Search

We study the coupling of axions to gauge bosons in heterotic string theory. The axion-gauge boson couplings in the low energy 4d theory are derived by matching mixed anomalies between higher-form global symmetries and the zero-form gauge symmetry in the 10d theory. When the standard model gauge group is embedded in a single simple group in the 10d theory -- as is the case for almost all heterotic models studied in the literature -- the ratio of the axion-photon coupling to the axion mass is bounded above by the QCD line. This bound is relevant for a large number of axion searches which have sensitivity to axion parameter space above this line. The discovery of an axion in these searches will rule out a large class of heterotic models, making such a signal challenging to explain within heterotic string theory., Comment: 22 pages, 1 figure

The hot inner flow in black-hole X-ray binaries is not just a static corona rotating around the black hole, but it must be partially outflowing. We have developed a model, in which Comptonization takes place in this outflowing corona. We are able to reproduce quantitatively five observed correlations: a) the time lag as a function of Fourier frequency, b) the time lag as a function of photon energy, c) the time lag as a function of $\Gamma$, d) the time lag as a function of the cut-off energy in the spectrum, and e) the long-standing radio - X-ray correlation. All of them with only two parameters (optical depth and width of the outflow), which vary in the same ranges for all the correlations. Our model does not require a compact, narrow relativistic jet, although its presence does not affect the results. The essential ingredient of our model is the parabolic shape of the Comptonizing corona. The outflow speed also plays a minor role. Furthermore, the bottom of the outflow, in the hard state, looks like a ``slab'' to the incoming soft photons from the disk, and this can explain the observed X-ray polarization, which is along the outflow., Comment: Accepted for publication in A&A

An ultra-light axion with CP violating interactions with a dark sector and CP preserving interactions with the visible sector can act as a novel portal between dark matter and the Standard Model. In such theories, dark matter sources an axion field extending over the entire galaxy, the gradient of which can be searched for with precise spin precession experiments. A reinterpretation of existing co-magnetometer data already constrains theories that are consistent with astrophysical bounds, and near-future experiments will begin probing well-motivated models. The required interactions can arise from a confining hidden sector without necessitating fine-tuning of the axion's mass., Comment: 6 pages, 1 figure; comments welcome!

Variability can be the pathway to understanding the physical processes in astrophysical jets, however, the high-cadence observations required to test particle acceleration models are still missing. Here we report on the first attempt to produce continuous, >24 hour polarization light curves of blazars using telescopes distributed across the globe and the rotation of the Earth to avoid the rising Sun. Our campaign involved 16 telescopes in Asia, Europe, and North America. We observed BL Lacertae and CGRaBS J0211+1051 for a combined 685 telescope hours. We find large variations in the polarization degree and angle for both sources in sub-hour timescales as well as a ~180 degree rotation of the polarization angle in CGRaBS J0211+1051 in less than two days. We compared our high-cadence observations to Particle-In-Cell magnetic reconnection and turbulent plasma simulations. We find that although the state of the art simulation frameworks can produce a large fraction of the polarization properties, they do not account for the entirety of the observed polarization behavior in blazar jets., Comment: 20 pages, 15 figures, 2 tables, accepted for publication in A&A. The data used in the paper are available here: https://doi.org/10.7910/DVN/IETSXS

Two-dimensional (2D) materials like transition metal dichalcogenides (TMD) have proved to be serious candidates to replace silicon in several technologies with enhanced performances. In this respect, the two remaining challenges are the wafer scale growth of TMDs and their integration into operational devices using clean room compatible processes. In this work, two different CMOS-compatible protocols are developed for the fabrication of MoS$_2$-based memristors, and the resulting performances are compared. The quality of MoS$_2$ at each stage of the process is characterized by Raman spectroscopy and x-ray photoemission spectroscopy. In the first protocol, the structure of MoS$_2$ is preserved during transfer and patterning processes. However, a polymer layer with a minimum thickness of 3 nm remains at the surface of MoS$_2$ limiting the electrical switching performances. In the second protocol, the contamination layer is completely removed resulting in improved electrical switching performances and reproducibility. Based on physico-chemical and electrical results, the switching mechanism is discussed in terms of conduction through grain boundaries., Comment: 11 pages, 6 figures

