Scaling of the atmosphere of self-avoiding walks

The number of free sites next to the end of a self-avoiding walk is known as the atmosphere. The average atmosphere can be related to the number of configurations. Here we study the distribution of atmospheres as a function of length and how the number of walks of fixed atmosphere scale. Certain bounds on these numbers can be proved. We use Monte Carlo estimates to verify our conjectures. Of particular interest are walks that have zero atmosphere, which are known as trapped. We demonstrate that these walks scale in the same way as the full set of self-avoiding walks, barring an overall constant factor

Adversarial Personalized Ranking for Recommendation

Item recommendation is a personalized ranking task. To this end, many recommender systems optimize models with pairwise ranking objectives, such as the Bayesian Personalized Ranking (BPR). Using matrix Factorization (MF) --- the most widely used model in recommendation --- as a demonstration, we show that optimizing it with BPR leads to a recommender model that is not robust. In particular, we find that the resultant model is highly vulnerable to adversarial perturbations on its model parameters, which implies the possibly large error in generalization. To enhance the robustness of a recommender model and thus improve its generalization performance, we propose a new optimization framework, namely Adversarial Personalized Ranking (APR). In short, our APR enhances the pairwise ranking method BPR by performing adversarial training. It can be interpreted as playing a minimax game, where the minimization of the BPR objective function meanwhile defends an adversary, which adds adversarial perturbations on model parameters to maximize the BPR objective function. To illustrate how it works, we implement APR on MF by adding adversarial perturbations on the embedding vectors of users and items. Extensive experiments on three public real-world datasets demonstrate the effectiveness of APR --- by optimizing MF with APR, it outperforms BPR with a relative improvement of 11.2% on average and achieves state-of-the-art performance for item recommendation. Our implementation is available at: https://github.com/hexiangnan/adversarial_personalized_ranking.Comment: SIGIR 201

An Exploratory Analysis of the Latent Structure of Process Data via Action Sequence Autoencoder

Computer simulations have become a popular tool of assessing complex skills such as problem-solving skills. Log files of computer-based items record the entire human-computer interactive processes for each respondent. The response processes are very diverse, noisy, and of nonstandard formats. Few generic methods have been developed for exploiting the information contained in process data. In this article, we propose a method to extract latent variables from process data. The method utilizes a sequence-to-sequence autoencoder to compress response processes into standard numerical vectors. It does not require prior knowledge of the specific items and human-computers interaction patterns. The proposed method is applied to both simulated and real process data to demonstrate that the resulting latent variables extract useful information from the response processes.Comment: 28 pages, 13 figure

Handheld Co-Axial Bioprinting: Application to in situ surgical cartilage repair

Three-dimensional (3D) bioprinting is driving major innovations in the area of cartilage tissue engineering. Extrusion-based 3D bioprinting necessitates a phase change from a liquid bioink to a semi-solid crosslinked network achieved by a photo-initiated free radical polymerization reaction that is known to be cytotoxic. Therefore, the choice of the photocuring conditions has to be carefully addressed to generate a structure stiff enough to withstand the forces phisiologically applied on articular cartilage, while ensuring adequate cell survival for functional chondral repair. We recently developed a handheld 3D printer called Biopen . To progress towards translating this freeform biofabrication tool into clinical practice, we aimed to define the ideal bioprinting conditions that would deliver a scaffold with high cell viability and structural stiffness relevant for chondral repair. To fulfill those criteria, free radical cytotoxicity was confined by a co-axial Core/Shell separation. This system allowed the generation of Core/Shell GelMa/HAMa bioscaffolds with stiffness of 200KPa, achieved after only 10seconds of exposure to 700mW/cm2 of 365nm UV-A, containing \u3e90% viable stem cells that retained proliferative capacity. Overall, the Core/Shell handheld 3D bioprinting strategy enabled rapid generation of high modulus bioscaffolds with high cell viability, with potential for in situ surgical cartilage engineering