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The circadian clock orchestrates daily changes in physiology and behavior to ensure internal temporal order and optimal timing across the day. In animals, a central brain clock coordinates circadian rhythms throughout the body and is characterized by a remarkable robustness that depends on synaptic connections between constituent neurons. The clock neuron network of Drosophila, which shares network motifs with clock networks in the mammalian brain yet is built of many fewer neurons, offers a powerful model for understanding the network properties of circadian timekeeping. Here, we report an assessment of synaptic connectivity within a clock network, focusing on the critical lateral neuron (LN) clock neuron classes within the Janelia hemibrain dataset. Our results reveal that previously identified anatomical and functional subclasses of LNs represent distinct connectomic types. Moreover, we identify a small number of non-clock cell subtypes representing highly synaptically coupled nodes within the clock neuron network. This suggests that neurons lacking molecular timekeeping likely play integral roles within the circadian timekeeping network. To our knowledge, this represents the first comprehensive connectomic analysis of a circadian neuronal network.

Recent advances in molecular transduction of odorants in the Olfactory Sensory Neurons (OSNs) of the Drosophila Antenna have shown that the odorant object identity is multiplicatively coupled with the odorant concentration waveform. The resulting combinatorial neural code is a confounding representation of odorant semantic information (identity) and syntactic information (concentration). To distill the functional logic of odor information processing in the Antennal Lobe (AL) a number of challenges need to be addressed including 1) how is the odorant semantic information decoupled from the syntactic information at the level of the AL, 2) how are these two information streams processed by the diverse AL Local Neurons (LNs) and 3) what is the end-to-end functional logic of the AL? By analyzing single-channel physiology recordings at the output of the AL, we found that the Projection Neuron responses can be decomposed into a concentration-invariant component, and two transient components boosting the positive/negative concentration contrast that indicate onset/offset timing information of the odorant object. We hypothesized that the concentration-invariant component, in the multi-channel context, is the recovered odorant identity vector presented between onset/offset timing events. We developed a model of LN pathways in the Antennal Lobe termed the differential Divisive Normalization Processors (DNPs), which robustly extract the semantics (the identity of the odorant object) and the ON/OFF semantic timing events indicating the presence/absence of an odorant object. For real-time processing with spiking PN models, we showed that the phase-space of the biological spike generator of the PN offers an intuit perspective for the representation of recovered odorant semantics and examined the dynamics induced by the odorant semantic timing events. Finally, we provided theoretical and computational evidence for the functional logic of the AL as a robust ON-OFF odorant object identity recovery processor across odorant identities, concentration amplitudes and waveform profiles.

The Drosophila brain has only a fraction of the number of neurons of higher organisms such as mice and humans. Yet the sheer complexity of its neural circuits recently revealed by large connectomics datasets suggests that computationally modeling the function of fruit fly brain circuits at this scale posits significant challenges.To address these challenges, we present here a programmable ontology that expands the scope of the current Drosophila brain anatomy ontologies to encompass the functional logic of the fly brain. The programmable ontology provides a language not only for modeling circuit motifs but also for programmatically exploring their functional logic. To achieve this goal, we tightly integrated the programmable ontology with the workflow of the interactive FlyBrainLab computing platform. As part of the programmable ontology, we developed NeuroNLP++, a web application that supports free-form English queries for constructing functional brain circuits fully anchored on the available connectome/synaptome datasets, and the published worldwide literature.In addition, we present a methodology for including a model of the space of odorants into the programmable ontology, and for modeling olfactory sensory circuits of the antenna of the fruit fly brain that detect odorant sources. Furthermore, we describe a methodology for modeling the functional logic of the antennal lobe circuit consisting of massive local feedback loops, a characteristic feature observed across Drosophila brain regions. Finally, using a circuit library, we demonstrate the power of our methodology for interactively exploring the functional logic of the massive number of feedback loops in the antennal lobe.

In recent years, a wealth of Drosophila neuroscience data have become available including cell type and connectome/synaptome datasets for both the larva and adult fly. To facilitate integration across data modalities and to accelerate the understanding of the functional logic of the fruit fly brain, we have developed FlyBrainLab, a unique open-source computing platform that integrates 3D exploration and visualization of diverse datasets with interactive exploration of the functional logic of modeled executable brain circuits. FlyBrainLab’s User Interface, Utilities Libraries and Circuit Libraries bring together neuroanatomical, neurogenetic and electrophysiological datasets with computational models of different researchers for validation and comparison within the same platform. Seeking to transcend the limitations of the connectome/synaptome, FlyBrainLab also provides libraries for molecular transduction arising in sensory coding in vision/olfaction. Together with sensory neuron activity data, these libraries serve as entry points for the exploration, analysis, comparison, and evaluation of circuit functions of the fruit fly brain.

