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Oja’s rule [Oja, Journal of mathematical biology 1982] is a well-known biologically-plausible algorithm using a Hebbian-type synaptic update rule to solve streaming principal component analysis (PCA). Computational neuroscientists have known that this biological version of Oja’s rule converges to the top eigenvector of the covariance matrix of the input in the limit. However, prior to this work, it was open to prove any convergence rate guarantee. In this work, we give the first convergence rate analysis for the biological version of Oja’s rule in solving streaming PCA. Moreover, our convergence rate matches the information theoretical lower bound up to logarithmic factors and outperforms the state-of-the-art upper bound for streaming PCA. Furthermore, we develop a novel framework inspired by ordinary differential equations (ODE) to analyze general stochastic dynamics. The framework abandons the traditional \textit{step-by-step} analysis and instead analyzes a stochastic dynamic in \textit{one-shot} by giving a closed-form solution to the entire dynamic. The one-shot framework allows us to apply stopping time and martingale techniques to have a flexible and precise control on the dynamic. We believe that this general framework is powerful and should lead to effective yet simple analysis for a large class of problems with stochastic dynamics. 

This paper presents the design and preliminary testing of an instrumented exoskeleton system, which is targeted at collecting gait data of the human locomotion to support the controller development of lower-limb wearable robots. This compact and lightweight device features a unique two-degree-of-freedom joint to minimize the interference to the user movement and a simple yet effective adjustment mechanism to fit subjects at different heights. For the gait measurement, the device incorporates embedded joint goniometers to obtain the knee and ankle positions, and inertial measurement units to obtain three-dimensional kinematic information. Force-sensing resistors are also incorporated into the shoe insole for plantar pressure measurement. Sensor signals are routed to an onboard microcontroller system for data storage and transfer, and the system is fully self-contained with onboard battery to facilitate data collection in various environments. A prototype of the exoskeleton was fabricated, and preliminary testing was conducted on two healthy subjects in various postures and modes of movement (walking, sitting, standing, stair climbing, etc.). The evaluation of a temporal event detection test showed no more than 5.5% mean variation in the measure of step counts by the sensory system and video annotation. These results indicate that the exoskeleton can provide an accurate measurement of gait information, using measurements taken from external video recordings as the benchmark in this preliminary validation study. 

Abstract We present the results of a search for gravitational-wave transients associated with core-collapse supernova SN 2023ixf, which was observed in the galaxy Messier 101 via optical emission on 2023 May 19, during the LIGO–Virgo–KAGRA 15th Engineering Run. We define a five-day on-source window during which an accompanying gravitational-wave signal may have occurred. No gravitational waves have been identified in data when at least two gravitational-wave observatories were operating, which covered ∼14% of this five-day window. We report the search detection efficiency for various possible gravitational-wave emission models. Considering the distance to M101 (6.7 Mpc), we derive constraints on the gravitational-wave emission mechanism of core-collapse supernovae across a broad frequency spectrum, ranging from 50 Hz to 2 kHz, where we assume the gravitational-wave emission occurred when coincident data are available in the on-source window. Considering an ellipsoid model for a rotating proto-neutron star, our search is sensitive to gravitational-wave energy 1 × 10⁻⁴M_⊙c²and luminosity 2.6 × 10⁻⁴M_⊙c²s⁻¹for a source emitting at 82 Hz. These constraints are around an order of magnitude more stringent than those obtained so far with gravitational-wave data. The constraint on the ellipticity of the proto-neutron star that is formed is as low as 1.08, at frequencies above 1200 Hz, surpassing past results. 

Abstract Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of general relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO–Virgo–KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering single-harmonic and dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the single-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical spin-down limit. The lowest upper limit on the amplitude is 6.4 × 10⁻²⁷for the young energetic pulsar J0537−6910, while the lowest constraint on the ellipticity is 8.8 × 10⁻⁹for the bright nearby millisecond pulsar J0437−4715. Additionally, for a subset of 16 targets, we performed a narrowband search that is more robust regarding the emission model, with no evidence of a signal. We also found no evidence of nonstandard polarizations as predicted by the Brans–Dicke theory. 

