ManifoldNet: A Deep Neural Network for Manifold-Valued Data With Applications.

Geometric deep learning is a relatively nascent field that has attracted significant attention in the past few years. This is partly due to the availability of data acquired from non-euclidean domains or features extracted from euclidean-space data that reside on smooth manifolds. For instance, pose data commonly encountered in computer vision reside in Lie groups, while covariance matrices that are ubiquitous in many fields and diffusion tensors encountered in medical imaging domain reside on the manifold of symmetric positive definite matrices. Much of this data is naturally represented as a grid of manifold-valued data. In this paper we present a novel theoretical framework for developing deep neural networks to cope with these grids of manifold-valued data inputs. We also present a novel architecture to realize this theory and call it the ManifoldNet. Analogous to vector spaces where convolutions are equivalent to computing weighted sums, manifold-valued data 'convolutions' can be defined using the weighted Fréchet Mean ([Formula: see text]). (This requires endowing the manifold with a Riemannian structure if it did not already come with one.) The hidden layers of ManifoldNet compute [Formula: see text]s of their inputs, where the weights are to be learnt. This means the data remain manifold-valued as they propagate through the hidden layers. To reduce computational complexity, we present a provably convergent recursive algorithm for computing the [Formula: see text]. Further, we prove that on non-constant sectional curvature manifolds, each [Formula: see text] layer is a contraction mapping and provide constructive evidence for its non-collapsibility when stacked in layers. This captures the two fundamental properties of deep network layers. Analogous to the equivariance of convolution in euclidean space to translations, we prove that the [Formula: see text] is equivariant to the action of the group of isometries admitted by the Riemannian manifold on which the data reside. To showcase the performance of ManifoldNet, we present several experiments using both computer vision and medical imaging data sets.

Display of Native Antigen on cDC1 That Have Spatial Access to Both T and B Cells Underlies Efficient Humoral Vaccination.

Follicular dendritic cells and macrophages have been strongly implicated in presentation of native Ag to B cells. This property has also occasionally been attributed to conventional dendritic cells (cDC) but is generally masked by their essential role in T cell priming. cDC can be divided into two main subsets, cDC1 and cDC2, with recent evidence suggesting that cDC2 are primarily responsible for initiating B cell and T follicular helper responses. This conclusion is, however, at odds with evidence that targeting Ag to Clec9A (DNGR1), expressed by cDC1, induces strong humoral responses. In this study, we reveal that murine cDC1 interact extensively with B cells at the border of B cell follicles and, when Ag is targeted to Clec9A, can display native Ag for B cell activation. This leads to efficient induction of humoral immunity. Our findings indicate that surface display of native Ag on cDC with access to both T and B cells is key to efficient humoral vaccination.

Cascade recurrent neural network-assisted nonlinear equalization for a 100 Gb/s PAM4 short-reach direct detection system.

We propose a novel, to the best of our knowledge, cascade recurrent neural network (RNN)-based nonlinear equalizer for a pulse amplitude modulation (PAM)4 short-reach direct detection system. A 100 Gb/s PAM4 link is experimentally demonstrated over 15 km standard single-mode fiber (SSMF), using a 16 GHz directly modulated laser (DML) in C-band. The link suffers from strong nonlinear impairments which is mainly induced by the mixture of linear channel effects with square-law detection, the DML frequency chirp, and the device nonlinearity. Experimental results show that the proposed cascade RNN-based equalizer outperforms other feedforward or non-cascade neural network (NN)-based equalizers owing to both its cascade and recurrent structure, showing the great potential to effectively tackle the nonlinear signal distortion. With the aid of a cascade RNN-based equalizer, a bit-error rate (BER) lower than the 7% hard-decision forward error correction (FEC) threshold can be achieved when the receiver power is larger than 5 dBm. Compared with traditional non-cascade NN-based equalizers, the training time could also be reduced by half with the help of the cascade structure.

Computational complexity comparison of feedforward/radial basis function/recurrent neural network-based equalizer for a 50-Gb/s PAM4 direct-detection optical link.