In recent years, a wealth of Drosophila neuroscience data have become available. These include cell type, connectome and synaptome datasets for both the larva and adult fly. To facilitate integration across data modalities and to accelerate the understanding of the functional logic of the fly brain, we developed an interactive computing environment called FlyBrainLab.FlyBrainLab is uniquely positioned to accelerate the discovery of the functional logic of the Drosophila brain. Its interactive open source architecture seamlessly integrates and brings together computational models with neuroanatomical, neurogenetic and electrophysiological data, changing the organization of neuroscientific fly brain data from a group of seemingly disparate databases, arrays and tables, to a well structured data and executable circuit repository.The FlyBrainLab User Interface supports a highly intuitive and automated work-flow that streamlines the 3D exploration and visualization of fly brain circuits, and the interactive exploration of the functional logic of executable circuits created directly from the explored and visualized fly brain data. Furthermore, efficient comparisons of circuit models are supported, across models developed by different researchers, across different developmental stages of the fruit fly and across different datasets.The FlyBrainLab Utility Libraries help untangle the graph structure of neural circuits from raw connectome and synaptome data. The Circuit Libraries facilitate the exploration of neural circuits of the neuropils of the central complex and, the development and implementation of models of the adult and larva fruit fly early olfactory systems.Seeking to transcend the limitations of the connectome, FlyBrainLab provides additional libraries for molecular transduction arising in sensory coding in vision and olfaction. Together with sensory neuron activity data, these libraries serve as entry points for discovering circuit function in the sensory systems of the fruit fly brain. They also enable the biological validation of developed executable circuits within the same platform.

Over the past two decades, substantial amount of work has been conducted to characterize different odorant receptors, neuroanatomy and odorant response properties of the early olfactory system of Drosophila melanogaster. Yet many odorant receptors remain only partially characterized, and the odorant transduction process and the axon hillock spiking mechanism of the olfactory sensory neurons (OSNs) have yet to be fully determined. Identity and concentration, two key characteristics of the space of odorants, are encoded by the odorant transduction process. Detailed molecular models of the odorant transduction process are, however, scarce for fruit flies. To address these challenges we advance a comprehensive model of fruit fly OSNs as a cascade consisting of an odorant transduction process (OTP) and a biophysical spike generator (BSG). We model odorant identity and concentration using an odorant-receptor binding rate tensor, modulated by the odorant concentration profile, and an odorant-receptor dissociation rate tensor, and quantitatively describe the mechanics of the molecular ligand binding/dissociation of the OTP. We model the BSG as a Connor-Stevens point neuron. The resulting spatio-temporal encoding model of the Drosophila antenna provides a theoretical foundation for understanding the neural code of both odorant identity and odorant concentration and advances the state-of-the-art in a number of ways. First, it quantifies on the molecular level the spatio-temporal level of complexity of the transformation taking place in the antennae. The concentration-dependent spatio-temporal code at the output of the antenna circuits determines the level of complexity of olfactory processing in the downstream neuropils, such as odorant recognition and olfactory associative learning. Second, the model is biologically validated using multiple electrophysiological recordings. Third, the model demonstrates that the currently available data for odorant-receptor responses only enable the estimation of the affinity of the odorant-receptor pairs. The odorant-dissociation rate is only available for a few odorant-receptor pairs. Finally, our model calls for new experiments for massively identifying the odorant-receptor dissociation rates of relevance to flies., Author summary Identity and concentration, intrinsically embedded in the odorant space, are two key characteristics of olfactory coding that define the level of complexity of neural processing throughout the olfactory system in the fruit fly. In this paper we advance a theoretical foundation for understanding these two characteristics by quantifying mathematically the odorant space and devising a biophysical model of the olfactory sensory neurons (OSNs). To validate our modeling approach, we propose and apply an algorithm to estimate the affinity value and the dissociation rate, the two characteristics that define odorant identity, of multiple odorant-receptor pairs. We then evaluate our model with a multitude of odorant waveforms and demonstrate that the model output reproduces the temporal responses of OSNs obtained from in vivo electrophysiology recordings. Furthermore, we evaluate the model at the OSN population level and quantify on the molecular level the spatio-temporal level of complexity of the transformation taking place between the odorant space and the OSNs. The resulting concentration-dependent spatio-temporal code determines the level of complexity of the input space driving olfactory processing in the downstream neuropils. Lastly, our model demonstrates that the currently available data for OSN responses only enables estimation of affinity value. This calls for new experiments for massively identifying the odorant-receptor dissociation rates of relevance to flies.

