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Compared to ground state electronic structure optimizations, accurate simulations of molecular real-time electron dynamics are usually much more difficult to perform. To simulate electron dynamics, the time-dependent density matrix renormalization group (TDDMRG) has been shown to offer an attractive compromise between accuracy and cost. However, many simulation parameters significantly affect the quality and efficiency of a TDDMRG simulation. So far, it is unclear whether common wisdom from ground state DMRG carries over to the TDDMRG, and a guideline on how to choose these parameters is missing. Here, in order to establish such a guideline, we investigate the convergence behavior of the main TDDMRG simulation parameters, such as time integrator, the choice of orbitals, and the choice of MPS representation for complex-valued non-singlet states. In addition, we propose a method to select orbitals that are tailored to optimize the dynamics. Lastly, we showcase the TDDMRG by applying it to charge migration ionization dynamics in furfural, where we reveal a rapid conversion from an ionized state with a $\sigma$ character to one with a $\pi$ character within less than a femtosecond.

We study a higher-dimensional analogue of the {Random Travelling Salesman Problem}: let the complete $d$-dimensional simplicial complex $K_n^{d}$ on $n$ vertices be equipped with i.i.d.\ volumes on its facets, uniformly random in $[0,1]$. What is the minimum volume $M_{n,d}$ of a sub-complex homeomorphic to the $d$-dimensional sphere $\mathbb{S}^d$, containing all vertices? We determine the growth rate of $M_{n,2}$, and prove that it is well-concentrated. For $d>2$ we prove such results to the extent that current knowledge about the number of triangulations of $\mathbb{S}^d$ allows. We remark that this can be thought of as a model of random geometry in the spirit of Angel \& Schramm's UIPT, and provide a generalised framework that interpolates between our model and the uniform random triangulation of $\mathbb{S}^d$., Comment: 25 pages, 1 figure

Recursive Fourier Sampling (RFS) is one of the earliest problems demonstrating a quantum advantage, and is known to lie outside the Merlin-Arthur complexity class. This paper contains a description of the phenomenon of phase kickback and its use in RFS, and how and why this is the enabling quantum computational property for the quantum advantage in RFS. Most importantly, describing the computational process of quantum computation in the terminology of phase kickback gives a much better understanding of why uncomputation is necessary when solving RFS, pointing to the underlying reason for the limitations of the quantum advantage., Comment: 6 pages, 1 figure

Relational databases often suffer from uninformative descriptors of table contents, such as ambiguous columns and hard-to-interpret values, impacting both human users and Text-to-SQL models. This paper explores the use of large language models (LLMs) to generate informative column descriptions as a semantic layer for relational databases. Using the BIRD-Bench development set, we created ColSQL, a dataset with gold-standard column descriptions generated and refined by LLMs and human annotators. We evaluated several instruction-tuned models, finding that GPT-4o and Command R+ excelled in generating high-quality descriptions. Additionally, we applied an LLM-as-a-judge to evaluate model performance. Although this method does not align well with human evaluations, we included it to explore its potential and to identify areas for improvement. More work is needed to improve the reliability of automatic evaluations for this task. We also find that detailed column descriptions significantly improve Text-to-SQL execution accuracy, especially when columns are uninformative. This study establishes LLMs as effective tools for generating detailed metadata, enhancing the usability of relational databases.

Attosecond X-ray pulses are the key to studying electron dynamics at their natural time scale involving specific electronic states. They are promising to build the conceptual bridge between physical and chemical photo-reaction processes. Free-electron lasers have demonstrated their capability of generating intense attosecond X-ray pulses. However, harnessing them for time-resolving experiments and investigations of nonlinear X-ray absorption mechanisms remains a cutting-edge challenge. We have characterised X-ray pulses with durations of down to 700$\,$attoseconds and peak powers up to 200$\,$GW at $\sim$ 1$\,$keV photon energy via angular streaking at the SQS instrument of the European XFEL. As direct application, we present results of nonlinear X-ray-matter interaction via state-specific spectroscopy on a transient system. Using the derived spectral and temporal information of each pulse, we deliberately steer the probability for formation of double-core vacancies in neon gas atoms through excitation or ionisation of the second inner-shell electron after K-shell ionisation. Our results advance the field of attosecond science with highly intense and fully characterised X-ray pulses to the site-specific investigation of electronic motion in transient media.

We propose a novel method for user-to-user interference (UUI) mitigation in dynamic time-division duplex multiple-input multiple-output communication systems with multi-antenna users. Specifically, we consider the downlink data transmission in the presence of UUI caused by a user that simultaneously transmits in uplink. Our method introduces an overhead for estimation of the user-to-user channels by transmitting pilots from the uplink user to the downlink users. Each downlink user obtains a channel estimate that is used to design a combining matrix for UUI mitigation. We analytically derive an achievable spectral efficiency for the downlink transmission in the presence of UUI with our mitigation technique. Through numerical simulations, we show that our method can significantly improve the spectral efficiency performance in cases of heavy UUI., Comment: Accepted for presentation at the 25th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Lucca, Italy, September 10-13, 2024

The Wasserstein distance $\mathcal{W}_p$ is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years. The adapted Wasserstein distance $\mathcal{A}\mathcal{W}_p$ extends this theory to laws of discrete time stochastic processes in their natural filtrations, making it particularly well suited for analyzing time-dependent stochastic optimization problems. While the topological differences between $\mathcal{A}\mathcal{W}_p$ and $\mathcal{W}_p$ are well understood, their differences as metrics remain largely unexplored beyond the trivial bound $\mathcal{W}_p\lesssim \mathcal{A}\mathcal{W}_p$. This paper closes this gap by providing upper bounds of $\mathcal{A}\mathcal{W}_p$ in terms of $\mathcal{W}_p$ through investigation of the smooth adapted Wasserstein distance. Our upper bounds are explicit and are given by a sum of $\mathcal{W}_p$, Eder's modulus of continuity and a term characterizing the tail behavior of measures. As a consequence, upper bounds on $\mathcal{W}_p$ automatically hold for $\mathcal{AW}_p$ under mild regularity assumptions on the measures considered. A particular instance of our findings is the inequality $\mathcal{A}\mathcal{W}_1\le C\sqrt{\mathcal{W}_1}$ on the set of measures that have Lipschitz kernels. Our work also reveals how smoothing of measures affects the adapted weak topology. In fact, we find that the topology induced by the smooth adapted Wasserstein distance exhibits a non-trivial interpolation property, which we characterize explicitly: it lies in between the adapted weak topology and the weak topology, and the inclusion is governed by the decay of the smoothing parameter.

