Dorian Florescu

The Fruit Fly Brain Observatory: from structure to function

The Fruit Fly Brain Observatory (FFBO) is a collaborative effort between experimentalists, theorists and computational neuroscientists at Columbia University, National Tsing Hua University and Sheffield University with the goal to (i) create an open platform for the emulation and biological validation of fruit fly brain models in health and disease, (ii) standardize tools and methods for graphical rendering, representation and manipulation of brain circuits, (iii) standardize tools for representation of fruit fly brain data and its abstractions and support for natural language queries, (iv) create a focus for the neuroscience community with interests in the fruit fly brain and encourage the sharing of fruit fly brain structural data and executable code worldwide. NeuroNLP and NeuroGFX, two key FFBO applications, aim to address two major challenges, respectively: i) seamlessly integrate structural and genetic data from multiple sources that can be intuitively queried, effectively visualized and extensively manipulated, ii) devise executable brain circuit models anchored in structural data for understanding and developing novel hypotheses about brain function. NeuroNLP enables researchers to use plain English (or other languages) to probe biological data that are integrated into a novel database system, called NeuroArch, that we developed for integrating biological and abstract data models of the fruit fly brain. With powerful 3D graphical visualization, NeuroNLP presents a highly accessible portal for the fruit fly brain data. NeuroGFX provides users highly intuitive tools to execute neural circuit models with Neurokernel, an open-source platform for emulating the fruit fly brain, with full data support from the NeuroArch database and visualization support from an interactive graphical interface. Brain circuits can be configured with high flexibility and investigated on multiple levels, e.g., whole brain, neuropil, and local circuit levels. The FFBO is publicly available and accessible at http://fruitflybrain.org from any modern web browsers, including those running on smartphones.

NeuroNLP: a natural language portal for aggregated fruit fly brain data

NeuroNLP, is a key application on the Fruit Fly Brain Observatory platform (FFBO, http://fruitflybrain.org), that provides a modern web-based portal for navigating fruit fly brain circuit data. Increases in the availability and scale of fruit fly connectome data, demand new, scalable and accessible methods to facilitate investigation into the functions of the latest complex circuits being uncovered. NeuroNLP enables in-depth exploration and investigation of the structure of brain circuits, using intuitive natural language queries that are capable of revealing the latent structure and information, obscured due to expansive yet independent data sources. NeuroNLP is built on top of a database system call NeuroArch that codifies knowledge about the fruit fly brain circuits, spanning multiple sources. Users can probe biological circuits in the NeuroArch database with plain English queries, such as “show glutamatergic local neurons in the left antennal lobe” and “show neurons with dendrites in the left mushroom body and axons in the fan-shaped body”. This simple yet powerful interface replaces the usual, cumbersome checkboxes and dropdown menus prevalent in today’s neurobiological databases. Equipped with powerful 3D visualization, NeuroNLP standardizes tools and methods for graphical rendering, representation, and manipulation of brain circuits, while integrating with existing databases such as the FlyCircuit. The userfriendly graphical user interface complements the natural language queries with additional controls for exploring the connectivity of neurons and neural circuits. Designed with an open-source, modular structure, it is highly scalable/flexible/extensible to additional databases or to switch between databases and supports the creation of additional parsers for other languages. By supporting access through a web browser from any modern laptop or smartphone, NeuroNLP significantly increases the accessibility of fruit fly brain data and improves the impact of the data in both scientific and educational exploration.

A novel reconstruction framework for time-encoded signals with integrate-and-fire neurons

Integrate-and-fire neurons are time encoding machines that convert the amplitude of an analog signal into a nonuniform, strictly increasing sequence of spike times. Under certain conditions, the encoded signals can be reconstructed from the nonuniform spike time sequences using a time decoding machine. Time encoding and time decoding methods have been studied using the nonuniform sampling theory for band-limited spaces, as well as for generic shift-invariant spaces. This letter proposes a new framework for studying IF time encoding and decoding by reformulating the IF time encoding problem as a uniform sampling problem. This framework forms the basis for two new algorithms for reconstructing signals from spike time sequences. We demonstrate that the proposed reconstruction algorithms are faster, and thus better suited for real-time processing, while providing a similar level of accuracy, compared to the standard reconstruction algorithm.

