Estimating null and potent modes of feedforward communication in a computational model of cortical activity

Communication across anatomical areas of the brain is key to both sensory and motor processes. Dimensionality reduction approaches have shown that the covariation of activity across cortical areas follows well-delimited patterns. Some of these patterns fall within the "potent space" of neural interactions and generate downstream responses; other patterns fall within the "null space" and prevent the feedforward propagation of synaptic inputs. Despite growing evidence for the role of null space activity in visual processing as well as preparatory motor control, a mechanistic understanding of its neural origins is lacking. Here, we developed a mean-rate model that allowed for the systematic control of feedforward propagation by potent and null modes of interaction. In this model, altering the number of null modes led to no systematic changes in firing rates, pairwise correlations, or mean synaptic strengths across areas, making it difficult to characterize feedforward communication with common measures of functional connectivity. A novel measure termed the null ratio captured the proportion of null modes relayed from one area to another. Applied to simultaneous recordings of primate cortical areas V1 and V2 during image viewing, the null ratio revealed that feedforward interactions have a broad null space that may reflect properties of visual stimuli.

A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block

Null-space methods have long been used to solve large sparse n × n symmetric saddle point systems of equations in which the (2, 2) block is zero. This paper focuses on the case where the (1, 1) block is ill conditioned or rank deficient and the k × k (2, 2) block is non zero and small (k ≪ n). Additionally, the (2, 1) block may be rank deficient. Such systems arise in a range of practical applications. A novel null-space approach is proposed that transforms the system matrix into a nicer symmetric saddle point matrix of order n that has a non zero (2, 2) block of order at most 2k and, importantly, the (1, 1) block is symmetric positive definite. Success of any null-space approach depends on constructing a suitable null-space basis. We propose methods for wide matrices having far fewer rows than columns with the aim of balancing stability of the transformed saddle point matrix with preserving sparsity in the (1, 1) block. Linear least squares problems that contain a small number of dense rows are an important motivation and are used to illustrate our ideas and to explore their potential for solving large-scale systems.

Simultaneous control of natural and extra degrees of freedom by isometric force and electromyographic activity in the muscle-to-force null space

Objective. Muscle activation patterns in the muscle-to-force null space, i.e., patterns that do not generate task-relevant forces, may provide an opportunity for motor augmentation by allowing to control additional end-effectors simultaneously to natural limbs. Here we tested the feasibility of muscular null space control for augmentation by assessing simultaneous control of natural and extra degrees of freedom. Approach. We instructed eight participants to control translation and rotation of a virtual 3D end-effector by simultaneous generation of isometric force at the hand and null space activity extracted in real-time from the electromyographic signals recorded from 15 shoulder and arm muscles. First, we identified the null space components that each participant could control more naturally by voluntary co-contraction. Then, participants performed several blocks of a reaching and holding task. They displaced an ellipsoidal cursor to reach one of nine targets by generating force, and simultaneously rotated the cursor to match the target orientation by activating null space components. We developed an information-theoretic metric, an index of difficulty defined as the sum of a spatial and a temporal term, to assess individual null space control ability for both reaching and holding. Main Results. On average, participants could reach the targets in most trials already in the first block (72%) and they improved with practice (maximum 93%) but holding performance remained lower (maximum 43%). As there was a high inter-individual variability in performance, we performed a simulation with different spatial and temporal task conditions to estimate those for which each individual participants would have performed best. Significance. Muscular null space control is feasible and may be used to control additional virtual or robotics end-effectors. However, decoding of motor commands must be optimized according to individual null space control ability.

A regularization method for solving dynamic problems with singular configuration

In the simulation process for multi-body systems, the generated redundant constraints will result in ill-conditioned dynamic equations, which are not good for stable simulations when the system motion proceeds near a singular configuration. In order to overcome the singularity problems, the paper presents a regularization method with an explicit expression based on Gauss principle, which does not need to eliminate the constraint violation after each iteration step compared with the traditional methods. Then the effectiveness and stability are demonstrated through two numerical examples, a slider-crank mechanism and a planar four-bar linkage. Simulation results obtained with the proposed method are analyzed and compared with augmented Lagrangian formulation and the null space formulation in terms of constraints violation, drift mechanical energy and computational efficiency, which shows that the proposed method is suitable to perform efficient and stable dynamic simulations for multi-body systems with singular configurations.

Event-Triggered Intervention Framework for UAV-UGV Coordination Systems

Air-ground coordination systems are usually composed of unmanned aerial vehicles (UAV) and unmanned ground vehicles (UGV). In such a system, UAVs can utilize their much more perceptive information to plan the path for UGVs. However, the correctness and accuracy of the planned route are often not guaranteed, and the communication and computation burdens increase with more sophisticated algorithms. This paper proposes a new type of air-ground coordination framework to enable UAVs intervention into UGVs tasks. An event-triggered mechanism in the null space behavior control (NSBC) framework is proposed to decide if an intervention is necessary and the timing of the intervention. Then, the problem of whether to accept the intervention is formulated as an integer programming problem and is solved using model predictive control (MPC). Simulation results show that the UAV can intervene in UGVs accurately and on time, and the UGVs can effectively decide whether to accept the intervention to get rid of troubles, thereby improving the intelligence of the air-ground coordination system.

A Modification of Gustavsen and Semlyen’s vector fitting algorithm for overestimated model order

Gustavsen and Semlyen’s vector fitting algorithm (VFA) is popular for the determination of the poles and residues of a sampled response function, modeled as a finite order rational function. However, it does not always perform well when the original function is of infinite order and/or the model order is overestimated. This article is concerned with a novel “null-space” modification of the VFA that provides an accurate representation of the original function when the model order is large and when the original VFA performs poorly. The null-space method is parameterized by a single control parameter, L, which can be adjusted to improve accuracy. Comparisons are made with the original VFA and another of Gustavsen’s modifications

A Modification of Gustavsen and Semlyen’s vector fitting algorithm for overestimated model order

Gustavsen and Semlyen’s vector fitting algorithm (VFA) is popular for the determination of the poles and residues of a sampled response function, modeled as a finite order rational function. However, it does not always perform well when the original function is of infinite order and/or the model order is overestimated. This article is concerned with a novel “null-space” modification of the VFA that provides an accurate representation of the original function when the model order is large and when the original VFA performs poorly. The null-space method is parameterized by a single control parameter, L, which can be adjusted to improve accuracy. Comparisons are made with the original VFA and another of Gustavsen’s modifications