Modeling Cultural Dynamics

EVOC (for EVOlution of Culture) is a computer model of culture that enables us to investigate how various factors such as barriers to cultural diffusion, the presence and choice of leaders, or changes in the ratio of innovation to imitation affect the diversity and effectiveness of ideas. It consists of neural network based agents that invent ideas for actions, and imitate neighbors actions. The model is based on a theory of culture according to which what evolves through culture is not memes or artifacts, but the internal models of the world that give rise to them, and they evolve not through a Darwinian process of competitive exclusion but a Lamarckian process involving exchange of innovation protocols. EVOC shows an increase in mean fitness of actions over time, and an increase and then decrease in the diversity of actions. Diversity of actions is positively correlated with population size and density, and with barriers between populations. Slowly eroding borders increase fitness without sacrificing diversity by fostering specialization followed by sharing of fit actions. Introducing a leader that broadcasts its actions throughout the population increases the fitness of actions but reduces diversity of actions. Increasing the number of leaders reduces this effect. Efforts are underway to simulate the conditions under which an agent immigrating from one culture to another contributes new ideas while still fitting in.

Dynamics of Neural Networks with Continuous Attractors

We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.

The Open Connectome Project Data Cluster: Scalable Analysis and Vision for High-Throughput Neuroscience

We describe a scalable database cluster for the spatial analysis and annotation of high-throughput brain imaging data, initially for 3-d electron microscopy image stacks, but for time-series and multi-channel data as well. The system was designed primarily for workloads that build connectomes---neural connectivity maps of the brain---using the parallel execution of computer vision algorithms on high-performance compute clusters. These services and open-science data sets are publicly available at http://openconnecto.me. The system design inherits much from NoSQL scale-out and data-intensive computing architectures. We distribute data to cluster nodes by partitioning a spatial index. We direct I/O to different systems---reads to parallel disk arrays and writes to solid-state storage---to avoid I/O interference and maximize throughput. All programming interfaces are RESTful Web services, which are simple and stateless, improving scalability and usability. We include a performance evaluation of the production system, highlighting the effectiveness of spatial data organization.

Searching for collective behavior in a network of real neurons

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such K-pairwise models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the populations capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.

Synchronization in random balanced networks

Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered neuronal networks with excitatory-inhibitory structure and balance constraints. We show how the interplay between structure and disorder in the connectivity leads to a universal transition from trivial to synchronized stationary or periodic states. This transition cannot be explained only through the analysis of the spectral density of the connectivity matrix. We provide a low dimensional approximation that shows the role of both the structure and disorder in the dynamics.

Resolution enhancement in neural networks with dynamical synapses

Conventionally, information is represented by spike rates in the neural system. Here, we consider the ability of temporally modulated activities in neuronal networks to carry information extra to spike rates. These temporal modulations, commonly known as population spikes, are due to the presence of synaptic depression in a neuronal network model. We discuss its relevance to an experiment on transparent motions in macaque monkeys by Treue et al. in 2000. They found that if the moving directions of objects are too close, the firing rate profile will be very similar to that with one direction. As the difference in the moving directions of objects is large enough, the neuronal system would respond in such a way that the network enhances the resolution in the moving directions of the objects. In this paper, we propose that this behavior can be reproduced by neural networks with dynamical synapses when there are multiple external inputs. We will demonstrate how resolution enhancement can be achieved, and discuss the conditions under which temporally modulated activities are able to enhance information processing performances in general.

Generalized cable theory for neurons in complex and heterogeneous media

Cable theory has been developed over the last decades, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion or capacitive effects, but their impact on cable properties is not known. In this paper, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for more complex media, for example in the presence of ionic diffusion, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.

Cross-talk and transitions between multiple spatial maps in an attractor neural network model of the hippocampus: phase diagram (I)

We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding 1D or 2D spatial maps or environments. Using statistical mechanics tools we show that, below critical values for the noise in the neural response and for the number of environments, the network activity is spatially localized in one environment. We calculate the number of stored environments. For high noise and loads the network activity extends over space, either uniformly or with spatial heterogeneities due to the cross-talk between the maps, and memory of environments is lost. Analytical predictions are corroborated by numerical simulations.

Design for a Darwinian Brain: Part 1. Philosophy and Neuroscience

Physical symbol systems are needed for open-ended cognition. A good way to understand physical symbol systems is by comparison of thought to chemistry. Both have systematicity, productivity and compositionality. The state of the art in cognitive architectures for open-ended cognition is critically assessed. I conclude that a cognitive architecture that evolves symbol structures in the brain is a promising candidate to explain open-ended cognition. Part 2 of the paper presents such a cognitive architecture.

Neurally Implementable Semantic Networks

We propose general principles for semantic networks allowing them to be implemented as dynamical neural networks. Major features of our scheme include: (a) the interpretation that each node in a network stands for a bound integration of the meanings of all nodes and external events the node links with; (b) the systematic use of nodes that stand for categories or types, with separate nodes for instances of these types; (c) an implementation of relationships that does not use intrinsically typed links between nodes.