Search

Let $G=(V,E,w)$ be a weighted directed graph without negative cycles. For two vertices $s,t\in V$, we let $d_{\le h}(s,t)$ be the minimum, according to the weight function $w$, of a path from $s$ to $t$ that uses at most $h$ edges, or hops. We consider algorithms for computing $d_{\le h}(s,t)$ for every $1\le h\le n$, where $n=|V|$, in various settings. We consider the single-pair, single-source and all-pairs versions of the problem. We also consider a distance oracle version of the problem in which we are not required to explicitly compute all distances $d_{\le h}(s,t)$, but rather return each one of these distances upon request. We consider both the case in which the edge weights are arbitrary, and in which they are small integers in the range $\{-M,\ldots,M\}$. For some of our results we obtain matching conditional lower bounds., Comment: To appear in SODA 2025

Integrated sensing and communication (ISAC) is a novel capability expected for sixth generation (6G) cellular networks. To that end, several challenges must be addressed to enable both mono- and bistatic sensing in existing deployments. A common impairment in both architectures is oscillator phase noise (PN), which not only degrades communication performance, but also severely impairs radar sensing. To enable a broader understanding of orthogonal-frequency division multiplexing (OFDM)-based sensing impaired by PN, this article presents an analysis of sensing peformance in OFDM-based ISAC for different waveform parameter choices and settings in both mono- and bistatic architectures. In this context, the distortion of the adopted digital constellation modulation is analyzed and the resulting PN-induced effects in range-Doppler radar images are investigated both without and with PN compensation. These effects include peak power loss of target reflections and higher sidelobe levels, especially in the Doppler shift direction. In the conducted analysis, these effects are measured by the peak power loss ratio, peak-to-sidelobe level ratio, and integrated sidelobe level ratio parameters, the two latter being evaluated in both range and Doppler shift directions. In addition, the signal-to-interference ratio is analyzed to allow not only quantifying the distortion of a target reflection, but also measuring the interference floor level in a radar image. The achieved results allow to quantify not only the PN-induced impairments to a single target, but also how the induced degradation may impair the sensing performance of OFDM-based ISAC systems in multi-target scenarios., Comment: This work has been submitted to the IEEE for possible publication

Anonymization plays a key role in protecting sensible information of individuals in real world datasets. Self-driving cars for example need high resolution facial features to track people and their viewing direction to predict future behaviour and react accordingly. In order to protect people's privacy whilst keeping important features in the dataset, it is important to replace the full body of a person with a highly detailed anonymized one. In contrast to doing face anonymization, full body replacement decreases the ability of recognizing people by their hairstyle or clothes. In this paper, we propose a workflow for full body person anonymization utilizing Stable Diffusion as a generative backend. Text-to-image diffusion models, like Stable Diffusion, OpenAI's DALL-E or Midjourney, have become very popular in recent time, being able to create photorealistic images from a single text prompt. We show that our method outperforms state-of-the art anonymization pipelines with respect to image quality, resolution, Inception Score (IS) and Frechet Inception Distance (FID). Additionally, our method is invariant with respect to the image generator and thus able to be used with the latest models available.

Numerical simulations rely on constructing accurate and detailed models to produce reliable results - a task that is often challenging. This task becomes notably more difficult when the model is of the human brain. We create an anatomically comprehensive hexahedral mesh of the human brain using an open-source digital brain atlas. Digital atlases are valuable tools currently used by medical professionals, medical students, and researchers for gathering, presenting, and discovering knowledge about the human brain. We demonstrate that the atlas can be used to efficiently create an accurate and detailed hexahedral finite element mesh of the brain for scientific computing. We present two case studies. The first case study constructs a biomechanical model of the brain to compute brain deformations and predict traumatic brain injury risk due to violent impact. In the second case study, we construct a bioelectrical model of the brain to solve the electroencephalography (EEG) forward problem, a frequent simulation process used in electrophysiology to study electromagnetic fields generated by the nervous system. We demonstrate efficient and accurate model construction using the meshed anatomical brain atlas, as well as emphasize the importance of effective communication and contextual analysis of results for enabling multi-disciplinary scientific computing research.