These lecture notes are designed to accompany an imaginary, virtual, undergraduate, one or two semester course on fundamentals of Parallel Computing as well as to serve as background and reference for graduate courses on High-Performance Computing, parallel algorithms and shared-memory multiprocessor programming. They introduce theoretical concepts and tools for expressing, analyzing and judging parallel algorithms and, in detail, cover the two most widely used concrete frameworks OpenMP and MPI as well as the threading interface pthreads for writing parallel programs for either shared or distributed memory parallel computers with emphasis on general concepts and principles. Code examples are given in a C-like style and many are actual, correct C code. The lecture notes deliberately do not cover GPU architectures and GPU programming, but the general concerns, guidelines and principles (time, work, cost, efficiency, scalability, memory structure and bandwidth) will be just as relevant for efficiently utilizing various GPU architectures. Likewise, the lecture notes focus on deterministic algorithms only and do not use randomization. The student of this material will find it instructive to take the time to understand concepts and algorithms visually. The exercises can be used for self-study and as inspiration for small implementation projects in OpenMP and MPI that can and should accompany any serious course on Parallel Computing. The student will benefit from actually implementing and carefully benchmarking the suggested algorithms on the parallel computing system that may or should be made available as part of such a Parallel Computing course. In class, the exercises can be used as basis for hand-ins and small programming projects for which sufficient, additional detail and precision should be provided by the instructor.

Backscatter communication (BC) has emerged as a key technology to satisfy the increasing need for low-cost and green Internet-of-Things (IoT) connectivity, especially in large-scale deployments. Unlike the monostatic BC (MoBC), the bistatic BC (BiBC) has the possibility to decrease the round-trip path loss by having the carrier emitter (CE) and the reader in different locations. Therefore, this work investigates the BiBC in the context of cell-free multiple-input multiple-output (MIMO) networks by exploring the optimal selection of CE and reader among all access points, leveraging prior knowledge about the area where the backscatter device (BD) is located. First, a maximum a posteriori probability (MAP) detector to decode the BD information bits is derived. Then, the exact probability of error for this detector is obtained. In addition, an algorithm to select the best CE-reader pair for serving the specified area is proposed. Finally, simulation results show that the error performance of the BC is improved by the proposed algorithm compared to the benchmark scenario.

We give optimally fast $O(\log p)$ time (per processor) algorithms for computing round-optimal broadcast schedules for message-passing parallel computing systems. This affirmatively answers difficult questions posed in a SPAA 2022 BA and a CLUSTER 2022 paper. We observe that the computed schedules and circulant communication graph can likewise be used for reduction, all-broadcast and all-reduction as well, leading to new, round-optimal algorithms for these problems. These observations affirmatively answer open questions posed in a CLUSTER 2023 paper. The problem is to broadcast $n$ indivisible blocks of data from a given root processor to all other processors in a (subgraph of a) fully connected network of $p$ processors with fully bidirectional, one-ported communication capabilities. In this model, $n-1+\lceil\log_2 p\rceil$ communication rounds are required. Our new algorithms compute for each processor in the network receive and send schedules each of size $\lceil\log_2 p\rceil$ that determine uniquely in $O(1)$ time for each communication round the new block that the processor will receive, and the already received block it has to send. Schedule computations are done independently per processor without communication. The broadcast communication subgraph is an easily computable, directed, $\lceil\log_2 p\rceil$-regular circulant graph also used elsewhere. We show how the schedule computations can be done in optimal time and space of $O(\log p)$, improving significantly over previous results of $O(p\log^2 p)$ and $O(\log^3 p)$, respectively. The schedule computation and broadcast algorithms are simple to implement, but correctness and complexity are not obvious. The schedules are used for new implementations of the MPI (Message-Passing Interface) collectives MPI_Bcast, MPI_Allgatherv, MPI_Reduce and MPI_Reduce_scatter. Preliminary experimental results are given., Comment: arXiv admin note: substantial text overlap with arXiv:2312.11236

Extremely large-scale antenna arrays (ELAA) play a critical role in enabling the functionalities of next generation wireless communication systems. However, as the number of antennas increases, ELAA systems face significant bottlenecks, such as excessive interconnection costs and high computational complexity. Efficient distributed signal processing (SP) algorithms show great promise in overcoming these challenges. In this paper, we provide a comprehensive overview of distributed SP algorithms for ELAA systems, tailored to address these bottlenecks. We start by presenting three representative forms of ELAA systems: single-base station ELAA systems, coordinated distributed antenna systems, and ELAA systems integrated with emerging technologies. For each form, we review the associated distributed SP algorithms in the literature. Additionally, we outline several important future research directions that are essential for improving the performance and practicality of ELAA systems., Comment: submitted to IEEE JSTSP special issue on "Distributed Signal Processing for Extremely Large-Scale Antenna Array Systems"

The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity assumptions. The analysis is set in the maximal regularity framework of UMD Banach spaces. Similar results were proved in an earlier work, based on the consistency analysis of Radau IIA methods. The present error analysis, which is based on variational techniques, is of independent interest, but the main motivation is that it extends to nonlinear parabolic equations; in contrast to the earlier work. Both autonomous and nonautonomous linear equations are considered., Comment: 14 pages

