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Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the…
In this paper we present a methodology to address the problem of brain tissue deformation referred to as 'brain-shift'. This deformation occurs throughout a neurosurgery intervention and strongly alters the accuracy of the neuronavigation…
Neuromorphic computing systems comprise networks of neurons that use asynchronous events for both computation and communication. This type of representation offers several advantages in terms of bandwidth and power consumption in…
A growing body of work underlines striking similarities between biological neural networks and recurrent, binary neural networks. A relatively smaller body of work, however, discusses similarities between learning dynamics employed in deep…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
Neurological diseases and injuries present some of the greatest challenges in modern medicine, often causing irreversible and lifelong burdens in the people whom they afflict. These diagnoses have devastating consequences on millions of…
Microscopic structural damage, such as lesions in neural systems or disruptions in urban transportation networks, can impair the dynamics crucial for systems' functionality, such as electrochemical signals or human flows, or any other type…
In the mammalian brain, newly acquired memories depend on the hippocampus for maintenance and recall, but over time the neocortex takes over these functions, rendering memories hippocampus-independent. The process responsible for this…
The basic units in our brain are neurons and each neuron has more than 1000 synapse connections. Synapse is the basic structure for information transfer in an ever-changing manner, and short-term plasticity allows synapses to perform…
We present an account of neuroplasticity with respect to cell-internal processing pathways in relation to membrane and synaptic plasticity. We think traditional synapse-centric, weight-based models of memorization are not sufficient or…
Previous mechanical meta-structures used for mechanical memory storage, computing and information processing are severely constrained by low information density and/or non-robust structural stiffness to stably protect the maintained…
The neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…
Recent breakthroughs in artificial intelligence (AI) are reshaping the way we construct computational counterparts of the brain, giving rise to a new class of ``surrogate brains''. In contrast to conventional hypothesis-driven biophysical…
The central dogma of molecular biology is the principal framework for understanding how nucleic acid information is propagated and used by living systems to create complex biomolecules. Here, by integrating the structural and dynamic…
Neurosurgery interventions involve complex tracking systems because a tissue deformation takesplace. The neuronavigation system relies only on preoperative images. In order to overcome the soft tissue deformations and guarantee the accuracy…
Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…
We propose to analyze dynamically changing brain networks by decomposing them into three orthogonal components through the Hodge decomposition. We propose to quantify the magnitude and relative strength of each component. We performed…
The integration of deep learning and neuroscience has been advancing rapidly, which has led to improvements in the analysis of brain activity and the understanding of deep learning models from a neuroscientific perspective. The…
Here we describe an "information based exchange" model of brain function that ascribes to neocortex, basal ganglia, and thalamus distinct network functions. The model allows us to analyze whole brain system set point measures, such as the…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…