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Many of the primal ingredients of convex optimization extend naturally from Euclidean to Hadamard spaces $\unicode{x2014}$ nonpositively curved metric spaces like Euclidean, Hilbert, and hyperbolic spaces, metric trees, and more general CAT(0) cubical complexes. Linear structure, however, and the duality theory it supports are absent. Nonetheless, we introduce a new type of subgradient for convex functions on Hadamard spaces, based on Busemann functions. This notion supports a splitting subgradient method with guaranteed complexity bounds. In particular, the algorithm solves $p$-mean problems in general Hadamard spaces: we illustrate by computing medians in BHV tree space., Comment: 41 pages, 5 figures

The ability to resolve photon numbers is crucial in quantum information science and technology, driving the development of detectors with intrinsic photon-number resolving (PNR) capabilities. Although transition edge sensors represent the state-of-the-art in PNR performance, superconducting nanowire single-photon detectors (SNSPDs) offer superior efficiency, speed, noise reduction, and timing precision. Directly inferring photon numbers, however, has only recently become feasible due to advances in readout technology. Despite this, photon-number discrimination remains constrained by the nanowire's electrical properties and readout jitter. In this work, we employ waveguide-integrated SNSPDs and time-resolved measurements to explore how the nanowire kinetic inductance and system jitter affect PNR capabilities. By analyzing the latency time of the photon detection, we can resolve changes in the rising edge of the detection pulse. We find that lower jitter as well as increased kinetic inductance enhances the pulse separation for different photon numbers and improves the PNR capability. Enhancing the kinetic inductance from 165 nH to 872 nH improves PNR quality by 12%, 31% and 23% over the first three photon numbers, though at the cost of reducing the detector's count rate from 165 Mcps to 19 Mcps. Our findings highlight the trade-off between PNR resolution and detector speed., Comment: 21 pages, 7 figures

Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case of feasible regions consisting of pre-images of convex sets under maps that are once (but not necessarily twice) continuously differentiable, the geometry is less transparent. We define a new approximate convexity property, that holds both for such feasible regions and also for all prox-regular sets. This new property requires that nearby points can always be joined by smooth feasible paths that are almost straight. In particular, in the terminology of real algebraic geometry, such feasible regions are locally normally embedded in the Euclidean space.

The treatment of Hall-effect thrusters as nonlinear, dynamical systems has emerged as a new perspective to understand and analyze data acquired from the thrusters. The acquisition of high-speed data that can resolve the characteristic high-frequency oscillations of these thruster enables additional levels of classification in these thrusters. Notably, these signals may serve as unique indicators for the full state of the system that can aid digital representations of thrusters and predictions of thruster dynamics. In this work, a Reservoir Computing framework is explored to build surrogate models from experimental time-series measurements of a Hall-effect thruster. Such a framework has shown immense promise for predicting the behavior of low-dimensional yet chaotic dynamical systems. In particular, the surrogates created by the Reservoir Computing framework are capable of both predicting the observed behavior of the thruster and estimating the values of certain measurements from others, known as inference.

This work explores the conditions under which global contraction manifests in the leaky continuous time reservoirs, thus guaranteeing Generalized Synchronization. Results on continuous time reservoirs make use of the logarithmic norm of the connectivity matrix. Further analysis yields some simple guidelines on how to better construct the connectivity matrix in these systems. Additionally, we outline how the Universal Approximation Property of discrete time reservoirs is readily satisfied by virtue of the activation function being contracting, and how continuous time reservoirs may inherit a limited form of universal approximation by virtue of them overlapping with Neural Ordinary Differential Equations. The ability of the Reservoir Computing framework to universally approximate topological conjugates, along with their fast training, make them a compelling data-driven, black-box surrogate of dynamical systems, and a potential mechanism for developing digital twins.

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally whether or not a given point is such an average, exactly or approximately. In nonpositively curved spaces, several averaging notions, including the usual weighted barycenter, produce the same "mean set". In such spaces, at points where the tangent cone is a Euclidean space, the recognition problem reduces to Euclidean projection onto a polytope. Hadamard manifolds comprise one example. Another consists of CAT(0) cubical complexes, at relative-interior points: the recognition problem is harder for general points, but we present an efficient semidefinite-programming-based algorithm.

Goldstein's 1977 idealized iteration for minimizing a Lipschitz objective fixes a distance - the step size - and relies on a certain approximate subgradient. That "Goldstein subgradient" is the shortest convex combination of objective gradients at points within that distance of the current iterate. A recent implementable Goldstein-style algorithm allows a remarkable complexity analysis (Zhang et al. 2020), and a more sophisticated variant (Davis and Jiang, 2022) leverages typical objective geometry to force near-linear convergence. To explore such methods, we introduce a new modulus, based on Goldstein subgradients, that robustly measures the slope of a Lipschitz function. We relate near-linear convergence of Goldstein-style methods to linear growth of this modulus at minimizers. We illustrate the idea computationally with a simple heuristic for Lipschitz minimization.