The computational complexity and system bit-error-rate (BER) performance of four types of neural-network-based nonlinear equalizers are analyzed for a 50-Gb/s pulse amplitude modulation (PAM)-4 direct-detection (DD) optical link. The four types are feedforward neural networks (F-NN), radial basis function neural networks (RBF-NN), auto-regressive recurrent neural networks (AR-RNN) and layer-recurrent neural networks (L-RNN). Numerical results show that, for a fixed BER threshold, the AR-RNN-based equalizers have the lowest computational complexity. Amongst all the nonlinear NN-based equalizers with the same number of inputs and hidden neurons, F-NN-based equalizers have the lowest computational complexity while the AR-RNN-based equalizers exhibit the best BER performance. Compared with F-NN or RNN, RBF-NN tends to require more hidden neurons with the increase of the number of inputs, making it not suitable for long fiber transmission distance. We also demonstrate that only a few tens of multiplications per symbol are needed for NN-based equalizers to guarantee a good BER performance. This relatively low computational complexity signifies that various NN-based equalizers can be potentially implemented in real time. More broadly, this paper provides guidelines for selecting a suitable NN-based equalizer based on BER and computational complexity requirements.

TGF-ß and IL-6 family signalling crosstalk: an integrated model.

Mathematical models for TGF-ß and IL-6 signalling have been linked, providing a platform for analyzing the crosstalk between the systems. An integrated IL-6:TGF-ß model was developed via a reduced set of reaction equations which incorporate both feedback loops and appropriate time-delays for transcription and translation processes. The model simulates stable, robust and realistic responses to both ligands. Pulsatile (multiple pulses) inputs for both TGF-ß and IL-6 have been simulated to investigate the effects of each ligand on the sensitivity, equilibrium and dynamic responses of the integrated signalling system. In our simulations the crosstalk between constant IL-6 and TGF-ß signalling via SMAD7 does not appear to be sufficient to render the cells resistant to TGF-ß inhibition. However, the simulations predict that pulsatile IL-6 stimulation would increase SMAD7 levels substantially and consequentially, lead to resistance to TGF-ß. The model also allows the prediction of the integrated signalling pathway responses to the mutation of key components, e.g. Gp130 F/F.

Mathematical model of TGF-ßsignalling: feedback coupling is consistent with signal switching.

BACKGROUND: Transforming growth factor ß (TGF-ß) signalling regulates the development of embryos and tissue homeostasis in adults. In conjunction with other oncogenic changes, long-term perturbation of TGF-ß signalling is associated with cancer metastasis. Although TGF-ß signalling can be complex, many of the signalling components are well defined, so it is possible to develop mathematical models of TGF-ß signalling using reduction and scaling methods. The parameterization of our TGF-ß signalling model is consistent with experimental data. RESULTS: We developed our mathematical model for the TGF-ß signalling pathway, i.e. the RF- model of TGF-ß signalling, using the "rapid equilibrium assumption" to reduce the network of TGF-ß signalling reactions based on the time scales of the individual reactions. By adding time-delayed positive feedback to the inherent time-delayed negative feedback for TGF-ß signalling. We were able to simulate the sigmoidal, switch-like behaviour observed for the concentration dependence of long-term (> 3 hours) TGF-ß stimulation. Computer simulations revealed the vital role of the coupling of the positive and negative feedback loops on the regulation of the TGF-ß signalling system. The incorporation of time-delays for the negative feedback loop improved the accuracy, stability and robustness of the model. This model reproduces both the short-term and long-term switching responses for the intracellular signalling pathways at different TGF-ß concentrations. We have tested the model against experimental data from MEF (mouse embryonic fibroblasts) WT, SV40-immortalized MEFs and Gp130 F/F MEFs. The predictions from the RF- model are consistent with the experimental data. CONCLUSIONS: Signalling feedback loops are required to model TGF-ß signal transduction and its effects on normal and cancer cells. We focus on the effects of time-delayed feedback loops and their coupling to ligand stimulation in this system. The model was simplified and reduced to its key components using standard methods and the rapid equilibrium assumption. We detected differences in short-term and long-term signal switching. The results from the RF- model compare well with experimental data and predict the dynamics of TGF-ß signalling in cancer cells with different mutations.

Tracking Electroencephalographic Changes Using Distributions of Linear Models: Application to Propofol-Based Depth of Anesthesia Monitoring.

