The Layer-Oriented Approach to Declarative Languages for Biological Modeling

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language

LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

Spatiotemporal network coding of physiological mossy fiber inputs by the cerebellar granular layer

The granular layer, which mainly consists of granule and Golgi cells, is the first stage of the cerebellar cortex and processes spatiotemporal information transmitted by mossy fiber inputs with a wide variety of firing patterns. To study its dynamics at multiple time scales in response to inputs approximating real spatiotemporal patterns, we constructed a large-scale 3D network model of the granular layer. Patterned mossy fiber activity induces rhythmic Golgi cell activity that is synchronized by shared parallel fiber input and by gap junctions. This leads to long distance synchrony of Golgi cells along the transverse axis, powerfully regulating granule cell firing by imposing inhibition during a specific time window. The essential network mechanisms, including tunable Golgi cell oscillations, on-beam inhibition and NMDA receptors causing first winner keeps winning of granule cells, illustrate how fundamental properties of the granule layer operate in tandem to produce (1) well timed and spatially bound output, (2) a wide dynamic range of granule cell firing and (3) transient and coherent gating oscillations. These results substantially enrich our understanding of granule cell layer processing, which seems to promote spatial group selection of granule cell activity as a function of timing of mossy fiber input

NineML: the network interchange for neuroscience modeling language

The growing number of large-scale neuronal network models has created a need for standards and guidelines to ease model sharing and facilitate the replication of results across different simulators. To foster community efforts towards such standards, the International Neuroinformatics Coordinating Facility (INCF) has formed its Multiscale Modeling program, and has assembled a task force of simulator developers to propose a declarative computer language for descriptions of large-scale neuronal networks. The name of the proposed language is "Network Interchange for Neuroscience Modeling Language" (NineML) and its initial focus is restricted to point neuron models. The INCF Multiscale Modeling task force has identified the key concepts of network modeling to be 1) spiking neurons 2) synapses 3) populations of neurons and 4) connectivity patterns across populations of neurons. Accordingly, the definition of NineML includes a set of mathematical abstractions to represent these concepts. NineML aims to provide tool support for explicit declarative definition of spiking neuronal network models both conceptually and mathematically in a simulator independent manner. In addition, NineML is designed to be self-consistent and highly flexible, allowing addition of new models and mathematical descriptions without modification of the previous structure and organization of the language. To achieve these goals, the language is being iteratively designed using several representative models with various levels of complexity as test cases. The design of NineML is divided in two semantic layers: the Abstraction Layer, which consists of core mathematical concepts necessary to express neuronal and synaptic dynamics and network connectivity patterns, and the User Layer, which provides constructs to specify the instantiation of a network model in terms that are familiar to computational neuroscience modelers. As part of the Abstraction Layer, NineML includes a flexible block diagram notation for describing spiking dynamics. The notation represents continuous and discrete variables, their evolution according to a set of rules such as a system of ordinary differential equations, and the conditions that induce a regime change, such as the transition from subthreshold mode to spiking and refractory modes. The User Layer provides syntax for specifying the structure of the elements of a spiking neuronal network. This includes parameters for each of the individual elements (cells, synapses, inputs) and the grouping of these entities into networks. In addition, the user layer defines the syntax for supplying parameter values to abstract connectivity patterns. The NineML specification is defined as an implementation-neutral object model representing all the concepts in the User and Abstraction Layers. Libraries for creating, manipulating, querying and serializing the NineML object model to a standard XML representation will be delivered for a variety of languages. The first priority of the task force is to deliver a publicly available Python implementation to support the wide range of simulators which provide a Python user interface (NEURON, NEST, Brian, MOOSE, GENESIS-3, PCSIM, PyNN, etc.). These libraries will allow simulator developers to quickly add support for NineML, and will thus catalyze the emergence of a broad software ecosystem supporting model definition interoperability around NineML

iraikov/9ML-toolkit: Support for adaptive solvers and precise event time interpolation

This release uses the new features in salt 0.20 to support adaptive solvers and precise even time interpolation