Cooperative Safe Trajectory Planning for Quadrotor Swarms.

In this paper, we propose a novel distributed algorithm based on model predictive control and alternating direction multiplier method (DMPC-ADMM) for cooperative trajectory planning of quadrotor swarms. First, a receding horizon trajectory planning optimization problem is constructed, in which the differential flatness property is used to deal with the nonlinear dynamics of quadrotors while we design a relaxed form of the discrete-time control barrier function (DCBF) constraint to balance feasibility and safety. Then, we decompose the original trajectory planning problem by ADMM and solve it in a fully distributed manner with peer-to-peer communication, which induces the quadrotors within the communication range to reach a consensus on their future trajectories to enhance safety. In addition, an event-triggered mechanism is designed to reduce the communication overhead. The simulation results verify that the trajectories generated by our method are real-time, safe, and smooth. A comprehensive comparison with the centralized strategy and several other distributed strategies in terms of real-time, safety, and feasibility verifies that our method is more suitable for the trajectory planning of large-scale quadrotor swarms.

Manifold alignment for heterogeneous single-cell multi-omics data integration using Pamona.

MOTIVATION: Single-cell multi-omics sequencing data can provide a comprehensive molecular view of cells. However, effective approaches for the integrative analysis of such data are challenging. Existing manifold alignment methods demonstrated the state-of-the-art performance on single-cell multi-omics data integration, but they are often limited by requiring that single-cell datasets be derived from the same underlying cellular structure. RESULTS: In this study, we present Pamona, a partial Gromov-Wasserstein distance-based manifold alignment framework that integrates heterogeneous single-cell multi-omics datasets with the aim of delineating and representing the shared and dataset-specific cellular structures across modalities. We formulate this task as a partial manifold alignment problem and develop a partial Gromov-Wasserstein optimal transport framework to solve it. Pamona identifies both shared and dataset-specific cells based on the computed probabilistic couplings of cells across datasets, and it aligns cellular modalities in a common low-dimensional space, while simultaneously preserving both shared and dataset-specific structures. Our framework can easily incorporate prior information, such as cell type annotations or cell-cell correspondence, to further improve alignment quality. We evaluated Pamona on a comprehensive set of publicly available benchmark datasets. We demonstrated that Pamona can accurately identify shared and dataset-specific cells, as well as faithfully recover and align cellular structures of heterogeneous single-cell modalities in a common space, outperforming the comparable existing methods. AVAILABILITYAND IMPLEMENTATION: Pamona software is available at https://github.com/caokai1073/Pamona. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

STV-SC: Segmentation and Temporal Verification Enhanced Scan Context for Place Recognition in Unstructured Environment.

Place recognition is an essential part of simultaneous localization and mapping (SLAM). LiDAR-based place recognition relies almost exclusively on geometric information. However, geometric information may become unreliable when faced with environments dominated by unstructured objects. In this paper, we explore the role of segmentation for extracting key structured information. We propose STV-SC, a novel segmentation and temporal verification enhanced place recognition method for unstructured environments. It contains a range image-based 3D point segmentation algorithm and a three-stage process to detect a loop. The three-stage method consists of a two-stage candidate loop search process and a one-stage segmentation and temporal verification (STV) process. Our STV process utilizes the time-continuous feature of SLAM to determine whether there is an occasional mismatch. We quantitatively demonstrate that the STV process can trigger false detections caused by unstructured objects and effectively extract structured objects to avoid outliers. Comparison with state-of-art algorithms on public datasets shows that STV-SC can run online and achieve improved performance in unstructured environments (Under the same precision, the recall rate is 1.4∼16% higher than Scan context). Therefore, our algorithm can effectively avoid the mismatching caused by the original algorithm in unstructured environment and improve the environmental adaptability of mobile agents.

Unsupervised topological alignment for single-cell multi-omics integration.

MOTIVATION: Single-cell multi-omics data provide a comprehensive molecular view of cells. However, single-cell multi-omics datasets consist of unpaired cells measured with distinct unmatched features across modalities, making data integration challenging. RESULTS: In this study, we present a novel algorithm, termed UnionCom, for the unsupervised topological alignment of single-cell multi-omics integration. UnionCom does not require any correspondence information, either among cells or among features. It first embeds the intrinsic low-dimensional structure of each single-cell dataset into a distance matrix of cells within the same dataset and then aligns the cells across single-cell multi-omics datasets by matching the distance matrices via a matrix optimization method. Finally, it projects the distinct unmatched features across single-cell datasets into a common embedding space for feature comparability of the aligned cells. To match the complex non-linear geometrical distorted low-dimensional structures across datasets, UnionCom proposes and adjusts a global scaling parameter on distance matrices for aligning similar topological structures. It does not require one-to-one correspondence among cells across datasets, and it can accommodate samples with dataset-specific cell types. UnionCom outperforms state-of-the-art methods on both simulated and real single-cell multi-omics datasets. UnionCom is robust to parameter choices, as well as subsampling of features. AVAILABILITY AND IMPLEMENTATION: UnionCom software is available at https://github.com/caokai1073/UnionCom. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Distributed Optimization With Projection-Free Dynamics: A Frank-Wolfe Perspective.

