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We determine the sharp mass threshold for Sobolev norm growth for the focusing continuum Calogero--Moser model. It is known that below the mass of $2\pi$, solutions to this completely integrable model enjoy uniform-in-time $H^s$ bounds for all $s \geq 0$. In contrast, we show that for arbitrarily small $\varepsilon > 0$ there exists initial data $u_0 \in H^\infty_+$ of mass $2\pi + \varepsilon$ such that the corresponding maximal lifespan solution $u : (T_-, T_+) \times \mathbb{R} \to \mathbb{C}$ satisfies $\lim_{t \to T_\pm} \|u(t)\|_{H^s} = \infty$ for all $s > 0$. As part of our proof, we demonstrate an orbital stability statement for the soliton and a dispersive decay bound for solutions with suitable initial data., Comment: 13 pages

A theoretical-computational framework is proposed for predicting the failure behavior of two anisotropic brittle materials, namely, single crystal magnesium and boron carbide. Constitutive equations are derived, in both small and large deformations, by using thermodynamics in order to establish a fully coupled and transient twin and crack system. To study the common deformation mechanisms (e.g., twinning and fracture), which can be caused by extreme mechanical loading, a monolithically-solved Ginzburg--Landau-based phase-field theory coupled with the mechanical equilibrium equation is implemented in a finite element simulation framework for the following problems: (i) twin evolution in two-dimensional single crystal magnesium and boron carbide under simple shear deformation; (ii) crack-induced twinning for magnesium under pure mode I and mode II loading; and (iii) study of fracture in homogeneous single crystal boron carbide under biaxial compressive loading. The results are verified by a steady-state phase-field approach and validated by available experimental data in the literature. The success of this computational method relies on using two distinct phase-field (order) parameters related to fracture and twinning. A finite element method-based code is developed within the Python-based open-source platform FEniCS. We make the code publicly available and the developed algorithm may be extended for the study of phase transformations under dynamic loading or thermally-activated mechanisms, where the competition between various deformation mechanisms is accounted for within the current comprehensive model approach.

Crater cataloging is an important yet time-consuming part of geological mapping. We present an automated Crater Detection Algorithm (CDA) that is competitive with expert-human researchers and hundreds of times faster. The CDA uses multiple neural networks to process digital terrain model and thermal infra-red imagery to identify and locate craters across the surface of Mars. We use additional post-processing filters to refine and remove potential false crater detections, improving our precision and recall by 10% compared to Lee (2019). We now find 80% of known craters above 3km in diameter, and identify 7,000 potentially new craters (13% of the identified craters). The median differences between our catalog and other independent catalogs is 2-4% in location and diameter, in-line with other inter-catalog comparisons. The CDA has been used to process global terrain maps and infra-red imagery for Mars, and the software and generated global catalog are available at https://doi.org/10.5683/SP2/CFUNII., Comment: 18 pages, 6 figures, 1 table. In press at Computers & Geosciences

Biological sequence comparison is a key step in inferring the relatedness of various organisms and the functional similarity of their components. Thanks to the Next Generation Sequencing efforts, an abundance of sequence data is now available to be processed for a range of bioinformatics applications. Embedding a biological sequence over a nucleotide or amino acid alphabet in a lower dimensional vector space makes the data more amenable for use by current machine learning tools, provided the quality of embedding is high and it captures the most meaningful information of the original sequences. Motivated by recent advances in the text document embedding literature, we present a new method, called seq2vec, to represent a complete biological sequence in an Euclidean space. The new representation has the potential to capture the contextual information of the original sequence necessary for sequence comparison tasks. We test our embeddings with protein sequence classification and retrieval tasks and demonstrate encouraging outcomes.