Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled inertial oscillators with constant delay. Building on the master stability formalism, our technique provides necessary and sufficient delay…
An integration by parts formula is the foundation for stochastic analysis on path spaces over a (finite dimensional) Riemannian manifold or over $R^n$, from which we may deduce the operator $d$ is closable and define the Laplacian operator on path spaces. A useful formula on the Riemannian manifold is $$dP_tf(v)=(1/t)E f(x_t) \int_0^t \langle d\{x_s\}, v_s\rangle…
We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and input constraints robustly. Using disturbance measurements after each iteration, we construct Confidence Support sets, which contain…
Integration by parts formulae are given for a class of measures on the space of paths of a smooth manifold $M$ determined by the laws of degenerate diffusions. The mother of such formulae, on the path space of diffeomorphism group of $M$ is shown to arise from a quasi-invariance property of measures determined by stochastic…
The morphological attributes of retinal vessels, such as length, width, tortuosity and branching pattern and angles, play an important role in diagnosis, screening, treatment, and evaluation of various cardiovascular and ophthalmologic diseases such as diabetes, hypertension and arteriosclerosis. The crucial step before extracting these morphological characteristics of retinal vessels from retinal fundus images is vessel…
We prove that every set of n points in the plane has at most $17^n$ rectangulations. This improves upon a long-standing bound of Ackerman. Our proof is based on the cross-graph charging-scheme technique.
The recovery of a low rank matrix from a subset of noisy low-precision quantized samples arises in several applications such as collaborative filtering, intelligent recommendation and millimeter wave channel estimation with few bit ADCs. In this paper, a generalized sparse Bayesian learning (Gr-SBL) combining expectation propagation (EP) is proposed to solve the matrix completion (MC),…
Human ratings are currently the most accurate way to assess the quality of an image captioning model, yet most often the only used outcome of an expensive human rating evaluation is a few overall statistics over the evaluation dataset. In this paper, we show that the signal from instance-level human caption ratings can be leveraged…
Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done in arbitrary precision rational arithmetic.In this paper, we present an approach where most of the computation is performed in floating-point arithmetic,…
In this paper, we propose to use pre-trained features from end-to-end ASR models to solve the speech sentiment analysis problem as a down-stream task. We show that end-to-end ASR features, which integrate both acoustic and text information from speech, achieve promising results. We use RNN with self-attention as the sentiment classifier, which also provides an…