Related papers: The Ising Model for Neural Data: Model Quality and…
Simultaneous behavioral and electrophysiological recordings call for new methods to reveal the interactions between neural activity and behavior. A milestone would be an interpretable model of the co-variability of spiking activity and…
We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously, and we explore them…
In this technical note, we address an unresolved challenge in neuroimaging statistics: how to determine which of several datasets is the best for inferring neuronal responses. Comparisons of this kind are important for experimenters when…
For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and…
Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…
We describe and analyze some novel approaches for studying the dynamics of Ising spin glass models. We first briefly consider the variational approach based on minimizing the Kullback-Leibler divergence between independent trajectories and…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
Human brain contains about 10 billion neurons, each of which has about 10~10,000 nerve endings from which neurotransmitters are released in response to incoming spikes, and the released neurotransmitters then bind to receptors located in…
A good understanding of how neurons use electrical pulses (i.e, spikes) to encode the signal information remains elusive. Analyzing spike sequences generated by individual neurons and by two coupled neurons (using the stochastic…
This article contains two main theoretical results on neural spike train models. The first assumes that the spike train is modeled as a counting or point process on the real line where the conditional intensity function is a product of a…
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen,…
For energy-efficient computation in specialized neuromorphic hardware, we present spiking neural coding, an instantiation of a family of artificial neural models grounded in the theory of predictive coding. This model, the first of its…
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for…
Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in…
Exact solutions for the learning problem of autoassociative networks with binary couplings are determined by a new method. The use of a branch-and-bound algorithm leads to a substantial saving of computational time compared with complete…
Demystifying effective connectivity among neuronal populations has become the trend to understand the brain mechanisms of Parkinson's disease, schizophrenia, mild traumatic brain injury, and many other unlisted neurological diseases.…
The network inference problem arises in biological research when one needs to quantitatively choose the best protein-interaction model for explaining a phenotype. The diverse nature of the data and nonlinear dynamics pose significant…