TRPO, PPO), and a critic that involves minimizing a closely connected objective.

Our contributions are summarized as follows.

These authors contributed equally to this work.

This paper investigates posterior sampling algorithms for competitive reinforcement learning (RL) in the context of general function approximations.

We study the problem of experiment planning with function approximation in contextual bandit problems.

This paper analyzes a fuzzy multiplex from a logical perspective in a way that has not been formalized so far. A fuzzy multiplex is a nested structure with inner nodes representing sub-system level agent traits and with outer nodes representing system agents; all while the ensemble is the system under consideration. Moreover, a mathematical framework is necessary to describe that structure which is formulated and then utilized. The system is firstly initialized using fuzzy set theory [2], inspired by Fuzzy Cognitive Maps [1]. Then a criterion that describes the structure is devised to implement a multiplex instead of a map [7] [8], and lastly system optimization is achieved. Furthermore, the theoretical context behind the multiplex is expounded in an attempt to establish a formal way of handling implications within a closed system using human intelligence. The paper is organized in sections following the reasoning process behind this unique idea. 1

We develop a novel characterization of extremal dependence between two cortical regions of the brain when its signals display extremely large amplitudes. We show that connectivity in the tails of the distribution reveals unique features of extreme events (e.g., seizures) that can help to identify their occurrence. Numerous studies have established that connectivity-based features are effective for discriminating brain states. Here, we demonstrate the advantage of the proposed approach: that tail connectivity provides additional discriminatory power, enabling more accurate identification of extreme-related events and improved seizure risk management. Common approaches in tail dependence modeling use pairwise summary measures or parametric models. However, these approaches do not identify channels that drive the maximal tail dependence between two groups of signals -- an information that is useful when analyzing electroencephalography of epileptic patients where specific channels are responsible for seizure occurrences. A familiar approach in traditional signal processing is canonical correlation, which we extend to the tails to develop a visualization of extremal channel-contributions. Through the tail pairwise dependence matrix (TPDM), we develop a computationally-efficient estimator for our canonical tail dependence measure. Our method is then used for accurate frequency-based soft clustering of neonates, distinguishing those with seizures from those without.

Classical Proportional-Integral-Derivative (PID) control has been widely successful across various industrial systems such as chemical processes, robotics, and power systems. However, as these systems evolved, the increase in the nonlinear dynamics and the complexity of interconnected variables have posed challenges that classical PID cannot effectively handle, often leading to instability, overshooting, or prolonged settling times. Researchers have proposed PIDNN models that combine the function approximation capabilities of neural networks with PID control to tackle these nonlinear challenges. However, these models require extensive, highly refined training data and have significant computational costs, making them less favorable for real-world applications. In this paper, We propose a novel EC-PIDUNN architecture, which integrates an untrained neural network with an improved PID controller, incorporating a stabilizing factor (\(τ\)) to generate the control signal. Like classical PID, our architecture uses the steady-state error \(e_t\) as input bypassing the need for explicit knowledge of the systems dynamics. By forming an input vector from \(e_t\) within the neural network, we increase the dimensionality of input allowing for richer data representation. Additionally, we introduce a vector of parameters \( ρ_t \) to shape the output trajectory and a \textit{dynamic compute} function to adjust the PID coefficients from predefined values. We validate the effectiveness of EC-PIDUNN on multiple nonlinear robotics applications: (1) nonlinear unmanned ground vehicle systems that represent the Ackermann steering mechanism and kinematics control, (2) Pan-Tilt movement system. In both tests, it outperforms classical PID in convergence and stability achieving a nearly critically damped response.

Traffic congestion is a major and complex challenge for cities worldwide with the rapid growth of urbanization and vehicle ownership. Longer commute times, excessive fuel consumption, and elevated air pollution levels are direct consequences of over-saturated roads. For instance, according to the 2024 INRIX Global Traffic Scorecard, individual commuters in Istanbul, New York City, and Chicago experienced total annual delay of about 105, 102, and 102 hours, respectively, underscoring the magnitude of intersection-driven delays in major metros (INRIX). Within urban networks, signalized intersections are the dominant bottlenecks: the policies implemented at these intersections allocate scarce space-time among competing traffic streams and therefore largely determine corridor-level delay, queues, and emissions. Reinforcement learning (RL) has become a standard practice for adaptive traffic signal control (ATSC), controlling phase selection and timing as a sequential decision problem that optimizes long-horizon objectives such as delay, throughput, and emissions under nonstationary demand (Yau et al., 2017). Deep RL (DRL) extends this by using function approximation to digest rich state representations--from detector queues to trajectories and graph-structured networks--enabling policies that generalize across varying traffic flows and topologies (Zhao et al., 2024). Collectively, this body of work motivates moving beyond single-intersection controllers toward coordinated, network-level solutions and setting the stage for multi-agent formulations.

This paper develops the foundations of Quantum Granular Computing (QGC), extending classical granular computing including fuzzy, rough, and shadowed granules to the quantum regime. Quantum granules are modeled as effects on a finite dimensional Hilbert space, so granular memberships are given by Born probabilities. This operator theoretic viewpoint provides a common language for sharp (projective) and soft (nonprojective) granules and embeds granulation directly into the standard formalism of quantum information theory. We establish foundational results for effect based quantum granules, including normalization and monotonicity properties, the emergence of Boolean islands from commuting families, granular refinement under Luders updates, and the evolution of granules under quantum channels via the adjoint channel in the Heisenberg picture. We connect QGC with quantum detection and estimation theory by interpreting the effect operators realizing Helstrom minimum error measurement for binary state discrimination as Helstrom type decision granules, i.e., soft quantum counterparts of Bayes optimal decision regions. Building on these results, we introduce Quantum Granular Decision Systems (QGDS) with three reference architectures that specify how quantum granules can be defined, learned, and integrated with classical components while remaining compatible with near term quantum hardware. Case studies on qubit granulation, two qubit parity effects, and Helstrom style soft decisions illustrate how QGC reproduces fuzzy like graded memberships and smooth decision boundaries while exploiting noncommutativity, contextuality, and entanglement. The framework thus provides a unified and mathematically grounded basis for operator valued granules in quantum information processing, granular reasoning, and intelligent systems.