A Nanophotonic Computing Paradigm: Problem-Solving and Decision-Making Systems Using Spatiotemporal Photoexcitation Transfer Dynamics

Brain function is understood to be regulated by complex spatiotemporal dynamics, and can be characterized by a combination of observed brain response patterns in time and space. Magnetoencephalography (MEG), with its high temporal resolution, and functional magnetic resonance imaging (fMRI), with its high spatial resolution, are complementary imaging techniques with great potential to reveal information about spatiotemporal brain dynamics. Hence, the complementary nature of these imaging techniques holds much promise to study brain function in time and space, especially when the two data types are allowed to fully interact. We employed coupled tensor/matrix factorization (CMTF) to extract joint latent components in the form of unique spatiotemporal brain patterns that can be used to study brain development and function on a millisecond scale. Using the CMTF model, we extracted distinct brain patterns that revealed fine-grained spatiotemporal brain dynamics and typical sensory processing pathways informative of high-level cognitive functions in healthy adolescents. The components extracted from multimodal tensor fusion possessed better discriminative ability between high- and low-performance subjects than single-modality data-driven models. Multimodal tensor fusion successfully identified spatiotemporal brain dynamics of brain function and produced unique components with high discriminatory power. The CMTF model is a promising tool for high-order, multimodal data fusion that exploits the functional resolution of MEG and fMRI, and provides a comprehensive picture of the developing brain in time and space.

All-optical schemes for controlling complex delay-induced and spatio-temporal dynamics in multi-stripe and broad-area semiconductor lasers are presented. The underlying control-principle is based on continuous delayed optical feedback. Its influence on the general spatiotemporal dynamics of semiconductor lasers is discussed. The delayed feedback control principle allows successful control of delay-induced chaotic behavior as well as the dynamic optical filamentation in broad-area and multi-stripe lasers. The suppression of spatiotemporal instabilities in semiconductor laser arrays is achieved by selectively stabilizing relevant transverse optical modes. The relevant values of delay-times and delay-phase are obtained from a nonlinear eigenmode analysis based on a complex extension of the Karhunen-Loeve decomposition. Thereby a destructive interference condition in the higher-order transverse modes conveying the instabilities is achieved. The stabilization technique is demonstrated on multi-stripe laser arrays. In high-power broad-area lasers the spatiotemporal filamentation processes occur on both macroscopic and microscopic scales. Numerical simulations on the basis of Maxwell-Bloch equations for spatially extended semiconductor lasers reveal the internal spatial and temporal scales on which control consequently has to occur. It is demonstrated that the combined filamentation and propagation effects may be controlled by suitable spatially structured delayed optical feedback allowing, in particular, the control of coherent regimes in originally temporally and spatially chaotic states.

Urban Foundation Models (UFMs) are emerging as a transformative paradigm for understanding and managing complex urban systems, offering new capabilities to improve and transform urban environments. Trajectory data (e.g., vehicle movements) contains rich spatio-temporal patterns of human mobility and urban dynamics that are crucial for understanding city-wide movement behaviors, traffic patterns, and transportation system operations. Effectively modeling such trajectory data is crucial for UFMs, yet this poses significant challenges due to the high-dimensional nature of raw trajectories and their complex spatio-temporal dynamics. Trajectory representation learning addresses these challenges by transforming raw trajectory data into compact, meaningful representations that capture essential mobility patterns and facilitates the application to various urban tasks, such as trajectory similarity computation, travel time estimation, or destination prediction. This is achieved by learning low-dimensional representations from high-dimensional and raw trajectory data. However, existing methods for trajectory representation learning either rely on grid-based or road-based representations, which are inherently different and thus, could lose information contained in the other modality. Moreover, these methods overlook the dynamic nature of urban traffic, relying on static road network features rather than time-varying traffic patterns. In this paper, we propose TIGR , a novel model designed to integrate grid and road network modalities while incorporating spatio-temporal dynamics to learn rich, general-purpose representations of trajectories. We evaluate TIGR on three real-world datasets and demonstrate the effectiveness of combining both modalities by substantially outperforming state-of-the-art methods, i.e., up to 59.34% for trajectory similarity, up to 16.65% for travel time estimation, and up to 14.81% for destination prediction.

Overtaking method based on sand-sifter mechanism: Why do optimistic value functions find optimal solutions in multi-armed bandit problems?

