Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Evaluating gravitational path integrals in the Lorentzian has been a long-standing challenge due to the numerical sign problem. We show that this challenge can be overcome in simplicial quantum gravity. By deforming the integration contour into the complex, the sign fluctuations can be suppressed, for instance using the holomorphic gradient flow algorithm. Working through simple models, we show that this algorithm enables efficient Monte Carlo simulations for Lorentzian simplicial quantum gravity. In order to allow complex deformations of the integration contour, we provide a manifestly holomorphic formula for Lorentzian simplicial gravity. This leads to a complex version of simplicial gravity that generalizes the Euclidean and Lorentzian cases. Outside the context of numerical computation, complex simplicial gravity is also relevant to studies of singularity resolving processes with complex semi-classical solutions. Along the way, we prove a complex version of the Gauss-Bonnet theorem, which may be of independent interest.

The static force from generalized Wilson loops using gradient flow

We explore a novel approach to compute the force between a static quark-antiquark pair with the gradient flow algorithm on the lattice. The approach is based on inserting a chromoelectric field in a Wilson loop. The renormalization issues, associated with the finite size of the chromoelectric field on the lattice, can be solved with the use of gradient flow. We compare numerical results for the flowed static potential to our previous measurement of the same observable without a gradient flow.

Fast flow algorithm prioritizing the most time-consuming source point by using a multi-source evacuation model

In many public spaces (e.g. colleges and shopping malls), people are frequently distributed discretely, and thus, single-source evacuation, which means there’s only one point of origin, is not always a feasible solution. Hence, this paper discusses a multi-source evacuation model and algorithm, which are intended to evacuate all the people that are trapped within the minimum possible time. This study presents a fast flow algorithm to prioritize the most time-consuming source point under the constraint of route and exit capacity to reduce the evacuation time. This fast flow algorithm overcomes the deficiencies in the existing global optimization fast flow algorithm and capacity constrained route planner (CCRP) algorithm. For the fast flow algorithm, the first step is to determine the optimal solution to single-source evacuation and use the evacuation time of the most time-consuming source and exit gate set as the initial solution. The second step is to determine a multi-source evacuation solution by updating the lower limit of the current evacuation time and the exit gate set continually. The final step is to verify the effectiveness and feasibility of the algorithm through comparison.

Uncertainty Estimation of Dense Optical Flow for Robust Visual Navigation

This paper presents a novel dense optical-flow algorithm to solve the monocular simultaneous localisation and mapping (SLAM) problem for ground or aerial robots. Dense optical flow can effectively provide the ego-motion of the vehicle while enabling collision avoidance with the potential obstacles. Existing research has not fully utilised the uncertainty of the optical flow—at most, an isotropic Gaussian density model has been used. We estimate the full uncertainty of the optical flow and propose a new eight-point algorithm based on the statistical Mahalanobis distance. Combined with the pose-graph optimisation, the proposed method demonstrates enhanced robustness and accuracy for the public autonomous car dataset (KITTI) and aerial monocular dataset.

A Sensitivity-Based Three-Phase Weather-Dependent Power Flow Algorithm for Networks with Local Controllers—Part I: Algorithm Development

<b>Local voltage controllers (LVCs) are important components of a modern distribution system for regulating the voltage within permissible limits. This manuscript presents a sensitivity-based three-phase weather-dependent power flow algorithm for distribution networks with LVCs. This Part I presents the theoretical development of the proposed algorithm, which has four distinct characteristics: a) it considers the three-phase unbalanced nature of distribution systems, b) the operating state of LVCs is calculated using sensitivity parameters, which accelerates the convergence speed of the algorithm, c) it considers the precise switching sequence of LVCs based on their reaction time delays, and d) the nonlinear influence of weather variations in the power flow is also taken into consideration. Simulations and validation results presented in Part II indicate that the proposed approach outperforms other existing algorithms with respect to the accuracy and speed of convergence, thus making it a promising power flow tool for accurate distribution system analysis. </b><div><b><br></b></div>

A Novel Three-Phase Harmonic Power Flow Algorithm for Unbalanced Radial Distribution Networks with the Presence of D-STATCOM Devices

Due to the rapid advancement in power electronic devices in recent years, there is a fast growth of non-linear loads in distribution networks (DNs). These non-linear loads can cause harmonic pollution in the networks. The harmonic pollution is low, and the resonance problem is absent in distribution static synchronous compensators (D-STATCOM), which is the not case in traditional compensating devices such as capacitors. The power quality issue can be enhanced in DNs with the interfacing of D-STATCOM devices. A novel three-phase harmonic power flow algorithm (HPFA) for unbalanced radial distribution networks (URDN) with the existence of linear and non-linear loads and the integration of a D-STATCOM device is presented in this paper. The bus number matrix (BNM) and branch number matrix (BRNM) are developed in this paper by exploiting the radial topology in DNs. These matrices make the development of HPFA simple. Without D-STATCOM integration, the accuracy of the fundamental power flow solution and harmonic power flow solution are tested on IEEE−13 bus URDN, and the results are found to be precise with the existing work. Test studies are conducted on the IEEE−13 bus and the IEEE−34 bus URDN with interfacing D-STATCOM devices, and the results show that the fundamental r.m.s voltage profile is improved and the fundamental harmonic power loss and total harmonic distortion (THD) are reduced.

An optical-flow-based monitoring method for measuring translational motion in infrared-thermographic images of AFP processes

This paper presents a novel method for a precise localization of the automated-fiber-placement head, without the need for a data access to the machine control. It is based on a sub-pixel accurate optical-flow-algorithm which determines information about the heads movement by means of the material flow in sequences of IR images. Using local curvatures in the temperature field of the IR images, feature matrices are created which can locally be compared to the features of successive images. Thus, the translation between images become visible. This enables the possibility to perform an accurate ($$16.8\,\upmu{\mathrm{m}}$$ 16.8 μ m ) and self-sufficient process monitoring that additionally is capable of capturing the motion and position information of the AFP system and can be linked to existing algorithms for defect detection and classification.

Empirical Study on the Relationship between Financial Development and Economic Growth in China Based on Maximum Flow Algorithm

Objectives: The relationship between finance and economic growth has always been one of the hot issues in theoretical research and empirical analysis. As one of the important factors affecting economic growth, finance has long been recognized by the majority of scholars. Methods: In the context of the development of Internet e-commerce, empirical research on the relationship between China’s financial development and economic growth is conducted based on the maximum traffic algorithm. Results: Based on this, this paper constructs the Probit and Logistic binary discrete selection model for economic growth, and the discrete particle swarm algorithm is used to solve the sequence of influencing factors, estimating the model parameters, and the degree of influence of each influencing factor is calculated. Conclusion: The degree of concurrent employment is a decisive factor in economic growth.