New Self-Adaptive Inertial-Like Proximal Point Methods for the Split Common Null Point Problem

Symmetry plays an important role in solving practical problems of applied science, especially in algorithm innovation. In this paper, we propose what we call the self-adaptive inertial-like proximal point algorithms for solving the split common null point problem, which use a new inertial structure to avoid the traditional convergence condition in general inertial methods and avoid computing the norm of the difference between xn and xn−1 before choosing the inertial parameter. In addition, the selection of the step-sizes in the inertial-like proximal point algorithms does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms. The proposed algorithms provide enlightenment for the further development of applied science in order to dig deep into symmetry under the background of technological innovation.

An Accelerated Error Convergence Design Criterion and Implementation of Lebesgue-p Norm ILC Control Topology for Linear Position Control Systems

Traditional and typical iterative learning control algorithm shows that the convergence rate of error is very low for a class of regular linear systems. A fast iterative learning control algorithm is designed to deal with this problem in this paper. The algorithm is based on the traditional P-type iterative learning control law, which increases the composition of adjacent two overlapping quantities, the tracking error of previous cycle difference signals, and the current error difference. Using convolution to promote Young inequalities proved strictly that, in terms of Lebesgue-p norm, when the number of iterations tends to infinity, the tracking error converges to zero in the system and presents the convergence condition of the algorithm. Compared with the traditional P-type iterative learning control algorithm, the proposed algorithm improves convergence speed and evades the defect using the norm metric’s tracking error. Finally, the validation of the effectiveness of the proposed algorithm is further proved by simulation results.

Time-independence of gravitational Rényi entropies and unitarity in quantum gravity

The Hubeny-Rangamani-Takayanagi surface γHRT computing the entropy S(D) of a domain of dependence D on an asymptotically AdS boundary is known to be causally inaccessible from D. We generalize this gravitational result to higher replica numbers n > 1 by considering the replica-invariant surfaces (aka ‘splitting surfaces’) γ of real-time replica-wormhole saddle-points computing Rényi entropies Sn(D) and showing that there is a sense in which D must again be causally inaccessible from γ when the saddle preserves both replica and conjugation symmetry. This property turns out to imply the Sn(D) to be independent of any choice of any Cauchy surface ΣD for D, and also that the Sn(D) are independent of the choice of boundary sources within D. This is a key hallmark of unitary evolution in any dual field theory. Furthermore, from the bulk point of view it adds to the evidence that time evolution of asymptotic observables in quantum gravity is implemented by a unitary operator in each baby universe superselection sector. Though we focus here on pure Einstein-Hilbert gravity and its Kaluza-Klein reductions, we expect the argument to extend to any two-derivative theory who satisfies the null convergence condition. We consider both classical saddles and the effect of back-reaction from quantum corrections.

Limits of multiplicative inhomogeneous random graphs and Lévy trees: limit theorems

We consider a natural model of inhomogeneous random graphs that extends the classical Erdős–Rényi graphs and shares a close connection with the multiplicative coalescence, as pointed out by Aldous (Ann Probab 25:812–854, 1997). In this model, the vertices are assigned weights that govern their tendency to form edges. It is by looking at the asymptotic distributions of the masses (sum of the weights) of the connected components of these graphs that Aldous and Limic (Electron J Probab 3:1–59, 1998) have identified the entrance boundary of the multiplicative coalescence, which is intimately related to the excursion lengths of certain Lévy-type processes. We, instead, look at the metric structure of these components and prove their Gromov–Hausdorff–Prokhorov convergence to a class of (random) compact measured metric spaces that have been introduced in a companion paper (Broutin et al. in Limits of multiplicative inhomogeneous random graphs and Lévy trees: the continuum graphs. arXiv:1804.05871, 2020). Our asymptotic regimes relate directly to the general convergence condition appearing in the work of Aldous and Limic. Our techniques provide a unified approach for this general “critical” regime, and relies upon two key ingredients: an encoding of the graph by some Lévy process as well as an embedding of its connected components into Galton–Watson forests. This embedding transfers asymptotically into an embedding of the limit objects into a forest of Lévy trees, which allows us to give an explicit construction of the limit objects from the excursions of the Lévy-type process. The mains results combined with the ones in the other paper allow us to extend and complement several previous results that had been obtained via model- or regime-specific proofs, for instance: the case of Erdős–Rényi random graphs obtained by Addario-Berry et al. (Probab Theory Relat Fields 152:367–406, 2012), the asymptotic homogeneous case as studied by Bhamidi et al. (Probab Theory Relat Fields 169:565–641, 2017), or the power-law case as considered by Bhamidi et al. (Probab Theory Relat Fields 170:387–474, 2018).