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them., Comment: TianQin Gravitational Wave Whitepaper, 72 pages, 30 figures

Computational biomechanics models of the brain have become an important tool for investigating the brain responses to mechanical loads. The geometry, loading conditions, and constitutive properties of such brain models are well-studied and generally accepted. However, there is a lack of experimental evidence to support models of the layers of tissues (brain-skull interface) connecting the brain with the skull which determine boundary conditions for the brain. We present a new protocol for determining the biomechanical properties of the brain-skull interface and present the preliminary results (for a small number of tissue samples extracted from sheep cadaver heads). The method consists of biomechanical experiments using brain tissue and brain-skull complex (consisting of the brain tissue, brain-skull interface, and skull bone) and comprehensive computer simulation of the experiments using the finite element (FE) method. Application of the FE simulations allowed us to abandon the traditionally used approaches that rely on analytical formulations that assume cuboidal (or cylindrical) sample geometry when determining the parameters that describe the biomechanical behaviour of the brain tissue and brain-skull interface. In the simulations, we used accurate 3D geometry of the samples obtained from magnetic resonance images (MRIs). Our results indicate that the behaviour of the brain-skull interface under compressive loading appreciably differs from that under tension. Rupture of the interface was clearly visible for tensile load while no obvious indication of mechanical failure was observed under compression. These results suggest that assuming a rigid connection or frictionless sliding contact between the brain tissue and skull bone, the approaches often used in computational biomechanics models of the brain, may not accurately represent the mechanical behaviour of the brain-skull interface., Comment: Computational Biomechanics for Medicine (accepted). Springer

We study the gravitational wave (GW) phase shift arising from center-of-mass accelerations of binary black hole mergers formed dynamically in three-body systems, where both the inner orbit of the merging binary and the outer orbit are eccentric. We provide a semi-analytical model and several analytical approximations that allow for fast evaluation of both the temporal evolution and the maximum value of the phase shift. The highest phase shifts occur when the binary merges close to the pericentre of the outer orbit, and can in this case be orders-of-magnitude larger compared to the circular limit. At high outer orbit eccentricities, the orbital curvature leaves distinct imprints onto the phase shift if the binary passes the outer pericentre during its inspiral. By comparing with phase shifts measured in numerical chaotic 3-body scatterings, we show that our model accurately describes the observed phase of dynamically assembled binary systems in realistic astrophysical scenarios, providing a way to directly determine their formation channel via single GW observations.

Enabling bistatic radar sensing within the context of integrated sensing and communication (ISAC) for future sixth generation mobile networks demands strict synchronization accuracy, which is particularly challenging to be achieved with over-the-air synchronization. Existing algorithms handle time and frequency offsets adequately, but provide insufficiently accurate sampling frequency offset (SFO) estimates that result in degradation of obtained radar images in the form of signal-to-noise ratio loss and migration of range and Doppler shift. This article introduces an SFO estimation algorithm named tilt inference of time offset (TITO) for orthogonal frequency-division multiplexing (OFDM)-based ISAC. Using available pilot subcarriers, TITO obtains channel impulse response estimates and extracts information on the SFO-induced delay migration to a dominant reference path with constant range, Doppler shift, and angle between transmit and receive ISAC nodes. TITO then adaptively selects the delay estimates that are only negligibly impaired by SFO-induced intersymbol interference, ultimately employing them to estimate the SFO. Assuming a scenario without a direct line-of-sight (LoS) between the aforementioned transmitting and receiving ISAC nodes, a system concept with a relay reflective intelligent surface (RIS) is used to create the aforementioned reference path is proposed. Besides a mathematical derivation of accuracy bounds, simulation and measurements at 26.2 GHz are presented to demonstrate TITO's superiority over existing methods in terms of SFO estimation accuracy and robustness., Comment: This work has been submitted to the IEEE for possible publication

The first stars formed over five orders of magnitude in mass by accretion in primordial dark matter halos. We study the evolution of massive, very massive and supermassive primordial (Pop III) stars over nine orders of magnitude in accretion rate. We use the stellar evolution code GENEC to evolve accreting Pop III stars from 10$^{-6}$ - 10$^3$ M$_\odot$/yr and study how these rates determine final masses. The stars are evolved until either the end of central Si burning or until they encounter the general relativistic instability (GRI). We also examine how metallicity affects the evolution of the stars. At rates below $2.5 x 10^{-5}$ M$_\odot$/yr the final mass of the star falls below that required for pair-instability supernovae. The minimum rate required to produce black holes with masses above 250 M$_\odot$ is $5 x 10^{-5}$ M$_\odot$/yr, well within the range of infall rates found in numerical simulations of halos that cool via H$_2$, $10^{-3}$ M$_\odot$/yr. At rates of $5 x 10^{-5}$ M$_\odot$/yr to $4 x 10^{-2}$ \Ms\ yr$^{-1}$, like those expected for halos cooling by both H$_2$ and Ly-alpha, the star collapses after Si burning. At higher accretion rates the GRI triggers the collapse of the star during central H burning. Stars that grow at above these rates are cool red hypergiants with effective temperatures $log(T_{\text{eff}}) = 3.8$ and luminosities that can reach 10$^{10.5}$ L$_\odot$. At accretion rates of 100 - 1000 M$_\odot$/yr the gas encounters the general relativistic instability prior to the onset of central hydrogen burning and collapses to a black hole with a mass of 10$^6$ M$_\odot$ without ever having become a star. We reveal for the first time the critical transition rate in accretion above which catastrophic baryon collapse, like that which can occur during galaxy collisions in the high-redshift Universe, produces supermassive black holes via dark collapse., Comment: 11 pages, 8 figures

