Path Space Research Articles

Rapidly Screening the Correlation between the Rotational Mobility and the Hydrogen Bonding Strength of Confined Water.

Automated Deuterium Relaxation-Ordered SpectroscopY in solution (ADROSYS), an automated two-dimensional deuterium NMR methodology, discriminates between D2O populations (as well as deuterium-labeled alcohol groups) whose properties differ as a result of being confined inside nanoscale volumes. In this contribution, a proof-of-principle demonstration on reverse micelles (RMs) yields the insight that as the length scale of the confinement decreases from several nanometers down to less than a nanometer, the position of the signal peak migrates through the two-dimensional (2D) spectrum, tracing out a distinctive path in the 2D space (of relaxation time vs chemical shift). The signals typically follow a relatively gentle linear path for water confined on the scale of several nanometers, before curving once the surfactants confine the water molecules to length scales smaller than 1-2 nm. The qualitative shape of this path, especially in the regime of strong confinement, can change with different choices of surfactants, i.e., a different choice of chemistry at the edges of the confining environment. An important facet of this research was to demonstrate the relatively wide applicability of these techniques by showing that both: (1) Standard modern NMR instrumentation is capable of deploying an automated measurement, even though the choice of a deuterium nucleus is nonstandard and frequently requires companion proton spectra in order to reference the chemical shifts; and (2) well-established (though underutilized) modern techniques can process the resulting signal even though it involves the somewhat unusual combination of chemical shifts along one dimension and a distribution of relaxation times along another dimension. In addition to demonstrating that this technique can be deployed across many samples of interest, detailed facts pertaining to the broadening or shifting of resulting signals upon inclusion of various guest molecules are also discussed.

Spin waves and orbital contribution to ferromagnetism in a topological metal

Honeycomb and kagome lattices can host propagating excitations with non-trivial topology as defined by their evolution along closed paths in momentum space. Excitations on such lattices can also be momentum-independent, and the associated flat bands are of interest due to strong interactions between heavy quasiparticles. Here, we report the discovery — using circularly polarized X-rays for the unambiguous isolation of magnetic signals — of a nearly flat spin-wave band and large (compared to elemental iron) orbital moment in the metallic ferromagnet Fe3Sn2 with compact AB-stacked kagome bilayers. As a function of out-of-plane momentum, the nearly flat optical mode and the global rotation symmetry-restoring acoustic mode are out of phase, consistent with a bilayer exchange coupling that is larger than the already large in-plane couplings. The defining units of this topological metal are therefore triangular lattices of octahedral iron clusters rather than weakly coupled kagome planes. The spin waves are strongly damped when compared to elemental iron, opening the topic of topological boson–fermion interactions for deeper exploration within this material platform.

Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes

In this paper, we study parameter identification for solutions to (possibly non-linear) SDEs driven by additive Rosenblatt process and singularity of the induced laws on the path space. We propose a joint estimator for the drift parameter, diffusion intensity, and Hurst index that can be computed from discrete-time observations with a bounded time horizon and we prove its strong consistency under in-fill asymptotics with a fixed time horizon. As a consequence of this strong consistency, singularity of measures generated by the solutions with different drifts is shown. This results in the invalidity of a Girsanov-type theorem for Rosenblatt processes.

Risk measures based on weak optimal transport

In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we discuss computational aspects related to the nonlinear transform as well as approximations of the risk measures using, for example, neural networks. Our setup comprises a variety of examples, such as classical optimal transport penalties, parametric families of models, divergence risk measures, uncertainty on path spaces, moment constraints, and martingale constraints. In a last step, we show how to use the theoretical results for the numerical computation of worst-case losses in an insurance context and no-arbitrage prices of European contingent claims after quoted maturities in a model-free setting.

Engineering flexible machine learning systems by traversing functionally invariant paths

Contemporary machine learning algorithms train artificial neural networks by setting network weights to a single optimized configuration through gradient descent on task-specific training data. The resulting networks can achieve human-level performance on natural language processing, image analysis and agent-based tasks, but lack the flexibility and robustness characteristic of human intelligence. Here we introduce a differential geometry framework—functionally invariant paths—that provides flexible and continuous adaptation of trained neural networks so that secondary tasks can be achieved beyond the main machine learning goal, including increased network sparsification and adversarial robustness. We formulate the weight space of a neural network as a curved Riemannian manifold equipped with a metric tensor whose spectrum defines low-rank subspaces in weight space that accommodate network adaptation without loss of prior knowledge. We formalize adaptation as movement along a geodesic path in weight space while searching for networks that accommodate secondary objectives. With modest computational resources, the functionally invariant path algorithm achieves performance comparable with or exceeding state-of-the-art methods including low-rank adaptation on continual learning, sparsification and adversarial robustness tasks for large language models (bidirectional encoder representations from transformers), vision transformers (ViT and DeIT) and convolutional neural networks.

