We consider exit problems for small white noise perturbations of a dynamical system generated by a vector field, and a domain containing a critical point with all positive eigenvalues of linearization. We prove that, in the vanishing noise limit, the probability of exit through a generic set on the boundary is asymptotically polynomial in the…
Let $X_0$ be a non-constant random variable with finite variance. Given an integer $k\ge2$, define a sequence $\{X_n\}_{n=1}^\infty$ of approximately linear recursions with small perturbations $\{\Delta_n\}_{n=0}^\infty$ by $$X_{n+1} = \sum_{i=1}^k a_{n,i} X_{n,i} + \Delta_n \quad \text{for all } n\ge0$$ where $X_{n,1},\dots,X_{n,k}$ are independent copies of the $X_n$ and $a_{n,1},\dots,a_{n,k}$ are real numbers. In 2004, Goldstein…
Convolutional neural networks (CNNs) with dilated filters such as the Wavenet or the Temporal Convolutional Network (TCN) have shown good results in a variety of sequence modelling tasks. However, efficiently modelling long-term dependencies in these sequences is still challenging. Although the receptive field of these models grows exponentially with the number of layers, computing the…
This paper introduces the Eighth Dialog System Technology Challenge. In line with recent challenges, the eighth edition focuses on applying end-to-end dialog technologies in a pragmatic way for multi-domain task-completion, noetic response selection, audio visual scene-aware dialog, and schema-guided dialog state tracking tasks. This paper describes the task definition, provided datasets, and evaluation set-up for…
Dynamic contrast enhanced computed tomography (CT) is an imaging technique that provides critical information on the relationship of vascular structure and dynamics in the context of underlying anatomy. A key challenge for image processing with contrast enhanced CT is that phase discrepancies are latent in different tissues due to contrast protocols, vascular dynamics, and metabolism…
Previous studies generally agree that face recognition accuracy is higher for older persons than for younger persons. But most previous studies were before the wave of deep learning matchers, and most considered accuracy only in terms of the verification rate for genuine pairs. This paper investigates accuracy for age groups 16-29, 30-49 and 50-70, using…
We present SMILES-embeddings derived from internal encoder state of a Transformer[1] model trained to canonize SMILES as a Seq2Seq problem. Using CharNN[2] architecture upon the embeddings results in a higher quality QSAR/QSPR models on diverse benchmark datasets including regression and classification tasks. The proposed Transformer-CNN method uses SMILES augmentation for training and inference, and thus…
To transform a single-celled zygote into an adult multicellular organism, development employs three basic processes — asymmetric cell division, signaling and gene regulation. These three processes can be combined in a multitude of ways, thus generating the huge diversity of plant and animal forms we see today. The wealth of possible developmental schemes created by…
One of the major goals of nanobionics and bottom-up synthetic biology is the development of artificial cell organelles for the creation of cell-like structures operating similar to biological systems with a minimalistic set of building blocks. In the present contribution, versatile strategies to develop artificial reaction centers for novel photoautotrophic processes and to provide fully…
This paper proposes to use deep radiomic features (DRFs) from a convolutional neural network (CNN) to model fine-grained texture signatures in the radiomic analysis of recurrent glioblastoma (rGBM). We use DRFs to predict survival of rGBM patients with preoperative T1-weighted post-contrast MR images (n=100). DRFs are extracted from regions of interest labelled by a radiation…