Functional identification is a key methodology for uncovering the logic of neuroinformation processing of brain circuits. For neural circuits modeling sensory systems as dynamical systems, the complexity of the identification algorithm largely depends on the number of stimuli used. Neurons in these circuits consist of dendritic stimulus processors modeling the signal processing in the dendritric tree and biological spike generators modeling the spiking mechanism at the axon hillock. Here, we review the identification of multi-sensory spatio-temporal dendritic stimulus processors that arise in the encoding of auditory scenes, color visual fields, and the mixing of auditory scenes and natural visual fields. We demonstrate the fundamental duality between the identification of the dendritic stimulus processor of a single neuron and the decoding of stimuli encoded by a population of neurons with a bank of dendritic stimulus processors. The duality enables us to reconstruct the originally encoded stimuli from all the generated spikes by using the identified neural circuit. The reconstruction leads to a simple and intuitive evaluation of the identified dendritic stimulus processors in the space of stimuli.

The fruit fly’s natural visual environment is often characterized by light intensities ranging across several orders of magnitude and by rapidly varying contrast across space and time. Fruit fly photoreceptors robustly transduce and, in conjunction with amacrine cells, process visual scenes and provide the resulting signal to downstream targets. Here, we model the first step of visual processing in the photoreceptor-amacrine cell layer. We propose a novel divisive normalization processor (DNP) for modeling the computation taking place in the photoreceptor-amacrine cell layer. The DNP explicitly models the photoreceptor feedforward and temporal feedback processing paths and the spatio-temporal feedback path of the amacrine cells. We then formally characterize the contrast gain control of the DNP and provide sparse identification algorithms that can efficiently identify each the feedforward and feedback DNP components. The algorithms presented here are the first demonstration of tractable and robust identification of the components of a divisive normalization processor. The sparse identification algorithms can be readily employed in experimental settings, and their effectiveness is demonstrated with several examples.

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.

In the past two decades, a substantial amount of work characterized the odorant receptors, neuroanatomy and odorant response properties of the early olfactory system of Drosophila melanogaster. Yet many odorant receptors remain only partially characterized and, the odorant transduction process and the axon hillock spiking mechanism of the olfactory sensory neurons (OSNs) have yet to be fully determined.Identity and concentration, two key aspects of olfactory coding, originate in the odorant transduction process. Detailed molecular models of the odorant transduction process are, however, scarce for fruit flies. To address these challenges we advance a comprehensive model of fruit fly OSNs as a cascade consisting of an odorant transduction process (OTP) and a biophysical spike generator (BSG). We model identity and concentration in OTP using an odorant-receptor binding rate tensor, modulated by the odorant concentration profile, and an odorant-receptor dissociation rate tensor, and quantitatively describe the ligand binding/dissociation process. We model the BSG as a Connor-Stevens point neuron.The resulting combinatorial encoding model of the Drosophila antenna provides a theoretical foundation for understanding the neural code of both odorant identity and odorant concentration and advances the state-of-the-art in a number of ways. First, it quantifies on the molecular level the combinatorial complexity of the transformation taking place in the antennae. The concentration-dependent combinatorial code determines the complexity of the input space driving olfactory processing in the downstream neuropils, such as odorant recognition and olfactory associative learning. Second, the model is biologically validated using multiple electrophysiology recordings. Third, the model demonstrates that the currently available data for odorant-receptor responses only enable the estimation of the affinity of the odorant-receptor pairs. The odorant-dissociation rate is only available for a few odorant-receptor pairs. Finally, our model calls for new experiments for massively identifying the odorant-receptor dissociation rates of relevance to flies.

We investigate the sparse functional identification of complex cells and the decoding of spatio-temporal visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm is formulated as a rank minimization problem that significantly reduces the number of sampling measurements (spikes) required for decoding. We also establish the duality between sparse decoding and functional identification and provide algorithms for identification of low-rank dendritic stimulus processors. The duality enables us to efficiently evaluate our functional identification algorithms by reconstructing novel stimuli in the input space. Finally, we demonstrate that our identification algorithms substantially outperform the generalized quadratic model, the nonlinear input model, and the widely used spike-triggered covariance algorithm. Electronic Supplementary Material The online version of this article (10.1186/s13408-017-0057-1) contains supplementary material.

