Neural Differential Equations (NDEs) excel at modeling continuous-time dynamics, effectively handling challenges such as irregular observations, missing values, and noise. Despite their advantages, NDEs face a fundamental challenge in adopting dropout, a cornerstone of deep learning regularization, making them susceptible to overfitting. To address this research gap, we introduce Continuum Dropout, a universally applicable regularization technique for NDEs built upon the theory of alternating renewal processes. Continuum Dropout formulates the on-off mechanism of dropout as a stochastic process that alternates between active (evolution) and inactive (paused) states in continuous time. This provides a principled approach to prevent overfitting and enhance the generalization capabilities of NDEs. Moreover, Continuum Dropout offers a structured framework to quantify predictive uncertainty via Monte Carlo sampling at test time. Through extensive experiments, we demonstrate that Continuum Dropout outperforms existing regularization methods for NDEs, achieving superior performance on various time series and image classification tasks. It also yields better-calibrated and more trustworthy probability estimates, highlighting its effectiveness for uncertainty-aware modeling.

LiDAR-inertial odometry (LIO) has been widely used in robotics due to its high accuracy. However, its performance degrades in degenerate environments, such as long corridors and high-altitude flights, where LiDAR measurements are imbalanced or sparse, leading to ill-posed state estimation. In this letter, we present LODESTAR, a novel LIO method that addresses these degeneracies through two key modules: degeneracy-aware adaptive Schmidt-Kalman filter (DA-ASKF) and degeneracy-aware data exploitation (DA-DE). DA-ASKF employs a sliding window to utilize past states and measurements as additional constraints. Specifically, it introduces degeneracy-aware sliding modes that adaptively classify states as active or fixed based on their degeneracy level. Using Schmidt-Kalman update, it partially optimizes active states while preserving fixed states. These fixed states influence the update of active states via their covariances, serving as reference anchors--akin to a lodestar. Additionally, DA-DE prunes less-informative measurements from active states and selectively exploits measurements from fixed states, based on their localizability contribution and the condition number of the Jacobian matrix. Consequently, DA-ASKF enables degeneracy-aware constrained optimization and mitigates measurement sparsity, while DA-DE addresses measurement imbalance. Experimental results show that LODESTAR outperforms existing LiDAR-based odometry methods and degeneracy-aware modules in terms of accuracy and robustness under various degenerate conditions.

We present a formal and constructive simulation framework for nondeterministic finite automata (NFAs) using time-shared, depth-unrolled feedforward networks (TS-FFNs), i.e., acyclic unrolled computations with shared parameters that are functionally equivalent to unrolled recurrent or state-space models. Unlike prior approaches that rely on explicit recurrent architectures or post hoc extraction methods, our formulation symbolically encodes automaton states as binary vectors, transitions as sparse matrix transformations, and nondeterministic branching-including $\varepsilon$-closures-as compositions of shared thresholded updates. We prove that every regular language can be recognized exactly by such a shared-parameter unrolled feedforward network, with parameter count independent of input length. Our construction yields a constructive equivalence between NFAs and neural networks and demonstrates \emph{empirical learnability}: these networks can be trained via gradient descent on supervised acceptance data to recover the target automaton behavior. This learnability, formalized in Proposition 5.1, is the crux of this work. Extensive experiments validate the theoretical results, achieving perfect or near-perfect agreement on acceptance, state propagation, and closure dynamics. This work clarifies the correspondence between automata theory and modern neural architectures, showing that unrolled feedforward networks can perform precise, interpretable, and trainable symbolic computation.

N eurotensin receptor 1 (NTSR1), a member of the C lass A G protein - coupled receptor superfamily, plays a n important role in modulating dopamine rgic neuronal activity and eliciting opioid - independent analgesia. Recent studies suggest that promoting β - arrestin - bias ed signaling in NTSR1 may diminish drugs of abuse, such as psychostimulants, thereby offering a potential avenue for treating human addiction - related disorders . In this study, we utiliz e d a novel computational and experimental approach that combined nudged elastic band - based molecular dynamics simulations, Markov state models, temporal communication network analysis, site - directed mutagenesis, and conformational biosensors, to explore the intricate mechanisms underlying NTSR1 activation and bias ed signal ing . Our study reveal s a dynamic stepwise transition mechanism and activat ed transmission network associated with NTSR1 activation. It also yield s valuable insights into the complex interplay between the unique polar network, non - conserved ion locks, and aromatic clusters in NTSR1 signaling. Moreover, we identif ied a cryptic allosteric site located in the intracellular r egion of the receptor that exists in an intermediate state within the activation pathway. Collectively, these findings contribute to a more profound understanding of NTSR1 activation and biased signal ing at the atomic level, thereby providing a potential strateg y for the development of NTSR1 allosteric modulators in the realm of G protein - coupled receptor biology, biophysics, and medicine.