We consider solving distributed constrained optimization in this article. To avoid projection operations due to constraints in the scenario with large-scale variable dimensions, we propose distributed projection-free dynamics by employing the Frank-Wolfe method, also known as the conditional gradient. Technically, we find a feasible descent direction by solving an alternative linear suboptimization. To make the approach available over multiagent networks with weight-balanced digraphs, we design dynamics to simultaneously achieve both the consensus of local decision variables and the global gradient tracking of auxiliary variables. Then, we present the rigorous convergence analysis of the continuous-time dynamical systems. Also, we derive its discrete-time scheme with an accordingly proved convergence rate of O(1/k) . Furthermore, to clarify the advantage of our proposed distributed projection-free dynamics, we make detailed discussions and comparisons with both existing distributed projection-based dynamics and other distributed Frank-Wolfe algorithms.

Zero-determinant strategy in stochastic Stackelberg asymmetric security game.

In a stochastic Stackelberg asymmetric security game, the strong Stackelberg equilibrium (SSE) strategy is a popular option for the defender to get the highest utility against an attacker with the best response (BR) strategy. However, the attacker may be a boundedly rational player, who adopts a combination of the BR strategy and a fixed stubborn one. In such a condition, the SSE strategy may not maintain the defensive performance due to the stubbornness. In this paper, we focus on how the defender can adopt the unilateral-control zero-determinate (ZD) strategy to confront the boundedly rational attacker. At first, we verify the existence of ZD strategies for the defender. We then investigate the performance of the defender's ZD strategy against a boundedly rational attacker, with a comparison of the SSE strategy. Specifically, when the attacker's strategy is close to the BR strategy, the ZD strategy admits a bounded loss for the defender compared with the SSE strategy. Conversely, when the attacker's strategy is close to the stubborn strategy, the ZD strategy can bring higher defensive performance for the defender than the SSE strategy does.

Distributed Time-Varying Convex Optimization With Dynamic Quantization.

In this work, we design a distributed algorithm for time-varying convex optimization over networks with quantized communications. Each agent has its local time-varying objective function, while the agents need to cooperatively track the optimal solution trajectories of global time-varying functions. The distributed algorithm is motivated by the alternating direction method of multipliers, but the agents can only share quantization information through an undirected graph. To reduce the tracking error due to information loss in quantization, we apply the dynamic quantization scheme with a decaying scaling function. The tracking error is explicitly characterized with respect to the limit of the decaying scaling function in quantization. Furthermore, we are able to show that the algorithm could asymptotically track the optimal solution when time-varying functions converge, even with quantization information loss. Finally, the theoretical results are validated via numerical simulation.

Efficient Algorithm for Approximating Nash Equilibrium of Distributed Aggregative Games.

In this article, we aim to design a distributed approximate algorithm for seeking Nash equilibria (NE) of an aggregative game. Due to the local set constraints of each player, projection-based algorithms have been widely employed for solving such problems actually. Since it may be quite hard to get the exact projection in practice, we utilize inscribed polyhedrons to approximate local set constraints, which yields a related approximate game model. We first prove that the NE of the approximate game is the ϵ -NE of the original game and then propose a distributed algorithm to seek the ϵ -NE, where the projection is then of a standard form in quadratic optimization with linear constraints. With the help of the existing developed methods for solving quadratic optimization, we show the convergence of the proposed algorithm and also discuss the computational cost issue related to the approximation. Furthermore, based on the exponential convergence of the algorithm, we estimate the approximation accuracy related to ϵ . In addition, we investigate the computational cost saved by approximation in numerical simulation.

Misperception influence on zero-determinant strategies in iterated Prisoner's Dilemma.

Zero-determinant (ZD) strategies have attracted wide attention in Iterated Prisoner's Dilemma (IPD) games, since the player equipped with ZD strategies can unilaterally enforce the two players' expected utilities subjected to a linear relation. On the other hand, uncertainties, which may be caused by misperception, occur in IPD inevitably in practical circumstances. To better understand the situation, we consider the influence of misperception on ZD strategies in IPD, where the two players, player X and player Y, have different cognitions, but player X detects the misperception and it is believed to make ZD strategies by player Y. We provide a necessary and sufficient condition for the ZD strategies in IPD with misperception, where there is also a linear relationship between players' utilities in player X's cognition. Then we explore bounds of players' expected utility deviation from a linear relationship in player X's cognition with also improving its own utility.

