We investigate the recovery dynamics of healthy cardiac activity after physical exertion using multimodal biosignals recorded with a polycardiograph. Multifractal features derived from the singularity spectrum capture the scale-invariant properties of cardiovascular regulation. Five supervised classification algorithms - Logistic Regression (LogReg), Suport Vector Machine with RBF kernel (SVM-RBF), k-Nearest Neighbors (kNN), Decision Tree (DT), and Random Forest (RF) - were evaluated to distinguish recovery states in a small, imbalanced dataset. Our results show that multifractal analysis, combined with multimodal sensing, yields reliable features for characterizing recovery and points toward nonlinear diagnostic methods for heart conditions.

Synthetic Aperture Radar (SAR), with its all-weather and wide-area observation capabilities, serves as a crucial tool for wake detection. However, due to its complex imaging mechanism, wake features in SAR images often appear abstract and noisy, posing challenges for accurate annotation. In contrast, optical images provide more distinct visual cues, but models trained on optical data suffer from performance degradation when applied to SAR images due to domain shift. To address this cross-modal domain adaptation challenge, we propose a Similarity-Guided and Memory-Guided Domain Adaptation (termed SimMemDA) framework for unsupervised domain adaptive ship wake detection via instance-level feature similarity filtering and feature memory guidance. Specifically, to alleviate the visual discrepancy between optical and SAR images, we first utilize WakeGAN to perform style transfer on optical images, generating pseudo-images close to the SAR style. Then, instance-level feature similarity filtering mechanism is designed to identify and prioritize source samples with target-like distributions, minimizing negative transfer. Meanwhile, a Feature-Confidence Memory Bank combined with a K-nearest neighbor confidence-weighted fusion strategy is introduced to dynamically calibrate pseudo-labels in the target domain, improving the reliability and stability of pseudo-labels. Finally, the framework further enhances generalization through region-mixed training, strategically combining source annotations with calibrated target pseudo-labels. Experimental results demonstrate that the proposed SimMemDA method can improve the accuracy and robustness of cross-modal ship wake detection tasks, validating the effectiveness and feasibility of the proposed method.

Humanoids are progressing toward practical deployment across healthcare, industrial, defense, and service sectors. While typically considered cyber-physical systems (CPSs), their dependence on traditional networked software stacks (e.g., Linux operating systems), robot operating system (ROS) middleware, and over-the-air update channels, creates a distinct security profile that exposes them to vulnerabilities conventional CPS models do not fully address. Prior studies have mainly examined specific threats, such as LiDAR spoofing or adversarial machine learning (AML). This narrow focus overlooks how an attack targeting one component can cascade harm throughout the robot's interconnected systems. We address this gap through a systematization of knowledge (SoK) that takes a comprehensive approach, consolidating fragmented research from robotics, CPS, and network security domains. We introduce a seven-layer security model for humanoid robots, organizing 39 known attacks and 35 defenses across the humanoid ecosystem-from hardware to human-robot interaction. Building on this security model, we develop a quantitative 39x35 attack-defense matrix with risk-weighted scoring, validated through Monte Carlo analysis. We demonstrate our method by evaluating three real-world robots: Pepper, G1 EDU, and Digit. The scoring analysis revealed varying security maturity levels, with scores ranging from 39.9% to 79.5% across the platforms. This work introduces a structured, evidence-based assessment method that enables systematic security evaluation, supports cross-platform benchmarking, and guides prioritization of security investments in humanoid robotics.

We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels among the class of weight-independent geometrically-coupled positive random feature (PRF) mechanisms, substantially outperforming the previously most accurate Orthogonal Random Features at no observable extra cost. We present a more computationally expensive SimRFs+ variant, which we prove is asymptotically optimal in the broader family of weight-dependent geometrical coupling schemes (which permit correlations between random vector directions and norms). In extensive empirical studies, we show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.

