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We present a comprehensive study of stationary states in a coherent medium with a quadratic or Kerr nonlinearity in the presence of localized potentials in one dimension (1D) for both positive and negative signs of the nonlinear term, as well as for barriers and wells. The description is in terms of the nonlinear Schr\"odinger equation (NLSE) and hence applicable to a variety of systems, including interacting ultracold atoms in the mean field regime and light propagation in optical fibers. We determine the full landscape of solutions, in terms of a potential step and build solutions for rectangular barrier and well potentials. It is shown that all the solutions can be expressed in terms of a Jacobi elliptic function with the inclusion of a complex-valued phase shift. Our solution method relies on the roots of a cubic polynomial associated with a hydrodynamic picture, which provides a simple classification of all the solutions, both bounded and unbounded, while the boundary conditions are intuitively visualized as intersections of phase space curves. We compare solutions for open boundary conditions with those for a barrier potential on a ring, and also show that numerically computed solutions for smooth barriers agree qualitatively with analytical solutions for rectangular barriers. A stability analysis of solutions based on the Bogoliubov equations for fluctuations show that persistent instabilities are localized at sharp boundaries, and are predicated by the relation of the mean density change across the boundary to the value of the derivative of the density at the edge. We examine the scattering of a wavepacket by a barrier potential and show that at any instant the scattered states are well described by the stationary solutions we obtain, indicating applications of our results and methods to nonlinear scattering problems., Comment: 22 pages, 15 figures, 1 table

Detecting sarcasm and verbal irony from people's subjective statements is crucial to understanding their intended meanings and real sentiments and positions in social scenarios. This paper describes the X-PuDu system that participated in SemEval-2022 Task 6, iSarcasmEval - Intended Sarcasm Detection in English and Arabic, which aims at detecting intended sarcasm in various settings of natural language understanding. Our solution finetunes pre-trained language models, such as ERNIE-M and DeBERTa, under the multilingual settings to recognize the irony from Arabic and English texts. Our system ranked second out of 43, and ninth out of 32 in Task A: one-sentence detection in English and Arabic; fifth out of 22 in Task B: binary multi-label classification in English; first out of 16, and fifth out of 13 in Task C: sentence-pair detection in English and Arabic., Comment: SemEval-2022 Task 6

We present Variational Aspect-based Latent Topic Allocation (VALTA), a family of autoencoding topic models that learn aspect-based representations of reviews. VALTA defines a user-item encoder that maps bag-of-words vectors for combined reviews associated with each paired user and item onto structured embeddings, which in turn define per-aspect topic weights. We model individual reviews in a structured manner by inferring an aspect assignment for each sentence in a given review, where the per-aspect topic weights obtained by the user-item encoder serve to define a mixture over topics, conditioned on the aspect. The result is an autoencoding neural topic model for reviews, which can be trained in a fully unsupervised manner to learn topics that are structured into aspects. Experimental evaluation on large number of datasets demonstrates that aspects are interpretable, yield higher coherence scores than non-structured autoencoding topic model variants, and can be utilized to perform aspect-based comparison and genre discovery.

We present the reinterpreted and reimplemented Copycat project, an architecture solving letter analogy domain problems. To support a flexible implementation change and rigor testing process, we propose a implementation method in DrRacket by using functional abstraction, naming system, initialization, and structural reference. Finally, benefits and limitations are analyzed for cognitive architectures along the lines of Copycat., Comment: 14 pages, 4 figures, 2 tables. Work in progress preprint. Research project spans 2 years both within my time in Northeastern University internships and class time in Viewpoint School, thus dual affiliation is accepted by both parties. More experimental comparison results will be added when conclusive experiments are completed