The importance of multi-armed bandit (MAB) problems is on the rise due to their recent application in a large variety of areas such as online advertising, news article selection, wireless networks, and medicinal trials, to name a few. The most common assumption made when solving such MAB problems is that the unknown reward probability θ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> of each bandit arm k is fixed. However, this assumption rarely holds in practice simply because real-life problems often involve underlying processes that are dynamically evolving. In this paper, we model problems where reward probabilities θ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> are drifting, and introduce a new method called Dynamic Thompson Sampling (DTS) that facilitates Order Statistics based Thompson Sampling for these dynamically evolving MABs. The DTS algorithm adapts its success probability estimates, hat θ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> , faster than traditional Thompson Sampling schemes and thus leads to improved performance in terms of lower regret. Extensive experiments demonstrate that DTS outperforms current state-of-the-art approaches, namely pure Thompson Sampling, UCB-Normal and UCB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> , for the case of dynamic reward probabilities. Furthermore, this performance advantage increases persistently with the number of bandit arms.

Spatiotemporal dynamics in a diffusive ratio-dependent predator–prey model near a Hopf–Turing bifurcation point

An amoeboid unicellular organism, a plasmodium of the true slime mold Physarum polycephalum, exhibits complex spatiotemporal oscillatory dynamics and sophisticated information processing capabilities while deforming its amorphous body. We previously devised an ‘amoeba-based computer (ABC),’ that implemented optical feedback control to lead this amoeboid organism to search for a solution to the traveling salesman problem (TSP). In the ABC, the shortest TSP route (the optimal solution) is represented by the shape of the organism in which the body area (nutrient absorption) is maximized while the risk of being exposed to aversive light stimuli is minimized. The shortness of the TSP route found by ABC, therefore, serves as a quantitative measure of the optimality of the decision made by the organism. However, it remains unclear how the decision-making ability of the organism originates from the oscillatory dynamics of the organism. We investigated the number of coexisting traveling waves in the spatiotemporal patterns of the oscillatory dynamics of the organism. We show that a shorter TSP route can be found when the organism exhibits a lower number of traveling waves. The results imply that the oscillatory dynamics are highly coordinated throughout the global body. Based on the results, we discuss the fact that the decision-making ability of the organism can be enhanced not by uncorrelated random fluctuations, but by its highly coordinated oscillatory dynamics.

The interplay between reaction kinetics and diffusion leads to a wide range of spatiotemporal behaviors in reaction–diffusion (RD) systems. This article presents a theoretical and computational study of a RD system inspired by experimental observations of the Rho-GEF-Myosin signaling network controlling cell contraction dynamics. The temporal reaction system dynamics range from periodicity to bistability. By employing a dual hybrid dynamical systems approach of numerical bifurcation analysis and Floquet theory, we characterize the spatiotemporal dynamics when stable limit-cycle oscillators or homogeneous time-periodic solutions undergo the process of Floquet–Turing-diffusion-driven-instability (FTDDI). FTDDI refers to the emergence of spatially nonuniform patterns when diffusion destabilizes an otherwise temporally stable limit cycle of the underlying reaction kinetics. For the temporal reaction system, numerical bifurcation allows us to identify regions in a two-parameter space defining the stability of the uniform steady states and regions where the system exhibits limit cycles, which are characterized by employing the Floquet theory. In the presence of spatial variations, Floquet theory classifies regions where diffusion destabilizes the limit cycle or maintains their homogeneous stability and the emerging spatiotemporal dynamics of the full system, far from equilibrium. In the bistable regime, diffusion differentiates regions into those that exhibit classical Turing diffusion-driven instability, leading to pattern formation; and those that exhibit FTDDI, leading to space-time periodic patterns, spatially inhomogeneous patterns, oscillatory pulses, and wave propagation, and those that remain unaffected by diffusion. These findings provide theoretical insights into understanding complex spatiotemporal dynamics relevant to biological, chemical, and ecological spatiotemporal systems.