SummaryRecently, multiple focused efforts have resulted in substantial increase in the availability of connectome data in the fruit fly brain. Elucidating neural circuit function from such structural data calls for a scalable computational modeling methodology. We propose such a methodology that includes i) a brain emulation engine, with an architecture that can tackle the complexity of whole brain modeling, ii) a database that supports tight integration of biological and modeling data along with support for domain specific queries and circuit transformations, and iii) a graphical interface that allows for total flexibility in configuring neural circuits and visualizing run-time results, both anchored on model abstractions closely reflecting biological structure. Towards the realization of such a methodology, we have developed NeuroGFX and integrated it into the architecture of the Fruit Fly Brain Observatory (http://fruitflybrain.org). The computational infrastructure in NeuroGFX is provided by Neurokernel, an open source platform for the emulation of the fruit fly brain, and NeuroArch, a database for querying and executing fruit fly brain circuits. The integration of the two enables the algorithmic construction/manipulation/revision of executable circuits on multiple levels of abstraction of the same model organism. The power of this computational infrastructure can be leveraged through an intuitive graphical interface that allows visualizing execution results in the context of biological structure. This provides an environment where computational researchers can present configurable, executable neural circuits, and experimental scientists can easily explore circuit structure and function ultimately leading to biological validation. With these capabilities, NeuroGFX enables the exploration of function from circuit structure at whole brain, neuropil, and local circuit level of abstraction. By allowing for independently developed models to be integrated at the architectural level, NeuroGFX provides an open plug and play, collaborative environment for whole brain computational modeling of the fruit fly.

SummaryNeuroNLP, 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.

SummaryThe 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.

The central complex (CX) is a set of neuropils in the center of the fly brain that have been implicated as playing an important role in vision-mediated behavior and integration of spatial information for locomotor control. In contrast to currently available data regarding the neural circuitry of neuropils in the fly's vision and olfactory systems, comparable data for the CX neuropils is relatively incomplete; many categories of neurons remain only partly characterized, and the synaptic connectivity between CX neurons has yet to be experimentally determined. Successful modeling of the information processing functions of the CX neuropils therefore requires a means of easily constructing and testing a range of hypotheses regarding both the high-level structure of their neural circuitry and the properties of their constituent neurons and synapses. This document demonstrates how NeuroArch and Neurokernel may be used to algorithmically construct and evaluate executable neural circuit models of the CX neuropils and their interconnects based upon currently available information regarding the geometry and polarity of the arborizations of identified local and projection neurons in the CX.

We have developed an open software platform called Neurokernel for collaborative development of comprehensive models of the brain of the fruit fly Drosophila melanogaster and their execution and testing on multiple Graphics Processing Units (GPUs). Neurokernel provides a programming model that capitalizes upon the structural organization of the fly brain into a fixed number of functional modules to distinguish between these modules' local information processing capabilities and the connectivity patterns that link them. By defining mandatory communication interfaces that specify how data is transmitted between models of each of these modules regardless of their internal design, Neurokernel explicitly enables multiple researchers to collaboratively model the fly's entire brain by integration of their independently developed models of its constituent processing units. We demonstrate the power of Neurokernel's model integration by combining independently developed models of the retina and lamina neuropils in the fly's visual system and by demonstrating their neuroinformation processing capability. We also illustrate Neurokernel's ability to take advantage of direct GPU-to-GPU data transfers with benchmarks that demonstrate scaling of Neurokernel's communication performance both over the number of interface ports exposed by an emulation's constituent modules and the total number of modules comprised by an emulation.

Previous research demonstrated thatglobalphase alone can be used to faithfully represent visual scenes. Here we provide a reconstruction algorithm by using onlylocalphase information. We also demonstrate that local phase alone can be effectively used to detect local motion. The local phase-based motion detector is akin to models employed to detect motion in biological vision, for example, the Reichardt detector. The local phase-based motion detection algorithm introduced here consists of two building blocks. The first building block measures/evaluates the temporal change of the local phase. The temporal derivative of the local phase is shown to exhibit the structure of a second order Volterra kernel with two normalized inputs. We provide an efficient, FFT-based algorithm for implementing the change of the local phase. The second processing building block implements the detector; it compares the maximum of the Radon transform of the local phase derivative with a chosen threshold. We demonstrate examples of applying the local phase-based motion detection algorithm on several video sequences. We also show how the locally detected motion can be used for segmenting moving objects in video scenes and compare our local phase-based algorithm to segmentation achieved with a widely used optic flow algorithm.

