We present a model based on the concept of saturation for small $Q^2$ and small $x$. With only three parameters we achieve a good description of all Deep Inelastic Scattering data below $x=0.01$. This includes a consistent treatment of charm and a successful extrapolation into the photoproduction regime. The same model leads to a roughly constant ratio of diffractive and inclusive cross section.
The technical virtual power plant (TVPP) is a promising paradigm to facilitate the integration of distributed energy resources (DERs) while incorporating operational constraints of both DERs and networks. Due to the volatility and limited predictability of DER generation and electric loads, the output capability of the TVPP is uncertain. In this regard, this paper proposes the robust capability curve (RCC) of the TVPP, which explicitly characterizes the allowable range of the scheduled power output that is executable for the TVPP under uncertainties. Implementing the RCC can secure the scheduling of the TVPP against unexpected fluctuations of operating conditions when the TVPP participates in the transmission-level dispatch. Mathematically, the RCC is the first-stage feasible set of an adjustable robust optimization problem. An uncertainty set model incorporating the variable correlation and uncertainty budget is employed, which makes the robustness and conservatism of the RCC adjustable. A novel methodology is proposed to estimate the RCC by the convex hull of several points on its perimeter. These perimeter points are obtained by solving a series of multi scenario-optimal power flow problems with worst-case uncertainty realizations identified based on a linearized network configuration. Case studies based on the IEEE-13 test feeder validate the effectiveness of the RCC to ensure the scheduling feasibility while hedging against uncertainties. The computational efficiency of the proposed RCC estimation method is also verified based on larger-scale test systems.
The problem of adaptive traffic signal control in the multi-intersection system has attracted the attention of researchers. Among the existing methods, reinforcement learning has shown to be effective. However, the complex intersection features, heterogeneous intersection structures, and dynamic coordination for multiple intersections pose challenges for reinforcement learning-based algorithms. This paper proposes a cooperative deep Q-network with Q-value transfer (QT-CDQN) for adaptive multi-intersection signal control. In QT-CDQN, a multi-intersection traffic network in a region is modeled as a multi-agent reinforcement learning system. Each agent searches the optimal strategy to control an intersection by a deep Q-network that takes the discrete state encoding of traffic information as the network inputs. To work cooperatively, the agent considers the influence of the latest actions of its adjacencies in the process of policy learning. Especially, the optimal Q-values of the neighbor agents at the latest time step are transferred to the loss function of the Q-network. Moreover, the strategy of the target network and the mechanism of experience replay are used to improve the stability of the algorithm. The advantages of QT-CDQN lie not only in the effectiveness and scalability for the multi-intersection system but also in the versatility to deal with the heterogeneous intersection structures. The experimental studies under different road structures show that the QT-CDQN is competitive in terms of average queue length, average speed, and average waiting time when compared with the state-of-the-art algorithms. Furthermore, the experiments of recurring congestion and occasional congestion validate the adaptability of the QT-CDQN to dynamic traffic environments.
We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by Guo. We also deduce a $q$-analogue of a congruence due to Apagodu and Zeilberger from Guo's $q$-congruence.
Q is a semi-qualitative methodology to identify typologies of perspectives. It is appropriate to address questions concerning diverse viewpoints, plurality of discourses, or participation processes across disciplines. Perspectives are interpreted based on rankings of a set of statements. These rankings are analysed using multivariate data reduction techniques in order to find similarities between respondents. Discussing the analytical process and looking for progress in Q methodology is becoming increasingly relevant. While its use is growing in social, health and environmental studies, the analytical process has received little attention in the last decades and it has not benefited from recent statistical and computational advances. Specifically, the standard procedure provides overall and arguably simplistic variability measures for perspectives and none of these measures are associated to individual statements, on which the interpretation is based. This paper presents an innovative approach of bootstrapping Q to obtain additional and more detailed measures of variability, which helps researchers understand better their data and the perspectives therein. This approach provides measures of variability that are specific to each statement and perspective, and additional measures that indicate the degree of certainty with which each respondent relates to each perspective. This supplementary information may add or subtract strength to particular arguments used to describe the perspectives. We illustrate and show the usefulness of this approach with an empirical example. The paper provides full details for other researchers to implement the bootstrap in Q studies with any data collection design.
We introduce new classes of q -starlike and q -convex functions of complex order involving the q -derivative operator defined in the open unit disc. Furthermore, we find estimates on the coefficients for second and third coefficients of these classes. Mathematics subject classification (2010): Primary 30C45; Secondary 30C80.