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Complex systems, such as in brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often difficult. We propose using a Vector Autoregressive model with eXogenous input (VARX) to capture delayed interactions between internal and external variables. Whereas this model aligns with Granger's statistical formalism for testing "causal relations", the connection between the two is not widely understood. Here, we bridge this gap by providing fundamental equations, user-friendly code, and demonstrations using simulated and real-world data from neuroscience, physiology, sociology, and economics. Our examples illustrate how the model avoids spurious correlation by factoring out external influences from internal dynamics, leading to more parsimonious explanations of these systems. For instance, in neural recordings we find that prolonged response of the brain can be explained as a short exogenous effect, followed by prolonged internal recurrent activity. In recordings of human physiology, we find that the model recovers established effects such as eye movements affecting pupil size and a bidirectional interaction of respiration and heart rate. We also provide methods for enhancing model efficiency, such as L2 regularization for limited data and basis functions to cope with extended delays. Additionally, we analyze model performance under various scenarios where model assumptions are violated. MATLAB, Python, and R code are provided for easy adoption: https://github.com/lcparra/varx. [ABSTRACT FROM AUTHOR]

Electrical motor cortex stimulation can produce corticospinal system plasticity and enhance motor function after injury. We investigate molecular mechanisms of structural and physiological plasticity following electrical neuromodulation, focusing on identifying molecular predictors, or biomarkers, for durable plasticity. We used two neuromodulation protocols, repetitive multipulse stimulation (rMPS) and patterned intermittent theta burst stimulation (iTBS), incorporating different stimulation durations and follow-up periods. We compared neuromodulation efficacy in promoting corticospinal tract (CST) sprouting, motor cortex muscle evoked potential (MEP) LTP-like plasticity, and their associated molecular underpinnings. Only iTBS produced CST sprouting after short-term neuromodulation (1 d of stimulation; 9-d survival for sprouting expression); both iTBS and rMPS produced sprouting with long-term (10-d) neuromodulation. Significant mTOR signaling activation and phosphatase and tensin homolog (PTEN) protein deactivation predicted axon growth across all neuromodulation conditions that produced significant sprouting. Both neuromodulation protocols, regardless of duration, were effective in producing MEP enhancement. However, persistent LTP-like enhancement of MEPs at 30 d was only produced by long-term iTBS. Statistical modeling suggests that Stat3 signaling is the key mediator of MEP enhancement. Cervical spinal cord injury (SCI) alone did not affect baseline molecular signaling. Whereas iTBS and rMPS after SCI produced strong mTOR activation and PTEN deactivation, only iTBS produced Stat3 activation. Our findings support differential molecular biomarkers for neuromodulation-dependent structural and physiological plasticity and show that motor cortex epidural neuromodulation produces molecular changes in neurons that support axonal growth after SCI. iTBS may be more suitable for repair after SCI because it promotes molecular signaling for both CST growth and MEP plasticity. [ABSTRACT FROM AUTHOR]

In the visual system of primates, image information propagates across successive cortical areas, and there is also local feedback within an area and long-range feedback across areas. Recent findings suggest that the resulting temporal dynamics of neural activity are crucial in several vision tasks. In contrast, artificial neural network models of vision are typically feedforward and do not capitalize on the benefits of temporal dynamics, partly due to concerns about stability and computational costs. In this study, we focus on recurrent networks with feedback connections for visual tasks with static input corresponding to a single fixation. We demonstrate mathematically that a network's dynamics can be stabilized by four key features of biological networks: layer-ordered structure, temporal delays between layers, longer distance feedback across layers, and nonlinear neuronal responses. Conversely, when feedback has a fixed distance, one can omit delays in feedforward connections to achieve more efficient artificial implementations. We also evaluated the effect of feedback connections on object detection and classification performance using standard benchmarks, specifically the COCO and CIFAR10 datasets. Our findings indicate that feedback connections improved the detection of small objects, and classification performance became more robust to noise. We found that performance increased with the temporal dynamics, not unlike what is observed in core vision of primates. These results suggest that delays and layered organization are crucial features for stability and performance in both biological and artificial recurrent neural networks. Author summary: The visual cortex is a part of the brain that receives, integrates, and processes visual information. It is made up of many interconnected areas that work together to help us see. Studies have shown that lateral and feedback connections between these areas are essential for us to be able to see and understand the world around us. However, most computer vision models only consider feedforward connections. In this study, we looked at the stability of networks with feedback. We used mathematical tools to discover that layered networks with long-range feedback favor stability, as do biologically realistic implementations with temporal delays in the feedforward connections. We also demonstrated the performance advantages of adding feedback connections to convolutional networks in image classification and detection tasks. These results suggest that the organization of the visual system favors stability. This implies that biologically more realistic implementations of computational vision networks may be easier to train. [ABSTRACT FROM AUTHOR]