Information Theory started and, according to some, ended with Shannon’s seminal paper “A Mathematical Theory of Communication” (Shannon 1948). Because its significance and flexibility were quickly recognized, there were numerous attempts to apply it to diverse fields outside of its original scope. This prompted Shannon to write his famous essay “The Bandwagon” (Shannon 1956), warning against indiscriminate use of the new tool. Nevertheless, non-standard applications of Information Theory persisted. Very soon after Shannon’s initial publication (Shannon 1948), several manuscripts provided the foundations of much of the current use of information theory in neuroscience. MacKay and McCulloch (1952) applied the concept of information to propose limits of the transmission capacity of a nerve cell. This work foreshadowed future work on what can be termed “Neural Information Flow”—how much information moves through the nervous system, and the constraints that information theory imposes on the capabilities of neural systems for communication, computation and behavior. A second set of manuscripts, by Attneave (1954) and Barlow (1961), discussed information as a constraint on neural system structure and function, proposing that neural structure in sensory system is matched to statistical structure of the sensory environment, in a way to optimize information transmission. This is the main idea behind the “Structure from Information” line of research that is still very active today. A third thread, “Reliable Computation with Noisy/Faulty Elements”, started both in the information-theoretic community (Shannon and McCarthy 1956) and neuro-science (Winograd and Cowan 1963). With the advent of integrated circuits that were essentially faultless, interest began to wane. However, as IC technology continues to push towards smaller and faster computational elements (even at the expense of reliability), and as neuromorphic systems are developed with variability designed in (Merolla and Boahen 2006), this topic is gaining in popularity again in the electronics community, and neuroscientists again may have something to contribute to the discussion.

We present a general framework for the reconstruction of natural video scenes encoded with a population of spiking neural circuits with random thresholds. The natural scenes are modeled as space-time functions that belong to a space of trigonometric polynomials. The visual encoding system consists of a bank of filters, modeling the visual receptive fields, in cascade with a population of neural circuits, modeling encoding in the early visual system. The neuron models considered include integrate-and-fire neurons and ON–OFF neuron pairs with threshold-and-fire spiking mechanisms. All thresholds are assumed to be random. We demonstrate that neural spiking is akin to taking noisy measurements on the stimulus both for time-varying and space-time-varying stimuli. We formulate the reconstruction problem as the minimization of a suitable cost functional in a finite-dimensional vector space and provide an explicit algorithm for stimulus recovery. We also present a general solution using the theory of smoothing splines in Reproducing Kernel Hilbert Spaces. We provide examples of both synthetic video as well as for natural scenes and demonstrate that the quality of the reconstruction degrades gracefully as the threshold variability of the neurons increases.

The lack of a deeper understanding of how olfactory sensory neurons (OSNs) encode odors has hindered the progress in understanding the olfactory signal processing in higher brain centers. Here we employ methods of system identification to investigate the encoding of time-varying odor stimuli and their representation for further processing in the spike domain by Drosophila OSNs. In order to apply system identification techniques, we built a novel low-turbulence odor delivery system that allowed us to deliver airborne stimuli in a precise and reproducible fashion. The system provides a 1% tolerance in stimulus reproducibility and an exact control of odor concentration and concentration gradient on a millisecond time scale. Using this novel setup, we recorded and analyzed the in-vivo response of OSNs to a wide range of time-varying odor waveforms. We report for the first time that across trials the response of OR59b OSNs is very precise and reproducible. Further, we empirically show that the response of an OSN depends not only on the concentration, but also on the rate of change of the odor concentration. Moreover, we demonstrate that a two-dimensional (2D) Encoding Manifold in a concentration-concentration gradient space provides a quantitative description of the neuron's response. We then use the white noise system identification methodology to construct one-dimensional (1D) and two-dimensional (2D) Linear-Nonlinear-Poisson (LNP) cascade models of the sensory neuron for a fixed mean odor concentration and fixed contrast. We show that in terms of predicting the intensity rate of the spike train, the 2D LNP model performs on par with the 1D LNP model, with a root mean-square error (RMSE) increase of about 5 to 10%. Surprisingly, we find that for a fixed contrast of the white noise odor waveforms, the nonlinear block of each of the two models changes with the mean input concentration. The shape of the nonlinearities of both the 1D and the 2D LNP model appears to be, for a fixed mean of the odor waveform, independent of the stimulus contrast. This suggests that white noise system identification of Or59b OSNs only depends on the first moment of the odor concentration. Finally, by comparing the 2D Encoding Manifold and the 2D LNP model, we demonstrate that the OSN identification results depend on the particular type of the employed test odor waveforms. This suggests an adaptive neural encoding model for Or59b OSNs that changes its nonlinearity in response to the odor concentration waveforms.

