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Neural networks successfully capture the computational power of the human brain for many tasks. Similarly inspired by the brain architecture, Nearest Neighbor (NN) representations is a novel approach of computation. We establish a firmer…
Endowing brain anatomy, dynamics, and function with a network structure is becoming standard in neuroscience. In its simplest form, a network is a collection of units and relationships between them. The pattern of relations among the units…
The brain has no direct access to physical stimuli, but only to the spiking activity evoked in sensory organs. It is unclear how the brain can structure its representation of the world based on differences between those noisy, correlated…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
This report discusses the application of neural networks (NNs) as small segments of the brain. The networks representing the biological connectome are altered both spatially and temporally. The degradation techniques applied here are…
The structure of the axon-dendrite connections of neurons of the brain creates a rich spatial structure in which provided various combinations of signals surrounding neurons. Structure of dendritic trees and shape of dendritic spines allow…
In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium…
Studies regarding knowledge organization and acquisition are of great importance to understand areas related to science and technology. A common way to model the relationship between different concepts is through complex networks. In such…
We apply the approach of the Google matrix, used in computer science and World Wide Web, to description of properties of neuronal networks. The Google matrix ${\bf G}$ is constructed on the basis of neuronal network of a brain model…
It has become increasingly popular to study the brain as a network due to the realization that functionality cannot be explained exclusively by independent activation of specialized regions. Instead, across a large spectrum of behaviors,…
A Parallel Self-Organizing Map (Parallel-SOM) is proposed to modify Kohonen's SOM in parallel computing environment. In this model, two separate layers of neurons are connected together. The number of neurons in both layers and connections…
We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed…
This paper proposes a novel framework for recurrent neural networks (RNNs) inspired by the human memory models in the field of cognitive neuroscience to enhance information processing and transmission between adjacent RNNs' units. The…
The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…
We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These…
Asymmetry in the synaptic interactions between neurons plays a crucial role in determining the memory storage and retrieval properties of recurrent neural networks. In this work, we analyze the problem of storing random memories in a…
The predictive power of neural networks often costs model interpretability. Several techniques have been developed for explaining model outputs in terms of input features; however, it is difficult to translate such interpretations into…
Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…