Cerebral aneurysm rupture, leading to subarachnoid hemorrhage with a high mortality rate, disproportionately affects younger populations, resulting in a significant loss of productive life years. A significant proportion of these deaths is due to aneurysmal re-bleeding within the first three days following the initial bleed, prior to treatment. While early aneurysm treatment is recommended, there is no consensus on the ideal timing, and emergency treatment offers only an incremental benefit at a significant cost. Although various multivariable prediction models have been proposed to provide personalized risk assessments, no validated patient-specific predictor is available to rationalize emergency treatment. Furthermore, no model has yet incorporated emerging computational biomechanics-based biomarkers such as wall tension. In this paper, we proposed and validated an efficient semi-automatic pipeline to compute patient-specific cerebral aneurysm wall tension as a potential biomarker for the likelihood of re-bleeding. Our pipeline uses the patient's computed tomography angiography (CTA) image obtained at the time of subarachnoid hemorrhage diagnosis to create a patient-specific biomechanical model of the cerebral aneurysm using the finite element method. A distinctive feature of our approach is the straightforward model creation and wall tension computation using shell finite elements, without requiring patient-specific material properties or aneurysm wall thickness. Our non-invasive, patient-specific method for cerebral aneurysm wall tension can potentially provide individualized risk prediction and enhance clinical decision-making.

With the rapid increase in mobile subscribers, there is a drive towards achieving higher data rates, prompting the use of higher frequencies in future wireless communication technologies. Wave propagation channel modeling for these frequencies must be considered in conjunction with measurement results. This paper presents a ray-launching (RL)-based simulation in a complex urban scenario characterized by an undulating terrain with a high density of trees. The simulation results tend to closely match the reported measurements when more details are considered. This underscores the benefits of using the RL method, which provides detailed space-time and angle-delay results., Comment: 6 pages, 7 figures, published on 2024 International Conference on Electromagnetics in Advanced Applications (ICEAA 2024)

With the recent announcement by NASA's Planetary Science and Astrobiology Decadal Survey 2023-2032, a priority flagship mission to the planet Uranus is anticipated. Here, we explore the prospects of using the mission's radio Doppler tracking equipment to detect gravitational waves (GWs) and other analogous signals related to dark matter (DM) over the duration of its interplanetary cruise. By employing a methodology to stack tracking data in combination with Monte-Carlo Markov-Chain parameter recovery tests, we show that the mission will be sensitive to GWs over the wide frequency range of $3\times 10^{-9}$ Hz to $10^{-1}$ Hz, provided that tracking data is taken consistently over a large fraction of the cruise duration. Thus, the mission has the potential to fill the gap between pulsar timing and space-based-interferometry GW observatories. Within this assumption, we forecast the detection of $\mathcal{\mathcal{O}}(1 - 100)$ individual massive black hole binaries using two independent population models. Additionally, we determine the mission's sensitivity to both astrophysical and primordial stochastic gravitational wave backgrounds, as well as its capacity to test, or even confirm via detection, ultralight DM models. In all these cases, the tracking of the spacecraft over its interplanetary cruise would enable coverage of unexplored regions of parameter space, where signals from new phenomena in our Universe may be lurking., Comment: Submitted to Pr.D. Comments welcome!

Changes in the nervous system due to neurological diseases take place at very small spatial scales, on the order of the micro and nanometers. Developing non-invasive imaging methods for obtaining this microscopic information as quantitative biomarkers is therefore crucial for improved medical diagnosis. In this context, diffusion-weighted magnetic resonance imaging has shown significant advances in revealing tissue microstructural features by probing molecular diffusion processes. Implementing modulated gradient spin-echo sequences allows monitoring time-dependent diffusion processes to reveal such detailed information. In particular, one of those sequences termed Non-uniform Oscillating Gradient Spin-Echo (NOGSE), has shown to selectively characterise microstructure sizes by generating an image contrast based on a signal decay-shift rather than on the conventionally used signal decay rate. In this work, we prove that such decay-shift is more pronounced with instantaneous switches of the magnetic field gradient strength sign. As fast gradient ramps need to be avoided in clinical settings, due to potential patient discomfort and artefacts in imaging, we evaluate the method's efficacy for estimating microstructure sizes using both idealised, sharp gradient modulations and more realistic, smooth modulations. In this more realistic scenario, we find that the signal decay shift might be lost as the diffusion time increases, likely hindering the accurate estimation of microstructural characteristics. We demonstrate, by a combination of numerical simulations, information theory analysis and proof-of-principle experiments with white-matter phantoms, that optimal sequence design to estimate microstructure size distributions can be achieved using either sharp or smooth gradient spin-echo modulations. This approach simplifies the translation of the NOGSE method for its use in clinical settings., Comment: 18 pages, 8 figures

