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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]

The broad utility of image distributions by applying hierarchical image probability (HIP) model to classification, synthesis, and compression, across a variety of image types, namely, electrooptical, synthetic aperture radar, and mammograms is demonstrated. The differences between the HIP and the hidden Markov tree (HMT) models include the use of multivariate Gaussians to model the distributions of local vectors of wavelet coefficients and the use of different numbers of hidden states at each resolution.

We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using [sup.31]P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on [sup.1]H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up. Index Terms--Blind source separation (BSS), chemical shift imaging (CSI), hierarchical decomposition, magnetic resonance (MR), magnetic resonance spectroscopy (MRS), nonnegative matrix factorization (NMF).