Consider a reinforcement learning problem where an agent has access to a very large amount of information about the environment, but it can only take very few actions to accomplish its task and to maximize its reward. Evidently, the main problem for the agent is to learn a map from a very high-dimensional space (which represents its environment) to a very low-dimensional space (which represents its actions). The high-to-low dimensional map implies that most of the information about the environment is irrelevant for the actions to be taken, and only a small fraction of information is relevant. In this paper we argue that the relevant information need not be learned by brute force (which is the standard approach), but can be identified from the intrinsic symmetries of the system. We analyze in details a reinforcement learning problem of autonomous driving, where the corresponding symmetry is the Galilean symmetry, and argue that the learning task can be accomplished with very few relevant parameters, or, more precisely, invariants. For a numerical demonstration, we show that the autonomous vehicles (which we call autonomous particles since they describe very primitive vehicles) need only four relevant invariants to learn how to drive very well without colliding with other particles. The simple model can be easily generalized to include different types of particles (e.g. for cars, for pedestrians, for buildings, for road signs, etc.) with different types of relevant invariants describing interactions between them. We also argue that there must exist a field theory description of the learning system where autonomous particles would be described by fermionic degrees of freedom and interactions mediated by the relevant invariants would be described by bosonic degrees of freedom. This suggests that the effectiveness of field theory descriptions of physical systems might be connected to the learning dynamics of some kinds of autonomous particles, supporting the claim that the entire universe is a neural network.

The paper proposes a numerically stable recursive algorithm for the exact computation of the linear-chain conditional random field gradient. It operates as a forward algorithm over the log-domain expectation semiring and has the purpose of enhancing memory efficiency when applied to long observation sequences. Unlike the traditional algorithm based on the forward-backward recursions, the memory complexity of our algorithm does not depend on the sequence length. The experiments on real data show that it can be useful for the problems which deal with long sequences.

Bisimulations have been widely used in many areas of computer science to model equivalence between various systems, and to reduce the number of states of these systems, whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets. Here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata. We prove that a uniform fuzzy relation between fuzzy automata $\cal A$ and $\cal B$ is a forward bisimulation if and only if its kernel and co-kernel are forward bisimulation fuzzy equivalences on $\cal A$ and $\cal B$ and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalences. As a consequence we get that fuzzy automata $\cal A$ and $\cal B$ are UFB-equivalent, i.e., there is a uniform forward bisimulation between them, if and only if there is a special isomorphism between the factor fuzzy automata of $\cal A$ and $\cal B$ with respect to their greatest forward bisimulation fuzzy equivalences. This result reduces the problem of testing UFB-equivalence to the problem of testing isomorphism of fuzzy automata, which is closely related to the well-known graph isomorphism problem. We prove some similar results for backward-forward bisimulations, and we point to fundamental differences. Because of the duality with the studied concepts, backward and forward-backward bisimulations are not considered separately. Finally, we give a comprehensive overview of various concepts on deterministic, nondeterministic, fuzzy, and weighted automata, which are related to bisimulations.

Recently, two types of simulations (forward and backward simulations) and four types of bisimulations (forward, backward, forward-backward, and backward-forward bisimulations) between fuzzy automata have been introduced. If there is at least one simulation/bisimulation of some of these types between the given fuzzy automata, it has been proved that there is the greatest simulation/bisimulation of this kind. In the present paper, for any of the above-mentioned types of simulations/bisimulations we provide an effective algorithm for deciding whether there is a simulation/bisimulation of this type between the given fuzzy automata, and for computing the greatest one, whenever it exists. The algorithms are based on the method developed in [J. Ignjatovi\'c, M. \'Ciri\'c, S. Bogdanovi\'c, On the greatest solutions to certain systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081-3113], which comes down to the computing of the greatest post-fixed point, contained in a given fuzzy relation, of an isotone function on the lattice of fuzzy relations.

In our recent paper we have established close relationships between state reduction of a fuzzy recognizer and resolution of a particular system of fuzzy relation equations. In that paper we have also studied reductions by means of those solutions which are fuzzy equivalences. In this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi-orders. Generally, fuzzy quasi-orders and fuzzy equivalences are equally good in the state reduction, but we show that right and left invariant fuzzy quasi-orders give better reductions than right and left invariant fuzzy equivalences. We also show that alternate reductions by means of fuzzy quasi-orders give better results than alternate reductions by means of fuzzy equivalences. Furthermore we study a more general type of fuzzy quasi-orders, weakly right and left invariant ones, and we show that they are closely related to determinization of fuzzy recognizers. We also demonstrate some applications of weakly left invariant fuzzy quasi-orders in conflict analysis of fuzzy discrete event systems.