A dual number abstraction for static analysis of Clarke Jacobians

We present a novel abstraction for bounding the Clarke Jacobian of a Lipschitz continuous, but not necessarily differentiable function over a local input region. To do so, we leverage a novel abstract domain built upon dual numbers, adapted to soundly over-approximate all first derivatives needed to compute the Clarke Jacobian. We formally prove that our novel forward-mode dual interval evaluation produces a sound, interval domain-based over-approximation of the true Clarke Jacobian for a given input region. Due to the generality of our formalism, we can compute and analyze interval Clarke Jacobians for a broader class of functions than previous works supported – specifically, arbitrary compositions of neural networks with Lipschitz, but non-differentiable perturbations. We implement our technique in a tool called DeepJ and evaluate it on multiple deep neural networks and non-differentiable input perturbations to showcase both the generality and scalability of our analysis. Concretely, we can obtain interval Clarke Jacobians to analyze Lipschitz robustness and local optimization landscapes of both fully-connected and convolutional neural networks for rotational, contrast variation, and haze perturbations, as well as their compositions.

BDNF-induced BDNF release mediates presynaptic LTP and is regulated by cannabinoids

Although brain-derived neurotrophic factor (BDNF) and its effector, Tropomyosin receptor kinase B (TrkB), are implicated in activity-dependent synaptic plasticity, the precise underlying mechanisms remain unclear. In the dentate gyrus, a hippocampal input region that expresses uniquely high levels of BDNF, repetitive activation of mossy cells (MCs) induces a presynaptic, BDNF/TrkB-dependent form of LTP at MC to granule cell (GC) synapses. Here, we report that activity-induced BDNF release from MC axons in mice elicits postsynaptic BDNF release in a TrkB- and calcium-dependent manner, and that BDNF-induced BDNF release is essential for LTP induction. Suppression of BDNF release by tonic and phasic activity of presynaptic type-1 cannabinoid receptors dampened LTP, revealing an unprecedented role of these receptors in controlling neuropeptide release. Lastly, BDNF-mediated MC-GC LTP can be elicited in vivo. Thus, BDNF-induced BDNF release emerges as a mechanism for activity-dependent LTP that may contribute to dentate gyrus-dependent learning, epilepsy, and neuropsychiatric disorders.

Flexible encoding of objects and space in single cells of the dentate gyrus

The hippocampus is involved in the formation of memories that require associations among stimuli to construct representations of space and the items and events within that space. Neurons in the dentate gyrus (DG), an initial input region of the hippocampus, have robust spatial tuning, but it is unclear how nonspatial information may be integrated with spatially modulated firing at this stage. We recorded from the DG of 21 adult mice as they foraged for food in an environment that contained discrete objects. By classifying recorded DG cells into putative granule cells and mossy cells, we examined how the addition or displacement of objects affected the spatial firing of these DG cell types. We found DG cells with multiple firing fields at a fixed distance and direction from objects (landmark vector cells) as well as cells that exhibited localized changes in spatial firing when objects in the environment were manipulated. When mice were exposed to a second environment with the same objects, DG spatial maps were completely reorganized, suggesting standard global remapping, and a largely different subset of cells responded to object manipulations. Together, these data reveal the capacity of DG cells to detect small changes in the environment, while preserving a stable spatial representation of the overall context.

Ultrastructural distribution of presynaptic active zones and dense core vesicles in olfactory projection neurons of Drosophila

In Drosophila melanogaster, olfactory projection neurons (PNs) convey odor information from peripheral olfactory center, antenna lobe, to central olfactory center, mushroom body (MB), and lateral horn (LH). In MB, the mechanisms underlining the transformation from coarse-coding PNs to sparse-coding MB intrinsic Kenyon cells (KCs) remain an open question. Here, we used HRP-labeled electron microscopy (EM) to volume reconstruct 89 PN axonal boutons in a reference area of the input region, the calyx of MB. The results showed that the number of presynaptic active zones (PAZs), neurotransmitter release site, is in positive linear correlation with the surface area of PN axonal boutons, while the number of dense core vesicles (DCVs), vesicles that containing neuropeptides, monoamines, or neurotrophic factors, is weakly related to the morphology of PN axonal boutons. Further analysis illustrated that DCVs preferentially exist in PN axonal boutons labeled by GH146-GAL4, a most widely used genetic marker for studying olfactory PNs. Our data suggest that synapses are uniformly distributed on the surface of all PN boutons, thus the neurotransmission capability of a PN axonal bouton could be predicted by its size, and PN subtypes release neuropeptides, monoamines, or neurotrophic factors, as well as classical neurotransmitters, to mediate the PN-KC transformation.