Time-dependent Bose-Einstein condensate (BEC) formation in ultracold atoms is investigated in a nonlinear diffusion model. For constant transport coefficients, the model has been solved analytically. Here, we extend it to include energy-dependent transport coeffcients and numerically solve the nonlinear equation. Our results are compared with the earlier analytical model for constant transport coeffcients, and with recent deep-quench data for K-39 at various scattering lengths. Some non-physical predictions from the constant-coefficient model are resolved using energy-dependent drift and diffusion., Comment: 10 pages, 7 figures; submitted to Phys. Rev. A

Given a finite set $S$, i.i.d. random weights $\{X_i\}_{i\in S}$, and a family of subsets $\mathcal{F}\subseteq 2^S$, we consider the minimum weight of an $F\in \mathcal{F}$: \[ M(\mathcal{F}):= \min_{F\in \mathcal{F}} \sum_{i\in F}X_i. \] In particular, we investigate under what conditions this random variable is sharply concentrated around its mean. We define the patchability of a family $\mathcal{F}$: essentially, how expensive is it to finish an almost-complete $F$ (that is, $F$ is close to $\mathcal{F}$ in Hamming distance) if the edge weights are re-randomized? Combining the patchability of $\mathcal{F}$, applying the Talagrand inequality to a dual problem, and a sprinkling-type argument, we prove a concentration inequality for the random variable $M(\mathcal{F})$.

We develop a geometric approximation theory for deep feed-forward neural networks with ReLU activations. Given a $d$-dimensional hypersurface in $\mathbb{R}^{d+1}$ represented as the graph of a $C^2$-function $\phi$, we show that a deep fully-connected ReLU network of width $d+1$ can implicitly construct an approximation as its zero contour with a precision bound depending on the number of layers. This result is directly applicable to the binary classification setting where the sign of the network is trained as a classifier, with the network's zero contour as a decision boundary. Our proof is constructive and relies on the geometrical structure of ReLU layers provided in [doi:10.48550/arXiv.2310.03482]. Inspired by this geometrical description, we define a new equivalent network architecture that is easier to interpret geometrically, where the action of each hidden layer is a projection onto a polyhedral cone derived from the layer's parameters. By repeatedly adding such layers, with parameters chosen such that we project small parts of the graph of $\phi$ from the outside in, we, in a controlled way, construct a network that implicitly approximates the graph over a ball of radius $R$. The accuracy of this construction is controlled by a discretization parameter $\delta$ and we show that the tolerance in the resulting error bound scales as $(d-1)R^{3/2}\delta^{1/2}$ and the required number of layers is of order $d\big(\frac{32R}{\delta}\big)^{\frac{d+1}{2}}$.

The nitrate radical NO$_3$ plays an important role in atmospheric chemistry, yet many aspects of its coupled and anharmonic vibronic structure remain elusive. Here, using an accurate, coupled full-dimensional diabatic potential that includes five electronic states, we revisit the vibronic spectrum associated with the electronic $\tilde X ^2A_2'$ state. Using recently developed tensor network state methods, we are able to compute more than 2500 vibronic states, thereby increasing the number of computed full-dimensional states by a factor of 50, compared to previous work. While we obtain good agreement with experiment for most of the assigned vibronic levels, for several others, we observe striking disagreement. Further, for the antisymmetric bending motion we find remarkably large symmetry-induced level splittings that are larger than the zero-order reference. We discuss non-negligible nonadiabatic effects and show that the Born-Oppenheimer approximation leads to significant errors in the spectrum., Comment: in press

The paper describes a number of dialogue phenomena associated with negotiative dialogue, as implemented in a development version of the Talkamatic Dialogue Manager (TDM). This implementation is an initial step towards full coverage of general features of negotiative dialogue in TDM.

We consider a cell-free massive multiple-input multiple-output (CFmMIMO) network operating in dynamic time division duplex (DTDD). The switching point between the uplink (UL) and downlink (DL) data transmission phases can be adapted dynamically to the instantaneous quality-of-service (QoS) requirements in order to improve energy efficiency (EE). To this end, we formulate a problem of optimizing the DTDD switching point jointly with the UL and DL power control coefficients, and the large-scale fading decoding (LSFD) weights for EE maximization. Then, we propose an iterative algorithm to solve the formulated challenging problem using successive convex approximation with an approximate stationary solution. Simulation results show that optimizing switching points remarkably improves EE compared with baseline schemes that adjust switching points heuristically., Comment: Presented at the Asilomar Conference on Signals, Systems, and Computers 2023

The impact of intrinsic compressibility effects -- changes in fluid volume due to pressure variations -- on high-speed wall-bounded turbulence has often been overlooked or incorrectly attributed to mean property variations. To unambiguously quantify these intrinsic compressibility effects, we perform direct numerical simulations of compressible turbulent channel flows with nearly uniform mean properties. Our simulations reveal that intrinsic compressibility effects yield a significant upward shift in the logarithmic mean velocity profile that can be attributed to the reduction in the turbulent shear stress. This reduction stems from the weakening of the near-wall quasi-streamwise vortices. We in turn attribute this weakening to the spontaneous opposition of sweeps and ejections from the near-wall expansions and contractions of the fluid, and provide a theoretical explanation for this mechanism. Our results also demonstrate that intrinsic compressibility effects are responsible for the increase in the inner-scaled streamwise turbulence intensity in compressible flows compared to incompressible flows, previously regarded to be an effect of mean property variations., Comment: 29 pages, 17 figures