The recovery of (weak) stimuli encoded with a population of Hodgkin-Huxley neurons is investigated. In the absence of a stimulus, the Hodgkin-Huxley neurons are assumed to be tonically spiking. The methodology employed calls for 1) finding an input-output (I/O) equivalent description of the Hodgkin-Huxley neuron and 2) devising a recovery algorithm for stimuli encoded with the I/O equivalent neuron(s). A Hodgkin-Huxley neuron with multiplicative coupling is I/O equivalent with an Integrate-and-Fire neuron with a variable threshold sequence. For bandlimited stimuli a perfect recovery of the stimulus can be achieved provided that a Nyquist-type rate condition is satisfied. A Hodgkin-Huxley neuron with additive coupling and deterministic conductances is first-order I/O equivalent with a Project-Integrate-and-Fire neuron that integrates a projection of the stimulus on the phase response curve. The stimulus recovery is formulated as a spline interpolation problem in the space of finite length bounded energy signals. A Hodgkin-Huxley neuron with additive coupling and stochastic conductances is shown to be first-order I/O equivalent with a Project-Integrate-and-Fire neuron with random thresholds. For stimuli modeled as elements of Sobolev spaces the reconstruction algorithm minimizes a regularized quadratic optimality criterion. Finally, all previous recovery results of stimuli encoded with Hodgkin-Huxley neurons with multiplicative and additive coupling, and deterministic and stochastic conductances are extended to stimuli encoded with a population of Hodgkin-Huxley neurons.

We consider a formal model of stimulus encoding with a circuit consisting of a bank of filters and an ensemble of integrate-and-fire neurons. Such models arise in olfactory systems, vision, and hearing. We demonstrate that bandlimited stimuli can be faithfully represented with spike trains generated by the ensemble of neurons. We provide a stimulus reconstruction scheme based on the spike times of the ensemble of neurons and derive conditions for perfect recovery. The key result calls for the spike density of the neural population to be above the Nyquist rate. We also show that recovery is perfect if the number of neurons in the population is larger than a threshold value. Increasing the number of neurons to achieve a faithful representation of the sensory world is consistent with basic neurobiological thought. Finally we demonstrate that in general, the problem of faithful recovery of stimuli from the spike train of single neurons is ill posed. The stimulus can be recovered, however, from the information contained in the spike train of a population of neurons.

We investigate a class of finite-dimensional time decoding algorithms that: (1) is insensitive with respect to the time-encoding parameters; (2) is highly efficient and stable; and (3) can be implemented in real time. These algorithms are based on the observation that the recovery of time encoded signals given a finite number of observations has the property that the quality of signal recovery is very high in a reduced time range. We show how to obtain a local representation of the time encoded signal in an efficient and stable manner using a Vandermonde formulation of the recovery algorithm. Once the signal values are obtained from a finite number of possibly overlapping observations, the reduced-range segments are stitched together. The signal obtained by segment stitching is subsequently filtered for improved performance in recovery. Finally, we evaluate the complexity of the algorithms and their computational requirements for real-time implementation.

We introduce a novel class of time encoding machines (TEMs) that exhibit multiplicative coupling, and, feedforward and feedback. We show that a machine with multiplicative coupling is I/O equivalent with an integrate-and-fire neuron with a variable threshold sequence. The same result holds for a TEM with feedforward while a machine with feedback is I/O equivalent with an asynchronous sigma/delta modulator with variable thresholds. For all TEMs, an input band-limited signal can be perfectly recovered from the zero crossings of the modulated signal and the threshold sequence. We present the optimal decoding algorithm and give conditions for perfect signal recovery

We describe a simple model of spike processing build with a number of neural hardware primitives including integrate-and-fire neurons, dendritic trees, integrators, inhibition logic and one-to-many axonal/dendritic tree connectivity. Functionally, our model consists of neuro-modulators, communication channels, neuro-demodulators and filters. Integrate-and-fire neurons play the role of neuro-modulators. They represent dendritic currents in the spike domain through a process of reversible computation. Neuro-demodulation and irreversible computation takes place in dendritic trees as time domain linear and/or non-linear operations. Assuming that the stimulus at the input of an integrate-and-fire sensory neuron is bandlimited, we demonstrate how to construct a linear operator that maps an arbitrary stimulus into a desired neuronal signal.

A time encoding machine is a real-time asynchronous mechanism for encoding amplitude information into a time sequence. We investigate the operating characteristics of a machine consisting of a feedback loop containing an adder, a linear filter, and a noninverting Schmitt trigger. We show that the amplitude information of a bandlimited signal can be perfectly recovered if the difference between any two consecutive values of the time sequence is bounded by the inverse of the Nyquist rate. We also show how to build a nonlinear inverse time decoding machine (TDM) that perfectly recovers the amplitude information from the time sequence. We demonstrate the close relationship between the recovery algorithms for time encoding and irregular sampling. We also show the close relationship between time encoding and a number of nonlinear modulation schemes including FM and asynchronous sigma-delta modulation. We analyze the sensitivity of the time encoding recovery algorithm and demonstrate how to construct a TDM that perfectly recovers the amplitude information from the time sequence and is trigger parameter insensitive. We derive bounds on the error in signal recovery introduced by the quantization of the time sequence. We compare these with the recovery error introduced by the quantization of the amplitude of the bandlimited signal when irregular sampling is employed. Under Nyquist-type rate conditions, quantization of a bandlimited signal in the time and amplitude domains are shown to be largely equivalent methods of information representation.