We study the gravitational wave (GW) emission of sources perturbed by periodic dynamical forces which do not cause secular evolution in the orbital elements. We construct a corresponding post-Newtonian waveform model and provide estimates for the detectability of the resulting GW phase perturbations, for both space-based and future ground-based detectors. We validate our results by performing a set of Bayesian parameter recovery experiments with post-Newtonian waveforms. We find that, in stark contrast to the more commonly studied secular dephasing, periodic phase perturbations do not suffer from degeneracies with any of the tested vacuum binary parameters. We discuss the applications of our findings to a range of possible astrophysical scenarios, finding that such periodic perturbations may be detectable for massive black hole binaries embedded in circum-binary discs, extreme mass-ratio inspirals in accretion discs, as well as stellar-mass compact objects perturbed by tidal fields. We argue that modelling conservative sub-orbital dynamics opens up a promising new avenue to detect environmental effects in binary sources of GWs that should be included in state-of-the-art waveform templates., Comment: Accepted in PRD. Comments welcome

Integrated sensing and communication (ISAC) has been defined as one goal for 6G mobile communication systems. In this context, this article introduces a bistatic ISAC system based on orthogonal frequency-division multiplexing (OFDM). While the bistatic architecture brings advantages such as not demanding full duplex operation with respect to the monostatic one, the need for synchronizing transmitter and receiver is imposed. In this context, this article introuces a bistatic ISAC signal processing framework where an incoming OFDM-based ISAC signal undergoes over-the-air synchronization based on preamble symbols and pilots. Afterwards, bistatic radar processing is performed using either only pilot subcarriers or the full OFDM frame. The latter approach requires estimation of the originally transmitted frame based on communication processing and therefore error-free communication, which can be achieved via appropriate channel coding. The performance and limitations of the introduced system based on both aforementioned approaches are assessed via an analysis of the impact of residual synchronization mismatches and data decoding failures on both communication and radar performances. Finally, the performed analyses are validated by proof-of-concept measurement results.

Advancing quantum sensing tools for investigating systems at atomic and nanoscales is crucial for the progress of quantum technologies. While numerous protocols employ quantum probes to extract information from stationary or weakly coupled environments, the challenges intensify at atomic- and nano-scales where the environment is inherently out-of-equilibrium or strongly coupled with the sensor. We here prove that the time-reversal symmetry in the quantum-sensor control dynamics is broken, when partial information is probed from an environment that is out-of-equilibrium with non stationary fluctuations or is described by quantum non-Gaussian, strongly coupled environmental correlations. We exploit this phenomenon as a quantum sensing paradigm with proof-of principle experimental quantum simulations using solid-state nuclear magnetic resonance (NMR). This introduces a signal contrast on a qubit-probe that quantifies how far the sensed environment is from equilibrium or its quantum non-Gaussian nature. Protocols are also presented to discern and filter a variety of environmental properties including stationary, non-stationary and non-Gaussian quantum noise fluctuations as a step toward sensing the ubiquitous environments of a quantum-sensor at atomic and nanoscales.

A substantial fraction of stars can be found in wide binaries with projected separations between $\sim10^2$ and $10^5\,\rm AU$. In the standard lore of binary physics, these would evolve as effectively single stars that remotely orbit one another on stationary Keplerian ellipses. However, embedded in their Galactic environment their low binding energy makes them exceptionally prone to perturbations from the gravitational potential of the Milky Way and encounters with passing stars. Employing a fully relativistic $N$-body integration scheme, we study the impact of these perturbations on the orbital evolution of wide binaries along their trajectory through the Milky Way. Our analysis reveals that the torques exerted by the Galaxy can cause large-amplitude oscillations of the binary eccentricity to $1-e\lesssim10^{-8}$. As a consequence, the wide binary members pass close to each other at periapsis, which, depending on the type of binary, potentially leads to a mass transfer or collision of stars or to an inspiral and subsequent merger of compact remnants due to gravitational-wave radiation. Based on a simulation of $10^5$ wide binaries across the Galactic field, we find that this mechanism could significantly contribute to the rate of stellar collisions and binary black hole mergers as inferred from observations of Luminous Red Novae and gravitational-wave events by LIGO/Virgo/Kagra. We conclude that the dynamics of wide binaries, despite their large mean separation, can give rise to extreme interactions between stars and compact remnants., Comment: 20 pages, 9 figures

Aims: To showcase and characterise the rich phenomenology of temperature fluctuation patterns that are imprinted on the CMB by the gravitational wave memory (GWM) of massive black hole (BH) mergers. Methods: We analyse both individual binaries as well as populations of binaries, distributed in local cosmological boxes at a given redshift. Results: The magnitude of the temperature fluctuations scales primarily as a function of binary total mass and pattern angular scale, and accumulates as a random-walk process when populations of mergers are considered. Fluctuations of order $\sim 10^{-10}$ K are easily reached across scales of $\sim 1'$ to $\sim 1^{\circ}$ for realistic volumetric merger rates of 10$^{-3}$ Mpc$^{-3}$ Gyr$^{-1}$, as appropriate for massive galaxies at $z=1$. We determine numerically that GWM temperature fluctuations result in a universal power spectrum with a scaling of $P(k)\propto k^{-2.7}$. Conclusion: While not detectable given the limitations of current all-sky CMB surveys, our work explicitly shows how every black hole merger in the Universe left us its unique faint signature., Comment: Accepted in A&A. Comments welcome!