From late September 2017 to February 2018, the Be X-ray binary (BeXB) Swift J0243.6+6124 underwent an unprecedently bright giant outburst. The reported X-ray luminosities were so high that the system was classified as an Ultraluminous X-ray source (ULX). It was also the first BeXB pulsar showing radio jet emission. The source was not only bright in X-rays and radio, but also in optical and UV wavelenghts. In this paper we aim to understand the origin of the observed optical/UV fluxes simultaneous to the X-ray emission. We studied the optical/UV light curves in comparison with the X-ray fluxes along the outburst, considering the main mechanisms that can explain the optical/UV emission in X-ray binaries. Due to the tight correlation observed between the optical/UV and X-ray light curves, reprocessing of X-rays seems to be the most plausible explanation. We calculated the timescales of the light curves decays and studied the correlation indexes between the optical and X-ray emission. Finally, we built a physical model considering X-ray heating of the surface of the donor star, irradiation of the accretion disk, and emission from a viscously heated accretion disk, in order to reproduce the observed optical/UV SEDs along the outburst. We considered in our model that the Be circumstellar disk was co-planar to the orbit, and then we neglected its irradiation in the current model. As an input of the model, we used as incident X-ray luminosities those calculated from the bolometric X-ray fluxes obtained from the spectral fit of the Swift/XRT and BAT observations. We conclude that reprocessing of X-rays as X-ray heating of the Be star surface and irradiation of the accretion disk are the two main mechanisms that can reproduce the observed optical/UV emission during the 2017-2018 giant outburst of Swift J0243.6+6124., Comment: Accepted for publication in A&A on 7 December 2023; 16 pages, 12 figures, 2 tables

KS 1947+300 is a Be/X-ray binary. Despite its nearly circular orbit, it displays both giant and regular less intense X-ray outbursts. According to the viscous decretion disk model, such low eccentric binaries should not show periodic outbursts. We have studied the long-term optical variability of KS 1947+300 and its relationship with X-ray activity. Our objective is to investigate the origin of this variability. KS 1947+300 exhibits changes in brightness and H$\alpha$ emission on time scales from months to years. The optical and IR variability shows small amplitude changes during the active X-ray state, and a long, smooth decrease during the quiescent state. The fact that the amplitude of variability increased with wavelength suggests that the long-term decrease of the optical emission is due to the weakening of the circumstellar disk. Structural changes in the disk may also be the origin of the periodic signals with periods $\sim200$ days detected in the ZTF-{\it g} and {\it r} band light curves. We speculate that these changes are related to the mechanism that ejects matter from the photosphere of the Be star into the disk. We have also studied the X-ray variability that manifested as a series of type I outbursts after the two giant outburst in 2000 and 2013 and found that the intensity and peak orbital phase differ from outburst to outburst. The type I outbursts in KS 1947+300 are not strictly periodic. This irregularity could result from precession of the interacting points between the neutron star and the disk, namely the disk apastron and the two nodes of the disk. The long-term changes in optical continuum and line emission and the X-ray variability patterns are attributed to an evolving and distorted decretion disk., Comment: 18 pages, 10 figures

In this note we consider Penning trap experiments as probes of axion-mediated forces. We show that the current measurement of electron's $g$-factor already sets a new exclusion limit for monopole-dipole axion forces acting on the electron spin. We also show that the Penning trap's capability of switching an electron and a positron can isolate the effect of an axion force and suppress systematic effects., Comment: 4 pages, 1 figure

We propose to use atoms and molecules as quantum sensors of axion-mediated monopole-dipole forces. We show that electron spin precession experiments using atomic and molecular beams are well-suited for axion searches thanks to the presence of co-magnetometer states and single-shot temporal resolution. Experimental strategies to detect axion gradients from localised sources and the earth are presented, taking ACME III as a prototype example. Other possibilities including atomic beams, and laser-cooled atoms and molecules are discussed., Comment: 9 pages, 2 figures. Comments welcome. V2: matches published version. Appendix on axion co-magnetometry added