We present algorithms for identifying multidimensional receptive fields directly from spike trains produced by biophysically-grounded neuron models. We demonstrate that only the projection of a receptive field onto the input stimulus space may be perfectly identified and derive conditions under which this identification is possible.We also provide detailed examples of identification of neural circuits incorporating spatiotemporal and spectrotemporal receptive fields.

We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a nonlinear dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The nonlinear dendritic processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

A rich set of genetic tools and extensive anatomical data make the olfactory system of the fruit fly a neural circuit of choice for studying function in sensory systems. Though a substantial amount of work has been published on the neural coding of olfactory sensory neurons (OSNs) of the fruit fly, yet little is known how projection neurons (PNs) encode time-varying odor stimuli [1]. Here we address this question with in vivo experiments coupled with a phenomenological characterization of the spiking activity of PNs. Recently, a new class of identification algorithms called Channel Identification Machines (CIMs) [2] was proposed for identifying dendritic processing in simple neural circuits using conditional phase response curves (cPRCs) [3]. By combining cPRCs with the reduced project-integrated-andfire neuron (PIF) model [4], the CIM algorithms identify a complete phenomenological description of spike generation of a biological neuron for weak to moderately strong stimuli. Moreover, the identification method employed does not require white noise stimuli nor an infinitesimal pulse injection protocol as widely used in the past [5]. Here we identify the PNs both in silico and in vivo. Starting with simulations, we investigate the feasibility of the CIM method on PNs modeled as pseudo uni-polar neurons in silico, as shown in Figures 1.(B) and 1.(C). We then systematically convert the CIM method into a stepby-step experimental protocol, and carry it out in vivo by injecting currents into PNs using the patch clamping technique [6,7]. A snapshot of PN patching is depicted in Figure 1.(A).

Consider an aggregate arrival process A N obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, A N approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period. Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process A t ∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable Q t P observed at the beginning of the arrival process activity periods where ρ = 𝔼A t ∞ < c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation. In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate 𝔼e t . This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value 𝔼e t .

The exponential growth of computer networking demands massive upgrades in the capacity of existing networks. Traditional capacity design methodologies, developed with the single-class networking paradigm in mind, overlook the non-cooperative structure of modern networks. Consequently, such design approaches entail the danger of degraded performance when resources are added to a network, a phenomenon known as the Braess paradox. The present paper proposes methods for adding resources efficiently to a non-cooperative network of general topology. It is shown that the paradox is avoided when resources are added across the network, rather than on a local scale, and when upgrades are focused on direct connections between the sources and destinations. The relevance of these results for modern networks is demonstrated.

ATM switching platforms are well suited for transporting multimedia streams with quality-of-service (QOS) requirements. This paper describes the system design of a high performance connection management system for xbind, a flexible open programmable signaling system for ATM switching platforms. The latency and throughput of call processing is improved by caching, message aggregation, and processing of requests in parallel. Using a set of general purpose UNIX work stations, we are able to attain a maximum throughput of close to 600000 call operations/h (setup and delete) with an average call setup time of 85 ms. With a low traffic load of 3600 call operations/h, an average call setup latency of 11 ms can be obtained. The system is adaptive. By adjusting various control parameters, the connection manager(s) can be dynamically configured to trade off between throughput and call setup time.

Let {(X n ,J n )} be a stationary Markov-modulated random walk on ℝ x E (E is finite), defined by its probability transition matrix measure F = {F ij }, F ij (B) = ℙ[X 1 ∈ B, J 1 = j | J 0 = i], B ∈ B (ℝ), i, j ∈ E. If F ij ([x,∞))/(1-H(x)) → W ij ∈ [0,∞), as x → ∞, for some long-tailed distribution function H, then the ascending ladder heights matrix distribution G +(x) (right Wiener-Hopf factor) has long-tailed asymptotics. If 𝔼X n < 0, at least one W ij > 0, and H(x) is a subexponential distribution function, then the asymptotic behavior of the supremum of this random walk is the same as in the i.i.d. case, and it is given by ℙ[sup n≥0 S n > x] → (−𝔼X n )−1 ∫ x ∞ ℙ[X n > u]du as x → ∞, where S n = ∑1 n X k , S 0 = 0. Two general queueing applications of this result are given. First, if the same asymptotic conditions are imposed on a Markov-modulated G/G/1 queue, then the waiting time distribution has the same asymptotics as the waiting time distribution of a GI/GI/1 queue, i.e., it is given by the integrated tail of the service time distribution function divided by the negative drift of the queue increment process. Second, the autocorrelation function of a class of processes constructed by embedding a Markov chain into a subexponential renewal process, has a subexponential tail. When a fluid flow queue is fed by these processes, the queue-length distribution is asymptotically proportional to its autocorrelation function.