An electric car equipped with a battery of a finite capacity travels on a road network with an infrastructure of charging stations. Each charging station has a possibly different cost per unit of energy. Traversing a given road segment requires a specified amount of energy that may be positive, zero or negative. The car can only traverse a road segment if it has enough charge to do so (the charge cannot drop below zero), and it cannot charge its battery beyond its capacity. To travel from one point to another the car needs to choose a \emph{travel plan} consisting of a path in the network and a recharging schedule that specifies how much energy to charge at each charging station on the path, making sure of having enough energy to reach the next charging station or the destination. The cost of the plan is the total charging cost along the chosen path. We reduce the problem of computing plans between every two junctions of the network to two problems: Finding optimal energetic paths when no charging is allowed and finding standard shortest paths. When there are no negative cycles in the network, we obtain an $O(n^3)$-time algorithm for computing all-pairs travel plans, where~$n$ is the number of junctions in the network. We obtain slightly faster algorithms under some further assumptions. We also consider the case in which a bound is placed on the number of rechargings allowed., Comment: 9 pages, 2 figures, SOSA 2024

Efficient quantum sensing technologies rely on precise control of quantum sensors, particularly two-level systems or qubits, to optimize estimation processes. We here exploit the Quantum Zeno Effect (QZE) as a tool for maximizing information obtainable by quantum sensors, with a specific focus on the level avoided crossing (LAC) phenomenon in qubit systems. While the estimation of the LAC energy splitting has been extensively studied, we emphasize the crucial role that the QZE can play in estimating the coupling strength. We introduce the concept of information amplification by the QZE for a LAC system under off-resonant conditions. The proposed approach has implications for AC magnetic field sensing and the caracterization of complex systems, including many-spin systems requiring the estimation of spin-spin couplings. Overall, our findings contribute to the advancement of quantum sensing by leveraging the QZE for improved control and information extraction., Comment: 14 pages, 6 figures

We quantify for the first time the gravitational wave (GW) phase shift appearing in the waveform of eccentric binary black hole (BBH) mergers formed dynamically in three-body systems. For this, we have developed a novel numerical method where we construct a reference binary, by evolving the post-Newtonian (PN) evolution equations backwards from a point near merger without the inclusion of the third object, that can be compared to the real binary that evolves under the influence from the third BH. From this we quantify how the interplay between dynamical tides, PN-effects, and the time-dependent Doppler shift of the eccentric GW source results in unique observable GW phase shifts that can be mapped to the gravitational dynamics taking place at formation. We further find a new analytical expression for the GW phase shift, which surprisingly has a universal functional form that only depends on the time-evolving BBH eccentricity. The normalization scales with the BH masses and initial separation, which can be linked to the underlying astrophysical environment. GW phase shifts from a chaotic 3-body BH scattering taking place in a cluster, and from a BBH inspiraling in a disk migration trap near a super-massive BH, are also shown for illustration. When current and future GW detectors start to observe eccentric GW sources with high enough signal-to-noise-ratio, we propose this to be among the only ways of directly probing the dynamical origin of individual BBH mergers using GWs alone., Comment: comments are warmly welcome. 27 pages. 12 figures

Colleges and universities have become increasingly concerned that requiring standardized test scores for admission is an impediment to campus diversity, and these objections have grown with the recent focus on societal inequities. In addition, the pandemic led to the cancellation of test administrations, which, in turn, caused many institutions to eliminate admissions test requirements. These developments present an opportunity to reconsider the role of college admissions testing. The report begins by recounting the history of college admissions in the US, the relationship of admissions tests to intelligence testing and military testing, and the motivations for developing standardized exams to replace the admissions methods used at the turn of the twentieth century. Next, it describes the college admissions tests used today, along with their role in the admissions process, their advantages and limitations, and the ongoing debates about their fairness. Finally it discusses the future of admissions and admissions testing and end with a discussion of the concept of meritocracy as it applies to college admissions.