Self-induced Bose glass phase in quantum quasicrystals

We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz–Petrich type. By using a mean-field variational method designed in momentum space as well as Gross–Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases.

Optimal Trajectory Planning for Wheeled Robots (OTPWR): A Globally and Dynamically Optimal Trajectory Planning Method for Wheeled Mobile Robots

In recent years, with the widespread application of indoor inspection robots, efficient motion planning has become crucial. Addressing the issue of discontinuous and suboptimal robot trajectories resulting from the independent nature of global and local planning, we propose a novel optimal path-planning method for wheeled mobile robots. This method leverages differential flatness to reduce dimensionality and decouple the problem, achieving globally optimal, collision-free paths in a two-dimensional flat output space through diagonal search and polynomial trajectory optimization. Comparative experiments in a simulated environment demonstrate that the proposed improved path search algorithm reduces search time by 46.6% and decreases the number of visited nodes by 43.1% compared to the original algorithm. This method not only ensures the optimal path and efficient planning but also ensures that the robot’s motion trajectory satisfies the dynamic constraints, verifying the effectiveness of the proposed optimal path planning algorithm for wheeled mobile robots.

EMPIRICAL STUDY OF SIGNAL STRENGTH PATH LOSS IN A UNIVERSITY CAMPUS ENVIRONMENT

Conducting performance analysis can be a valuable tool for mobile network operators (MNO) in optimizing network performance, improving user experience, and ensuring services, such as voice calls, data transmission, and video streaming, as well as to adhere to quality standards. This approach facilitates capacity planning, resource allocation, and the prompt identification and resolution of network congestion, hardware failures, or security breaches. In this paper, the performance of three MNOs around Papua New Guinea University of Technology (PNGUoT) is examined. The downlink frequency signal was measured and collected using the MST207T spectrum analyzer. The allocated frequency spectrum for each mobile network evolution from 3G to 4G-LTE was analyzed and calculated for signal strength path loss utilizing Free Space Path Loss (FSPL) and the Cost 231 Hata Model methods. 5G is not discussed in this paper as the technology is awaiting PNG market entry approval. The findings indicate that Digicel towers exhibit a decrease in downlink signal intensity and quality in areas with poor signal reception. Certain technical issues were observed to be responsible for the identified poor performances, including overcrowding of base stations (BS). The signal strength qualities of Bmobile Vodafone and Telikom exhibit variations, suggesting a moderate to poor level of quality. The data results from the path loss calculation also show an increase in fading signal strength quality. The findings of this empirical study would provide valuable insights for enhancing the efficiency and coverage of mobile communication networks around PNGUoT.

FF-RRT*: A Sampling-Based Planner for Multirobot Global Formation Path Planning

Abstract This article presents a collision-free global path planning approach for multirobot systems called flexible formation—rapidly exploring randomized trees* (FF-RRT*). The algorithm is based on RRT* and provides a flexible and efficient representation of the formation geometry independent of the number of robots. It is designed to generate optimal paths for multirobot systems in a five-dimensional configuration space comprising the formation centroid, orientation, and scaling. An affine transformation is used to convert the path in the configuration space to the workspace of the robots. The proposed method employs a new distance function that eliminates the need for tuning weights and a sampling scheme for scaling factors to avoid inter-robot collisions. FF-RRT* is experimentally demonstrated using nonholonomic wheeled mobile robots and is effective in planning the collective motion of the robots. Robots could collectively reach goals by squeezing through narrow gaps and splitting and merging around large obstacles.

Sub-terahertz near field channel measurements and analysis with beamforming and Bessel beams

Sub-terahertz communications (100–300 GHz) are explored today as a candidate technology to enable extremely high-rate, low-latency data services and high-resolution sensing in beyond-fifth-generation (beyond-5G) wireless networks. However, these sub-terahertz wireless systems will often have to operate in the near field, where the signal propagation does not follow canonical far-field models, including the commonly used free space path loss equation. Instead, the signal propagation in the near field follows more complex patterns that are not well-captured with analytical far-field models standardized for 5G research. Moreover, state-of-the-art beamforming solutions exploited heavily in fourth-generation (4G) and 5G networks are notably less efficient in the near field. In this article, the near-field sub-terahertz channel is accurately measured and analyzed. In addition to state-of-the-art beamforming, the article also analyzes the sub-terahertz channel measurements when using near-field-specific Bessel beams that demonstrate fewer power fluctuations in the near field in addition to higher focusing gain. Novel distance-centric and angle-centric dependencies reported in this article may serve as a reference when developing next-generation channel models for sixth-generation (6G) and beyond-6G near-field sub-terahertz wireless systems.

