相关论文: Neuron Growth Output-Feedback Control by PDE Backs…

State estimation is important for a variety of tasks, from forecasting to substituting for unmeasured states in feedback controllers. Performing real-time state estimation for PDEs using provably and rapidly converging observers, such as…

For the quite extensively developed PDE backstepping methodology for coupled linear hyperbolic PDEs, we provide a generalization from finite collections of such PDEs, whose states at each location in space are vector-valued, to previously…

Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded noise gain is typically proven. In recent work it has been shown, in both the pole placement…

The Stefan PDE system is a representative model for thermal phase change phenomena, such as melting and solidification, arising in numerous science and engineering processes. The mathematical description is given by a Partial Differential…

Regulation of cell growth and division is essential to achieve cell-size homeostasis. Recent advances in imaging technologies, such as ``mother machines" for bacteria or yeast, have allowed long-term tracking of cell-size dynamics across…

Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach…

This paper develops output feedback boundary control to mitigate traffic congestion of a unidirectional two-lane freeway segment. The macroscopic traffic dynamics are described by the Aw-Rascle-Zhang (ARZ) model respectively for both the…

Consider a large number $n$ of neurons, each being connected to approximately $N$ other ones, chosen at random. When a neuron spikes, which occurs randomly at some rate depending on its electric potential, its potential is set to a minimum…

Modern neural networks can achieve high accuracy while remaining poorly calibrated, producing confidence estimates that do not match empirical correctness. Yet calibration is often treated as a post-hoc attribute. We take a different…

Dense prediction models are widely used for image segmentation. One important challenge is to sufficiently train these models to yield good generalizations for hard-to-learn pixels. A typical group of such hard-to-learn pixels are…

Cultured stem cells have become a standard platform not only for regenerative medicine and developmental biology but also for biophysical studies. Yet, the characterization of cultured stem cells at the level of morphology and macroscopic…

Brains can process sensory information from different modalities at astonishing speed; this is surprising as the integration of inputs through the membrane of each individual neuron already causes a delayed response. Neuronal recordings…

Aggregates of misfolded tau proteins (or just 'tau' for brevity) play a crucial role in the progression of Alzheimer's disease (AD) as they correlate with cell death and accelerated tissue atrophy. Longitudinal positron emission tomography…

Living organisms must actively maintain themselves in order to continue existing. Autopoiesis is a key concept in the study of living organisms, where the boundaries of the organism is not static by dynamically regulated by the system…

In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes chemotaxis term directed to vasculature. First, we obtain some a priori estimates for the (possible) solutions of the model. In particular,…

It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead…

The main goal of this study is to propose a mathematical model describing paths of the axon growth cones and differences in the behavior of normal and mutant axons. We introduce a probabilistic model for axon growing, such that each family…

While tumor dynamic modeling has been widely applied to support the development of oncology drugs, there remains a need to increase predictivity, enable personalized therapy, and improve decision-making. We propose the use of Tumor Dynamic…

In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature. First, we prove the existence of…

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…