Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, morphology has compositional properties responsible for word formation, organized into a magma of morphological trees. However, unlike syntax, we do not have movement within morphology. A coproduct decomposition exists, but it requires extending the set of morphological trees beyond those which are generated solely by the magma, to a larger set of possible morphological inputs to syntactic trees. These participate in the formation of morphosyntactic trees as an algebra over an operad, and a correspondence between algebras over an operad . The process of structure formation for morphosyntactic trees can then be described in terms of this operadic correspondence that pairs syntactic and morphological data and the morphology coproduct. We reinterpret in this setting certain operations of Distributed Morphology as transformation that allow for flexibility in moving the boundary between syntax and morphology within the morphosyntactic objects.

Multiple sclerosis is a disease that affects the brain and spinal cord, it can lead to severe disability and has no known cure. The majority of prior work in machine learning for multiple sclerosis has been centered around using Magnetic Resonance Imaging scans or laboratory tests; these modalities are both expensive to acquire and can be unreliable. In a recent paper it was shown that disease progression can be predicted effectively using performance outcome measures and demographic data. In our work we build on this to investigate the modeling side, using continuous time models to predict progression. We benchmark four continuous time models using a publicly available multiple sclerosis dataset. We find that the best continuous model is often able to outperform the best benchmarked discrete time model. We also carry out an extensive ablation to discover the sources of performance gains, we find that standardizing existing features leads to a larger performance increase than interpolating missing features.

Recent studies have shown that deep convolutional neural networks (DCNN) are vulnerable to adversarial examples and sensitive to perceptual quality as well as the acquisition condition of images. These findings raise a big concern for the adoption of DCNN-based applications for critical tasks. In the literature, various defense strategies have been introduced to increase the robustness of DCNN, including re-training an entire model with benign noise injection, adversarial examples, or adding extra layers. In this paper, we investigate the connection between adversarial manipulation and image quality, subsequently propose a protective mechanism that doesnt require re-training a DCNN. Our method combines image quality assessment with knowledge distillation to detect input images that would trigger a DCCN to produce egregiously wrong results. Using the ResNet model trained on ImageNet as an example, we demonstrate that the detector can effectively identify poor quality and adversarial images.