Containment Control of First-Order Multi-Agent Systems under PI Coordination Protocol

This paper investigates the containment control problem of discrete-time first-order multi-agent system composed of multiple leaders and followers, and we propose a proportional-integral (PI) coordination control protocol. Assume that each follower has a directed path to one leader, and we consider several cases according to different topologies composed of the followers. Under the general directed topology that has a spanning tree, the frequency-domain analysis method is used to obtain the sufficient convergence condition for the followers achieving the containment-rendezvous that all the followers reach an agreement value in the convex hull formed by the leaders. Specially, a less conservative sufficient condition is obtained for the followers under symmetric and connected topology. Furthermore, it is proved that our proposed protocol drives the followers with unconnected topology to converge to the convex hull of the leaders. Numerical examples show the correctness of the theoretical results.

Iterative Learning Control for Switched Systems with Sensor Saturation Constraints

To solve trajectory tracking problem of switched system with sensor saturation, an iterative learning control algorithm is proposed. The method uses actual measurement error to modify the control variable of system on the premise that switched rule does not change along iteration axis, but it randomly changes along time axis. Moreover, by dealing with the saturation via diagonal matrix method, the convergence of the algorithm is strictly proved in the sense of λ-norm, and the convergence condition is derived. The algorithm can achieve complete tracking of desired trajectory in the finite time interval under the random switched rule, as iterations increase. The simulation example verifies the validity of the proposed algorithm.

Recursive Genetic Micro-Aggregation Technique: Information Loss, Disclosure Risk and Scoring Index

This research investigates the micro-aggregation problem in secure statistical databases by integrating the divide and conquer concept with a genetic algorithm. This is achieved by recursively dividing a micro-data set into two subsets based on the proximity distance similarity. On each subset the genetic operation “crossover” is performed until the convergence condition is satisfied. The recursion will be terminated if the size of the generated subset is satisfied. Eventually, the genetic operation “mutation” will be performed over all generated subsets that satisfied the variable group size constraint in order to maximize the objective function. Experimentally, the proposed micro-aggregation technique was applied to recommended real-life data sets. Results demonstrated a remarkable reduction in the computational time, which sometimes exceeded 70% compared to the state-of-the-art. Furthermore, a good equilibrium value of the Scoring Index (SI) was achieved by involving a linear combination of the General Information Loss (GIL) and the General Disclosure Risk (GDR).

A fast and effective detection framework for whole-slide histopathology image analysis

Pathologists generally pan, focus, zoom and scan tissue biopsies either under microscopes or on digital images for diagnosis. With the rapid development of whole-slide digital scanners for histopathology, computer-assisted digital pathology image analysis has attracted increasing clinical attention. Thus, the working style of pathologists is also beginning to change. Computer-assisted image analysis systems have been developed to help pathologists perform basic examinations. This paper presents a novel lightweight detection framework for automatic tumor detection in whole-slide histopathology images. We develop the Double Magnification Combination (DMC) classifier, which is a modified DenseNet-40 to make patch-level predictions with only 0.3 million parameters. To improve the detection performance of multiple instances, we propose an improved adaptive sampling method with superpixel segmentation and introduce a new heuristic factor, local sampling density, as the convergence condition of iterations. In postprocessing, we use a CNN model with 4 convolutional layers to regulate the patch-level predictions based on the predictions of adjacent sampling points and use linear interpolation to generate a tumor probability heatmap. The entire framework was trained and validated using the dataset from the Camelyon16 Grand Challenge and Hubei Cancer Hospital. In our experiments, the average AUC was 0.95 in the test set for pixel-level detection.

A novel optimization approach for sub-hourly unit commitment with large numbers of units and virtual transactions

Unit Commitment (UC) is an important problem in power system operations. It is traditionally scoped for 24 hours with one-hour time intervals. To improve system flexibility by accommodating the increasing net-load variability, sub-hourly UC has been suggested. Such a problem is larger and more complicated than hourly UC because of the increased number of periods and reduced unit ramping capabilities per period. The computational burden is further exacerbated for systems with large numbers of virtual transactions leading to dense transmission constraints matrices. Consequently, the state-of-the-art and practice method, branch-and-cut (B&C), suffers from poor performance. In this paper, our recent Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) is enhanced by embedding ordinal-optimization concepts for a drastic reduction in subproblem solving time. Rather than formally solving subproblems by using B&C, subproblem solutions that satisfy SAVLR’s convergence condition are obtained by modifying solutions from previous iterations or solving crude subproblems. All virtual transactions are included in each subproblem to reduce major changes in solutions across iterations. A parallel version is also developed to further reduce the computation time. Testing on MISO’s large cases demonstrates that our ordinal-optimization embedded approach obtains near-optimal solutions efficiently, is robust, and provides a new way on solving other MILP problems.