The observed correlation between the radio and X-ray fluxes in the hard state of black-hole X-ray binaries (BHXRBs) has been around for more than two decades. It is currently accepted that the hard X-rays in BHXRBs come from Comptonization in the corona and the radio emission from the relativistic jet (Lorentz $\gamma >> 1$), which is a narrow structure of a few $R_g=GM/c^2$ at its base. The relativistic jet and the corona, however, are separate entities with hardly any communication between them, apart from the fact that both are fed from the accreting matter. It is also widely accepted that the accretion flow around black holes in BHXRBs consists of an outer thin disk and an inner hot flow. From this hot inner flow, an outflow emanates in the hard and hard-intermediate states of the source. By considering Compton up-scattering of soft disk photons in the outflow (i.e., in the outflowing corona, which is a wider structure, tens to hundreds of $R_g$ at its base, with low Lorentz gamma) as the mechanism that produces the hard X-ray spectrum, we have been able to explain quantitatively a number of observed correlations. Here, we demonstrate that this outflowing corona can also explain quantitatively the observed radio - X-ray correlation. In addition, we make the following theoretical predictions for GX 339-4: 1) the radio flux in the hard and hard-intermediate states should be a bell-shaped curve as a function of the photon-number spectral index Gamma, 2) the radio - X-ray correlation should break down when the source moves from the hard to the hard-intermediate state and instead the radio flux should first increase sharply in the hard-intermediate state and then decrease also sharply, in a very narrow range of the X-ray flux, and 3) the X-ray polarization will be parallel to the outflow in the hard state and perpendicular to it in the hard-intermediate one., Comment: Accepted for publication in A&A

We consider electroweak (EW) gauge boson corrections to the masses of pseudoscalar mesons to next to leading order (NLO) in $\alpha_s$ and $1/N_C$. The pion mass shift induced by the $Z$-boson is shown to be $m_{\pi^\pm}-m_{\pi^0} = -0.00201(12)$ MeV. While being small compared to the electromagnetic mass shift, the prediction lies about a factor of $\sim 4$ above the precision of the current experimental measurement, and a factor $O(10)$ below the precision of current lattice calculations. This motivates future implementations of these EW gauge boson effects on the lattice. Finally, we consider BSM contributions to the pion mass difference., Comment: 6 pages, 1 figure

Optical polarimeters are typically calibrated using measurements of stars with known and stable polarization parameters. However, there is a lack of such stars available across the sky. Many of the currently available standards are not suitable for medium and large telescopes due to their high brightness. Moreover, as we find, some of the used polarimetric standards are in fact variable or have polarization parameters that differ from their cataloged values. Our goal is to establish a sample of stable standards suitable for calibrating linear optical polarimeters with an accuracy down to $10^{-3}$ in fractional polarization. For five years, we have been running a monitoring campaign of a sample of standard candidates comprised of 107 stars distributed across the northern sky. We analyzed the variability of the linear polarization of these stars, taking into account the non-Gaussian nature of fractional polarization measurements. For a subsample of nine stars, we also performed multiband polarization measurements. We created a new catalog of 65 stars (see Table 2) that are stable, have small uncertainties of measured polarimetric parameters, and can be used as calibrators of polarimeters at medium- and large-size telescopes.

This work presents a novel and promising approach to the clinical management of acute stroke. Using machine learning techniques, our research has succeeded in developing accurate diagnosis and prediction real-time models from hemodynamic data. These models are able to diagnose stroke subtype with 30 minutes of monitoring, to predict the exitus during the first 3 hours of monitoring, and to predict the stroke recurrence in just 15 minutes of monitoring. Patients with difficult access to a \acrshort{CT} scan, and all patients that arrive at the stroke unit of a specialized hospital will benefit from these positive results. The results obtained from the real-time developed models are the following: stroke diagnosis around $98\%$ precision ($97.8\%$ Sensitivity, $99.5\%$ Specificity), exitus prediction with $99.8\%$ precision ($99.8\%$ Sens., $99.9\%$ Spec.) and $98\%$ precision predicting stroke recurrence ($98\%$ Sens., $99\%$ Spec.).