OBJECTIVE: Tracking brain states with electrophysiological measurements often relies on short-term averages of extracted features and this may not adequately capture the variability of brain dynamics. The objective is to assess the hypotheses that this can be overcome by tracking distributions of linear models using anesthesia data, and that anesthetic brain state tracking performance of linear models is comparable to that of a high performing depth of anesthesia monitoring feature. METHODS: Individuals' brain states are classified by comparing the distribution of linear (auto-regressive moving average-ARMA) model parameters estimated from electroencephalographic (EEG) data obtained with a sliding window to distributions of linear model parameters for each brain state. The method is applied to frontal EEG data from 15 subjects undergoing propofol anesthesia and classified by the observers assessment of alertness/sedation (OAA/S) scale. Classification of the OAA/S score was performed using distributions of either ARMA parameters or the benchmark feature, Higuchi fractal dimension. RESULTS: The highest average testing sensitivity of 59% (chance sensitivity: 17%) was found for ARMA (2,1) models and Higuchi fractal dimension achieved 52%, however, no statistical difference was observed. For the same ARMA case, there was no statistical difference if medians are used instead of distributions (sensitivity: 56%). CONCLUSION: The model-based distribution approach is not necessarily more effective than a median/short-term average approach, however, it performs well compared with a distribution approach based on a high performing anesthesia monitoring measure. SIGNIFICANCE: These techniques hold potential for anesthesia monitoring and may be generally applicable for tracking brain states.

Liver-Resident Memory CD8+ T Cells Form a Front-Line Defense against Malaria Liver-Stage Infection.

In recent years, various intervention strategies have reduced malaria morbidity and mortality, but further improvements probably depend upon development of a broadly protective vaccine. To better understand immune requirement for protection, we examined liver-stage immunity after vaccination with irradiated sporozoites, an effective though logistically difficult vaccine. We identified a population of memory CD8+ T cells that expressed the gene signature of tissue-resident memory T (Trm) cells and remained permanently within the liver, where they patrolled the sinusoids. Exploring the requirements for liver Trm cell induction, we showed that by combining dendritic cell-targeted priming with liver inflammation and antigen recognition on hepatocytes, high frequencies of Trm cells could be induced and these cells were essential for protection against malaria sporozoite challenge. Our study highlights the immune potential of liver Trm cells and provides approaches for their selective transfer, expansion, or depletion, which may be harnessed to control liver infections or autoimmunity.

Expansion-maximization-compression algorithm with spherical harmonics for single particle imaging with x-ray lasers.

In three-dimensional (3D) single particle imaging with x-ray free-electron lasers, particle orientation is not recorded during measurement but is instead recovered as a necessary step in the reconstruction of a 3D image from the diffraction data. Here we use harmonic analysis on the sphere to cleanly separate the angular and radial degrees of freedom of this problem, providing new opportunities to efficiently use data and computational resources. We develop the expansion-maximization-compression algorithm into a shell-by-shell approach and implement an angular bandwidth limit that can be gradually raised during the reconstruction. We study the minimum number of patterns and minimum rotation sampling required for a desired angular and radial resolution. These extensions provide new avenues to improve computational efficiency and speed of convergence, which are critically important considering the very large datasets expected from experiment.

Neural mass model-based tracking of anesthetic brain states.

Neural mass model-based tracking of brain states from electroencephalographic signals holds the promise of simultaneously tracking brain states while inferring underlying physiological changes in various neuroscientific and clinical applications. Here, neural mass model-based tracking of brain states using the unscented Kalman filter applied to estimate parameters of the Jansen-Rit cortical population model is evaluated through the application of propofol-based anesthetic state monitoring. In particular, 15 subjects underwent propofol anesthesia induction from awake to anesthetised while behavioral responsiveness was monitored and frontal electroencephalographic signals were recorded. The unscented Kalman filter Jansen-Rit model approach applied to frontal electroencephalography achieved reasonable testing performance for classification of the anesthetic brain state (sensitivity: 0.51; chance sensitivity: 0.17; nearest neighbor sensitivity 0.75) when compared to approaches based on linear (autoregressive moving average) modeling (sensitivity 0.58; nearest neighbor sensitivity: 0.91) and a high performing standard depth of anesthesia monitoring measure, Higuchi Fractal Dimension (sensitivity: 0.50; nearest neighbor sensitivity: 0.88). Moreover, it was found that the unscented Kalman filter based parameter estimates of the inhibitory postsynaptic potential amplitude varied in the physiologically expected direction with increases in propofol concentration, while the estimates of the inhibitory postsynaptic potential rate constant did not. These results combined with analysis of monotonicity of parameter estimates, error analysis of parameter estimates, and observability analysis of the Jansen-Rit model, along with considerations of extensions of the Jansen-Rit model, suggests that the Jansen-Rit model combined with unscented Kalman filtering provides a valuable reference point for future real-time brain state tracking studies. This is especially true for studies of more complex, but still computationally efficient, neural models of anesthesia that can more accurately track the anesthetic brain state, while simultaneously inferring underlying physiological changes that can potentially provide useful clinical information.

