Sign-Balanced Pattern-Avoiding Permutation Classes

A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations. Let $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ be the set of permutations in the symmetric group $S_n$ which avoids patterns $\sigma_1, \sigma_2, \ldots, \sigma_r$. The aim of this paper is to investigate when, for certain patterns $\sigma_1, \sigma_2, \ldots, \sigma_r$, $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ is sign-balanced for every integer $n>1$. We prove that for any $\{\sigma_1, \sigma_2, \ldots, \sigma_r\}\subseteq S_3$, if $\{\sigma_1, \sigma_2, \ldots, \sigma_r\}$ is sign-balanced except $\{132, 213, 231, 312\}$, then $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ is sign-balanced for every integer $n>1$. In addition, we give some results in the case of avoiding some patterns of length $4$

Development Strategy, Viability, and Economic Institutions: The Case of China

development strategy, institution, viability, trinity system

The weather affects air conditioner purchases to fill the energy efficiency gap

Energy efficiency improvement is often hindered by the energy efficiency gap. This paper examines the effect of short-run temperature fluctuations on the Energy Star air conditioner purchases in the United States from 2006 to 2019 using transaction-level data. Results show that the probability of purchasing an Energy Star air conditioner increases as the weekly temperature before the transaction deviates from 20–22 °C. A larger response is related to fewer cooling degree days in the previous years, higher electricity prices/income/educational levels/age/rate of owners, more common use of electricity, and stronger concern about climate change. 1 °C increase and decrease from 21 °C would lead to a reduction of total energy expenditure by 35.46 and 17.73 million dollars nationwide (0.13% and 0.06% of the annual total energy expenditure on air conditioning), respectively. Our findings have important policy implications for demand-end interventions to incorporate the potential impact of the ambient physical environment

Accelerated Computation of Free Energy Profile at ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semi-Empirical Reference Potential. I. Weighted Thermodynamics Perturbation

Free energy profile (FE Profile) is an essential quantity for the estimation of reaction rate and the validation of reaction mechanism. For chemical reactions in condensed phase or enzymatic reactions, the computation of FE profile at ab initio (ai) quantum mechanical/molecular mechanics (QM/MM) level is still far too expensive. Semiempirical (SE) method can be hundreds or thousands of times faster than the ai methods. However, the accuracy of SE methods is often unsatisfactory, due to the approximations that have been adopted in these methods. In this work, we proposed a new method termed MBAR+wTP, in which the ai QM/MM free energy profile is computed by a weighted thermodynamic perturbation (TP) correction to the SE profile generated by the multistate Bennett acceptance ratio (MBAR) analysis of the trajectories from umbrella samplings (US). The weight factors used in the TP calculations are a byproduct of the MBAR analysis in the post-processing of the US trajectories, which are often discarded after the free energy calculations. The results show that this approach can enhance the efficiency of ai FE profile calculations by several orders of magnitude