Hybrid LLC Converter with Wide Range of Zero-Voltage Switching and Wide Input Voltage Operation

A new hybrid inductor-inductor-capacitor (LLC) converter is investigated to have wide voltage input operation capability and zero-voltage turn-on characteristics. The presented circuit topology can be applied for consumer power units without power factor correction or with long hold-up time requirement, photovoltaic energy conversion and renewable energy power transfer. To overcome the weakness of narrow voltage gain of resonant converter, the hybrid LLC converter with different turns ratio of transformer is presented and the experimental investigation is provided to achieve wide voltage input capability (400 V–50 V). On the input-side, the converter can operate as full bridge resonant circuit or half bridge resonant circuit with input split capacitors for high or low voltage input region. On the output-side, the less or more winding turns is selected to overcome wide voltage input operation. According to the circuit structures and transformer turns ratio, the single stage LLC converter with wide voltage input operation capability (400 V–50 V) is accomplished. The laboratory prototype has been developed and the experimental waveforms are measured and demonstrated to investigate the effectiveness of the presented hybrid LLC converter.

Analysis of Synaptic Microcircuits in the Mushroom Bodies of the Honeybee

Mushroom bodies (MBs) are multisensory integration centers in the insect brain involved in learning and memory formation. In the honeybee, the main sensory input region (calyx) of MBs is comparatively large and receives input from mainly olfactory and visual senses, but also from gustatory/tactile modalities. Behavioral plasticity following differential brood care, changes in sensory exposure or the formation of associative long-term memory (LTM) was shown to be associated with structural plasticity in synaptic microcircuits (microglomeruli) within olfactory and visual compartments of the MB calyx. In the same line, physiological studies have demonstrated that MB-calyx microcircuits change response properties after associative learning. The aim of this review is to provide an update and synthesis of recent research on the plasticity of microcircuits in the MB calyx of the honeybee, specifically looking at the synaptic connectivity between sensory projection neurons (PNs) and MB intrinsic neurons (Kenyon cells). We focus on the honeybee as a favorable experimental insect for studying neuronal mechanisms underlying complex social behavior, but also compare it with other insect species for certain aspects. This review concludes by highlighting open questions and promising routes for future research aimed at understanding the causal relationships between neuronal and behavioral plasticity in this charismatic social insect.

The hippocampus as a perceptual map: neuronal and behavioral discrimination during memory encoding

The hippocampus is thought to encode similar events as distinct memory representations that are used for behavioral decisions. Where and how this “pattern separation” function is accomplished in the hippocampal circuit, and how it relates to behavior, is still unclear. Here we perform in vivo 2-photon Ca2+ imaging from hippocampal subregions of head-fixed mice performing a virtual-reality spatial discrimination task. We find that population activity in the input region of the hippocampus, the dentate gyrus, robustly discriminates small changes in environments, whereas spatial discrimination in CA1 reflects the behavioral performance of the animals and depends on the degree of differences between environments. Our results demonstrate that the dentate gyrus amplifies small differences in its inputs, while downstream hippocampal circuits will act as the final arbiter on this decorrelated information, thereby producing a “perceptual map” that will guide behaviour.