Identification of Linear and Nonlinear Sensory Processing Circuits from Spiking Neuron Data

Inferring mathematical models of sensory processing systems directly from input-output observations, while making the fewest assumptions about the model equations and the types of measurements available, is still a major issue in computational neuroscience. This letter introduces two new approaches for identifying sensory circuit models consisting of linear and nonlinear filters in series with spiking neuron models, based only on the sampled analog input to the filter and the recorded spike train output of the spiking neuron. For an ideal integrate-and-fire neuron model, the first algorithm can identify the spiking neuron parameters as well as the structure and parameters of an arbitrary nonlinear filter connected to it. The second algorithm can identify the parameters of the more general leaky integrate-and-fire spiking neuron model, as well as the parameters of an arbitrary linear filter connected to it. Numerical studies involving simulated and real experimental recordings are used to demonstrate the applicability and evaluate the performance of the proposed algorithms.

A New Method for Implementing Linear Filters in the Spike Domain

This chapter proposes a new model for processing information using spike trains, by developing a direct relationship between the input and output of a linear filter, both encoded into spike time sequences by a TEM. The TEM considered in this study is the IF neuron model. The proposed representation forms the basis for a new algorithm to compute the time encoded output directly from the input spike time sequence. The approximation error introduced by the proposed implementation is characterized by deriving an error bound between the real and estimated spike times that is a function of the IF neuron parameters. The proposed direct encoding approach is much faster than the indirect approach, involving simulating the filter output and subsequent encoding. A numerical simulation study is used to illustrate the approach.

A New Approach to the Identification of Sensory Processing Circuits Based on Spiking Neuron Data

The cascade model, comprising a filter in series with a spiking neuron, have been widely used as representation for spiking neural circuits. Although the state-of-the-art identification methods for cascade models can accommodate a wide range of filters and spiking neurons, the assumptions proposed can in some cases be considered restrictive. Specifically, for [Filter]-[IF] circuits, it is assumed that the IF model is known, or that the filter output is available for measurement. In this chapter, two new identification methodologies are proposed for neural circuits comprising a linear or nonlinear filter in cascade with a spiking neuron. A [Nonlinear Filter]-[Ideal IF] circuit is reformulated as a scaled nonlinear filter in series with a modified ideal IF neuron. The identification is subsequently carried out by employing the NARMAX nonlinear system identification methodology to infer the structure and parameters of a discrete-time representation for the scaled nonlinear filter. An equivalent [Linear Filter]-[Leaky IF] circuit is identified, assuming that input-output measurements of the spiking neuron are not available and that all parameters are unknown. The leaky IF model is identified by solving an equation whose solution is proven to be unique. An algorithm is provided that computes the solution with arbitrary precision. Subsequently, the structure and parameters of the filter are inferred using the NARMAX identification methodology. Numerical simulations are given to test the performance of the new methods.

Time Encoding and Decoding in Bandlimited and Shift-Invariant Spaces

The IF neuron represents one of the most common models for describing the behaviour of the spiking neurons. The IF model belongs to the more general class of time encoding machines (TEM). Using mathematical tools from nonuniform sampling theory, it was proven that, the input of a TEM belonging to a bandlimited space can be perfectly reconstructed from the corresponding output sequence of spike times. This result was subsequently generalised for inputs belonging to the more general shift-invariant spaces. All the state-of-the-art reconstruction algorithms for TEMs are studied in a unifying manner with the reconstruction algorithms from nonuniform sampling theory. In this case, the sampling times are different for every input, and thus the algorithms become computationally demanding when processing a large number of inputs. This chapter reviews the nonuniform sampling theory and the state-of-the-art mathematical formulation describing the encoding and decoding for TEMs, for inputs belonging to bandlimited as well as shift-invariant spaces.