Quantum machine learning aims to use quantum computers to enhance machine learning, but it is often limited by the required number of samples due to quantum noise and statistical limits on expectation value estimates. While efforts are made to reduce quantum noise, less attention is given to boosting the confidence of Variational Quantum Classifiers (VQCs) and reducing their sampling needs. This paper focuses on multiclass classification, introducing a parameter-free post-processing technique that treats circuit outputs as edges of an n-dimensional simplex, representing independent binary decisions between each pair of classes. We prove and show in our experiments that this method improves few-sample accuracy by a factor of two by disentangling the wire outputs and compelling the VQC to avoid uncertain outputs. We describe this method and provide comparisons of accuracy, confidence, and entanglement, advocating for few-sample accuracy as a primary goal for effective VQCs., Comment: 10 pages, 4 figures, 3 tables

5G systems are being deployed all over the world and one key enabler of these systems is massive multiple-input multiple-output (MIMO). This technology has brought large performance gains in terms of serving many users. Despite the possibility to further exploit the spatial domain, there are situations where it is not possible to offer more than a single, or a few, data streams per user and where cell-edge coverage is an issue due to the lack of enough efficient channel scatterers. Looking ahead, distributed MIMO systems, where the antennas are spread over a larger area, are investigated for next generation systems. However, distributed MIMO comes with many practical deployment issues, making it a big challenge to adopt. As another way forward, we envision repeater-assisted cellular massive MIMO, where repeaters are deployed to act as channel scatterers to increase the rank of the channel and provide macro diversity for improved coverage and reliability. After elaborating on the requirements and hardware aspects of repeaters that enable this vision, we demonstrate through simulations the potential of repeater-assisted cellular massive MIMO to achieve distributed MIMO performance. Following this, we discuss open questions and future research directions., Comment: Submitted to IEEE Communications Magazine

In this survey we revisit {\sc finite subtraction}, one-heap subtraction games on finite rulesets. The main purpose is to give a general overview of the development, and specifically to draw attention to Flammenkamp's thesis (1997), where he, contrary to other studies, experimentally observes exponential eventual period length of the outcomes, for a carefully selected subclass of games. In addition, we contribute an appendix on {\sc finite excluded subtraction} by Suetsugu., Comment: 15 pages, 2 figures, Appendix by Koki Suetsugu

In federated learning, a server must periodically broadcast a model to the agents. We propose to use multi-resolution coding and modulation (also known as non-uniform modulation) for this purpose. In the simplest instance, broadcast transmission is used, whereby all agents are targeted with one and the same transmission (typically without any particular favored beam direction), which is coded using multi-resolution coding/modulation. This enables high-SNR agents, with high path gains to the server, to receive a more accurate model than the low-SNR agents do, without consuming more downlink resources. As one implementation, we use transmission with a non-uniform 8-PSK constellation, where a high-SNR receiver (agent) can separate all 8 constellation points (hence receive 3 bits) whereas a low-SNR receiver can only separate 4 points (hence receive 2 bits). By encoding the least significant information in the third bit, the high-SNR receivers can obtain the model with higher accuracy, while the low-SNR receiver can still obtain the model although with reduced accuracy, thereby facilitating at least some basic participation of the low-SNR receiver. We show the effectiveness of our proposed scheme via experimentation using federated learning with the MNIST data-set.

Federated learning (FL) has received significant attention in recent years for its advantages in efficient training of machine learning models across distributed clients without disclosing user-sensitive data. Specifically, in federated edge learning (FEEL) systems, the time-varying nature of wireless channels introduces inevitable system dynamics in the communication process, thereby affecting training latency and energy consumption. In this work, we further consider a streaming data scenario where new training data samples are randomly generated over time at edge devices. Our goal is to develop a dynamic scheduling and resource allocation algorithm to address the inherent randomness in data arrivals and resource availability under long-term energy constraints. To achieve this, we formulate a stochastic network optimization problem and use the Lyapunov drift-plus-penalty framework to obtain a dynamic resource management design. Our proposed algorithm makes adaptive decisions on device scheduling, computational capacity adjustment, and allocation of bandwidth and transmit power in every round. We provide convergence analysis for the considered setting with heterogeneous data and time-varying objective functions, which supports the rationale behind our proposed scheduling design. The effectiveness of our scheme is verified through simulation results, demonstrating improved learning performance and energy efficiency as compared to baseline schemes., Comment: Submitted to IEEE journals for possible publication

Single-shot volumetric fluorescence (SVF) imaging offers a significant advantage over traditional imaging methods that require scanning across multiple axial planes as it can capture biological processes with high temporal resolution across a large field of view. The key challenges in SVF imaging include requiring sparsity constraints to meet the multiplexing requirements of compressed sensing, eliminating depth ambiguity in the reconstruction, and maintaining high resolution across a large field of view. In this paper, we introduce the QuadraPol point spread function (PSF) combined with neural fields, a novel approach for SVF imaging. This method utilizes a custom polarizer at the back focal plane and a polarization camera to detect fluorescence, effectively encoding the 3D scene within a compact PSF without depth ambiguity. Additionally, we propose a reconstruction algorithm based on the neural fields technique that provides improved reconstruction quality and addresses the inaccuracies of phase retrieval methods used to correct imaging system aberrations. This algorithm combines the accuracy of experimental PSFs with the long depth of field of computationally generated retrieved PSFs. QuadraPol PSF, combined with neural fields, significantly reduces the acquisition time of a conventional fluorescence microscope by approximately 20 times and captures a 100 mm$^3$ cubic volume in one shot. We validate the effectiveness of both our hardware and algorithm through all-in-focus imaging of bacterial colonies on sand surfaces and visualization of plant root morphology. Our approach offers a powerful tool for advancing biological research and ecological studies.

