Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks

In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Networks (VPINNs). Such conditions are usually imposed by adding penalization terms in the loss function and properly choosing the corresponding scaling coefficients; however, in practice, this requires an expensive tuning phase. We show through several numerical tests that modifying the output of the neural network to exactly match the prescribed values leads to more efficient and accurate solvers. The best results are achieved by exactly enforcing the Dirichlet boundary conditions by means of an approximate distance function. We also show that variationally imposing the Dirichlet boundary conditions via Nitsche's method leads to suboptimal solvers.Comment: 22 pages, 45 figure

Updating the orbital ephemeris of the dipping source XB 1254-690 and the distance to the source

XB 1254-690 is a dipping low mass X-ray binary system hosting a neutron star and showing type I X-ray bursts. We aim at obtaining more accurate orbital ephemeris and at constraining the orbital period derivative of the system for the first time. In addition, we want to better constrain the distance to the source in order to locate the system in a well defined evolutive scenario. We apply for the first time an orbital timing technique to XB 1254-690, using the arrival times of the dips present in the light curves that have been collected during 26 years of X-ray pointed observations performed from different space missions. We estimate the dip arrival times using a statistical method that weights the count-rate inside the dip with respect to the level of the persistent emission outside the dip. We fit the obtained delays as a function of the orbital cycles both with a linear and a quadratic function. We infer the orbital ephemeris of XB 1254-690 improving the accuracy of the orbital period with respect to previous estimates. We infer a mass of M$_{2}=0.42\pm 0.04$ M$_{\odot}$ for the donor star, in agreement with the estimations already present in literature, assuming that the star is in thermal equilibrium while it transfers part of its mass via the inner Lagrangian point, and assuming a neutron star mass of 1.4 M$_{\odot}$. Using these assumptions, we also constrain the distance to the source, finding a value of 7.6$\pm 0.8$ kpc. Finally, we discuss the evolution of the system suggesting that it is compatible with a conservative mass transfer driven by magnetic braking.Comment: 13 pages, 5 figures, accepted for publication in Research in Astronomy and Astrophysics (RAA

New orbital ephemerides for the dipping source 4U 1323-619: constraining the distance to the source

4U 1323-619 is a low mass X-ray binary system that shows type I X-ray bursts and dips. The most accurate estimation of the orbital period is 2.941923(36) hrs and a distance from the source that is lower than 11 kpc has been proposed. We aim to obtain the orbital ephemeris, the orbital period of the system, as well as its derivative to compare the observed luminosity with that predicted by the theory of secular evolution. We took the advantage of about 26 years of X-ray data and grouped the selected observations when close in time. We folded the light curves and used the timing technique, obtaining 12 dip arrival times. We fit the delays of the dip arrival times both with a linear and a quadratic function. We locate 4U 1323-619 within a circular area centred at RA (J2000)= 201.6543\degree and DEC (J2000)= -62.1358\degree with an associated error of 0.0002\degree, and confirm the detection of the IR counterpart already discussed in literature. We estimate an orbital period of P=2.9419156(6) hrs compatible with the estimations that are present in the literature, but with an accuracy ten times higher. We also obtain a constraint on the orbital period derivative for the first time, estimating $\dot{P}=(8\pm 13)\times 10^{-12}$ s/s. Assuming that the companion star is in thermal equilibrium in the lower main sequence, and is a neutron star of 1.4 M$_{\odot}$, we infer a mass of 0.28$\pm$0.03 M$_{\odot}$ for the companion star. Assuming a distance of 10 kpc, we obtained a luminosity of (4.3$\pm$0.5)$\times 10^{36}$ erg s$^{-1}$, which is not in agreement with what is predicted by the theory of secular evolution. Using a 3D extinction map of the K$_{s}$ radiation in our Galaxy, we obtain a distance of 4.2$^{+0.8}_{-0.7}$ kpc at 68\% confidence level. (Abridged)Comment: 10 pages, 8 figures, accepted for publication in Astronomy & Astrophysic