Reconstruction, identification and implementation methods for spiking neural circuits

Integrate-and-fire (IF) neurons are time encoding machines (TEMs) that convert the amplitude of an analog signal into a non-uniform, strictly increasing sequence of spike times. This thesis addresses three major issues in the field of computational neuroscience as well as neuromorphic engineering. The first problem is concerned with the formulation of the encoding performed by an IF neuron. The encoding mechanism is described mathematically by the t-transform equation, whose standard formulation is given by the projection of the stimulus onto a set of input dependent frame functions. As a consequence, the standard methods reconstruct the input of an IF neuron in a space spanned by a set of functions that depend on the stimulus. The process becomes computationally demanding when performing reconstruction from long sequences of spike times. The issue is addressed in this work by developing a new framework in which the IF encoding process is formulated as a problem of uniform sampling on a set of input independent time points. Based on this formulation, new algorithms are introduced for reconstructing the input of an IF neuron belonging to bandlimited as well as shift-invariant spaces. The algorithms are significantly faster, whilst providing a similar level of accuracy, compared to the standard reconstruction methods. Another important issue calls for inferring mathematical models for sensory processing systems directly from input-output observations. This problem was addressed before by performing identification of sensory circuits consisting of linear filters in series with ideal IF neurons, by reformulating the identification problem as one of stimulus reconstruction. The result was extended to circuits in which the ideal IF neuron was replaced by more biophysically realistic models, under the additional assumptions that the spiking neuron parameters are known a priori, or that input-output measurements of the spiking neuron are available. This thesis develops two new identification methodologies for [Nonlinear Filter]-[Ideal IF] and [Linear Filter]-[Leaky IF] circuits consisting of two steps: the estimation of the spiking neuron parameters and the identification of the filter. The methodologies are based on the reformulation of the circuit as a scaled filter in series with a modified spiking neuron. The first methodology identifies an unknown [Nonlinear Filter]-[Ideal IF] circuit from input-output data. The scaled nonlinear filter is estimated using the NARMAX identification methodology for the reconstructed filter output. The [Linear Filter]-[Leaky IF] circuit is identified with the second proposed methodology by first estimating the leaky IF parameters with arbitrary precision using specific stimuli sequences. The filter is subsequently identified using the NARMAX identification methodology. The third problem addressed in this work is given by the need of developing neuromorphic engineering circuits that perform mathematical computations in the spike domain. In this respect, this thesis developed a new representation between the time encoded input and output of a linear filter, where the TEM is represented by an ideal IF neuron. A new practical algorithm is developed based on this representation. The proposed algorithm is significantly faster than the alternative approach, which involves reconstructing the input, simulating the linear filter, and subsequently encoding the resulting output into a spike train.

Implementation of linear filters in the spike domain

This paper proposes a model and algorithm to compute the time encoded output of a linear filter directly from the time encoded input. The time encoding machine considered in this study is the integrate-and-fire neuron model. The proposed direct encoding approach is much faster than the indirect approach, involving simulating the filter output and subsequent encoding. A numerical simulation study is used to illustrate the approach.

Nonlinear system identification of receptive fields from spiking neuron data

Identification of a linear filter in cascade with a spiking neuron has been previously considered [1] under the assumption that the input of the Hodgkin-Huxley spiking neuron can be measured in addition to the input and output of the circuit. An alternative method to identify a linear filter given the input to the circuit and the spike time sequence, has been proposed [2] for Integrate-and-Fire (IAF) neurons. The method was further extended [3] to nonlinear receptive fields that can be described by a Volterra series. Here we propose a new system identification methodology to identify a more general NARMAX representation of the nonlinear receptive field in cascade with an ideal-IAF neuron, based only on measurements of the input stimulus and the spike time sequence of the IAF neuron. By using an orthogonal forward selection algorithm we are able to derive the NARMAX representation of a scaled version of the nonlinear filter directly from the reconstructed input of an ideal IAF neuron. The method is further extended to leaky-IAF neurons which require estimating an additional spiking neuron parameter. We use the NARMAX methodology to identify recursively the nonlinear filter and the spiking neuron parameter in the presence of noise. Statistical and dynamical model validation tests are used to check if the identified nonlinear filter models are an adequate representation of the underlying nonlinear information processing mechanisms. The performance and robustness to noise of the proposed methods is demonstrated through numerical simulation studies. Specifically, we compared the generalized (higher-order) frequency response functions (GFRFs) of the original and the identified nonlinear filter (Figures 1 A-D) and evaluated, for different noise levels, the SNR of the model predicted output on a validation data set (Figure 1 E). Figure 1 A&B - GFRF functions of the original filter, C&D - Difference between the original GFRFs and the scaled versions for the identified filter, E - SNR between the validation signal and the identified filter output.