The wireless channel is undergoing continuous changes, and the block-fading assumption, despite its popularity in theoretical contexts, never holds true in practical scenarios. This discrepancy is particularly critical for user activity detection in grant-free random access, where joint processing across multiple resource blocks is usually undesirable. In this paper, we propose employing a low-dimensional approximation of the channel to capture variations over time and frequency and robustify activity detection algorithms. This approximation entails projecting channel fading vectors onto their principal directions to minimize the approximation order. Through numerical examples, we demonstrate a substantial performance improvement achieved by the resulting activity detection algorithm., Comment: 5 pages, 11 figures. Asilomar SSC 2023 Conference

Out-of-system (OoS) interference is a potential limitation for distributed networks that operate in unlicensed spectrum or in a spectrum sharing scenario. The OoS interference differs from the in-system interference in that OoS signals and their associated channels (or even their statistics) are completely unknown. In this paper, we propose a novel distributed algorithm that can mitigate OoS interference in the uplink and suppress the signal transmission in the OoS direction in the downlink. To estimate the OoS interference, each access point (AP), upon receiving an estimate of OoS interference from a previous AP, computes a better estimate of OoS interference by rotate-and-average using Procrustes method and forwards the estimates to the next AP. This process continues until the central processing unit (CPU) receives the final estimate. Our method has comparable performance to that of a fully centralized interference rejection combining algorithm and has much lower fronthaul load requirements., Comment: 5 pages, 2 figures, to be published in IEEE Wireless Communications Letters

We consider a wireless network with multiple single-antenna repeaters that amplify and instantaneously re-transmit the signals they receive to improve the channel rank and system coverage. Due to the positive feedback formed by inter-repeater interference, stability could become a critical issue. We investigate the problem of determining the maximum amplification gain that the repeaters can use without breaking the system stability. Specifically, we obtain a bound by using the Gershgorin disc theorem, which reveals that the maximum amplification gain is restricted by the sum of channel amplitude gains. We show by case studies the usefulness of the so-obtained bound and provide insights on how the repeaters should be deployed., Comment: Accepted to SPAWC 2024. 5 pages, 7 figures

We explore the impact of optical excitation using two interfering ultrashort optical pulses on ultrafast magnetization dynamics. Our investigation focuses on Pt/Co/Pt multilayers and TbCo alloy samples, employing a dual pump approach. We observe significant variations in the dynamics of magnetization suppression and subsequent recovery when triggered with two optical pulses of the same polarization-essentially meeting conditions for interference. Conversely, dynamics triggered with cross-polarized pump beams exhibit expected similarity to that triggered with a single pulse. Delving into the underlying physical processes contributing to laser-induced demagnetization and recovery dynamics, we find that our current understanding cannot elucidate the observed trends. Consequently, we propose that optical excitation with interfering light possesses not previously acknowledged capacity to induce long-lasting alterations in the dynamics of angular momentum.

JWST/NIRCam obtained high angular-resolution (0.05-0.1''), deep near-infrared 1--5 micron imaging of Supernova (SN) 1987A taken 35 years after the explosion. In the NIRCam images, we identify: 1) faint H2 crescents, which are emissions located between the ejecta and the equatorial ring, 2) a bar, which is a substructure of the ejecta, and 3) the bright 3-5 micron continuum emission exterior to the equatorial ring. The emission of the remnant in the NIRCam 1-2.3 micron images is mostly due to line emission, which is mostly emitted in the ejecta and in the hot spots within the equatorial ring. In contrast, the NIRCam 3-5 micron images are dominated by continuum emission. In the ejecta, the continuum is due to dust, obscuring the centre of the ejecta. In contrast, in the ring and exterior to the ring, synchrotron emission contributes a substantial fraction to the continuum. Dust emission contributes to the continuum at outer spots and diffuse emission exterior to the ring, but little within the ring. This shows that dust cooling and destruction time scales are shorter than the synchrotron cooling time scale, and the time scale of hydrogen recombination in the ring is even longer than the synchrotron cooling time scale. With the advent of high sensitivity and high angular resolution images provided by JWST/NIRCam, our observations of SN 1987A demonstrate that NIRCam opens up a window to study particle-acceleration and shock physics in unprecedented details, probed by near-infrared synchrotron emission, building a precise picture of how a SN evolves., Comment: Accepted for publication in MNRAS; 18 pages

We propose a direct (non-recursive) algorithm for applying a rotation $R_{\theta^\ast}$, $\epsilon$-close to a desired rotation $R_\theta$, to a single qubit using the Clifford+Toffoli gate set. Our algorithm does not rely on repeatedly applying a fixed rotation, but immediately applies $R_{\theta^\ast}$. It succeeds with probability strictly greater than $1/2$, has an expected number of repetitions strictly less than 2, expected Toffoli count logarithmic in $\tfrac{1}{\epsilon}$, and expected gate depth also logarithmic in $\tfrac{1}{\epsilon}$., Comment: 6 pages, 3 figures, v3: improved introduction

We present a reciprocity calibration method for dual-antenna repeaters in wireless networks. The method uses bi-directional measurements between two network nodes, A and B, where for each bi-directional measurement, the repeaters are configured in different states. The nodes A and B could be two access points in a distributed MIMO system, or they could be a base station and a mobile user terminal, for example. From the calibration measurements, the differences between the repeaters' forward and reverse gains are estimated. The repeaters are then (re-)configured to compensate for these differences such that the repeaters appear, transparently to the network, as reciprocal components of the propagation environment, enabling reciprocity-based beamforming in the network., Comment: published version, misprint corrected

Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for complex system models remains a challenge. This paper presents NonlinearSolve.jl - a suite of high-performance open-source nonlinear equation solvers implemented natively in the Julia programming language. NonlinearSolve.jl distinguishes itself by offering a unified API that accommodates a diverse range of solver specifications alongside features such as automatic algorithm selection based on runtime analysis, support for GPU-accelerated computation through static array kernels, and the utilization of sparse automatic differentiation and Jacobian-free Krylov methods for large-scale problem-solving. Through rigorous comparison with established tools such as Sundials and MINPACK, NonlinearSolve.jl demonstrates unparalleled robustness and efficiency, achieving significant advancements in solving benchmark problems and challenging real-world applications. The capabilities of NonlinearSolve.jl unlock new potentials in modeling and simulation across various domains, making it a valuable addition to the computational toolkit of researchers and practitioners alike.

