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This extended abstracts presents a method to generate energy-optimal trajectories for multi-agent systems as a strategic-form game. Using recent results in optimal control, we demonstrate that an energy-optimal trajectory can be generated in milliseconds if the sequence of constraint activations is known a priori. Thus, rather than selecting an infinite-dimensional action from a function space, the agents select their actions from a finite number of constraints and determine the time that each becomes active. Furthermore, the agents can exactly encode their trajectory in a set of real numbers, rather than communicating their control action as an infinite-dimensional function. We demonstrate the performance of this algorithm in simulation and find an optimal trajectory in 45 milliseconds on a tablet PC., Comment: 4 pages, 3 figures. Extended abstract for the 2023 IEEE International Symposium on Multi-Robot and Multi-Agent Systems (MRS 2023)

In confirmatory clinical trials, survival outcomes are frequently studied and interim analyses for efficacy and/or futility are often desirable. Methods such as the log rank test and Cox regression model are commonly used to compare treatments in this setting. They rely on a proportional hazards (PH) assumption and are subject to type I error rate inflation and loss of power when PH are violated. Such violations may be expected a priori, particularly when the mechanisms of treatments differ such as immunotherapy vs. chemotherapy for treating cancer. We develop group sequential tests for comparing survival curves with covariate adjustment that allow for interim analyses in the presence of non-PH and offer easily interpreted, clinically meaningful summary measures of the treatment effect. The joint distribution of repeatedly computed test statistics converges to the canonical joint distribution with a Markov structure. The asymptotic distribution of the test statistics allows marginal comparisons of survival probabilities at multiple fixed time points and facilitates both critical value specification to maintain type I error control and sample size/power determination. Simulations demonstrate that the achieved type I error rate and power of the proposed tests meet targeted levels and are robust to the PH assumption and covariate influence. The proposed tests are illustrated using a clinical trial dataset from the Blood and Marrow Transplant Clinical Trials Network 1101 trial.

We study the conditions under which the CP violation in the quark mixing matrix can leak into the scalar potential of the real two-Higgs-doublet model (2HDM) via divergent radiative corrections, thereby spoiling the renormalizability of the model. We show that any contributing diagram must involve 12 Yukawa-coupling insertions and a factor of the $U(1)_{PQ}$-breaking scalar potential parameter $\lambda_5$, thereby requiring at least six loops; this also implies that the 2HDM with only softly-broken $U(1)_{PQ}$ is safe from divergent leaks of CP violation to all orders. We demonstrate that additional symmetries of the six-loop diagrams in the type I and II 2HDMs guarantee that all of the divergent CP-violating contributions cancel at this order. We also show that these symmetries are violated at seven loops and enumerate the classes of diagrams that can contribute to CP-violating divergences, providing evidence that the real 2HDM is theoretically inconsistent starting at the seven-loop level., Comment: 27 pages, 14 figures

In this article we address the multi-robot task allocation problem, where robots must cooperatively assign themselves to accomplish a set of tasks. We consider the colony maintenance problem as an example, where a team of robots are tasked with continuously maintaining the energy supply of a central colony. We model this as a global game, where each robot measures the energy level of the colony, and the current number of assigned robots, to determine whether or not to forage for energy sources. The key to our approach is introducing a negative feedback term into the robots' utility, which also eliminates the trivial solution where foraging or not foraging are strictly dominant strategies. We compare our approach qualitatively to existing an global games approach, where a positive positive feedback term admits threshold-based decision making that encourages many robots to forage. We discuss how positive feedback can lead to a cascading failure when robots are removed from the system, and we demonstrate the resilience of our approach in simulation., Comment: 8 pages, 5 figures

The ongoing development of single electron, nano and atomic scale semiconductor devices would benefit greatly from a characterization tool capable of detecting single electron charging events with high spatial resolution, at low temperature. In this work, we introduce a novel Atomic Force Microscope (AFM) instrument capable of measuring critical device dimensions, surface roughness, electrical surface potential, and ultimately the energy levels of quantum dots and single electron transistors in ultra miniaturized semiconductor devices. Characterization of nanofabricated devices with this type of instrument presents a challenge: finding the device. We therefore also present a process to efficiently find a nanometre size quantum dot buried in a $10 \times 10~\text{mm}^2$ silicon sample using a combination of optical positioning, capacitive sensors and AFM topography in vacuum.