Computational simulations using methods such as the finite element (FE) method rely on high-quality meshes for achieving accurate results. This study introduces a method for creating a high-quality hexahedral mesh using the Open Anatomy Project's brain atlas. Our atlas-based FE hexahedral mesh of the brain mitigates potential inaccuracies and uncertainties due to segmentation - a process that often requires input of an inexperienced analyst. It accomplishes this by leveraging existing segmentation from the atlas. We further extend the mesh's usability by forming a two-way correspondence between the atlas and mesh. This feature facilitates property assignment for computational simulations and enhances result analysis within an anatomical context. We demonstrate the application of the mesh by solving the electroencephalography (EEG) forward problem. Our method simplifies the mesh creation process, reducing time and effort, and provides a more comprehensive and contextually enriched visualisation of simulation outcomes.

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

Direct-write multi-photon laser lithography (MPL) combines highest resolution on the nanoscale with essentially unlimited 3D design freedom. Over the previous years, the groundbreaking potential of this technique has been demonstrated in various application fields, including micromechanics, material sciences, microfluidics, life sciences as well as photonics, where in-situ printed optical coupling elements offer new perspectives for package-level system integration. However, millimeter-wave (mmW) and terahertz (THz) devices could not yet leverage the unique strengths of MPL, even though the underlying devices and structures could also greatly benefit from 3D freeform microfabrication. One of the key challenges in this context is the fact that functional mmW and THz structures require materials with high electrical conductivity and low dielectric losses, which are not amenable to structuring by multi-photon polymerization. In this work, we introduce and experimentally demonstrate a novel approach that allows to leverage MPL for fabricating high-performance mmW and THz structures with hitherto unachieved functionalities. Our concept exploits in-situ printed polymer templates that are selectively coated through highly directive metal deposition techniques in combination with precisely aligned 3D-printed shadowing structures. The resulting metal-coated freeform structures offer high surface quality in combination with low dielectric losses and conductivities comparable to bulk material values, while lending themselves to fabrication on planar mmW/THz circuits. We experimentally show the viability of our concept by demonstrating a series of functional THz structures such as THz interconnects, probe tips, and suspended antennas. We believe that our approach offers disruptive potential in the field of mmW and THz technology and may unlock an entirely new realm of laser-based 3D manufacturing.

Many studies have recently documented the orbital response of eccentric binaries accreting from thin circumbinary disks, characterizing the change in binary semi-major axis and eccentricity. We extend these calculations to include the precession of the binary's longitude of periapse induced by the circumbinary disk, and we characterize this precession continuously with binary eccentricity $e_b$ for equal mass components. This disk-induced apsidal precession is prograde with a weak dependence on binary eccentricity when $e_b \lesssim 0.4$ and decreases approximately linearly for $e_b \gtrsim 0.4$; yet at all $e_b$ binary precession is faster than the rates of change to the semi-major axis and eccentricity by an order of magnitude. We estimate that such precession effects are likely most important for sub-parsec separated binaries with masses $\lesssim 10^7 M_\odot$, like LISA precursors. We find that accreting, equal-mass LISA binaries with $M < 10^6 M_\odot$ (and the most massive $M \sim 10^7 M_\odot$ binaries out to $z \sim 3$) may acquire a detectable phase offset due to the disk-induced precession. Moreover, disk-induced precession can compete with General Relativistic precession in vacuum, making it important for observer-dependent electromagnetic searches for accreting massive binaries -- like Doppler boost and binary self-lensing models -- after potentially only a few orbital periods., Comment: 16 pages and 10 figures

The most massive black holes in our Universe form binaries at the centre of merging galaxies. The recent evidence for a gravitational-wave (GW) background from pulsar timing may constitute the first observation that these supermassive black hole binaries (SMBHBs) merge. Yet, the most massive SMBHBs are out of reach of interferometric {GW} detectors and are exceedingly difficult to resolve individually with pulsar timing. These limitations call for unexplored strategies to detect individual SMBHBs in the uncharted frequency band $\lesssim10^{-5}\,\rm Hz$ in order to establish their abundance and decipher the coevolution with their host galaxies. Here we show that SMBHBs imprint detectable long-term modulations on GWs from stellar-mass binaries residing in the same galaxy. We determine that proposed deci-Hz GW interferometers sensitive to numerous stellar-mass binaries could uncover modulations from $\sim\mathscr{O}(10^{-1}$ - $10^4)$ SMBHBs with masses $\sim\mathscr{O}(10^7$ - $10^8)\,\rm M_\odot$ out to redshift $z\sim3.5$. This offers a unique opportunity to map the population of SMBHBs through cosmic time, which might remain inaccessible otherwise., Comment: 20 pages, 6 figures. Nature Astronomy (2024)

This text will appear as Section II of Chapter 5 of the book "Black Holes in the Era of Gravitational-Wave Astronomy". As a stand alone text, it serves as a brief overview of astrophysics and gravitational wave radiation of extreme mass ratio inspirals, or EMRIs. Topics covered consist of: dynamical and gas-assisted formation channels, basics of EMRI dynamics and gravitational radiation, and science potential for both astrophysics and fundamental physics., Comment: To appear in Chapter 5 in the book Black Holes in the Era of Gravitational Wave Astronomy, ed. Arca Sedda, Bortolas, Spera, pub. Elsevier. All authors equally contributed to the Chapter writing