The distribution of streaming data often changes over time as conditions change, a phenomenon known as concept drift. Only a subset of previous experience, collected in similar conditions, is relevant to learning an accurate classifier for current data. Learning from irrelevant experience describing a different concept can degrade performance. A system learning from streaming data must identify which recent experience is irrelevant when conditions change and which past experience is relevant when concepts reoccur, \textit{e.g.,} when weather events or financial patterns repeat. Existing streaming approaches either do not consider experience to change in relevance over time and thus cannot handle concept drift, or only consider the recency of experience and thus cannot handle recurring concepts, or only sparsely evaluate relevance and thus fail when concept drift is missed. To enable learning in changing conditions, we propose SELeCT, a probabilistic method for continuously evaluating the relevance of past experience. SELeCT maintains a distinct internal state for each concept, representing relevant experience with a unique classifier. We propose a Bayesian algorithm for estimating state relevance, combining the likelihood of drawing recent observations from a given state with a transition pattern prior based on the system's current state.

We study networks of processes that all execute the same finite protocol and communicate synchronously in two different ways: a process can broadcast one message to all other processes or send it to at most one other process. In both cases, if no process can receive the message, it will still be sent. We establish a precise complexity class for two coverability problems with a parameterised number of processes: the state coverability problem and the configuration coverability problem. It is already known that these problems are Ackermann-hard (but decidable) in the general case. We show that when the protocol is Wait-Only, i.e., it has no state from which a process can send and receive messages, the complexity drops to P and PSpace, respectively.

Federated learning is an emerging distributed machine learning framework in the Internet of Vehicles (IoV). In IoV, millions of vehicles are willing to train the model to share their knowledge. Maintaining an active state means the participants must update their state to the FL server in a fixed interval and participate to next round. However, the cost by maintaining an active state is very large when there are a huge number of participating vehicles. In this paper, we proposed a distributed client selection scheme to reduce the cost of maintaining the active state for all participants. The clients with the highest evaluation are elected among the neighbours. In the evaluator, four variables are considered including sample quantity, throughput available, computational capability and the quality of the local dataset. We adopted fuzzy logic as the evaluator since the closed-form solution over four variables does not exist. Extensive simulation results show our proposal approximates the centralized client selection in terms of accuracy and can significantly reduce the communication overhead.

This work targets the identification of a class of models for hybrid dynamical systems characterized by nonlinear autoregressive exogenous (NARX) components, with finite-dimensional polynomial expansions, and by a Markovian switching mechanism. The estimation of the model parameters is performed under a probabilistic framework via Expectation Maximization, including submodel coefficients, hidden state values and transition probabilities. Discrete mode classification and NARX regression tasks are disentangled within the iterations. Soft-labels are assigned to latent states on the trajectories by averaging over the state posteriors and updated using the parametrization obtained from the previous maximization phase. Then, NARXs parameters are repeatedly fitted by solving weighted regression subproblems through a cyclical coordinate descent approach with coordinate-wise minimization. Moreover, we investigate a two stage selection scheme, based on a l1-norm bridge estimation followed by hard-thresholding, to achieve parsimonious models through selection of the polynomial expansion. The proposed approach is demonstrated on a SMNARX problem composed by three nonlinear sub-models with specific regressors.

We show how well known rules of back propagation arise from a weighted combination of finite automata. By redefining a finite automata as a predictor we combine the set of all $k$-state finite automata using a weighted majority algorithm. This aggregated prediction algorithm can be simplified using symmetry, and we prove the equivalence of an algorithm that does this. We demonstrate that this algorithm is equivalent to a form of a back propagation acting in a completely connected $k$-node neural network. Thus the use of the weighted majority algorithm allows a bound on the general performance of deep learning approaches to prediction via known results from online statistics. The presented framework opens more detailed questions about network topology; it is a bridge to the well studied techniques of semigroup theory and applying these techniques to answer what specific network topologies are capable of predicting. This informs both the design of artificial networks and the exploration of neuroscience models.

We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite automata. We generate a set of biased sequences by applying a finite state automata with a specified number, m, of states to the set of all binary sequences. We detail optimal algorithms to predict sequences generated in this way. We explore a finite setting for the problem of prediction.