Study of the reflection spectrum of the LMXB 4U 1702-429

The source 4U 1702-429 (Ara X-1) is a low-mass X-ray binary system hosting a neutron star. Albeit the source is quite bright ( $\sim10^{37}$ erg s$^{-1}$) its broadband spectrum has never been studied. Neither dips nor eclipses have been observed in the light curve suggesting that its inclination angle is smaller than 60$^{\circ}$.We analysed the broadband spectrum of 4U 1702-429 in the 0.3-60 keV energy range, using XMM-Newton and INTEGRAL data, to constrain its Compton reflection component if it is present. After excluding the three time intervals in which three type-I X-ray bursts occurred, we fitted the joint XMM-Newton and INTEGRAL spectra obtained from simultaneous observations. A broad emission line at 6.7 keV and two absorption edges at 0.87 and 8.82 keV were detected. We found that a self-consistent reflection model fits the 0.3-60 keV spectrum well. The broadband continuum is composed of an emission component originating from the inner region of the accretion disc, a Comptonised direct emission coming from a corona with an electron temperature of $2.63 \pm 0.06$ keV and an optical depth $\tau=13.6 \pm 0.2$, and, finally, a reflection component. The best-fit indicates that the broad emission line and the absorption edge at 8.82 keV, both associated with the presence of \ion{Fe}{xxv} ions, are produced by reflection in the region above the disc with a ionisation parameter of $Log(\xi) \simeq 2.7$. We have inferred that the inner radius, where the broad emission line originates, is $64^{+52}_{-15}$ km, and the inner radius of the accretion disc is $39^{+6}_{-8}$ km. (Abridged)Comment: 9 pages, 9 figures, accepted for publication by A&

Testing Rate Dependent corrections on timing mode EPIC-pn spectra of the accreting Neutron Star GX 13+1

When the EPIC-pn instrument on board XMM-Newton is operated in Timing mode, high count rates (>100 cts/s) of bright sources may affect the calibration of the energy scale, resulting in a modification of the real spectral shape. The corrections related to this effect are then strongly important in the study of the spectral properties. Tests of these calibrations are more suitable in sources which spectra are characterised by a large number of discrete features. Therefore, in this work, we carried out a spectral analysis of the accreting Neutron Star GX 13+1, which is a dipping source with several narrow absorption lines and a broad emission line in its spectrum. We tested two different correction approaches on an XMM-Newton EPIC-pn observation taken in Timing mode: the standard Rate Dependent CTI (RDCTI or epfast) and the new, Rate Dependent Pulse Height Amplitude (RDPHA) corrections. We found that, in general, the two corrections marginally affect the properties of the overall broadband continuum, while hints of differences in the broad emission line spectral shape are seen. On the other hand, they are dramatically important for the centroid energy of the absorption lines. In particular, the RDPHA corrections provide a better estimate of the spectral properties of these features than the RDCTI corrections. Indeed the discrete features observed in the data, applying the former method, are physically more consistent with those already found in other Chandra and XMM-Newton observations of GX 13+1.Comment: Accepted for publication in MNRAS; 10 pages, 8 figure

Global QSAR models of skin sensitisers for regulatory purposes

Abstract Background The new European Regulation on chemical safety, REACH, (Registration, Evaluation, Authorisation and Restriction of CHemical substances), is in the process of being implemented. Many chemicals used in industry require additional testing to comply with the REACH regulations. At the same time EU member states are attempting to reduce the number of animals used in experiments under the 3 Rs policy, (refining, reducing, and replacing the use of animals in laboratory procedures). Computational techniques such as QSAR have the potential to offer an alternative for generating REACH data. The FP6 project CAESAR was aimed at developing QSAR models for 5 key toxicological endpoints of which skin sensitisation was one. Results This paper reports the development of two global QSAR models using two different computational approaches, which contribute to the hybrid model freely available online. Conclusions The QSAR models for assessing skin sensitisation have been developed and tested under stringent quality criteria to fulfil the principles laid down by the OECD. The final models, accessible from CAESAR website, offer a robust and reliable method of assessing skin sensitisation for regulatory use.</p