We consider geodesically convex optimization problems involving distances to a finite set of points $A$ in a CAT(0) cubical complex. Examples include the minimum enclosing ball problem, the weighted mean and median problems, and the feasibility and projection problems for intersecting balls with centers in $A$. We propose a decomposition approach relying on standard Euclidean cutting plane algorithms. The cutting planes are readily derivable from efficient algorithms for computing geodesics in the complex.

To explore convex optimization on Hadamard spaces, we consider an iteration in the style of a subgradient algorithm. Traditionally, such methods assume that the underlying spaces are manifolds and that the objectives are geodesically convex: the methods are described using tangent spaces and exponential maps. By contrast, our iteration applies in a general Hadamard space, is framed in the underlying space itself, and relies instead on horospherical convexity of the objective level sets. For this restricted class of objectives, we prove a complexity result of the usual form. Notably, the complexity does not depend on a lower bound on the space curvature. We illustrate our subgradient algorithm on the minimal enclosing ball problem in Hadamard spaces.

This technical report details our work towards building an enhanced audio-visual sound event localization and detection (SELD) network. We build on top of the audio-only SELDnet23 model and adapt it to be audio-visual by merging both audio and video information prior to the gated recurrent unit (GRU) of the audio-only network. Our model leverages YOLO and DETIC object detectors. We also build a framework that implements audio-visual data augmentation and audio-visual synthetic data generation. We deliver an audio-visual SELDnet system that outperforms the existing audio-visual SELD baseline.

Sound event localization and detection (SELD) is an important task in machine listening. Major advancements rely on simulated data with sound events in specific rooms and strong spatio-temporal labels. SELD data is simulated by convolving spatialy-localized room impulse responses (RIRs) with sound waveforms to place sound events in a soundscape. However, RIRs require manual collection in specific rooms. We present SpatialScaper, a library for SELD data simulation and augmentation. Compared to existing tools, SpatialScaper emulates virtual rooms via parameters such as size and wall absorption. This allows for parameterized placement (including movement) of foreground and background sound sources. SpatialScaper also includes data augmentation pipelines that can be applied to existing SELD data. As a case study, we use SpatialScaper to add rooms to the DCASE SELD data. Training a model with our data led to progressive performance improves as a direct function of acoustic diversity. These results show that SpatialScaper is valuable to train robust SELD models., Comment: 5 pages, 4 figures, 1 table, to be presented at ICASSP 2024 in Seoul, South Korea

A central tool for understanding first-order optimization algorithms is the Kurdyka-Lojasiewicz inequality. Standard approaches to such methods rely crucially on this inequality to leverage sufficient decrease conditions involving gradients or subgradients. However, the KL property fundamentally concerns not subgradients but rather "slope", a purely metric notion. By highlighting this view, and avoiding any use of subgradients, we present a simple and concise complexity analysis for first-order optimization algorithms on metric spaces. This subgradient-free perspective also frames a short and focused proof of the KL property for nonsmooth semi-algebraic functions.

Differentiable structure ensures that many of the basics of classical convex analysis extend naturally from Euclidean space to Riemannian manifolds. Without such structure, however, extensions are more challenging. Nonetheless, in Alexandrov spaces with curvature bounded above (but possibly positive), we develop several basic building blocks. We define subgradients via projection and the normal cone, prove their existence, and relate them to the classical affine minorant property. Then, in what amounts to a simple calculus or duality result, we develop a necessary optimality condition for minimizing the sum of two convex functions.

The dynamical stability of quadruple-star systems has traditionally been treated as a problem involving two `nested' triples which constitute a quadruple. In this novel study, we employed a machine learning algorithm, the multi-layer perceptron (MLP), to directly classify 2+2 and 3+1 quadruples based on their stability (or long-term boundedness). The training data sets for the classification, comprised of $5\times10^5$ quadruples each, were integrated using the highly accurate direct $N$-body code MSTAR. We also carried out a limited parameter space study of zero-inclination systems to directly compare quadruples to triples. We found that both our quadruple MLP models perform better than a `nested' triple MLP approach, which is especially significant for 3+1 quadruples. The classification accuracies for the 2+2 MLP and 3+1 MLP models are 94% and 93% respectively, while the scores for the `nested' triple approach are 88% and 66% respectively. This is a crucial implication for quadruple population synthesis studies. Our MLP models, which are very simple and almost instantaneous to implement, are available on GitHub, along with Python3 scripts to access them., Comment: Accepted for publication by MNRAS

The complexity of applications addressed with photonic integrated circuits is steadily rising and poses increasingly challenging demands on individual component functionality, performance and footprint. Inverse design methods have recently shown great promise to address these demands using fully automated design procedures that enable access to non-intuitive device layouts beyond conventional nanophotonic design concepts. Here we present a dynamic binarization method for the objective-first algorithm that lies at the core of the currently most successful inverse design algorithms. Our results demonstrate significant performance advantages over previous implementations of objective first algorithms, which we show for a fundamental TE00 to TE20 waveguide mode converter both in simulation and in experiments with fabricated devices., Comment: 10 pages, 4 figures

In recent years, Artificial Intelligence (AI) and Computer Vision (CV) have become the pinnacle of technology with new developments seemingly every day. This technology along with more powerful drone technology have made autonomous surveillance more sought after. Here an overview of the Automated Logging Drone (ALD) project is presented along with examples of how this project can be used with more refining and added features.