The sesquioxide, Ce$_{2}$O$_{3}$, has been a material of intense interest in recent years due to reports of an anomalous giant magnetodielectric effect and emergent mixed crystal field-phonon (vibronic) excitations below a putative antiferromagnetic transition at T$_{N}$ = 6.2 K. The claim of long-range magnetic order in this material is based on heat capacity and temperature-dependent susceptibility measurements; however, multiple neutron diffraction studies have been unable to distinguish any magnetic Bragg peaks. In this article, we present the results of a comprehensive investigation of the low-temperature phase in symmetry-broken polycrystalline Ce$_{2}$O$_{3}$ using a combination of magnetic susceptibility, heat capacity, neutron diffraction, triple-axis and time-of-flight (TOF) inelastic neutron scattering (INS), and muon spin rotation ($\mu$SR). Our measurements and subsequent analysis confirm that the transition at T$_{N}$ can be associated with the ordering of moments on the Ce$^{3+}$ site. Both a spontaneous magnetic order observed with $\mu$SR and a dispersive spin-wave spectrum observed with inelastic neutron scattering suggest a model wherein planar dipoles order antiferromagnetically. Notable inconsistencies between $\mu$SR and neutron scattering data within the dipole picture provide strong evidence for the ordering of higher-order moments., Comment: 12 pages, 8 figures

Technology, especially the smartphone, is villainized for taking meaning and time away from in-person interactions and secluding people into "digital bubbles". We believe this is not an intrinsic property of digital gadgets, but evidence of a lack of imagination in technology design. Leveraging augmented reality (AR) toward this end allows us to create experiences for multiple people, their pets, and their environments. In this work, we explore the design of AR technology that "piggybacks" on everyday leisure to foster co-located interactions among close ties (with other people and pets. We designed, developed, and deployed three such AR applications, and evaluated them through a 41-participant and 19-pet user study. We gained key insights about the ability of AR to spur and enrich interaction in new channels, the importance of customization, and the challenges of designing for the physical aspects of AR devices (e.g., holding smartphones). These insights guide design implications for the novel research space of co-located AR.

We investigate the long-term optical variability of the Be/X-ray binary GRO J2058+42 and the possible connection with periods of enhanced X-ray activity. We performed an optical spectroscopic and photometric analysis on data collected during about 18 years. We also present the first optical polarimetric observations of this source. The long-term optical light curves in the $BVRI$ bands and the evolution of the H$\alpha$ equivalent width display a sinusoidal pattern with maxima and minima that repeat every $\sim$9.5 years. The amplitude of this variability increases as the wavelength increases. The H$\alpha$ equivalent width varied from about $-0.3$ to $-15$ \AA. We found a significant decrease in the polarization degree during the low optical state. The optical maxima occur near periods of enhanced X-ray activity and are followed by a drop in the optical emission. Unlike many other Be/X-ray binaries, GRO 2058+42 does not display $V/R$ variability. The long-term optical variability agrees with the standard model of a Be/X-ray binary, where the circumstellar disk of the Be star grows and dissipates on timescales of 9--10 years. We find that the dissipation of the disk started after a major X-ray outburst. However, the stability of the H$\alpha$ line shape as a double-peak profile and the lack of asymmetries suggest the absence of a warped disk and argue against the presence of a highly distorted disk during major X-ray outbursts.

Diffusion is one of the most ubiquitous transport phenomena in nature. Experimentally, it can be tracked by following point spreading in space and time. Here, we introduce a spatiotemporal pump-probe microscopy technique that exploits the residual spatial temperature profile obtained through the transient reflectivity when probe pulses arrive before pump pulses. This corresponds to an effective pump-probe time delay of 13 ns, determined by the repetition rate of our laser system (76 MHz). This pre-time-zero technique enables probing the diffusion of long-lived excitations created by previous pump pulses with nanometer accuracy, and is particularly powerful for following in-plane heat diffusion in thin films. In contrast to existing techniques for quantifying thermal transport it does not require any material input parameters or strong heating. We demonstrate the direct determination of the thermal diffusivities of the layered materials MoSe$_2$ (0.18 cm$^2$/s), WSe$_2$ (0.20 cm$^2$/s), MoS$_2$ (0.35 cm$^2$/s), and WS$_2$ (0.59 cm$^2$/s). This technique paves the way for observing novel nanoscale thermal transport phenomena and tracking diffusion of a broad range of species.

