

Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…