How some people's brains make an extraordinary recovery from stroke A well-known actor who had experienced a stroke was treated by stroke specialist Sandor Nardai. The actor had been left with aphasia, or an impaired ability to speak - brutal for anyone, but "probably the most devastating thing that could happen to an actor", says Nardai. After three months of recovery, though, the actor was able to say some words. After a year, he voiced a commercial. Remarkably, he eventually got well enough to return to live theatre, says Nardai, who is at Semmelweis University in Hungary.

Understanding how animals learn is a central challenge in neuroscience, with growing relevance to the development of animal-or human-aligned artificial intelligence. However, existing approaches tend to assume fixed parametric forms for the learning rule (e.g., Q-learning, policy gradient), which may not accurately describe the complex forms of learning employed by animals in realistic settings. Here we address this gap by developing a framework to infer learning rules directly from behavioral data collected during task learning. We assume that animals follow a decision policy parameterized by a generalized linear model (GLM), and we model their learning rule--the mapping from task covariates to per-trial weight updates--using a deep neural network (DNN). This formulation allows flexible, data-driven inference of learning rules while maintaining an interpretable form of the decision policy itself.

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Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses. These biases affect key parameters such as variance, prevalence, correlation, slope, and explained variance. The root cause is that imputed values optimized for MSE are averages, which reduce the natural variability in the data. This paper demonstrates that adding noise to imputed values can effectively eliminate these biases. The required noise level is proportional to the MSE. Using a toy example in a multivariate normal setting, we compare two methods: predictive imputation, which minimizes MSE, and stochastic imputation, which incorporates random noise. Simulation results show that predictive methods systematically introduce bias, while stochastic methods preserve the data's natural variability and produce unbiased estimates. We also evaluate three popular imputation tools -- missForest, softImpute, and mice -- and observe consistent biases in predictive methods. These findings highlight that MSE is an inadequate measure of imputation quality, as it prioritizes accuracy over variability. Incorporating noise into imputation methods is essential to prevent biases and ensure valid downstream analyses, underscoring the importance of stochastic approaches for handling incomplete data.

Time-series analysis is often affected by missing data, a common problem across several fields, including healthcare and environmental monitoring. Multiple Imputation by Chained Equations (MICE) has been prominent for imputing missing values through "fully conditional specification". We extend MICE using the Bayesian framework (tBayes-MICE), utilising Bayesian inference to impute missing values via Markov Chain Monte Carlo (MCMC) sampling to account for uncertainty in MICE model parameters and imputed values. We also include temporally informed initialisation and time-lagged features in the model to respect the sequential nature of time-series data. We evaluate the tBayes-MICE method using two real-world datasets (AirQuality and PhysioNet), and using both the Random Walk Metropolis (RWM) and the Metropolis-Adjusted Langevin Algorithm (MALA) samplers. Our results demonstrate that tBayes-MICE reduces imputation errors relative to the baseline methods over all variables and accounts for uncertainty in the imputation process, thereby providing a more accurate measure of imputation error. We also found that MALA mixed better than RWM across most variables, achieving comparable accuracy while providing more consistent posterior exploration. Overall, these findings suggest that the tBayes-MICE framework represents a practical and efficient approach to time-series imputation, balancing increased accuracy with meaningful quantification of uncertainty in various environmental and clinical settings.

Social conflict is a survival mechanism yielding both normal and pathological behaviors. Tounderstand its underlying principles, we collected behavioral and whole-brain neural data from mice advancing through stages of social conflict.

In this paper, we tackled just the first one in the list to show the effectiveness of9 ouralgorithm. Weagree that computations aresimple, i.e., elegant,once the18 aforementioned requirements have been elicited. Eliciting them, however,is definitely non-trivial and has not been19 explored in the literature so far for expectations. Our circuits are expressive enough to model larger datasets24 (see our answer to R#1.2) and learning them would scale: in manycases it is easier to learn aLC than aneural net25 (e.g., see [3]). 3. Approximate inference alternatives. Whenever we are able to compute expectations exactly for26 regression (Thm 1), we might want to consider approximations only to speed computations.

For our synthetic datasets, we conduct two additional rounds of instruction evolution to increase complexity. As shown in Figure 3, the scores of instructions across the three datasets consistently increase.