Achieving efficient, high-power harmonic generation in the terahertz spectral domain has technological applications, for example in sixth generation (6G) communication networks. Massless Dirac fermions possess extremely large terahertz nonlinear susceptibilities and harmonic conversion efficiencies. However, the observed maximum generated harmonic power is limited, because of saturation effects at increasing incident powers, as shown recently for graphene. Here, we demonstrate room-temperature terahertz harmonic generation in a Bi$_2$Se$_3$ topological insulator and topological-insulator-grating metamaterial structures with surface-selective terahertz field enhancement. We obtain a third-harmonic power approaching the milliwatt range for an incident power of 75 mW - an improvement by two orders of magnitude compared to a benchmarked graphene sample. We establish a framework in which this exceptional performance is the result of thermodynamic harmonic generation by the massless topological surface states, benefiting from ultrafast dissipation of electronic heat via surface-bulk Coulomb interactions. These results are an important step towards on-chip terahertz (opto)electronic applications.

We consider different types of storage rings as precision probes of axion-mediated monopole-dipole forces. We show that current and planned experiments aiming to measure magnetic and electric dipole moments of protons, muons and electrons very precisely may explore new parts of the parameter space beyond existing laboratory bounds and, in some cases, beyond astrophysical constraints. Remarkably, a light axion coupled to muons may explain the FNAL/BNL $(g-2)_\mu$ anomaly as an environmental effect -- the coherent axion field generated by the earth nucleons induces an extra contribution to the anomalous precession frequency of the muon explaining the discrepancy with respect to the SM prediction., Comment: 12 pages, 3 figures. v2: references added, version accepted in PRD

3D imaging enables accurate diagnosis by providing spatial information about organ anatomy. However, using 3D images to train AI models is computationally challenging because they consist of 10x or 100x more pixels than their 2D counterparts. To be trained with high-resolution 3D images, convolutional neural networks resort to downsampling them or projecting them to 2D. We propose an effective alternative, a neural network that enables efficient classification of full-resolution 3D medical images. Compared to off-the-shelf convolutional neural networks, our network, 3D Globally-Aware Multiple Instance Classifier (3D-GMIC), uses 77.98%-90.05% less GPU memory and 91.23%-96.02% less computation. While it is trained only with image-level labels, without segmentation labels, it explains its predictions by providing pixel-level saliency maps. On a dataset collected at NYU Langone Health, including 85,526 patients with full-field 2D mammography (FFDM), synthetic 2D mammography, and 3D mammography, 3D-GMIC achieves an AUC of 0.831 (95% CI: 0.769-0.887) in classifying breasts with malignant findings using 3D mammography. This is comparable to the performance of GMIC on FFDM (0.816, 95% CI: 0.737-0.878) and synthetic 2D (0.826, 95% CI: 0.754-0.884), which demonstrates that 3D-GMIC successfully classified large 3D images despite focusing computation on a smaller percentage of its input compared to GMIC. Therefore, 3D-GMIC identifies and utilizes extremely small regions of interest from 3D images consisting of hundreds of millions of pixels, dramatically reducing associated computational challenges. 3D-GMIC generalizes well to BCS-DBT, an external dataset from Duke University Hospital, achieving an AUC of 0.848 (95% CI: 0.798-0.896).

We studied the millihertz quasi-periodic oscillation (mHz QPO) in the 2020 outburst of the Be/X-ray binary 1A 0535+262 using Insight-HXMT data over a broad energy band. The mHz QPO is detected in the 27-120 keV energy band. The QPO centroid frequency is correlated with the source flux, and evolves in the 35-95 mHz range during the outburst. The QPO is most significant in the 50-65 keV band, with a significance of ~ 8 sigma, but is hardly detectable (<2 sigma) in the lowest (1-27 keV) and highest (>120 keV) energy bands. Notably, the detection of mHz QPO above 80 keV is the highest energy at which mHz QPOs have been detected so far. The fractional rms of the mHz QPO first increases and then decreases with energy, reaching the maximum amplitude at 50-65 keV. In addition, at the peak of the outburst, the mHz QPO shows a double-peak structure, with the difference between the two peaks being constant at ~0.02 Hz, twice the spin frequency of the neutron star in this system. We discuss different scenarios explaining the generation of the mHz QPO, including the beat frequency model, the Keplerian frequency model, the model of two jets in opposite directions, and the precession of the neutron star, but find that none of them can explain the origin of the QPO well. We conclude that the variability of non-thermal radiation may account for the mHz QPO, but further theoretical studies are needed to reveal the physical mechanism., Comment: 13 pages, 7 figures. Accepted for publication in MNRAS