Austrin showed that the approximation ratio $\beta\approx 0.94016567$ obtained by the MAX 2-SAT approximation algorithm of Lewin, Livnat and Zwick (LLZ) is optimal modulo the Unique Games Conjecture (UGC) and modulo a Simplicity Conjecture that states that the worst performance of the algorithm is obtained on so called simple configurations. We prove Austrin's conjecture, thereby showing the optimality of the LLZ approximation algorithm, relying only on the Unique Games Conjecture. Our proof uses a combination of analytic and computational tools. We also present new approximation algorithms for two restrictions of the MAX 2-SAT problem. For MAX HORN-$\{1,2\}$-SAT, i.e., MAX CSP$(\{x\lor y,\bar{x}\lor y,x,\bar{x}\})$, in which clauses are not allowed to contain two negated literals, we obtain an approximation ratio of $0.94615981$. For MAX CSP$(\{x\lor y,x,\bar{x}\})$, i.e., when 2-clauses are not allowed to contain negated literals, we obtain an approximation ratio of $0.95397990$. By adapting Austrin's and our arguments for the MAX 2-SAT problem we show that these two approximation ratios are also tight, modulo only the UGC conjecture. This completes a full characterization of the approximability of the MAX 2-SAT problem and its restrictions., Comment: 32 pages, 1 figure; to appear in SODA 2024

We present an efficient and accurate immersed boundary (IB) finite element (FE) method for internal flow problems with complex geometries (e.g., blood flow in the vascular system). In this study, we use a voxelized flow domain (discretized with hexahedral and tetrahedral elements) instead of a box domain, which is frequently used in IB methods. The proposed method utilizes the well-established incremental pressure correction scheme (IPCS) FE solver, and the boundary condition-enforced IB (BCE-IB) method to numerically solve the transient, incompressible Navier--Stokes flow equations. We verify the accuracy of our numerical method using the analytical solution for the Poiseuille flow in a cylinder, and the available experimental data (laser Doppler velocimetry) for the flow in a three-dimensional 90{\deg} angle tube bend. We further examine the accuracy and applicability of the proposed method by considering flow within complex geometries, such as blood flow in aneurysmal vessels and the aorta, flow configurations that would otherwise be difficult to solve by most IB methods. Our method offers high accuracy, as demonstrated by the verification examples, and high applicability, as demonstrated through the solution of blood flow within complex geometry. The proposed method is efficient, since it is as fast as the traditional finite element method used to solve the Navier--Stokes flow equations, with a small overhead (not more than 5$\%$) due to the numerical solution of a linear system formulated for the IB method., Comment: arXiv admin note: substantial text overlap with arXiv:2007.02082

We revisit the precessing black hole binary model, a candidate to explain the bizarre quasi-periodic optical flares in OJ-287's light curve, from first principles. We deviate from existing work in three significant ways: 1) Including crucial aspects of relativistic dynamics related to the accretion disc's gravitational moments. 2) Adopting a model-agnostic prescription for the disc's density and scale height. 3) Using monte-carlo Markhov-chain methods to recover reliable system parameters and uncertainties. We showcase our model's predictive power by timing the 2019 Eddington flare within 40 hr of the observed epoch, exclusively using data available prior to it. Additionally, we obtain a novel direct measurement of OJ-287's disc mass and quadrupole moment exclusively from the optical flare timings. Our improved methodology can uncover previously unstated correlations in the parameter posteriors and patterns in the flare timing uncertainties. According to the model, the 26th optical flare is expected to occur on the 21st of August 2023 $\pm$ 32 days, shifted by approximately a year with respect to previous expectations., Comment: Accepted in MNRAS. Comments welcome!

A weighted directed graph $G=(V,A,c)$, where $A\subseteq V\times V$ and $c:A\to R$, describes a road network in which an electric car can roam. An arc $uv$ models a road segment connecting the two vertices $u$ and $v$. The cost $c(uv)$ of an arc $uv$ is the amount of energy the car needs to traverse the arc. This amount may be positive, zero or negative. To make the problem realistic, we assume there are no negative cycles. The car has a battery that can store up to $B$ units of energy. It can traverse an arc $uv\in A$ only if it is at $u$ and the charge $b$ in its battery satisfies $b\ge c(uv)$. If it traverses the arc, it reaches $v$ with a charge of $\min(b-c(uv),B)$. Arcs with positive costs deplete the battery, arcs with negative costs charge the battery, but not above its capacity of $B$. Given $s,t\in V$, can the car travel from $s$ to $t$, starting at $s$ with an initial charge $b$, where $0\le b\le B$? If so, what is the maximum charge with which the car can reach $t$? Equivalently, what is the smallest $\delta_{B,b}(s,t)$ such that the car can reach $t$ with a charge of $b-\delta_{B,b}(s,t)$, and which path should the car follow to achieve this? We refer to $\delta_{B,b}(s,t)$ as the energetic cost of traveling from $s$ to $t$. We let $\delta_{B,b}(s,t)=\infty$ if the car cannot travel from $s$ to $t$ starting with an initial charge of $b$. The problem of computing energetic costs is a strict generalization of the standard shortest paths problem. We show that the single-source minimum energetic paths problem can be solved using simple, but subtle, adaptations of the Bellman-Ford and Dijkstra algorithms. To make Dijkstra's algorithm work in the presence of negative arcs, but no negative cycles, we use a variant of the $A^*$ search heuristic. These results are explicit or implicit in some previous papers. We provide a simpler and unified description of these algorithms., Comment: 11 pages