On an analogue signal processing circuit in the Nematode C. elegans.

In this work we will work on analogue signal processing in the neural circuit of C. elegans which is able to detect the analogue signals from the environment and produce locomotive behaviours which are in accordance with experiments. The signals in C. elegans are processed in a purely analogue procedure, since no action potential has been recorded in its neural activity. We aim to show how signal processing can be executed in analogue domain in a living creature. In order to do that we will model two different behaviours of C. elegans which are generated in the same network of neurons, klinotaxis behaviour and isothermal tracking. We will implement a Genetic Algorithm to find appropriate sets of parameters of the model. Our contribution is to show how relatively straight forward differential equations can lead to relatively complex and different behaviours.

C. elegans locomotion analysis using algorithmic information theory.

This article investigates the use of algorithmic information theory to analyse C. elegans datasets. The ability of complexity measures to detect similarity in animals' behaviours is demonstrated and their strengths are compared to methods such as histograms. Introduced quantities are illustrated on a couple of real two-dimensional C. elegans datasets to investigate the thermotaxis and chemotaxis behaviours.

Persistence of skin-resident memory T cells within an epidermal niche.

Barrier tissues such as the skin contain various populations of immune cells that contribute to protection from infections. These include recently identified tissue-resident memory T cells (TRM). In the skin, these memory CD8(+) T cells reside in the epidermis after being recruited to this site by infection or inflammation. In this study, we demonstrate prolonged persistence of epidermal TRM preferentially at the site of prior infection despite sustained migration. Computational simulation of TRM migration within the skin over long periods revealed that the slow rate of random migration effectively constrains these memory cells within the region of skin in which they form. Notably, formation of TRM involved a concomitant local reduction in dendritic epidermal γδ T-cell numbers in the epidermis, indicating that these populations persist in mutual exclusion and may compete for local survival signals. Accordingly, we show that expression of the aryl hydrocarbon receptor, a transcription factor important for dendritic epidermal γδ T-cell maintenance in skin, also contributes to the persistence of skin TRM. Together, these data suggest that skin tissue-resident memory T cells persist within a tightly regulated epidermal T-cell niche.

Approximate, computationally efficient online learning in Bayesian spiking neurons.

Bayesian spiking neurons (BSNs) provide a probabilistic interpretation of how neurons perform inference and learning. Online learning in BSNs typically involves parameter estimation based on maximum-likelihood expectation-maximization (ML-EM) which is computationally slow and limits the potential of studying networks of BSNs. An online learning algorithm, fast learning (FL), is presented that is more computationally efficient than the benchmark ML-EM for a fixed number of time steps as the number of inputs to a BSN increases (e.g., 16.5 times faster run times for 20 inputs). Although ML-EM appears to converge 2.0 to 3.6 times faster than FL, the computational cost of ML-EM means that ML-EM takes longer to simulate to convergence than FL. FL also provides reasonable convergence performance that is robust to initialization of parameter estimates that are far from the true parameter values. However, parameter estimation depends on the range of true parameter values. Nevertheless, for a physiologically meaningful range of parameter values, FL gives very good average estimation accuracy, despite its approximate nature. The FL algorithm therefore provides an efficient tool, complementary to ML-EM, for exploring BSN networks in more detail in order to better understand their biological relevance. Moreover, the simplicity of the FL algorithm means it can be easily implemented in neuromorphic VLSI such that one can take advantage of the energy-efficient spike coding of BSNs.