Given a general It\^o semimartingale, its Markovian projection is an It\^o process, with Markovian differential characteristics, that matches the one-dimensional marginal laws of the original process. We construct Markovian projections for It\^o semimartingales with jumps, whose flows of one-dimensional marginal laws are solutions to non-local Fokker--Planck--Kolmogorov equations (FPKEs). As an application, we show how Markovian projections appear in building calibrated diffusion/jump models with both local and stochastic features.

One of the main challenges in multi-agent reinforcement learning is scalability as the number of agents increases. This issue is further exacerbated if the problem considered is temporally dependent. State-of-the-art solutions today mainly follow centralized training with decentralized execution paradigm in order to handle the scalability concerns. In this paper, we propose time-dependent multi-agent transformers which can solve the temporally dependent multi-agent problem efficiently with a centralized approach via the use of transformers that proficiently handle the large input. We highlight the efficacy of this method on two problems and use tools from statistics to verify the probability that the trajectories generated under the policy satisfy the task. The experiments show that our approach has superior performance against the literature baseline algorithms in both cases., Comment: Submitted to L4DC 2024 conference

Supernova (SN) 1987A offers a unique opportunity to study how a spatially resolved SN evolves into a young supernova remnant (SNR). We present and analyze Hubble Space Telescope (HST) imaging observations of SN 1987A obtained in 2022 and compare them with HST observations from 2009 to 2021. These observations allow us to follow the evolution of the equatorial ring (ER), the rapidly expanding ejecta, and emission from the center over a wide range in wavelength from 2000 to 11 000 AA. The ER has continued to fade since it reached its maximum ~8200 days after the explosion. In contrast, the ejecta brightened until day ~11000 before their emission levelled off; the west side brightened more than the east side, which we attribute to the stronger X-ray emission by the ER on that side. The asymmetric ejecta expand homologously in all filters, which are dominated by various emission lines from hydrogen, calcium, and iron. From this overall similarity, we infer the ejecta are chemically well-mixed on large scales. The exception is the diffuse morphology observed in the UV filters dominated by emission from the Mg II resonance lines that get scattered before escaping. The 2022 observations do not show any sign of the compact object that was inferred from highly-ionized emission near the remnant's center observed with JWST. We determine an upper limit on the flux from a compact central source in the [O III] HST image. The non-detection of this line indicates that the S and Ar lines observed with JWST originate from the O free inner Si - S - Ar rich zone and/or that the observed [O III] flux is strongly affected by dust scattering.

The supernova remnant SNR 0540-69.3, twin of the Crab Nebula, offers an excellent opportunity to study the continuum emission from a young pulsar and pulsar-wind nebula (PWN). We present observations taken with the VLT instruments MUSE and X-shooter in the wavelength range 3000-25,000 \r{A}, which allow us to study spatial variations of the optical spectra, along with the first near-infrared (NIR) spectrum of the source. We model the optical spectra with a power law (PL) $F_\nu\propto\nu^{-\alpha}$ and find clear spatial variations (including a torus-jet structure) in the spectral index across the PWN. Generally, we find spectral hardening toward the outer parts, from $\alpha\sim1.1$ to $\sim0.1$, which may indicate particle reacceleration by the PWN shock at the inner edge of the ejecta or alternatively time variability of the pulsar wind. The optical-NIR spectrum of the PWN is best described by a broken PL, confirming that several breaks are needed to model the full spectral energy distribution of the PWN, suggesting the presence of more than one particle population. Finally, subtracting the PWN contribution from the pulsar spectrum we find that the spectrum is best described with a broken-PL model with a flat and a positive spectral index, in contrast to the Crab pulsar that has a negative spectral index and no break in the optical. This might imply that pulsar differences propagate to the PWN spectra., Comment: 29 pages, 19 Figures, 1 Table. Accepted for publication in ApJ

In the framework of stochastic portfolio theory we introduce rank volatility stabilized models for large equity markets over long time horizons. These models are rank-based extensions of the volatility stabilized models introduced by Fernholz & Karatzas in 2005. On the theoretical side we establish global existence of the model and ergodicity of the induced ranked market weights. We also derive explicit expressions for growth-optimal portfolios and show the existence of relative arbitrage with respect to the market portfolio. On the empirical side we calibrate the model to sixteen years of CRSP US equity data matching (i) rank-based volatilities, (ii) stock turnover as measured by market weight collisions, (iii) the average market rate of return and (iv) the capital distribution curve. Assessment of model fit and error analysis is conducted both in and out of sample. To the best of our knowledge this is the first model exhibiting relative arbitrage that has statistically been shown to have a good quantitative fit with the empirical features (i)-(iv). We additionally simulate trajectories of the calibrated model and compare them to historical trajectories, both in and out of sample., Comment: 35 pages, 10 figures

The nearby Supernova 1987A was accompanied by a burst of neutrino emission, which indicates that a compact object (a neutron star or black hole) was formed in the explosion. There has been no direct observation of this compact object. In this work, we observe the supernova remnant with JWST spectroscopy finding narrow infrared emission lines of argon and sulphur. The line emission is spatially unresolved and blueshifted in velocity relative to the supernova rest frame. We interpret the lines as gas illuminated by a source of ionizing photons located close to the center of the expanding ejecta. Photoionization models show that the line ratios are consistent with ionization by a cooling neutron star or pulsar wind nebula. The velocity shift could be evidence for a neutron star natal kick., Comment: Authors version of manuscript published in Science on 22 Feb 2024

The main respiratory muscle, the diaphragm, is an example of a thin structure. We aim to perform detailed numerical simulations of the muscle mechanics based on individual patient data. This requires a representation of the diaphragm geometry extracted from medical image data. We design an adaptive reconstruction method based on a least-squares radial basis function partition of unity method. The method is adapted to thin structures by subdividing the structure rather than the surrounding space, and by introducing an anisotropic scaling of local subproblems. The resulting representation is an infinitely smooth level set function, which is stabilized such that there are no spurious zero level sets. We show reconstruction results for 2D cross sections of the diaphragm geometry as well as for the full 3D geometry. We also show solutions to basic PDE test problems in the reconstructed geometries., Comment: 25 pages, 15 figures, preprint