Abstract We present results from a search for X-ray/gamma-ray counterparts of gravitational-wave (GW) candidates from the third observing run (O3) of the LIGO–Virgo–KAGRA network using the Swift Burst Alert Telescope (Swift-BAT). The search includes 636 GW candidates received with low latency, 86 of which have been confirmed by the offline analysis and included in the third cumulative Gravitational-Wave Transient Catalogs (GWTC-3). Targeted searches were carried out on the entire GW sample using the maximum-likelihood Non-imaging Transient Reconstruction and Temporal Search pipeline on the BAT data made available via the GUANO infrastructure. We do not detect any significant electromagnetic emission that is temporally and spatially coincident with any of the GW candidates. We report flux upper limits in the 15–350 keV band as a function of sky position for all the catalog candidates. For GW candidates where the Swift-BAT false alarm rate is less than 10⁻³Hz, we compute the GW–BAT joint false alarm rate. Finally, the derived Swift-BAT upper limits are used to infer constraints on the putative electromagnetic emission associated with binary black hole mergers. 

Abstract Indistinguishability of particles is a fundamental principle of quantum mechanics 1 . For all elementary and quasiparticles observed to date—including fermions, bosons and Abelian anyons—this principle guarantees that the braiding of identical particles leaves the system unchanged 2,3 . However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions 4–8 . Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well-developed mathematical description of non-Abelian anyons and numerous theoretical proposals 9–22 , the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the many-body wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons 9,10 , we implement a generalized stabilizer code and unitary protocol 23 to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards fault-tolerant quantum computing. 

Abstract The magnetar SGR 1935+2154 is the only known Galactic source of fast radio bursts (FRBs). FRBs from SGR 1935+2154 were first detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME)/FRB and the Survey for Transient Astronomical Radio Emission 2 in 2020 April, after the conclusion of the LIGO, Virgo, and KAGRA Collaborations’ O3 observing run. Here, we analyze four periods of gravitational wave (GW) data from the GEO600 detector coincident with four periods of FRB activity detected by CHIME/FRB, as well as X-ray glitches and X-ray bursts detected by NICER and NuSTAR close to the time of one of the FRBs. We do not detect any significant GW emission from any of the events. Instead, using a short-duration GW search (for bursts ≤1 s) we derive 50% (90%) upper limits of 10⁴⁸(10⁴⁹) erg for GWs at 300 Hz and 10⁴⁹(10⁵⁰) erg at 2 kHz, and constrain the GW-to-radio energy ratio to ≤10¹⁴−10¹⁶. We also derive upper limits from a long-duration search for bursts with durations between 1 and 10 s. These represent the strictest upper limits on concurrent GW emission from FRBs. 

Abstract Despite the growing number of binary black hole coalescences confidently observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include the effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that have already been identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total source-frame massM> 70M_⊙) binaries covering eccentricities up to 0.3 at 15 Hz emitted gravitational-wave frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place a conservative upper limit for the merger rate density of high-mass binaries with eccentricities 0 <e≤ 0.3 at 16.9 Gpc⁻³yr⁻¹at the 90% confidence level. 

Abstract We report the observation of a coalescing compact binary with component masses 2.5–4.5M_⊙and 1.2–2.0M_⊙(all measurements quoted at the 90% credible level). The gravitational-wave signal GW230529_181500 was observed during the fourth observing run of the LIGO–Virgo–KAGRA detector network on 2023 May 29 by the LIGO Livingston observatory. The primary component of the source has a mass less than 5M_⊙at 99% credibility. We cannot definitively determine from gravitational-wave data alone whether either component of the source is a neutron star or a black hole. However, given existing estimates of the maximum neutron star mass, we find the most probable interpretation of the source to be the coalescence of a neutron star with a black hole that has a mass between the most massive neutron stars and the least massive black holes observed in the Galaxy. We provisionally estimate a merger rate density of ${55}_{-47}^{+127}{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$for compact binary coalescences with properties similar to the source of GW230529_181500; assuming that the source is a neutron star–black hole merger, GW230529_181500-like sources may make up the majority of neutron star–black hole coalescences. The discovery of this system implies an increase in the expected rate of neutron star–black hole mergers with electromagnetic counterparts and provides further evidence for compact objects existing within the purported lower mass gap.