On the path of spin-[formula omitted] Berry phase

This paper investigates the relation between the Berry phase of a spinor accumulated along a path corresponding to an adiabatically varying magnetic field and the conformal deformation along the path in the parameter space. The first part demonstrates that the accumulated phase can be controlled by continuous deformation characterized by a single conformal parameter. The source of the corresponding field strength responsible for the deformed phase path is shown to be a conformally deformed monopole located at the origin in the parameter space with the fundamental strength g=±1/2. In the second part, we model a rotating magnetic field coupled to a charged spinor with a time-varying amplitude subjected to the conformal deformation, realizing a single-variable deformation of the evolution process of the phase path.

Impact of Antenna Orientation on Localization Accuracy Using RSSI-based Trilateration

The goal of the indoor localization is to determine the position and orientation of people, devices, and mobile robots. With the rise of Industry 4.0, wireless communication technologies have emerged as a rapidly evolving and crucial area for achieving this goal. Various radiocommunication-based technologies, including Bluetooth, Bluetooth Low Energy (BLE), Wi-Fi, Ultra-Wideband (UWB), and ZigBee offer means to indirectly estimate distance. These methods leverage diverse principles such as time-based measurements, signal strength, and angle of arrival. Indoor positioning systems can be categorized into two approaches: distance-based and distance-independent techniques. The Free Space Path Loss (FSPL) model describes the connection between distance and Received Signal Strength Indicator (RSSI). The parameters within this model significantly impact distance estimation and localization accuracy. Therefore, a method that accurately characterizes the model is critical. This work proposes an orientation-based localization technique utilizing RSSI and trilateration. Measurements were conducted between two ESP32 units in various orientations to obtain optimal parameters for each specific scenario. To assess the effectiveness of this approach, two scenarios were evaluated: one considering orientation and another neglecting it. The results show that incorporating orientation information leads to significantly more accurate positioning compared to the orientation-agnostic approach.

Application of Artificial Intelligence in the Design of 2D Escape From Pirates Game with A Star Algorithm Search Method

This research is designed to provide a challenging gaming experience by integrating strategy and problem-solving elements. The A* algorithm was chosen due to its efficient ability to find the shortest path in a complex search space. The implementation of this algorithm allows the main character to dynamically avoid obstacles and pirate threats and reach the destination in an optimal way. The test results show that the A* algorithm not only improves game performance but also provides a more realistic and challenging experience for the player. For testing this application, using obstacles and measured based on the value of nodes on the game map. Based on the test results, the A Star algorithm was successfully applied when comparing the computations in the game and manual calculations in the Escape from Pirates game in the test. Thus, this research contributes to the development of artificial intelligence-based games and opens opportunities for further innovation in interactive game design.

Complex behavior from intrinsic motivation to occupy future action-state path space

Most theories of behavior posit that agents tend to maximize some form of reward or utility. However, animals very often move with curiosity and seem to be motivated in a reward-free manner. Here we abandon the idea of reward maximization and propose that the goal of behavior is maximizing occupancy of future paths of actions and states. According to this maximum occupancy principle, rewards are the means to occupy path space, not the goal per se; goal-directedness simply emerges as rational ways of searching for resources so that movement, understood amply, never ends. We find that action-state path entropy is the only measure consistent with additivity and other intuitive properties of expected future action-state path occupancy. We provide analytical expressions that relate the optimal policy and state-value function and prove convergence of our value iteration algorithm. Using discrete and continuous state tasks, including a high-dimensional controller, we show that complex behaviors such as “dancing”, hide-and-seek, and a basic form of altruistic behavior naturally result from the intrinsic motivation to occupy path space. All in all, we present a theory of behavior that generates both variability and goal-directedness in the absence of reward maximization.