Robotic and mechatronic systems, autonomous vehicles, electric power systems and smart grids, as well as manufacturing and industrial production systems can exhibit complex nonlinear dynamics or spatio-temporal dynamics which need to be controlled to ensure good functioning and performance. In this comprehensive reference, the authors present new and innovative control and estimation methods and techniques based on dynamical nonlinear and partial differential equation systems. Such results can be classified in five main domains for the control of complex nonlinear dynamical systems using respectively methods of approximate (local) linearization, methods of exact (global) linearization, Lyapunov stability approaches, control and estimation of distributed parameter systems and stochastic estimation and fault diagnosis methods. Control and Estimation of Dynamical Nonlinear and Partial Differential Equation Systems: Theory and applications will be of interest to electrical engineering, physics, computer science, robotics and mechatronics researchers and professionals working on control problems, condition monitoring, estimation and fault diagnosis and isolation problems. It will also be useful to skilled technical personnel working on applications in robotics, energy conversion, transportation and manufacturing.

Modelling the spatio-temporal dynamics of multi-species host–parasitoid interactions: Heterogeneous patterns and ecological implications

The coherent spatiotemporal dynamical interplay among neurons, neuronal populations, cortical circuits, and networks cross the micro-, meso- and macro-scales of the human brain, providing the functional organization of the brain and supporting our daily life. The details of how these multiple scales of organization in the brain influence one another and produce a multitude of human behaviors remains a clouded mystery. Mathematical, computational, and experimental neuroscientists employ a variety of cutting-edge methods, techniques, and algorithms in both humans and animals to identify the core mechanisms that govern the perception and action characteristics of the human brain. Integration of functional MRI (fMRI)–as an indirect measure of brain activity-with electroencephalogram (EEG) and magnetoencephalogram (MEG) as direct measures of spatiotemporal and spectral fingerprints of brain dynamics has provided novel insights into how the human brain operates in the resting state and in goal-oriented task performance. The ultimate goal is to identify the fundamental mechanisms that explain brain function across multiple spatiotemporal dynamics. Although our knowledge has grown exponentially in the past few decades, the integration of this knowledge to provide a conceptual framework of emergent behavior and pattern formation occurring on different levels of spatial organization remains challenging.

A multiarmed bandit problem is studied when the arms are not always available. The arms are first assumed to be intermittently available with some state/action-dependent probabilities. It is proven that no index policy can attain the maximum expected total discounted reward in every instance of that problem. The Whittle index policy is derived, and its properties are studied. Then it is assumed that the arms may break down, but repair is an option at some cost, and the new Whittle index policy is derived. Both problems are indexable. The proposed index policies cannot be dominated by any other index policy over all multiarmed bandit problems considered here. Whittle indices are evaluated for Bernoulli arms with unknown success probabilities.

The multi-armed bandit (MAB) model is one of the most classical models to study decision-making in an uncertain environment. In this model, a player chooses one of K possible arms of a bandit machine to play at each time step, where the corresponding arm returns a random reward to the player, potentially from a specific unknown distribution. The target of the player is to collect as many rewards as possible during the process. Despite its simplicity, the MAB model offers an excellent playground for studying the trade-off between exploration vs exploitation and designing effective algorithms for sequential decision-making under uncertainty. Although many asymptotically optimal algorithms have been established, the finite-time behaviors of the stochastic dynamics of the MAB model appear much more challenging to analyze due to the intertwine between the decision-making and the rewards being collected. In this paper, we employ techniques in statistical physics to analyze the MAB model, which facilitates the characterization of the distribution of cumulative regrets at a finite short time, the central quantity of interest in an MAB algorithm, as well as the intricate dynamical behaviors of the model. Our analytical results, in good agreement with simulations, point to the emergence of an interesting multimodal regret distribution, with large regrets resulting from excess exploitation of sub-optimal arms due to an initial unlucky output from the optimal one.

The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often ...

This paper characterizes creative cognition as a multi-armed bandit problem involving a trade-off between exploration and exploitation in sequential decisions from experience taking place in novel uncertain environments. Creative cognition implements an efficient learning process in this kind of dynamic decision. Special emphasis is put on the optimal sequencing of divergent and convergent behavior by showing that divergence must be inhibited at one point to converge toward creative behavior so that excessive divergence is counterproductive. We test this hypothesis in two behavioral experiments, using both novel and well-known tasks and precise measures of individual differences in creative potential in middle and high school students. Results in both studies confirmed that a task-dependent mix of divergence and convergence predicted high performance in a production task and better satisfaction in a consumption task, but exclusively in novel uncertain environments. These predictions were maintained after controlling for gender, personality, incentives, and other factors. As hypothesized, creative cognition was shown to be necessary for high performance under the appropriate conditions. However, it was not necessary for getting high grades in a traditional school system.