This article discusses the need for standard software interfaces for programming of networks, specifically for service and signaling control, through programming interfaces. The objective is to enable the development of open signaling, control, and management applications as well as higher-level multimedia services on networks. The scope of this effort includes ATM switches, circuit switches, IP routers, and hybrid switches such as those that provide for fast switching of IP packets over an ATM backbone. The basic ideas represented herein are in the process of development as a standard for application programming interfaces for networks under IEEE Standards Project IEEE P1520.

MPEG-4 is an emerging international standard based on the encoding of audiovisual data using object description techniques. This novel approach to encoding allows MPEG-4-based multimedia applications to dynamically compose complex scenes from one or more elementary stream objects. These stream objects are carried within potentially hundreds of channels. As a result, the underlying transport system must support the rapid creation and release of such channels with QoS guarantees. In addition to defining the format, structure and rules of composition of these objects, MPEG-4 also specifies a general application and transport delivery framework called the delivery multimedia integration framework (DMIF). DMIF's main purpose is to hide the details of the transport network from the user, as well as to ensure signaling and transport interoperability between end-systems. We describe the first reference implementation of the MPEG-4 DMIF standard for the ISO, including a full specification of the DMIF application interface. The DAI offers the required functionality for realizing multimedia applications without any concerns regarding the selected communication protocol. The realization of DMIF is greatly facilitated by xbind, a broadband kernel that provides connection management, routing, QoS mapping, and intelligent selection of suitable transport protocol stacks. The resulting system, called XDMIF, supports different QoS requirements, and the rapid creation and release of numerous transport channels, along with efficient management of network resources.

The capacity allocation problem in a network that is to be shared by noncooperative users is considered. Each user decides independently upon its routing strategy so as to optimize its individual performance objective. The operating points of the network are the Nash equilibria of the underlying routing game,. The network designer aims to allocate link capacities, so that the resulting Nash equilibria are efficient, according to some systemwide performance criterion. In general, the solution of such design problems is complex and at times counterintuitive, since adding link capacity might lead to degradation of user performance. For systems of parallel links, we show that such paradoxes do not occur and that the capacity allocation problem has a simple and intuitive optimal solution that coincides with the solution in the single-user case.

Recent advances in distributed systems and transportable software and increasing demand for better quality of service (QoS) control in multiservice networks are driving a reexamination of network software architectures. We established the Comet (Control, Management, and Telemedia) Group at Columbia University's Center for Telecommunications Research to provide comprehensive understanding of network software architecture for the 1990s and beyond. This research focuses on developing new network architectures that support service creation, QoS control, and the joint allocation of computing and communications resources. This provides an opportunity to reconcile the perspectives of the computing and communication communities. Future multiservice (multimedia) networks will carry traffic such as video, audio, and computer data with diverse QoS requirements. Such networks will thus require that we develop ways to manage many physical and logical entities, services, and users.

The move toward market deregulation and open competition has sparked a wave of serious introspection in the telecommunications service industry. Telecom providers and operators are now required to open up their primary revenue channels to competing industries. The competition for product differentiation increasingly depends on the level of sophistication, degree of flexibility, and speed of deployment of services that a future provider can offer. These factors in turn depend heavily on the flexibility of the software architecture in place in a provider's operational infrastructure. Within this context, we examine the service architecture of two major global communication networks-the telephone network and the Internet and explore their weaknesses and strengths. We discuss the realization of an open programmable networking environment based on a new service architecture for advanced telecommunication services that overcomes the limitations of the existing networks. Our approach to network programmability stems from two angles-one conceptual, the other implementational. In the first, we attempt to develop a service model that is open and reflects the economic market structure of the future telecommunications service industry. Furthermore, we introduce an extended reference model for realizing the service marketplace and present it as a vehicle for creating multimedia services with QoS guarantees. In the second, we investigate the feasibility of engineering the reference model from an implementation standpoint. We describe a realization of the open programmable networking environment as a broadband kernel. Called xbind, the broadband kernel incorporates IP and CORBA technologies for signaling, management, and service creation, and ATM for transport. We also address some of the important QoS, performance, scalability, and implementation issues.