Using density functional theory (DFT) and linear response approaches, we compute the on-site Hubbard interaction $U$ of elemental Terbium (Tb) metal in the pressure range $\sim 0-65$ GPa. The resulting first-principles $U$ values with experimental crystal structures enable us to examine the magnetic properties of Tb using a self-consistent DFT+U method. The lowest-energy magnetic states in our calculations for different high-pressure Tb phases -- including hcp, $\alpha$-Sm, and dhcp -- are found to be compatible with the corresponding magnetic ordering vectors reported in experiments. The result shows that the inclusion of Hubbard $U$ substantially improves the accuracy and efficiency in modeling correlated rare-earth materials. Our study also provides the necessary $U$ information for other quantum many-body techniques to study Tb under extreme pressure conditions., Comment: 7 pages, 4 figures

In this letter, we address the problem of improving the feasible domain of the solution of a decentralized control framework for coordinating connected and automated vehicles (CAVs) at signal-free intersections as the traffic volume increases. The framework provides the optimal trajectories of CAVs to cross the intersection safely without stop-and-go driving. However, as the traffic volume increases, the domain of the feasible trajectories decreases. We use concepts of numerical interpolation to identify appropriate polynomials that can serve as alternative trajectories of the CAVs, expanding the domain of the feasible CAV trajectories. We provide the conditions under which such polynomials exist. Finally, we demonstrate the efficacy of our approach through numerical simulations.

The operational space and global performance of plasmas with edge-localized modes (ELMs) suppressed by resonant magnetic perturbations (RMPs) are surveyed by comparing AUG, DIII-D, EAST, and KSTAR stationary operating points. RMP-ELM suppression is achieved over a range of plasma currents, toroidal fields, and RMP toroidal mode numbers. Consistent operational windows in edge safety factor are found across devices, while windows in plasma shaping parameters are distinct. Accessed pedestal parameters reveal a quantitatively similar pedestal-top density limit for RMP-ELM suppression in all devices of just over 3x1019 m-3. This is surprising given the wide variance of many engineering parameters and edge collisionalities, and poses a challenge to extrapolation of the regime. Wide ranges in input power, confinement time, and stored energy are observed, with the achieved triple product found to scale like the product of current, field, and radius. Observed energy confinement scaling with engineering parameters for RMP-ELM suppressed plasmas are presented and compared with expectations from established H and L-mode scalings, including treatment of uncertainty analysis. Different scaling exponents for individual engineering parameters are found as compared to the established scalings. However, extrapolation to next-step tokamaks ITER and SPARC find overall consistency within uncertainties with the established scalings, finding no obvious performance penalty when extrapolating from the assembled multi-device RMP-ELM suppressed database. Overall this work identifies common physics for RMP-ELM suppression and highlights the need to pursue this no-ELM regime at higher magnetic field and different plasma physical size., Comment: 22 pages, 11 figures

Digital health technologies (DHT), such as wearable devices, provide personalized, continuous, and real-time monitoring of patient. These technologies are contributing to the development of novel therapies and personalized medicine. Gaining insight from these technologies requires appropriate modeling techniques to capture clinically-relevant changes in disease state. The data generated from these devices is characterized by being stochastic in nature, may have missing elements, and exhibits considerable inter-individual variability - thereby making it difficult to analyze using traditional longitudinal modeling techniques. We present a novel pharmacology-informed neural stochastic differential equation (SDE) model capable of addressing these challenges. Using synthetic data, we demonstrate that our approach is effective in identifying treatment effects and learning causal relationships from stochastic data, thereby enabling counterfactual simulation., Comment: 6 figures

This letter addresses the constraint compatibility problem of control barrier functions (CBFs), which occurs when a safety-critical CBF requires a system to apply more control effort than it is capable of generating. This inevitably leads to a safety violation, which transitions the system to an unsafe (and possibly dangerous) trajectory. We resolve the constraint compatibility problem by constructing a control barrier function that maximizes the feasible action space for first and second-order constraints, and we prove that the optimal CBF encodes a dynamical motion primitive. Furthermore, we show that this dynamical motion primitive contains an implicit model for the future trajectory for time-varying components of the system. We validate our optimal CBF in simulation, and compare its behavior with a linear CBF., Comment: 6 pages, 2 figures

