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We investigated the neural representation of locomotion in the nematode C. elegans by recording population calcium activity during movement. We report that population activity more accurately decodes locomotion than any single neuron. Relevant signals are distributed across neurons with diverse tunings to locomotion. Two largely distinct subpopulations are informative for decoding velocity and curvature, and different neurons’ activities contribute features relevant for different aspects of a behavior or different instances of a behavioral motif. To validate our measurements, we labeled neurons AVAL and AVAR and found that their activity exhibited expected transients during backward locomotion. Finally, we compared population activity during movement and immobilization. Immobilization alters the correlation structure of neural activity and its dynamics. Some neurons positively correlated with AVA during movement become negatively correlated during immobilization and vice versa. This work provides needed experimental measurements that inform and constrain ongoing efforts to understand population dynamics underlying locomotion in C. elegans.

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We present an automated method to track and identify neurons in C. elegans, called 'fast Deep Neural Correspondence' or fDNC, based on the transformer network architecture. The model is trained once on empirically derived semi-synthetic data and then predicts neural correspondence across held-out real animals. The same pre-trained model both tracks neurons across time and identifies corresponding neurons across individuals. Performance is evaluated against hand-annotated datasets, including NeuroPAL [1]. Using only position information, the method achieves 79.1% accuracy at tracking neurons within an individual and 64.1% accuracy at identifying neurons across individuals. Accuracy at identifying neurons across individuals is even higher (78.2%) when the model is applied to a dataset published by another group [2]. Accuracy reaches 74.7% on our dataset when using color information from NeuroPAL. Unlike previous methods, fDNC does not require straightening or transforming the animal into a canonical coordinate system. The method is fast and predicts correspondence in 10ms making it suitable for future real-time applications.

Keywords:Fractional Laplacian Gagliardo-Nirenberg inequality Sobolev inequality Logarithmic Sobolev inequality Hardy inequality a b s t r a c tIn this paper, we establish the Gagliardo-Nirenberg inequality under Lorentz norms for fractional Laplacian. Based on special cases of this inequality under Lebesgue norms, we prove the L p -logarithmic Gagliardo-Nirenberg and Sobolev inequalities. Motivated by the L 2 -logarithmic Sobolev inequality, we obtain a fractional logarithmic Sobolev trace inequality in terms of the restriction τ k u of u from R n to R n−k . Finally, we prove the fractional Hardy inequality under Lorentz norms.

In many industrial plants, multiple, interconnected control loops are common. Their maintenance and improvement requires detailed controller performance assessment to determine not only whether they are behaving well, but also to determine the potential cause of any observed problems. Techniques for performance assessment can be divided into two broad categories (1) performance assessment of regulatory control loops; and (2) performance assessment of supervisory control loops that evaluate the economic performance of advanced control strategies, such as model predictive control (MPC). A comprehensive review of the literature on the industrial applications of performance assessment, as well as some of the currently available software, is also presented. © 2011 Canadian Society for Chemical Engineering

This paper investigates the channel estimations in a relay network with multiple transmit and receive antennas, including the estimation of the end-to-end channel matrix and the individual estimation of the transmitter-relay channels and the relay-receiver channels. For the end-to-end channel estimation, instead of directly estimating entries of the channel matrix, we use singular value decomposition (SVD) and estimate its largest singular value and singular vectors, which are then combined to form an estimation of the channel matrix. An approximate maximum-likelihood (ML) estimation is proposed, which is shown to become the exact ML estimation when the time duration of each training step equals the number of antennas at the transmitter. Simulation on the mean square error (MSE) shows that the SVD-based approximate ML estimation performs about the same as the exact ML estimation and is superior to entry-based estimations. For the individual channel estimation, we decompose each channel vector into the product of its length and direction, and find the ML estimation of each. By using an approximation on the probability density function (PDF) of the observations during training, an analytical ML estimation is derived. The ML estimation with the exact PDF is also investigated and a solution is obtained numerically. Simulation on the MSE shows that the two have similar performance. Compared with cascade channel estimations, its performance is superior for the relay-receiver channel estimation and comparable for the transmitter-relay channel estimation. Extension to the general multiple-antenna multiple-relay network is also provided.