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Long linear polymers in a depinned interfaces environment have been studied for a long time, for instance in \cite{Caravenna2009depinning} when the temperature is constant. In this paper, we study an extension of this model by making the temperature and the distance between interfaces goes to infinity. We give a full phase diagram for this model, and show that a new behaviour appears in this extension. Our key tool include new sharp results on the simple random walk evolving between interfaces.

This paper studies the feasibility of synthetic data generation for mission-critical applications. The emphasis is on synthetic data generation for anomalous detection in complex social networks. In particular, the development of a heuristic generative model, capable of creating data for anomalous rare activities in complex social networks is sought. To this end, lessons from social and political literature are applied to prototype a novel implementation of the Agent-based Modeling (ABM) framework, based on simple social interactions between agents, for synthetic data generation in the context of terrorist profile desegregation. The conclusion offers directions for further verification, fine-tuning, and proposes future directions of work for the ABM prototype, as a complex-societal approach to synthetic data generation, by identifying heuristic hyper-parameter tuning methodologies to further ensure the generated data distribution is similar to the true distribution of the original data-sets. While a rigorous mathematical optimization for reducing the distances in distributions is not offered in this work, we opine that this prototype of an autonomous-agent generative complex social model is useful for studying and researching on pattern of life and anomaly detection where there is strict limitation or lack of sufficient data for using practical machine learning solutions in mission-critical applications., Comment: Presented at AAAI FSS-20: Artificial Intelligence in Government and Public Sector, Washington, DC, USA

Optimal Bayesian design techniques provide an estimate for the best parameters of an experiment in order to maximize the value of measurements prior to the actual collection of data. In other words, these techniques explore the space of possible observations and determine an experimental setup that produces maximum information about the system parameters on average. Generally, optimal Bayesian design formulations result in multiple high-dimensional integrals that are difficult to evaluate without incurring significant computational costs as each integration point corresponds to solving a coupled system of partial differential equations. In the present work, we propose a novel approach for development of polynomial chaos expansion (PCE) surrogate model for the design utility function. In particular, we demonstrate how the orthogonality of PCE basis polynomials can be utilized in order to replace the expensive integration over the space of possible observations by direct construction of PCE approximation for the expected information gain. This novel technique enables the derivation of a reasonable quality response surface for the targeted objective function with a computational budget comparable to several single-point evaluations. Therefore, the proposed technique reduces dramatically the overall cost of optimal Bayesian experimental design. We evaluate this alternative formulation utilizing PCE on few numerical test cases with various levels of complexity to illustrate the computational advantages of the proposed approach., Comment: 30 pages, 9 figures. Published in Computer Methods in Applied Mechanics and Engineering