A robust adaptive model predictive control (MPC) algorithm is presented for linear, time invariant systems with unknown dynamics and subject to bounded measurement noise. The system is characterized by an impulse response model, which is assumed to lie within a bounded set called the feasible system set. Online set-membership identification is used to reduce uncertainty…
We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its neighbors. This process provides a continuous analog of majority dynamics. We deduce properties of median dynamics…
The crystalline period map is a tool for linearizing $p$-divisible groups. It has been applied to study the Langlands correspondences, and has possible applications to the homotopy groups of spheres. The original construction of the period map is inherently local. We present an alternative construction, giving a map on the entire moduli stack of $p$-divisbile…
We consider cell line classification using multivariate time series data obtained from electric cell-substrate impedance sensing (ECIS) technology. The ECIS device, which monitors the attachment and spreading of mammalian cells in real time through the collection of electrical impedance data, has historically been used to study one cell line at a time. However, we show…
The specific connectivity of a neuronal network is reflected in the dynamics of the signals recorded on its nodes. The analysis of how the activity in one node predicts the behaviour of another gives the directionality in their relationship. However, each node is composed of many different elements which define the properties of the links.…
We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their derivatives. A neural network approximates the data and constructs the function library, but it also performs the sparse regression. This construction makes it…
Gene interaction graphs aim to capture various relationships between genes and represent decades of biology research. When trying to make predictions from genomic data, those graphs could be used to overcome the curse of dimensionality by making machine learning models sparser and more consistent with biological common knowledge. In this work, we focus on assessing…
Postural Orthostatic Tachycardia Syndrome (POTS) is associated with the onset of tachycardia upon postural change. The current diagnosis involves the measurement of heart rate (HR) and blood pressure (BP) during head-up tilt (HUT) or active standing test. A positive diagnosis is made if HR changes with more than 30 bpm (40 bpm in patients aged…
Adverse drug-drug interactions (DDIs) remain a leading cause of morbidity and mortality. Identifying potential DDIs during the drug design process is critical for patients and society. Although several computational models have been proposed for DDI prediction, there are still limitations: (1) specialized design of drug representation for DDI predictions is lacking; (2) predictions are based…
We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function can be non convex and needs not to…