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.

Cambodia's orphan dance shows: From cultural salvation to child exploitation?

In Cambodia, orphan dance shows were once popular as a way to preserve endangered art forms and to cultivate children's dignity and well-being. But they came to be seen as exploitative instead, and today are nearly nonexistent. This article examines the confluence of changes that caused this reversal of opinion. The reversal is due to both covert factors such as changes in constructions of childhood, and overt factors such as changes in audience composition. The rise and fall of Cambodian orphan dance shows took place largely within foreign communities, with little local input.

Input-specific control of interneuron numbers in nascent striatal networks

The assembly of functional neuronal circuits requires appropriate numbers of distinct classes of neurons, but the mechanisms through which their relative proportions are established remain poorly defined. Investigating the mouse striatum, here we found that the two most prominent subtypes of striatal interneurons, parvalbumin-expressing (PV+) GABAergic and cholinergic (ChAT+) interneurons, undergo extensive programmed cell death between the first and second postnatal weeks. Remarkably, the survival of PV+ and ChAT+ interneurons is regulated by distinct mechanisms mediated by their specific afferent connectivity. While long-range cortical inputs control PV+ interneuron survival, ChAT+ interneuron survival is regulated by local input from the medium spiny neurons. Our results identify input-specific circuit mechanisms that operate during the period of programmed cell death to establish the final number of interneurons in nascent striatal networks.

Input to layer 1 of somatosensory cortex: Local input outweighs long-range and can modulate the activity of layer 1 interneurons

Neocortical layer (L) 1 is a locus for interactions between long-range inputs, L1 interneurons and apical tuft dendrites of pyramidal neurons. Even though we have a wealth of information about L1, the level and effect of local input to this layer have not been quantified. Here we characterized the input to L1 of mouse somatosensory cortex with fast blue, monosynaptic rabies and optogenetics. Our work shows that most of the input to L1 is local, and that both local and long-range inputs to this layer arise predominantly from L2/3 and L5 neurons. Subtypes of L5 and L6b neurons project to the overlying L1 with different probabilities. VIP and SST interneurons in L2/3 and L5 also innervate L1. A subset of local L5, the intratelencephalic, pyramidal neurons, drive L1 interneurons but have no effect on L5 apical tuft dendrites. Monosynaptic rabies-based retrograde labelling reveals presynaptic boutons covering the entire somato-dendritic axis of pyramidal neurons, including in L1. When fast blue application was combined with rabies virus, we found that only a fraction of local and long-range neurons was both presynaptic to L5 neurons and projected to L1. These results demonstrate that L1 receives a large proportion of its input from local neurons, and that some of these inputs specifically target interneurons. We conclude that L1 is not just a site for interaction between long-range feedback and apical tuft dendrites of pyramidal cells, it is also a site for complex modulation of pyramidal neurons and interneurons by local inputs.

Cascades of Periodic Solutions in a Neural Circuit With Delays and Slow-Fast Dynamics

We analyse periodic solutions in a system of four delayed differential equations forced by periodic inputs representing two competing neural populations connected with fast mutual excitation and slow delayed inhibition. The combination of mechanisms generates a rich dynamical structure that we are able to characterize using slow-fast dissection and a binary classification of states. We previously proved the existence conditions of all possible states 1:1 locked to the inputs and applied this analysis to the tracking of the rhythms perceived when listening to alternating sequences of low and high tones. Here we extend this analysis using analytical and computational tools by proving the existence a set of n:1 periodically locked states and their location in parameter space. Firstly we examine cycle skipping states and find that they accumulate in an infinite cascade of period-incrementing bifurcations with increasing periods for decreasing values of the local input strength. Secondly we analyse periodic solutions that alternate between 1:1 locked states that repeat after an integer multiple of the input period (swapping states). We show that such states accumulate in similar bifurcation cascades with decreasing values of the lateral input strength. We report a parameter-dependent scaling constant for the ratio of widths of successive regions in the cascades, which generalises across cycle skipping and swapping states. The periodic states reported here - emergent behaviours in the model - can be linked to known phenomena in auditory perception that are beyond the original scope of the model’s design.

Harnessing Local Input for Job Creation-the Need for Collaboration Between the Academia and Industry; A Case Study of Carnegie African Diaspora Fellowship Program

This paper is an attempt to design a practical model of mutually-beneficial collaboration between the academia and industry for training and graduate mentoring. This ideal collaboration is modeled for efficacy and sustainability. This paper seeks to bring to the fore, an ideal collaborative framework whereby sustainability is the key. The paper will identify several key factors and prescribe pragmatic processes for achieving an ideal mutually-beneficial collaboration for graduate mentoring, training and skill acquisition. More so, the paper will identify and prescribe the kind and level of expertise, qualification for personnel and the necessary facility needed for such trainings. Funding has been identified as one the key factors militating against the success of any collaboration. The paper will address the process of attracting funding as well as managing such funds. Areas of funding and potential collaborators will be identified. Organizational expertise is critical to the success of any ideal collaboration. The paper will match desired expertise with potential corporations as well as institutions capable of incubating such expertise and technology.

Correction to: A local input-to-state stability result w.r.t. attractors of nonlinear reaction–diffusion equations

The article “A local input-to-state stability result w.r.t. attractors of nonlinear reaction–diffusion equations” written by Sergey Dashkovskiy, Oleksiy Kapustyan, and Jochen Schmid, was originally published online on 6 May 2020, without Open Access.

Non-canonical role for Lpar1-EGFP subplate neurons in early postnatal mouse somatosensory cortex

Subplate neurons (SPNs) are thought to play a role in nascent sensory processing in neocortex. To better understand how heterogeneity within this population relates to emergent function, we investigated the synaptic connectivity of Lpar1-EGFP SPNs through the first postnatal week in whisker somatosensory cortex (S1BF). These SPNs comprise of two morphological subtypes: fusiform SPNs with local axons, and pyramidal SPNs with axons that extend through the marginal zone. The former receive translaminar synaptic input up until the emergence of the whisker barrels; a timepoint coincident with significant cell death. In contrast, pyramidal SPNs receive local input from the subplate at early ages but then – during the later time window, acquire input from overlying cortex. Combined electrical and optogenetic activation of thalamic afferents identified that Lpar1-EGFP SPNs receive sparse thalamic innervation. These data reveal components of the postnatal network that interpret sparse thalamic input to direct the emergent columnar structure of S1BF.