Distributed Optimization Design for Computation of Algebraic Riccati Inequalities.

This article proposes a distributed optimization design to compute continuous-time algebraic Riccati inequalities (ARIs), where the information of matrices is distributed among agents. We propose a design procedure to tackle the nonlinearity, the inequality, and the coupled information structure of ARI; then, we design a distributed algorithm based on an optimization approach and analyze its convergence properties. The proposed algorithm is able to verify whether ARI is feasible in a distributed way and converges to a solution if ARI is feasible for any initial condition.

A unified computational framework for single-cell data integration with optimal transport.

Single-cell data integration can provide a comprehensive molecular view of cells. However, how to integrate heterogeneous single-cell multi-omics as well as spatially resolved transcriptomic data remains a major challenge. Here we introduce uniPort, a unified single-cell data integration framework that combines a coupled variational autoencoder (coupled-VAE) and minibatch unbalanced optimal transport (Minibatch-UOT). It leverages both highly variable common and dataset-specific genes for integration to handle the heterogeneity across datasets, and it is scalable to large-scale datasets. uniPort jointly embeds heterogeneous single-cell multi-omics datasets into a shared latent space. It can further construct a reference atlas for gene imputation across datasets. Meanwhile, uniPort provides a flexible label transfer framework to deconvolute heterogeneous spatial transcriptomic data using an optimal transport plan, instead of embedding latent space. We demonstrate the capability of uniPort by applying it to integrate a variety of datasets, including single-cell transcriptomics, chromatin accessibility, and spatially resolved transcriptomic data.

Achieving consensus in multilateral international negotiations: The case study of the 2015 Paris Agreement on climate change.

The purpose of this paper is to propose a dynamical model describing the achievement of the 2015 Paris Agreement on climate change. To represent the complex, decade-long, multiparty negotiation process that led to the accord, we use a two time scale dynamical model. The short time scale corresponds to the discussion process occurring at each meeting and is represented as a Friedkin-Johnsen model, a dynamical multiparty model in which the parties show stubbornness, i.e., tend to defend their positions during the discussion. The long time scale behavior is determined by concatenating multiple Friedkin-Johnsen models (one for each meeting). The proposed model, tuned on real data extracted from the Paris Agreement meetings, achieves consensus on a time horizon similar to that of the real negotiations. Remarkably, the model is also able to identify a series of parties that exerted a key leadership role in the Paris Agreement negotiation process.

Optimal Output Consensus of High-Order Multiagent Systems With Embedded Technique.

In this paper, we study an optimal output consensus problem for a multiagent network with agents in the form of multi-input multioutput minimum-phase dynamics. Optimal output consensus can be taken as an extended version of the existing output consensus problem for higher-order agents with an optimization requirement, where the output variables of agents are driven to achieve a consensus on the optimal solution of a global cost function. To solve this problem, we first construct an optimal signal generator, and then propose an embedded control scheme by embedding the generator in the feedback loop. We give two kinds of algorithms based on different available information along with both state feedback and output feedback, and prove that these algorithms with the embedded technique can guarantee the solvability of the problem for high-order multiagent systems under standard assumptions.

Observability of Automata Networks: Fixed and Switching Cases.

Automata networks are a class of fully discrete dynamical systems, which have received considerable interest in various different areas. This brief addresses the observability of automata networks and switched automata networks in a unified framework, and proposes simple necessary and sufficient conditions for observability. The results are achieved by employing methods from symbolic computation, and are suited for implementation using computer algebra systems. Several examples are presented to demonstrate the application of the results.

Distributed Continuous-Time Algorithms for Resource Allocation Problems Over Weight-Balanced Digraphs.

In this paper, a distributed resource allocation problem with nonsmooth local cost functions is considered, where the interaction among agents is depicted by strongly connected and weight-balanced digraphs. Here the decision variable of each agent is within a local feasibility constraint described as a convex set, and all the decision variables have to satisfy a network resource constraint, which is the sum of available resources. To solve the problem, a distributed continuous-time algorithm is developed by virtue of differentiated projection operations and differential inclusions, and its convergence to the optimal solution is proved via the set-valued LaSalle invariance principle. Furthermore, the exponential convergence of the proposed algorithm can be achieved when the local cost functions are differentiable with Lipschitz gradients and there are no local feasibility constraints. Finally, numerical examples are given to verify the effectiveness of the proposed algorithms.

Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection.

The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.