Cell-free massive multiple-input multiple-output (MIMO) is a promising technology for next-generation communication systems. This work proposes a novel partially coherent (PC) transmission framework to cope with the challenge of phase misalignment among the access points (APs), which is important for unlocking the full potential of cell-free massive MIMO technology. With the PC operation, the APs are only required to be phase-aligned within clusters. Each cluster transmits the same data stream towards each user equipment (UE), while different clusters send different data streams. We first propose a novel algorithm to group APs into clusters such that the distance between two APs is always smaller than a reference distance ensuring the phase alignment of these APs. Then, we propose new algorithms that optimize the combining at UEs and precoding at APs to maximize the downlink sum data rates. We also propose a novel algorithm for data stream allocation to further improve the sum data rate of the PC operation. Numerical results show that the PC operation using the proposed framework with a sufficiently small reference distance can offer a sum rate close to the sum rate of the ideal fully coherent (FC) operation that requires network-wide phase alignment. This demonstrates the potential of PC operation in practical deployments of cell-free massive MIMO networks., Comment: 17 pages, 10 figures. Published in IEEE Open Journal of the Communications Society

We consider testing a composite null hypothesis $\mathcal{P}$ against a point alternative $\mathsf{Q}$ using e-variables, which are nonnegative random variables $X$ such that $\mathbb{E}_\mathsf{P}[X] \leq 1$ for every $\mathsf{P} \in \mathcal{P}$. This paper establishes a fundamental result: under no conditions whatsoever on $\mathcal{P}$ or $\mathsf{Q}$, there exists a special e-variable $X^*$ that we call the numeraire, which is strictly positive and satisfies $\mathbb{E}_\mathsf{Q}[X/X^*] \leq 1$ for every other e-variable $X$. In particular, $X^*$ is log-optimal in the sense that $\mathbb{E}_\mathsf{Q}[\log(X/X^*)] \leq 0$. Moreover, $X^*$ identifies a particular sub-probability measure $\mathsf{P}^*$ via the density $d \mathsf{P}^*/d \mathsf{Q} = 1/X^*$. As a result, $X^*$ can be seen as a generalized likelihood ratio of $\mathsf{Q}$ against $\mathcal{P}$. We show that $\mathsf{P}^*$ coincides with the reverse information projection (RIPr) when additional assumptions are made that are required for the latter to exist. Thus $\mathsf{P}^*$ is a natural definition of the RIPr in the absence of any assumptions on $\mathcal{P}$ or $\mathsf{Q}$. In addition to the abstract theory, we provide several tools for finding the numeraire and RIPr in concrete cases. We discuss several nonparametric examples where we can indeed identify the numeraire and RIPr, despite not having a reference measure. Our results have interpretations outside of testing in that they yield the optimal Kelly bet against $\mathcal{P}$ if we believe reality follows $\mathsf{Q}$. We end with a more general optimality theory that goes beyond the ubiquitous logarithmic utility. We focus on certain power utilities, leading to reverse R\'enyi projections in place of the RIPr, which also always exist.

There exist very few mid-infrared (IR) observations of supernovae (SNe) in general. Therefore, SN 1987A, the closest visible SN in 400 years, gives us the opportunity to explore the mid-IR properties of SNe, the dust in their ejecta and surrounding medium, and to witness the birth of a SN remnant (SNR). The James Webb Space Telescope (JWST), with its high spatial resolution and extreme sensitivity, gives a new view on these issues. We report on the first imaging observations obtained with the Mid-InfraRed Instrument (MIRI). We build temperature maps and discuss the morphology of the nascent SNR. Our results show that the temperatures in the equatorial ring (ER) are quite non-uniform. This could be due to dust destruction in some parts of the ring, as had been assumed in some previous works. We show that the IR emission extends beyond the ER, illustrating the fact that the shock wave has now passed through this ring to affect the circumstellar medium on a larger scale. Finally, while sub-mm Atacama Large Millimeter Array (ALMA) observations have hinted at the location of the compact remnant of SN 1987A, we note that our MIRI data have found no such evidence., Comment: 19 pages, 19 figures, 2 tables; Accepted for publication in the Astrophysical Journal (February 2, 2024)

We present our optical photometric observations of the 2022 eruption of the recurrent nova U Scorpii (U Sco) using 49,152 data points over 70 d following the optical peak. We have also analyzed its soft X-ray (0.3--1 keV) light curve by the Neil Gehrels Swift Observatory. During the 2022 eruption, the optical plateau stage started 13.8--15.0 d and ended 23.8--25.0 d after the optical peak. The soft X-ray stage started 14.6--15.3 d and ended 38.7--39.5 d after the optical peak. Both stages started later and had shorter durations, and the soft X-ray light curve peaked earlier and was less luminous compared to those during the U Sco 2010 eruption. These points suggest that there were differences in the envelope mass between the different cycles of the nova eruption. Furthermore, we have analyzed the optical eclipses during the 2022 eruption. The primary eclipse was first observed 10.4--11.6 d after the optical peak, earlier than the beginning of the optical plateau stage. This sequence of events can be explained by the receding ejecta photosphere associated with the expanding nova ejecta. We have determined the ingress and egress phases of the primary eclipses and estimated the outer radius of the optical light source centered at the white dwarf (WD). During the optical plateau stage, the source radius remained $\sim$1.2 times larger than the Roche volume radius of the primary WD, being close to the L1 point. When the optical plateau stage ended, the source radius drastically shrank to the tidal truncation radius within a few orbital periods. This previously unresolved phenomenon can be interpreted as a structural change in U Sco where the temporarily expanded accretion disk due to the nova wind returned to a steady state., Comment: 16 pages, 7 figures, 7 tables, accepted for publication in PASJ; doi:10.1093/pasj/psae010