On-chip photonic processors for neural networks have potential benefits in both speed and energy efficiency but have not yet reached the scale at which they can outperform electronic processors. The dominant paradigm for designing on-chip photonics is to make networks of relatively bulky discrete components connected by one-dimensional waveguides. A far more compact alternative is to avoid explicitly defining any components and instead sculpt the continuous substrate of the photonic processor to directly perform the computation using waves freely propagating in two dimensions. We propose and demonstrate a device whose refractive index as a function of space, $n(x,z)$, can be rapidly reprogrammed, allowing arbitrary control over the wave propagation in the device. Our device, a 2D-programmable waveguide, combines photoconductive gain with the electro-optic effect to achieve massively parallel modulation of the refractive index of a slab waveguide, with an index modulation depth of $10^{-3}$ and approximately $10^4$ programmable degrees of freedom. We used a prototype device with a functional area of $12\,\text{mm}^2$ to perform neural-network inference with up to 49-dimensional input vectors in a single pass, achieving 96% accuracy on vowel classification and 86% accuracy on $7 \times 7$-pixel MNIST handwritten-digit classification. This is a scale beyond that of previous photonic chips relying on discrete components, illustrating the benefit of the continuous-waves paradigm. In principle, with large enough chip area, the reprogrammability of the device's refractive index distribution enables the reconfigurable realization of any passive, linear photonic circuit or device. This promises the development of more compact and versatile photonic systems for a wide range of applications, including optical processing, smart sensing, spectroscopy, and optical communications.

We call a continuous path of polygons decreasing if the convex hulls of the polygons form a decreasing family of sets. For an arbitrary polygon of more than three vertices, we characterize the polygons contained in it that can be reached by a decreasing path (attainability problem), and we show that this can be done by a finite application of "pull-in" moves (bang-bang problem). In the case of triangles, this problems was investigated by Goodman, Johansen, Ramsey, and Frydman among others, in connection with the embeddability problem for non-homogeneous Markov processes.

We carry out three-dimensional computations of the accretion rate onto an object (of size $R_{\rm sink}$ and mass $m$) as it moves through a uniform medium at a subsonic speed $v_{\infty}$. The object is treated as a fully-absorbing boundary (e.g. a black hole). In contrast to early conjectures, we show that when $R_{\rm sink}\ll R_{A}=2Gm/v^2$ the accretion rate is independent of $v_{\infty}$ and only depends on the entropy of the ambient medium, its adiabatic index, and $m$. Our numerical simulations are conducted using two different numerical schemes via the Athena++ and Arepo hydrodynamics solvers, which reach nearly identical steady-state solutions. We find that pressure gradients generated by the isentropic compression of the flow near the accretor are sufficient to suspend much of the surrounding gas in a near-hydrostatic equilibrium, just as predicted from the spherical Bondi-Hoyle calculation. Indeed, the accretion rates for steady flow match the Bondi-Hoyle rate, and are indicative of isentropic flow for subsonic motion where no shocks occur. We also find that the accretion drag may be predicted using the Safronov number, $\Theta=R_{A}/R_{\rm sink}$, and is much less than the dynamical friction for sufficiently small accretors ($R_{\rm sink}\ll R_{A}$)., Comment: 14 pages, 7 figures. Submitted to ApJ. Comments welcome!

Kahn Process Networks (KPNs) are a deterministic Model of Computation (MoC) for distributed systems. KPNs supports non-blocking writes and blocking reads, with the consequent assumption of unbounded buffers between processes. Variants such as Finite FIFO Platforms (FFP) have been developed, which enforce boundedness. One issue with existing models is that they mix process synchronisation with process execution. In this paper we address how these two facets may be decoupled. This paper explores a recent alternative called bittide, which decouples the execution of a process from the control needed for process synchronisation, and thus preserves determinism and boundedness while ensuring pipelined execution for better throughput. Our intuition is that such an approach could leverage not only determinism and buffer boundedness but may potentially offer better overall throughput. To understand the behavior of these systems we define a formal model -- a deterministic MoC called Logical Synchrony Networks (LSNs). LSNs describes a network of processes modelled as a graph, with edges representing invariant logical delays between a producer process and the corresponding consumer process. We show that this abstraction is satisfied by KPNs. Subsequently, we show that both FFPs and bittide faithfully implement this abstraction. Thus, we show for the first time that FFPs and bittide offer two alternative ways of implementing deterministic distributed systems with the latter being more performant.

Cortical surface analysis has gained increased prominence, given its potential implications for neurological and developmental disorders. Traditional vision diffusion models, while effective in generating natural images, present limitations in capturing intricate development patterns in neuroimaging due to limited datasets. This is particularly true for generating cortical surfaces where individual variability in cortical morphology is high, leading to an urgent need for better methods to model brain development and diverse variability inherent across different individuals. In this work, we proposed a novel diffusion model for the generation of cortical surface metrics, using modified surface vision transformers as the principal architecture. We validate our method in the developing Human Connectome Project (dHCP), the results suggest our model demonstrates superior performance in capturing the intricate details of evolving cortical surfaces. Furthermore, our model can generate high-quality realistic samples of cortical surfaces conditioned on postmenstrual age(PMA) at scan., Comment: 4 pages