Mixed state on a sparsely encoded associative memory model.

T Kimoto; M Okada

doi:10.1007/s004220100263

Home/Archive/PubMed

PubMed · 11592629

Mixed state on a sparsely encoded associative memory model.

T Kimoto·M Okada

View original source ↗Export metadata ↓

Abstract

We analyzed symmetric mixed states corresponding to the so-called concept formation on a sparsely encoded associative memory model with 0-1 neurons. Three types of mixed states--OR, AND, and a majority decision--are described as typical examples. Each element of the OR mixed state is composed of corresponding memory pattern elements by means of the OR operation. The other two types are similarly defined. By analyzing their equilibrium properties through self-consistent signal-to-noise analysis and computer simulation, we found that the storage capacity of the OR mixed state diverges in a sparse limit, but that the other states do not diverge. In addition, we found that the optimal threshold values, which maximize the storage capacity for the memory pattern and the OR mixed state, coincide with each other in the spare limit. We conclude that the OR mixed state is a reasonable representative of mixed state in the sparse limit.

Explore related subjects

Computer Simulation Memory Models, Neurological Journal Article Research Support, Non-U.S. Gov't

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

T Kimoto, M Okada. 2001. Mixed state on a sparsely encoded associative memory model.. https://doi.org/10.1007/s004220100263

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2025

Generating correlated data for omics simulation.

Simulation of realistic omics data is a key input for benchmarking studies that help users obtain optimal computational pipelines. Omics data involves large numbers of measured features on each sample and these measures are generally correlated with each other. However, simulation too often ignores these correlations, perhaps due to computational and statistical hurdles of doing so. To alleviate this, we describe three approaches for generating omics-scale data with correlated measures which mimic real datasets. These approaches are all based on a Gaussian copula approach with a covariance matrix that decomposes into a diagonal part and a low-rank part. This decomposition allows for extremely efficient simulation, overcoming a hurdle for adoption of past methods. We use these approaches to demonstrate the importance of including correlation in two benchmarking applications. First, we show that variance of results from the popular DESeq2 method increases when dependence is included. Second, we demonstrate that CYCLOPS, a method for inferring circadian time of collection from transcriptomics, improves in performance when given gene-gene dependencies in some circumstances. We provide an R package, dependentsimr, that has efficient implementations of these methods and can generate dependent data with arbitrary marginal distributions, including discrete (binary, ordered categorical, Poisson, negative binomial), continuous (normal), or with an empirical distribution.

Computer Simulation↗

PubMed2017

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development.

Computer Simulation↗

PubMed2003

Reconstructing metabolic flux vectors from extreme pathways: defining the alpha-spectrum.

The move towards genome-scale analysis of cellular functions has necessitated the development of analytical (in silico) methods to understand such large and complex biochemical reaction networks. One such method is extreme pathway analysis that uses stoichiometry and thermodynamic irreversibly to define mathematically unique, systemic metabolic pathways. These extreme pathways form the edges of a high-dimensional convex cone in the flux space that contains all the attainable steady state solutions, or flux distributions, for the metabolic network. By definition, any steady state flux distribution can be described as a nonnegative linear combination of the extreme pathways. To date, much effort has been focused on calculating, defining, and understanding these extreme pathways. However, little work has been performed to determine how these extreme pathways contribute to a given steady state flux distribution. This study represents an initial effort aimed at defining how physiological steady state solutions can be reconstructed from a network's extreme pathways. In general, there is not a unique set of nonnegative weightings on the extreme pathways that produce a given steady state flux distribution but rather a range of possible values. This range can be determined using linear optimization to maximize and minimize the weightings of a particular extreme pathway in the reconstruction, resulting in what we have termed the alpha-spectrum. The alpha-spectrum defines which extreme pathways can and cannot be included in the reconstruction of a given steady state flux distribution and to what extent they individually contribute to the reconstruction. It is shown that accounting for transcriptional regulatory constraints can considerably shrink the alpha-spectrum. The alpha-spectrum is computed and interpreted for two cases; first, optimal states of a skeleton representation of core metabolism that include transcriptional regulation, and second for human red blood cell metabolism under various physiological, non-optimal conditions.

Computer Simulation↗