Characterisation Free Space Path Loss: Sub-6ghz and Millimetre Wave Frequency

There is a free-space route loss in free-space propagation, which is the propagation path with no obstacles between the transmitter and the receiver. This is characterized as the radio wave signal’s loss during free space transit. In order to build communication systems that can function as efficiently as possible despite potential problems, it is imperative to determine the path loss. Path loss has also been utilized in wireless survey instruments and radio communications to determine the antennas’ signal strength. Given the growing significance of wireless devices, including software and survey instruments, it is now beneficial to comprehend the idea of radio path loss in its entirety. In order to gain a comprehensive understanding of the free space propagation path loss and the factors influencing it, the main objective of this paper is to simulate the phenomenon. MATLAB software is utilized in this process to generate graphs that provide a clear and easy-to-understand representation of the path loss. Four frequencies were chosen two from the sub-6 frequency range and another two from the milliwave frequency range, Results showed a trend of an increasing free space path loss with increase in distance and frequencies with a greater loss at milliwave, but loss can be mitigated with antenna gain and following other recommendations.

Phase space path integral approach to the kinetics of black hole phase transition

Phase space path integral approach to the kinetics of black hole phase transition

Link attributes based multi-service routing for software-defined satellite networks

As the potential complement to terrestrial networks, satellite networks are expected to facilitate full coverage and broadband access at anytime and anywhere. However, satellite networks are characterized by highly dynamic topology and load, and how to design an adaptive routing algorithm to meet diverse application needs faces significant challenges. In this paper, we propose a Link-Attributes-based multi-service On-Demand Routing (LAODR) algorithm to provide highly reliable and service-aware data forwarding for Software -Defined Satellite Networks (SDSN). Specifically, we construct a quantitative model of link reliability which provides a fine-grained state description of the dynamic topology. Furthermore, we select the K-shortest path as the solution space and plan routing paths based on NSGA-II to allocate link resources reasonably. Extensive experiments on the Iridium validate that LAODR outperforms state-of-art routing algorithms in terms of end-to-end average latency, packet loss, throughput and node congestion degree, as well as meets the requirements of diverse services.

Residual path integrals for re‐rendering

AbstractConventional rendering techniques are primarily designed and optimized for single‐frame rendering. In practical applications, such as scene editing and animation rendering, users frequently encounter scenes where only a small portion is modified between consecutive frames. In this paper, we develop a novel approach to incremental re‐rendering of scenes with dynamic objects, where only a small part of a scene moves from one frame to the next. We formulate the difference (or residual) in the image between two frames as a (correlated) light‐transport integral which we call the residual path integral. Efficient numerical solution of this integral then involves (1) devising importance sampling strategies to focus on paths with non‐zero residual‐transport contributions and (2) choosing appropriate mappings between the native path spaces of the two frames. We introduce a set of path importance sampling strategies that trace from the moving object(s) which are the sources of residual energy. We explore path mapping strategies that generalize those from gradient‐domain path tracing to our importance sampling techniques specially for dynamic scenes. Additionally, our formulation can be applied to material editing as a simpler special case. We demonstrate speed‐ups over previous correlated sampling of path differences and over rendering the new frame independently. Our formulation brings new insights into the re‐rendering problem and paves the way for devising new types of sampling techniques and path mappings with different trade‐offs.

Hybrid trajectory planning of two permanent magnets for medical robotic applications

Independent robotic manipulation of two large permanent magnets, in the form of the dual External Permanent Magnet (dEPM) system has demonstrated the possibility for enhanced magnetic control by allowing for actuation up to eight magnetic degrees of freedom (DOFs) at clinically relevant scales. This precise off-board control has facilitated the use of magnetic agents as medical devices, including catheter-like soft continuum robots (SCRs). The use of multiple robotically actuated permanent magnets poses the risk of collision between the robotic arms, the environment, and the patient. Furthermore, unconstrained transitions between actuation inputs can lead to undesired spikes in magnetic fields potentially resulting in unsafe manipulator deformation. This paper presents a hybrid approach to trajectory planning for the dEPM platform. This is performed by splitting the planning problem in two: first finding a collision-free physical path for the two robotically actuated permanent magnets before combining this with a path in magnetic space, which permits for a smooth change in magnetic fields and gradients. This algorithm was characterized by actuating each of the eight magnetic DOFs sequentially, eliminating any potential collisions and reducing the maximum undesired actuation value by 203.7 mT for fields and by 418.7 mT/m for gradients. The effect of this planned magnetic field actuation on a SCR was then examined through two case studies. First, a tip-driven SCR was moved to set points within a confined area. Actuation using the proposed planner reduced movement outside the restricted area by an average of 41.3%. Lastly, the use of the proposed magnetic planner was shown to be essential in navigating a multi-segment magnetic SCR to the site of an aneurysm within a silicone brain phantom.

The invariant measure of a walking droplet in hydrodynamic pilot–wave theory

We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential.