MOTIVATION: A protein can be represented in several forms, including its 1D sequence, 3D atom coordinates, and molecular surface. A protein surface contains rich structural and chemical features directly related to the protein's function such as its ability to interact with other molecules. While many methods have been developed for comparing the similarity of proteins using the sequence and structural representations, computational methods based on molecular surface representation are limited. RESULTS: Here, we describe "Surface ID," a geometric deep learning system for high-throughput surface comparison based on geometric and chemical features. Surface ID offers a novel grouping and alignment algorithm useful for clustering proteins by function, visualization, and in silico screening of potential binding partners to a target molecule. Our method demonstrates top performance in surface similarity assessment, indicating great potential for protein functional annotation, a major need in protein engineering and therapeutic design. AVAILABILITY AND IMPLEMENTATION: Source code for the Surface ID model, trained weights, and inference script are available at https://github.com/Sanofi-Public/LMR-SurfaceID.

In this paper, we introduce cooperative autonomous driving algorithms for vehicular networks with nonlinear mobile robot dynamics in urban environments that take human safety into account and are capable of performing vehicle-to-vehicle (V2V) and vehicle-to-pedestrian (V2P) collision avoidance. We argue that “flocks” are multi-agent models of vehicular traffic on roads and propose novel autonomous driving architectures and algorithms for cyber-physical vehicles capable of performing autonomous driving tasks such as lane-driving, lane-changing, braking, passing, and making turns. Our proposed autonomous driving algorithms are inspired by Olfati-Saber's flocking theory. Though, there are notable differences between autonomous driving on urban roads and flocking behavior - flocks have a single desired destination whereas most drivers on road do not share the same destination. We refer to this collective behavior (driving) as “multi-objective flocking.” The self-driving vehicles in our framework turn out to be hybrid systems with a finite number of discrete states that are related to the driving modes of vehicles. Complex driving maneuvers can be performed using a sequence of mode switchings. We use near-identity nonlinear transformations to extend the application of particle-based autonomous driving algorithms to multi-robot networks with nonlinear dynamics. The derivation of the mode switching conditions that preserve safety is non-trivial and an important part of the design of autonomous driving algorithms. We present several examples of driving tasks that can be effectively performed using our proposed driving algorithms.

There are essentially four points that Dr. Chebotarev's raises in [1]. Point 1. Chebotarev claims that Lemma 2 is not correct as stated and gives a counter example consisting of a simple directed tree. This counterexample points out two issues with the lemma as stated. The second portion of Lemma 2, referring to the case in which there are c components, only applies to graphs in which there are disjoint components of the graph (no edges between the components). This is clear from the proof of this fact (which simply consists of separating the nodes so that the Laplacian is block diagonal, implying a disjoint set of nodes), but is ambiguous in the statement of the lemma.

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations.

We analyze the performance of an approximate distributed Kalman filter proposed in recent work on distributed coordination. This approach to distributed estimation is novel in that it admits a systematic analysis of its performance as various network quantities such as connection density, topology, and bandwidth are varied. Our main contribution is a frequency-domain characterization of the distributed estimator's steady-state performance; this is quantified in terms of a special matrix associated with the connection topology called the graph Laplacian, and also the rate of message exchange between immediate neighbors in the communication network.