Applications of Stein's method for concentration inequalities

Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the theory and three applications: (1) We obtain a concentration inequality for the magnetization in the Curie--Weiss model at critical temperature (where it obeys a nonstandard normalization and super-Gaussian concentration). (2) We derive exact large deviation asymptotics for the number of triangles in the Erd\H{o}s--R\'{e}nyi random graph $G(n,p)$ when $p\ge0.31$. Similar results are derived also for general subgraph counts. (3) We obtain some interesting concentration inequalities for the Ising model on lattices that hold at all temperatures.Comment: Published in at http://dx.doi.org/10.1214/10-AOP542 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Central limit theorem for first-passage percolation time across thin cylinders

We prove that first-passage percolation times across thin cylinders of the form $[0,n]\times [-h_n,h_n]^{d-1}$ obey Gaussian central limit theorems as long as $h_n$ grows slower than $n^{1/(d+1)}$. It is an open question as to what is the fastest that $h_n$ can grow so that a Gaussian CLT still holds. Under the natural but unproven assumption about existence of fluctuation and transversal exponents, and strict convexity of the limiting shape in the direction of $(1,0,...,0)$, we prove that in dimensions 2 and 3 the CLT holds all the way up to the height of the unrestricted geodesic. We also provide some numerical evidence in support of the conjecture in dimension 2.Comment: Final version, accepted in Probability Theory and Related Fields. 40 pages, 7 figure

The Circular Economy of Dharavi: Making Building Materials from Waste

As developing nations continue to progress, people of these countries face problems of shortages in building materials and rising production of solid waste. The purpose of this research study is to explore the potential of establishing a circular economy by recycling/reusing solid waste as alternative building materials. Focused on the slum of Dharavi in Mumbai, a settlement well-known for its existing recycling business, this article explores the concept of a circular economy utilizing local informal labor by considering the flow of waste materials in the slum. This article presents an analysis of the case studies where waste is reused as a building product and identifies the gaps, advantages, and disadvantages related to how and where the building materials from the case studies could be adapted in the context of the Dharavi slum

Making Reinforcement Learning Practical for Building Energy Management

Conventional building controls rely on pre-programmed logic and fixed control strategies. Thus, they are typically not flexible and often not adaptive to real-time external and internal conditions. Moreover, with the incorporation of emerging technologies, including solar photovoltaics, electric vehicles, smart devices, Internet of Things (IoT) devices andsensors in buildings, operational control objectives are becoming increasingly complex, calling for advanced controls approaches. Reinforcement learning (RL) is an emerging model-free control method that has the ability to handle complex competing objectives and learning to continuously improve performance by repeatedly interacting with the controlled system in its environment. Although RL is an effective control strategy that can self-learn and adapt to changes in an environment without extensive modeling efforts, it can take an unacceptably long time to learn an effective control strategy. Additionally, the RL controller is unstable in its initial interactions, where it has insufficient system behavior knowledge. This process of trial-and-error and long training time make it unsuitable for an RL controller to be applied directly to a building for direct application. The challenges of rapid learning and early unstable behavior were addressed through the evaluation of various methodologies, including the utilization of surrogate models. Strategies such as imitation learning and offline learning from historical rule-based data were juxtaposed against metamodel training, inverse reinforcement learning, and online learningcomplemented by guided exploration. It was discovered that an synthesis of online learning and imitation learning was adept at decreasing the training duration and curtailing early exploration. This was achieved without the need for detailed and costly building models and could be executed exclusively through data-driven methods. Nonetheless, the computational cost of this method was found to be substantial. Moreover, the challenge of transfer learning in buildings was tackled to foster scalability of data-driven control approaches. A novel method of rule extraction was explored, which was coupled with the capability of a human stakeholder to interpret, engage with, and adapt the learned policies from one trained agent to another, targeting a specific building of interest.</p

Comparison of Reinforcement Learning Algorithms Applied to High-Fidelity Building Models

Reinforcement learning has been shown to be a promising approach to sequential decision making after its recent success in the autonomous vehicles, robotics, marketing, and gaming industries. Reinforcement learning has gained traction due to the advancement in deep learning. It has enabled RL to scale to decision making problems in high dimensional state and action spaces. With its recent success, RL has also attracted the attention in the building automation and controls field. Building automation and controls is responsible for maintaining a comfortable, safe, and healthy indoor environment in an energy efficient way. Building controls have become more complicated and need to balance the trade-off between multiple goals of occupant comfort, energy efficiency, and the provision of grid flexibility. This set of competing operational objectives is difficult to balance with conventional rule based feedback controls. The application of reinforcement learning in advanced building controls is both emerging and promising due to the recent availability of rich building data, higher computational resources, while avoiding the time to develop and calibrate a controls model for every individual building and energy system. This thesis compares the performance of an online policy-gradient based method with an offline value-based reinforcement learning method applied to a high fidelity commercial building control problem. The two algorithms chosen for this purpose are Deep Q Network (DQN) and Proximal Policy Optimization (PPO), which are among the most popular reinforcement learning algorithms. DQN has been found to be successful in the building controls arena for quite some time now. Conversely, the PPO algorithm is relatively new and thus fewer studies exist related to the application of PPO to building controls. An OpenAI Gym interface is developed here for the BOPTEST framework, which is an open-source advanced building controls test bed developed by the International Building Performance Simulation Association. The building model used here is a high-fidelity Spawn of EnergyPlus model, which is a combination of an EnergyPlus envelope model with a detailed Modelica model for HVAC systems and components. The aim of this research is to evaluate the difference in performance of the two algorithms and also to provide recommendations for the design of the observed states, the reward shaping, the duration and selection of the training (sample efficiency), the control time step, and several hyperparameter values providing the desired output in the context of building controls.</p

Entanglement thermodynamics for an excited state of Lifshitz system

A class of (2+1)-dimensional quantum many body system characterized by an anisotropic scaling symmetry (Lifshitz symmetry) near their quantum critical point can be described by a (3+1)-dimensional dual gravity theory with negative cosmological constant along with a massive vector field, where the scaling symmetry is realized by the metric as an isometry. We calculate the entanglement entropy of an excited state of such a system holographically, i.e., from the asymptotic perturbation of the gravity dual using the prescription of Ryu and Takayanagi, when the subsystem is sufficiently small. With suitable identifications, we show that this entanglement entropy satisfies an energy conservation relation analogous to the first law of thermodynamics. The non-trivial massive vector field here plays a crucial role and contributes to an additional term in the energy relation.Comment: 12 pages, no figure; v2: some typos fixed, few references adde