114 research outputs found
Complex Systems Science and Brain Dynamics
Brain systems with their complex and temporally intricate dynamics have been difficult to unravel and comprehend. While great advances have been made in understanding genetics, neural behavior, gray versus white matter and synaptic plasticity, it remains a particular challenge to understand how human diseases and disorders develop from internal neural level irregularities, e.g., in channels, membranes and mutations before they lead to an observable disease. The field of system biology has advanced significantly, giving rise to high expectations of tying separate biological phenomena into more expansive rational systems. Denis Noble, a pioneer of systems biology, who developed the first viable mathematical model of the working heart in 1960, has been influential in calling the community to focus on creating computer and mathematical models of organic life to interpret functions from the molecular level to that of the whole organism (Noble, 2006). Our approach to modelin
Discontinuities in recurrent neural networks
This paper studies the computational power of various discontinuous
real computational models that are based on the classical analog
recurrent neural network (ARNN). This ARNN consists of finite number
of neurons; each neuron computes a polynomial net-function and a
sigmoid-like continuous activation-function.
The authors introducePostprint (published version
Multiscale Agent-based Model of Tumor Angiogenesis
AbstractComputational models of cancer complement the biological study of tumor growth. However, existing modeling approaches can be both inefficient and inaccurate due to the difficulties of representing the complex interactions between cells and tissues. We present a three-dimensional multiscale agent-based model of tumor growth with angiogenesis. The model is designed to easily adapt to various cancer types, although we focus on breast cancer. It includes cellular (genetic control), tissue (cells, blood vessels, angiogenesis), and molecular (VEGF, diffusion) levels of representation. Unlike in most cancer models, both normally functioning tissue cells and tumor cells are included in the model. Tumors grow following the expected spheroid cluster pattern, with growth limited by available oxygen. Angiogenesis, the process by which tumors may encourage new vessel growth for nutrient diffusion, is modeled with a new discrete approach that we propose will decrease computational cost. Our results show that despite proposing these new abstractions, we see similar results to previously accepted angiogenesis models. This may indicate that a more discrete approach should be considered by modelers in the future
Probabilistic analysis of a differential equation for linear programming
In this paper we address the complexity of solving linear programming
problems with a set of differential equations that converge to a fixed point
that represents the optimal solution. Assuming a probabilistic model, where the
inputs are i.i.d. Gaussian variables, we compute the distribution of the
convergence rate to the attracting fixed point. Using the framework of Random
Matrix Theory, we derive a simple expression for this distribution in the
asymptotic limit of large problem size. In this limit, we find that the
distribution of the convergence rate is a scaling function, namely it is a
function of one variable that is a combination of three parameters: the number
of variables, the number of constraints and the convergence rate, rather than a
function of these parameters separately. We also estimate numerically the
distribution of computation times, namely the time required to reach a vicinity
of the attracting fixed point, and find that it is also a scaling function.
Using the problem size dependence of the distribution functions, we derive high
probability bounds on the convergence rates and on the computation times.Comment: 1+37 pages, latex, 5 eps figures. Version accepted for publication in
the Journal of Complexity. Changes made: Presentation reorganized for
clarity, expanded discussion of measure of complexity in the non-asymptotic
regime (added a new section
Unsupervised Learning with Self-Organizing Spiking Neural Networks
We present a system comprising a hybridization of self-organized map (SOM)
properties with spiking neural networks (SNNs) that retain many of the features
of SOMs. Networks are trained in an unsupervised manner to learn a
self-organized lattice of filters via excitatory-inhibitory interactions among
populations of neurons. We develop and test various inhibition strategies, such
as growing with inter-neuron distance and two distinct levels of inhibition.
The quality of the unsupervised learning algorithm is evaluated using examples
with known labels. Several biologically-inspired classification tools are
proposed and compared, including population-level confidence rating, and
n-grams using spike motif algorithm. Using the optimal choice of parameters,
our approach produces improvements over state-of-art spiking neural networks
Energy-based General Sequential Episodic Memory Networks at the Adiabatic Limit
The General Associative Memory Model (GAMM) has a constant state-dependant
energy surface that leads the output dynamics to fixed points, retrieving
single memories from a collection of memories that can be asynchronously
preloaded. We introduce a new class of General Sequential Episodic Memory
Models (GSEMM) that, in the adiabatic limit, exhibit temporally changing energy
surface, leading to a series of meta-stable states that are sequential episodic
memories. The dynamic energy surface is enabled by newly introduced asymmetric
synapses with signal propagation delays in the network's hidden layer. We study
the theoretical and empirical properties of two memory models from the GSEMM
class, differing in their activation functions. LISEM has non-linearities in
the feature layer, whereas DSEM has non-linearity in the hidden layer. In
principle, DSEM has a storage capacity that grows exponentially with the number
of neurons in the network. We introduce a learning rule for the synapses based
on the energy minimization principle and show it can learn single memories and
their sequential relationships online. This rule is similar to the Hebbian
learning algorithm and Spike-Timing Dependent Plasticity (STDP), which describe
conditions under which synapses between neurons change strength. Thus, GSEMM
combines the static and dynamic properties of episodic memory under a single
theoretical framework and bridges neuroscience, machine learning, and
artificial intelligence
Forward Signal Propagation Learning
We propose a new learning algorithm for propagating a learning signal and
updating neural network parameters via a forward pass, as an alternative to
backpropagation. In forward signal propagation learning (sigprop), there is
only the forward path for learning and inference, so there are no additional
structural or computational constraints on learning, such as feedback
connectivity, weight transport, or a backward pass, which exist under
backpropagation. Sigprop enables global supervised learning with only a forward
path. This is ideal for parallel training of layers or modules. In biology,
this explains how neurons without feedback connections can still receive a
global learning signal. In hardware, this provides an approach for global
supervised learning without backward connectivity. Sigprop by design has better
compatibility with models of learning in the brain and in hardware than
backpropagation and alternative approaches to relaxing learning constraints. We
also demonstrate that sigprop is more efficient in time and memory than they
are. To further explain the behavior of sigprop, we provide evidence that
sigprop provides useful learning signals in context to backpropagation. To
further support relevance to biological and hardware learning, we use sigprop
to train continuous time neural networks with Hebbian updates and train spiking
neural networks without surrogate functions
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