A quantitative technique for assessing the change in severity over time in psoriatic lesions using computer aided image analysis.

Psoriasis is a chronic skin disease affecting an estimated 125 million people worldwide. One of the key problems in the management of this condition is the objective measurement of lesion severity over time. Currently, severity is scored by clinicians using visual protocols leading to intra and inter observer variability that makes measurement of treatment efficacy subjective. In this paper, an automatic computer aided image analysis system is proposed that quantitatively assess the changes of erythema and scaling severity of psoriatic lesions in long-term treatment. The algorithm proposed in this paper works on 2D digital images by selecting features that can be used to accurately segment erythema and scaling in psoriasis lesions and assess their changes in severity, according to the popular psoriasis area and severity index (PASI). The algorithms are validated by developing linear models that correlate well with changes in severity scores given by dermatologists. To the best of our knowledge, no such computer assisted method for psoriasis severity assessment in a long-term treatment exists.

Automatic segmentation of scaling in 2-D psoriasis skin images.

Psoriasis is a chronic inflammatory skin disease that affects over 3% of the population. Various methods are currently used to evaluate psoriasis severity and to monitor therapeutic response. The PASI system of scoring is widely used for evaluating psoriasis severity. It employs a visual analogue scale to score the thickness, redness (erythema), and scaling of psoriasis lesions. However, PASI scores are subjective and suffer from poor inter- and intra-observer concordance. As an integral part of developing a reliable evaluation method for psoriasis, an algorithm is presented for segmenting scaling in 2-D digital images. The algorithm is believed to be the first to localize scaling directly in 2-D digital images. The scaling segmentation problem is treated as a classification and parameter estimation problem. A Markov random field (MRF) is used to smooth a pixel-wise classification from a support vector machine (SVM) that utilizes a feature space derived from image color and scaling texture. The training sets for the SVM are collected directly from the image being analyzed giving the algorithm more resilience to variations in lighting and skin type. The algorithm is shown to give reliable segmentation results when evaluated with images with different lighting conditions, skin types, and psoriasis types.

An introductory review of information theory in the context of computational neuroscience.

This article introduces several fundamental concepts in information theory from the perspective of their origins in engineering. Understanding such concepts is important in neuroscience for two reasons. Simply applying formulae from information theory without understanding the assumptions behind their definitions can lead to erroneous results and conclusions. Furthermore, this century will see a convergence of information theory and neuroscience; information theory will expand its foundations to incorporate more comprehensively biological processes thereby helping reveal how neuronal networks achieve their remarkable information processing abilities.

Capacity of a single spiking neuron channel.

Information transfer through a single neuron is a fundamental component of information processing in the brain, and computing the information channel capacity is important to understand this information processing. The problem is difficult since the capacity depends on coding, characteristics of the communication channel, and optimization over input distributions, among other issues. In this letter, we consider two models. The temporal coding model of a neuron as a communication channel assumes the output is tau where tau is a gamma-distributed random variable corresponding to the interspike interval, that is, the time it takes for the neuron to fire once. The rate coding model is similar; the output is the actual rate of firing over a fixed period of time. Theoretical studies prove that the distribution of inputs, which achieves channel capacity, is a discrete distribution with finite mass points for temporal and rate coding under a reasonable assumption. This allows us to compute numerically the capacity of a neuron. Numerical results are in a plausible range based on biological evidence to date.

Ancient jades map 3,000 years of prehistoric exchange in Southeast Asia.

We have used electron probe microanalysis to examine Southeast Asian nephrite (jade) artifacts, many archeologically excavated, dating from 3000 B.C. through the first millennium A.D. The research has revealed the existence of one of the most extensive sea-based trade networks of a single geological material in the prehistoric world. Green nephrite from a source in eastern Taiwan was used to make two very specific forms of ear pendant that were distributed, between 500 B.C. and 500 A.D., through the Philippines, East Malaysia, southern Vietnam, and peninsular Thailand, forming a 3,000-km-diameter halo around the southern and eastern coastlines of the South China Sea. Other Taiwan nephrite artifacts, especially beads and bracelets, were distributed earlier during Neolithic times throughout Taiwan and from Taiwan into the Philippines.