It is well established that neural responses to visual stimuli are enhanced at select locations in the visual field. Although spatial selectivity and the effects of spatial attention are well understood for discrete tasks (e.g. visual cueing), little is known for naturalistic experience that involves continuous dynamic visual stimuli (e.g. driving). Here, we assess the strength of neural responses across the visual space during a kart‐race game. Given the varying relevance of visual location in this task, we hypothesized that the strength of neural responses to movement will vary across the visual field, and it would differ between active play and passive viewing. To test this, we measure the correlation strength of scalp‐evoked potentials with optical flow magnitude at individual locations on the screen. We find that neural responses are strongly correlated at task‐relevant locations in visual space, extending beyond the focus of overt attention. Although the driver's gaze is directed upon the heading direction at the centre of the screen, neural responses were robust at the peripheral areas (e.g. roads and surrounding buildings). Importantly, neural responses to visual movement are broadly distributed across the scalp, with visual spatial selectivity differing across electrode locations. Moreover, during active gameplay, neural responses are enhanced at select locations in the visual space. Conventionally, spatial selectivity of neural response has been interpreted as an attentional gain mechanism. In the present study, the data suggest that different brain areas focus attention on different portions of the visual field that are task‐relevant, beyond the focus of overt attention. [ABSTRACT FROM AUTHOR]

Impaired inhibitory control accompanied by enhanced salience attributed to drug‐related cues, both associated with function of the dorsolateral prefrontal cortex (dlPFC), are hallmarks of drug addiction, contributing to worse symptomatology including craving. dlPFC modulation with transcranial direct current stimulation (tDCS) previously showed craving reduction in inpatients with cocaine use disorder (CUD). Our study aimed at assessing feasibility of a longer tDCS protocol in CUD (15 versus the common five/10 sessions) and replicability of previous results. In a randomized double‐blind sham‐controlled protocol, 17 inpatients with CUD were assigned to either a real‐tDCS (right anodal/left cathodal) or a sham‐tDCS condition for 15 sessions. Following the previous report, primary outcome measures were self‐reported craving, anxiety, depression, and quality of life. Secondary measures included sleepiness, readiness to change drug use, and affect. We also assessed cognitive function including impulsivity. An 88% retention rate demonstrated feasibility. Partially supporting the previous results, there was a trend for self‐reported craving to decrease in the real‐tDCS group more than the sham‐group, an effect that would reach significance with 15 subjects per group. Quality of life and impulsivity improved over time in treatment in both groups. Daytime sleepiness and readiness to change drug use showed significant Group × Time interactions whereby improvements were noted only in the real‐tDCS group. One‐month follow‐up suggested transient effects of tDCS on sleepiness and craving. These preliminary results suggest the need for including more subjects to show a unique effect of real‐tDCS on craving and examine the duration of this effect. After replication in larger sample sizes, increased vigilance and motivation to change drug use in the real‐tDCS group may suggest fortification of dlPFC‐supported executive functions. [ABSTRACT FROM AUTHOR]