We present evolutionary pathways for creating hot subdwarf OB (sdOB) stars from hierarchical triple configurations. We use the population synthesis code Multiple Stellar Evolution (MSE) to follow the stellar, binary, and gravitational dynamical evolution of triple-star systems. To ascertain the effect of the outer tertiary, we also consider the evolution of the inner binary with the tertiary component removed. We find we are able to create sdOB stars in single, binary and triple configurations. We also demonstrate that it is possible to form sdOBs in systems which undergo triple common envelope evolution, when the tertiary star undergoes unstable mass transfer onto the inner binary. We are unable to create single or wide sdOB systems without involving a merger earlier in the evolution. The triples can produce sdOBs in binaries with wide, non-interacting companions through binary interactions, which is impossible in isolated binaries. Owing to the closeness of the inner binary in hierarchical triples the formation channels associated with stable mass transfer are suppressed when compared to the isolated binary case., Comment: 10 Pages, 10 Figures, Accepted for publication

We present two approaches to determine the dynamical stability of a hierarchical triple-star system. The first is an improvement on the Mardling-Aarseth stability formula from 2001, where we introduce a dependence on inner orbital eccentricity and improve the dependence on mutual orbital inclination. The second involves a machine learning approach, where we use a multilayer perceptron (MLP) to classify triple-star systems as `stable' and `unstable'. To achieve this, we generate a large training data set of 10^6 hierarchical triples using the N-body code MSTAR. Both our approaches perform better than previous stability criteria, with the MLP model performing the best. The improved stability formula and the machine learning model have overall classification accuracies of 93 % and 95 % respectively. Our MLP model, which accurately predicts the stability of any hierarchical triple-star system within the parameter ranges studied with almost no computation required, is publicly available on Github in the form of an easy-to-use Python script., Comment: Accepted for publication by MNRAS

We present an updated prescription for the equilibrium tides suitable for population synthesis codes. A grid of 1D evolutionary models was created and the viscous time-scale was calculated for each detailed model. A metallicity dependent power-law relation was fitted to both the convective cores and convective envelopes of the models. The prescription was implemented into the population synthesis code BSE and predicts an 16.5% reduction in the overall number of merges, with those involving main-sequence stars most affected. The new prescription also reduces the overall supernova rate by 3.6% with individual channels being differently affected. The single degenerate Ia supernova occurrence is reduced by 12.8%. The merging of two Carbon Oxygen white dwarfs to cause a Ia supernova occurs 16% less frequently. The number of sub-synchronously rotating stars in close binaries is substantially increased with our prescription, as is the number of non-circularized systems at the start of common-envelope evolution., Comment: 22 pages, 17 Figures, Accepted for publication 13/05/22

We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with system parameter labels. Our goal is to identify system parameters of new trajectories. The given trajectories may or may not encompass the full state of the system, and we may only observe a one-dimensional time series. In the latter case, we reconstruct the full state by using delay embeddings, and under sufficient conditions, Taken's Embedding Theorem assures us the reconstruction is diffeomorphic to the original. This allows our method to work on time series. Our method works by first learning the velocity operator (as given or reconstructed) with a neural network having both state and system parameters as variable inputs. Then on new trajectories we backpropagate prediction errors to the system parameter inputs giving us a gradient. We then use gradient descent to infer the correct system parameter. We demonstrate the efficacy of our approach on many numerical examples: the Lorenz system, Lorenz96, Lotka-Volterra Predator-Prey, and the Compound Double Pendulum. We also apply our algorithm on a real-world dataset: propulsion of the Hall-effect Thruster (HET).

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is smooth at every iterate, the corresponding local models are unstable and the number of cutting planes invoked by traditional remedies is difficult to bound, leading to convergences guarantees that are sublinear relative to the cumulative number of gradient evaluations. We instead propose a multipoint generalization of the gradient descent iteration for local optimization. While designed with general objectives in mind, we are motivated by a ``max-of-smooth'' model that captures the subdifferential dimension at optimality. We prove linear convergence when the objective is itself max-of-smooth, and experiments suggest a more general phenomenon., Comment: Accepted to SIAM Journal on Optimization (SIOPT)