This article introduces adaptations to the conventional frame structure in binary phase-modulated continuous wave (PMCW) radars with sequence generation via linear-feedbck shift registers and additional processing steps to enable joint radar-communication (RadCom) operation. In this context, a preamble structure based on pseudorandom binary sequences (PRBSs) that is compatible with existing synchronization algorithms is outlined, and the allocation of pilot PRBS blocks is discussed. Finally, results from proof-of-concept measurements are presented to illustrate the effects of the choice of system and signal parameters and validate the investigated PMCW-based RadCom system and synchronization strategy., Comment: Accepted for presentation at the focused session "Automotive PMCW Radars'' of the EuMW 2023

This article introduces a bistatic joint radar-communication (RadCom) system based on orthogonal frequency-division multiplexing (OFDM). In this context, the adopted OFDM frame structure is described and system model encompassing time, frequency, and sampling synchronization mismatches between the transmitter and receiver of the bistatic system is outlined. Next, the signal processing approaches for synchronization and communication are discussed, and radar sensing processing approaches using either only pilots or a reconstructed OFDM frame based on the estimated receive communication data are presented. Finally, proof-of-concept measurement results are presented to validate the investigated system and a trade-off between frame size and the performance of the aforementioned processing steps is observed., Comment: Accepted for presentation at the focused session "Joint Communication and Radar Sensing - a step towards 6G'' of the EuMW 2023

We present the results of the first fully cosmological hydrodynamical simulations studying the merger-driven model for massive black hole (BH) seed formation via direct collapse. Using the zoom-in technique as well as particle splitting, we achieve a final spatial resolution of $2$ pc. We show that the major merger of two massive galaxies at redshift $z \sim 8$ results in the formation of a nuclear supermassive disk (SMD) of only $4$ pc in radius, owing to a prodigious gas inflow sustained at $100$-$1000$ $M_{\odot}$ yr$^{-1}$. The core of the merger remnant is metal-rich, well above solar abundance, and the SMD reaches a gaseous mass of $3 \times 10^8$ $M_{\odot}$ in less than a million years after the merger, despite a concurrent prominent nuclear starburst. Dynamical heating as gas falls into the deepest part of the potential well, and heating and stirring by supernova blastwaves, generate a turbulent multi-phase interstellar medium, with a gas velocity dispersion exceeding 100 km s$^{-1}$. As a result, only moderate fragmentation occurs in the inner $10$-$20$ pc despite the temperature falls below $1000$ K. The SMD is Jeans-unstable as well as bar-unstable and will collapse further adiabatically, becoming warm and ionized. We show that the SMD, following inevitable contraction, will become general relativistic unstable and directly form a supermassive BH of mass in the range $10^6$-$10^8$ $M_{\odot}$, essentially skipping the stage of BH seed formation. These results confirm that mergers between the most massive galaxies at $z \sim 8$-$10$ can naturally explain the rapid emergence of bright high-redshift quasars., Comment: 14 pages, 8 figures, submitted to ApJ

We propose and demonstrate a novel scheme for optical arbitrary waveform measurement (OAWM) that exploits chip-scale Kerr soliton combs as highly scalable multiwavelength local oscillators (LO) for ultra-broadband full-field waveform acquisition. In contrast to earlier concepts, our approach does not require any optical slicing filters and thus lends itself to efficient implementation on state-of-the-art high-index-contrast integration platforms such as silicon photonics. The scheme allows to measure truly arbitrary waveforms with high accuracy, based on a dedicated system model which is calibrated by means of a femtosecond laser with known pulse shape. We demonstrated the viability of the approach in a proof-of-concept experiment by capturing an optical waveform that contains multiple 16 QAM and 64 QAM wavelength-division multiplexed (WDM) data signals with symbol rates of up to 80 GBd, reaching overall line rates of up to 1.92 Tbit/s within an optical acquisition bandwidth of 610 GHz. To the best of our knowledge, this is the highest bandwidth that has so far been demonstrated in an OAWM experiment.