Soma-axon coupling configurations that enhance neuronal coincidence detection

Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the “input” region (soma and dendrite) and the spike-generating “output” region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on the interaction between coupling configuration and two currents that provide dynamic, voltage-gated, negative feedback in subthreshold voltage range: sodium current with rapid inactivation and low-threshold potassium current, IKLT. These currents reduce synaptic summation and can prevent spike generation unless inputs arrive with near simultaneity. We show that strong soma-to-axon coupling promotes the negative feedback effects of sodium inactivation and is, therefore, advantageous for coincidence detection. Furthermore, the “feedforward” combination of strong soma-to-axon coupling and weak axon-to-soma coupling enables spikes to be generated efficiently (few sodium channels needed) and with rapid recovery that enhances high-frequency coincidence detection. These observations detail the functional benefit of the strongly feedforward configuration that has been observed in physiological studies of MSO neurons. We find that IKLT further enhances coincidence detection sensitivity, but with effects that depend on coupling configuration. For instance, in weakly-coupled models, IKLT in the spike-generator compartment enhances coincidence detection more effectively than IKLT in the input compartment. By using a minimal model of soma-to-axon coupling, we connect structure, dynamics, and computation. Here, we consider the particular case of MSO coincidence detectors. In principle, our method for creating and exploring a parameter space of two-compartment models can be applied to other neurons.Author summaryBrain cells (neurons) are spatially extended structures. The locations at which neurons receive inputs and generate outputs are often distinct. We formulate and study a minimal mathematical model that describes the dynamical coupling between the input and output regions of a neuron. We construct our model to reflect known properties of neurons in the auditory brainstem that play an important role in our ability to locate sound sources. These neurons are known as “coincidence detectors” because they are most likely to respond when they receive simultaneous inputs. We use simulations to explore coincidence detection sensitivity throughout the parameter space of input-output coupling and to identify the coupling configurations that are best for neural coincidence detection. We find that strong forward coupling (from input region to output region), enhances coincidence detection sensitivity in our model and that low-threshold potassium current further improves coincidence detection. Our study is significant in that we detail how cell structure affects neuronal dynamics and, consequently, the ability of neurons to perform as temporally-precise coincidence detectors.

Octopaminergic neurons have multiple targets in Drosophila larval mushroom body calyx and regulate behavioral odor discrimination

Discrimination of sensory signals is essential for an organism to form and retrieve memories of relevance in a given behavioural context. Sensory representations are modified dynamically by changes in behavioral state, facilitating context-dependent selection of behavior, through signals carried by noradrenergic input in mammals, or octopamine (OA) in insects. To understand the circuit mechanisms of this signaling, we characterized the function of two OA neurons, sVUM1 neurons, that originate in the subesophageal zone (SEZ) and target the input region of the memory center, the mushroom body (MB) calyx, in larval Drosophila. We find that sVUM1 neurons target multiple neurons, including olfactory projection neurons (PNs), the inhibitory neuron APL, and a pair of extrinsic output neurons, but relatively few mushroom body intrinsic neurons, Kenyon cells. PN terminals carried the OA receptor Oamb, a Drosophila α1-adrenergic receptor ortholog. Using an odor discrimination learning paradigm, we showed that optogenetic activation of OA neurons compromised discrimination of similar odors but not learning ability. Our results suggest that sVUM1 neurons modify odor representations via multiple extrinsic inputs at the sensory input area to the MB olfactory learning circuit.

Density of mushroom body synaptic complexes limits intraspecies brain miniaturization in highly polymorphic leaf-cutting ant workers

Hymenoptera possess voluminous mushroom bodies (MBs), brain centres associated with sensory integration, learning and memory. The mushroom body input region (calyx) is organized in distinct synaptic complexes (microglomeruli, MG) that can be quantified to analyse body size-related phenotypic plasticity of synaptic microcircuits in these small brains. Leaf-cutting ant workers ( Atta vollenweideri ) exhibit an enormous size polymorphism, which makes them outstanding to investigate neuronal adaptations underlying division of labour and brain miniaturization. We particularly asked how size-related division of labour in polymorphic workers is reflected in volume and total numbers of MG in olfactory calyx subregions. Whole brains of mini, media and large workers were immunolabelled with anti-synapsin antibodies, and mushroom body volumes as well as densities and absolute numbers of MG were determined by confocal imaging and three-dimensional analyses. The total brain volume and absolute volumes of olfactory mushroom body subdivisions were positively correlated with head widths, but mini workers had significantly larger MB to total brain ratios. Interestingly, the density of olfactory MG was remarkably independent from worker size. Consequently, absolute numbers of olfactory MG still were approximately three times higher in large compared with mini workers. The results show that the maximum packing density of synaptic microcircuits may represent a species-specific limit to brain miniaturization.