Classical Be stars, regardless of spectral subtype, display multiperiodic light modulations in the frequency range 0.1-12 d$^{-1}$, when observed with high-cadence and long duration. This behaviour is attributed to non-radial pulsations and/or rotation of the Be star. The main goal of this work is to investigate the fast photometric variability of the optical counterparts to Be/X-ray binaries and compare the general patterns of such variability with the Galactic population of classical Be stars. We analyzed 21 sources with TESS. High-cadence photometry with two ground-based telescopes was also performed for 15 sources. Standard Fourier analysis and least-squares fitting methods were employed in the frequency analysis. All sources exhibit intra-night light variations with intensity variations of 0.01-0.06 mag in the ground-based observations and up to 5% in flux in TESS observations. This variability manifests itself as multi-periodic signals in the frequency range 0.2-12 d$^{-1}$. We find that the patterns of variability of the Be stars in Be/X-ray binaries agree with that of classical early-type Be stars in terms of the general shape of the periodograms. Based on the general shape and number of peaks in the periodograms, Be/X-ray binaries can be classified into different types. The most common case is the presence of groups of closely-spaced frequencies (67%), followed by sources that exhibit isolated signals (18%). The remaining type of sources displays frequency spectra characterized by a mixed pattern of stochastic variability and high-frequency peaks. This study reveals that short-term optical photometric variability is a very common, if not ubiquitous, feature intrinsic to the Be optical companions in Be/X-ray binaries. This variability is mainly attributed to pulsations that originate in the stellar interior.

Modern machine learning models use an ever-increasing number of parameters to train (175 billion parameters for GPT-3) with large datasets to obtain better performance. Bigger is better has been the norm. Optical computing has been reawakened as a potential solution to large-scale computing through optical accelerators that carry out linear operations while reducing electrical power. However, to achieve efficient computing with light, creating and controlling nonlinearity optically rather than electronically remains a challenge. This study explores a reservoir computing (RC) approach whereby a 14 mm long few-mode waveguide in LiNbO3 on insulator is used as a complex nonlinear optical processor. A dataset is encoded digitally on the spectrum of a femtosecond pulse which is then launched in the waveguide. The output spectrum depends nonlinearly on the input. We experimentally show that a simple digital linear classifier with 784 parameters using the output spectrum from the waveguide as input increased the classification accuracy of several databases compared to non-transformed data, approximately 10$\%$. In comparison, a deep digital neural network (NN) with 40000 parameters was necessary to achieve the same accuracy. Reducing the number of parameters by a factor of $\sim$50 illustrates that a compact optical RC approach can perform on par with a deep digital NN., Comment: 13 pages, 3 figures and 1 table

The idea that discourse relations are construed through explicit content and shared, or implicit, knowledge between producer and interpreter is ubiquitous in discourse research and linguistics. However, the actual contribution of the lexical semantics of arguments is unclear. We propose a computational approach to the analysis of contrast and concession relations in the PDTB corpus. Our work sheds light on the extent to which lexical semantics contributes to signaling explicit and implicit discourse relations and clarifies the contribution of different parts of speech in both. This study contributes to bridging the gap between corpus linguistics and computational linguistics by proposing transparent and explainable models of discourse relations based on the synonymy and antonymy of their arguments., Comment: 20 pages, 13 figures

We have obtained optical spectroscopy and photometry data during four years after the event. The long-term photometric light-curve and the equivalent widths of the Halpha and He I 6678 lines were used to monitor the state of the Be star disk. The Halpha line profiles show evidence for V/R variability that was accounted for by fitting the Halpha spectral line profile with two Gaussian functions. We divided our data into three phases according to the intensity of the X-ray, optical, and infrared emission. Phase I covers the rise and decay of the giant X-ray outburst that took place in October to November 2017. We interpret phase II as the dissipation of the Be star equatorial disk and phase III as its recovery. The timescale of a complete formation and dissipation process is about 1250 days. The epoch when the dissipation process stopped and the reformation period began is estimated to be around MJD 58530. We find a delay of about 100 to 200 days between the minimum of the optical or infrared intensity and the strength of the Halpha line after the X-ray outburst, which may indicate that the dissipation of the disk begins from the inner parts. The motion of the density perturbation inside the disk is prograde, with a V/R quasi-period of about four years. The source shows a positive correlation in the (B-V) color index versus V-band magnitude diagram, which implies that the system is seen at a small or moderate inclination angle., Comment: 15 pages, 5 figures