There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of the classical normal play structure. To analyze these games, an algebraic extension is necessary, including infinities as elements. In this work, affine normal play, the algebraic structure resulting from that extension, is analyzed. We prove that it is possible to compare two affine games using only their forms. Furthermore, affine games can still be reduced, although the reduced forms are not unique. We establish that the classical normal play is order-embedded in the extended structure, constituting its substructure of invertible elements. Additionally, as in classical theory, affine games born by day n form a lattice with respect to the partial order of games., Comment: 68 pages, 24 figures

We revisit the question of whether the strong law of large numbers (SLLN) holds uniformly in a rich family of distributions, culminating in a distribution-uniform generalization of the Marcinkiewicz-Zygmund SLLN. These results can be viewed as extensions of Chung's distribution-uniform SLLN to random variables with uniformly integrable $q^\text{th}$ absolute central moments for $0 < q < 2;\ q \neq 1$. Furthermore, we show that uniform integrability of the $q^\text{th}$ moment is both sufficient and necessary for the SLLN to hold uniformly at the Marcinkiewicz-Zygmund rate of $n^{1/q - 1}$. These proofs centrally rely on distribution-uniform analogues of some familiar almost sure convergence results including the Khintchine-Kolmogorov convergence theorem, Kolmogorov's three-series theorem, a stochastic generalization of Kronecker's lemma, and the Borel-Cantelli lemmas. The non-identically distributed case is also considered., Comment: 35 pages

We study an opinion dynamics model in which each agent takes a random Bernoulli distributed action whose probability is updated at each discrete time step, and we prove that this model converges almost surely to consensus. We also provide a detailed critique of a claimed proof of this result in the literature. We generalize the result by proving that the assumption of irreducibility in the original model is not necessary. Furthermore, we prove as a corollary of the generalized result that the almost sure convergence to consensus holds also in the presence of a stubborn agent which never changes its opinion. In addition, we show that the model, in both the original and generalized cases, converges to consensus also in $r$th mean., Comment: 15 pages, 9 figures and 1 table. Accepted at IEEE Transactions on Signal and Information Processing over Networks

Consensus-based decentralized stochastic gradient descent (D-SGD) is a widely adopted algorithm for decentralized training of machine learning models across networked agents. A crucial part of D-SGD is the consensus-based model averaging, which heavily relies on information exchange and fusion among the nodes. Specifically, for consensus averaging over wireless networks, communication coordination is necessary to determine when and how a node can access the channel and transmit (or receive) information to (or from) its neighbors. In this work, we propose $\texttt{BASS}$, a broadcast-based subgraph sampling method designed to accelerate the convergence of D-SGD while considering the actual communication cost per iteration. $\texttt{BASS}$ creates a set of mixing matrix candidates that represent sparser subgraphs of the base topology. In each consensus iteration, one mixing matrix is sampled, leading to a specific scheduling decision that activates multiple collision-free subsets of nodes. The sampling occurs in a probabilistic manner, and the elements of the mixing matrices, along with their sampling probabilities, are jointly optimized. Simulation results demonstrate that $\texttt{BASS}$ enables faster convergence with fewer transmission slots compared to existing link-based scheduling methods. In conclusion, the inherent broadcasting nature of wireless channels offers intrinsic advantages in accelerating the convergence of decentralized optimization and learning., Comment: 11 pages, 5 figures, submitted for possible journal publication. arXiv admin note: text overlap with arXiv:2310.16106

Purpose: To evaluate the quality of deep learning reconstruction for prospectively accelerated intraoperative magnetic resonance imaging (iMRI) during resective brain tumor surgery. Materials and Methods: Accelerated iMRI was performed during brain surgery using dual surface coils positioned around the area of resection. A deep learning (DL) model was trained on the fastMRI neuro dataset to mimic the data from the iMRI protocol. Evaluation was performed on imaging material from 40 patients imaged between 01.11.2021 - 01.06.2023 that underwent iMRI during tumor resection surgery. A comparative analysis was conducted between the conventional compressed sense (CS) method and the trained DL reconstruction method. Blinded evaluation of multiple image quality metrics was performed by two working neuro-radiologists and a working neurosurgeon on a 1 to 5 Likert scale (1=non diagnostic, 2=poor, 3=acceptable, 4=good, 5=excellent), and the favored reconstruction variant. Results: The DL reconstruction was strongly favored or favored over the CS reconstruction for 33/40, 39/40, and 8/40 of cases for reader 1, 2, and 3, respectively. Two of three readers consistently assigned higher ratings for the DL reconstructions, and the DL reconstructions had a higher score than their respective CS counterparts for 72%, 72%, and 14% of the cases for reader 1, 2, and 3, respectively. Still, the DL reconstructions exhibited shortcomings such as a striping artifact and reduced signal. Conclusion: DL shows promise to allow for high-quality reconstructions of intraoperative MRI with equal to or improved perceived spatial resolution, signal-to-noise ratio, diagnostic confidence, diagnostic conspicuity, and spatial resolution compared to compressed sense.

Distributed antennas must be phase-calibrated (phase-synchronized) for certain operations, such as reciprocity-based joint coherent downlink beamforming, to work. We use rigorous signal processing tools to analyze the accuracy of calibration protocols that are based on over-the-air measurements between antennas, with a focus on scalability aspects for large systems. We show that (i) for some who-measures-on-whom topologies, the errors in the calibration process are unbounded when the network grows; and (ii) despite that conclusion, it is optimal -- irrespective of the topology -- to solve a single calibration problem for the entire system and use the result everywhere to support the beamforming. The analyses are exemplified by investigating specific topologies, including lines, rings, and two-dimensional surfaces.