On Maximizing Sums of Non-Monotone Submodular and Linear Functions

We study the problem of Regularized Unconstrained Submodular Maximization (RegularizedUSM) as defined by [Bodek and Feldman \u2722]. In this problem, we are given query access to a non-negative submodular function f: 2^N ? ?_{? 0} and a linear function ?: 2^N ? ? over the same ground set N, and the objective is to output a set T ? N approximately maximizing the sum f(T)+?(T). Specifically, an algorithm is said to provide an (?,?)-approximation for RegularizedUSM if it outputs a set T such that E[f(T)+?(T)] ? max_{S ? N}[? ? f(S)+?? ?(S)]. We also study the setting where S and T are constrained to be independent in a given matroid, which we refer to as Regularized Constrained Submodular Maximization (RegularizedCSM). The special case of RegularizedCSM with monotone f has been extensively studied [Sviridenko et al. \u2717, Feldman \u2718, Harshaw et al. \u2719]. On the other hand, we are aware of only one prior work that studies RegularizedCSM with non-monotone f [Lu et al. \u2721], and that work constrains ? to be non-positive. In this work, we provide improved (?,?)-approximation algorithms for both {RegularizedUSM} and {RegularizedCSM} with non-monotone f. In particular, we are the first to provide nontrivial (?,?)-approximations for RegularizedCSM where the sign of ? is unconstrained, and the ? we obtain for RegularizedUSM improves over [Bodek and Feldman \u2722] for all ? ? (0,1). In addition to approximation algorithms, we provide improved inapproximability results for all of the aforementioned cases. In particular, we show that the ? our algorithm obtains for {RegularizedCSM} with unconstrained ? is essentially tight for ? ? e/(e+1). Using similar ideas, we are also able to show 0.478-inapproximability for maximizing a submodular function where S and T are subject to a cardinality constraint, improving a 0.491-inapproximability result due to [Oveis Gharan and Vondrak \u2710]

Theory of variational quantum simulation

The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles, including the Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel variational principle, the McLachlan's variational principle, and the time-dependent variational principle, for simulating real time dynamics. We focus on the simulation of dynamics and discuss the connections of the three variational principles. Previous works mainly focus on the unitary evolution of pure states. In this work, we introduce variational quantum simulation of mixed states under general stochastic evolution. We show how the results can be reduced to the pure state case with a correction term that takes accounts of global phase alignment. For variational simulation of imaginary time evolution, we also extend it to the mixed state scenario and discuss variational Gibbs state preparation. We further elaborate on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits. Our work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware.Comment: 41 pages, accepted by Quantu

Does regulation reduce productivity? Evidence from regulation of the U.S. beet-sugar manufacturing industry during the Sugar Acts, 1934-74

We study the impact of regulation on productivity and welfare in the U.S. sugar manufacturing industry. While this U.S. industry has been protected from foreign competition for nearly 150 years, it was regulated only during the Sugar Act period, 1934-74. We show that regulation significantly reduced productivity, with these productivity losses leading to large welfare losses. Our initial results indicate that the welfare losses are many times larger than those typically studied ? those arising from higher prices. We also argue that the channels through which regulation led to large productivity and welfare declines in this industry were also present in many other regulated industries, like banking and trucking.Productivity ; Regulation ; Competition ; Sugar

Energy Consumption and Habit Formation: Evidence from High Frequency Thermostat Data

Using minute-by-minute data from over 60,000 smart thermostats in households distributed across the United States, we analyze the persistence of energy consumption behaviors in response to external weather shocks. The analysis examines habitual behavior and provides insight into what affects long term change and what triggers the decision to reconsider one’s passive choices. Our preferences for indoor temperatures demonstrate habituation to outdoor temperatures. This habituation is asymmetrical between positive and negative changes and non-linear at the extremes. While our indoor temperature preferences habituate to match small outdoor changes, our preferences revert to long term means in response to extreme temperature change. We also find people are more likely to make active choices when outdoor temperature is salient. Finally, we show there is heterogeneity in how preferences respond as a function of social norms, political preferences, and change costs. Results provide guidance on how conservation policies impact energy use–failure to understand the influence of habit on decision making can lead us to over-estimate the impact of short term policy nudges but underestimate the long run impact of small changes. Our results also inform how changing average temperatures and changing cultural attitudes may affect energy conservation behaviors

Effects of POD control on a DFIG wind turbine structural system

This paper investigates the effects power oscillation damping (POD) controller could have on a wind turbine structural system. Most of the published work in this area has been done using relatively simple aerodynamic and structural models of a wind turbine which cannot be used to investigate the detailed interactions between electrical and mechanical components of the wind turbine. Therefore, a detailed model that combines electrical, structural and aerodynamic characteristics of a grid-connected Doubly Fed Induction Generator (DFIG) based wind turbine has been developed by adapting the NREL (National Renewable Energy Laboratory) 5MW wind turbine model within FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code. This detailed model is used to evaluate the effects of POD controller on the wind turbine system. The results appear to indicate that the effects of POD control on the WT structural system are comparable or less significant as those caused by wind speed variations. Furthermore, the results also reveal that the effects of a transient three-phase short circuit fault on the WT structural system are much larger than those caused by the POD controller