A possible cyclotron resonance scattering feature near 0.7 keV in X1822-371

We analyse all available X-ray observations of X1822-371 made with XMM-Newton, Chandra, Suzaku and INTEGRAL satellites. The observations were not simultaneous. The Suzaku and INTEGRAL broad band energy coverage allows us to constrain the spectral shape of the continuum emission well. We use the model already proposed for this source, consisting of a Comptonised component absorbed by interstellar matter and partially absorbed by local neutral matter, and we added a Gaussian feature in absorption at $\sim 0.7$ keV. This addition significantly improves the fit and flattens the residuals between 0.6 and 0.8 keV. We interpret the Gaussian feature in absorption as a cyclotron resonant scattering feature (CRSF) produced close to the neutron star surface and derive the magnetic field strength at the surface of the neutron star, $(8.8 \pm 0.3) \times 10^{10}$ G for a radius of 10 km. We derive the pulse period in the EPIC-pn data to be 0.5928850(6) s and estimate that the spin period derivative of X1822-371 is $(-2.55 \pm 0.03) \times 10^{-12}$ s/s using all available pulse period measurements. Assuming that the intrinsic luminosity of X1822-371is at the Eddington limit and using the values of spin period and spin period derivative of the source, we constrain the neutron star and companion star masses. We find the neutron star and the companion star masses to be $1.69 \pm 0.13$ M$_{\odot}$ and $0.46 \pm 0.02$ M$_{\odot}$, respectively, for a neutron star radius of 10 km.In a self-consistent scenario in which X1822-371 is spinning-up and accretes at the Eddington limit, we estimate that the magnetic field of the neutron star is $(8.8 \pm 0.3) \times 10^{10}$ G for a neutron star radius of 10 km. If our interpretation is correct, the Gaussian absorption feature near 0.7 keV is the very first detection of a CRSF below 1 keV in a LMXB. (abridged)Comment: 14 pages, 12 figures, accepted for publication in A&

Signature of the presence of a third body orbiting around XB 1916-053

The ultra-compact dipping source \object{XB 1916-053} has an orbital period of close to 50 min and a companion star with a very low mass (less than 0.1 M$_{\odot}$). The orbital period derivative of the source was estimated to be $1.5(3) \times 10^{-11}$ s/s through analysing the delays associated with the dip arrival times obtained from observations spanning 25 years, from 1978 to 2002. The known orbital period derivative is extremely large and can be explained by invoking an extreme, non-conservative mass transfer rate that is not easily justifiable. We extended the analysed data from 1978 to 2014, by spanning 37 years, to verify whether a larger sample of data can be fitted with a quadratic term or a different scenario has to be considered. We obtained 27 delays associated with the dip arrival times from data covering 37 years and used different models to fit the time delays with respect to a constant period model.We find that the quadratic form alone does not fit the data. The data are well fitted using a sinusoidal term plus a quadratic function or, alternatively, with a series of sinusoidal terms that can be associated with a modulation of the dip arrival times due to the presence of a third body that has an elliptical orbit. We infer that for a conservative mass transfer scenario the modulation of the delays can be explained by invoking the presence of a third body with mass between 0.10-0.14 M$_{\odot}$, orbital period around the X-ray binary system of close to 51 yr and an eccentricity of $0.28 \pm 0.15$. In a non-conservative mass transfer scenario we estimate that the fraction of matter yielded by the degenerate companion star and accreted onto the neutron star is $\beta = 0.08$, the neutron star mass is $\ge 2.2$ M$_{\odot}$, and the companion star mass is 0.028 M$_{\odot}$. (Abridged)Comment: 13 pages, 9 figures. Accepted for publication in A&

GRO J1744-28: an intermediate B-field pulsar in a low mass X-ray binary

The bursting pulsar, GRO J1744-28, went again in outburst after $\sim$18 years of quiescence in mid-January 2014. We studied the broad-band, persistent, X-ray spectrum using X-ray data from a XMM-Newton observation, performed almost at the peak of the outburst, and from a close INTEGRAL observation, performed 3 days later, thus covering the 1.3-70.0 keV band. The spectrum shows a complex continuum shape that cannot be modelled with standard high-mass X-ray pulsar models, nor by two-components models. We observe broadband and peaked residuals from 4 to 15 keV, and we propose a self-consistent interpretation of these residuals, assuming they are produced by cyclotron absorption features and by a moderately smeared, highly ionized, reflection component. We identify the cyclotron fundamental at $\sim$ 4.7 keV, with hints for two possible harmonics at 10.4 keV and 15.8 keV. The position of the cyclotron fundamental allows an estimate for the pulsar magnetic field of (5.27 $\pm$ 0.06) $\times$ 10$^{11}$ G, if the feature is produced at its surface. From the dynamical and relativistic smearing of the disk reflected component, we obtain a lower limit estimate for the truncated accretion disk inner radius, ($\gtrsim$ 100 R$_g$), and for the inclination angle (18$^{\circ}$-48$^{\circ}$). We also detect the presence of a softer thermal component, that we associate with the emission from an accretion disk truncated at a distance from the pulsar of 50-115 R$_g$. From these estimates, we derive the magneto-spheric radius for disk accretion to be $\sim$ 0.2 times the classical Alfv\'en radius for radial accretion.Comment: Accepted for publication in MNRA

Fibroblast proliferation and migration in wound healing by phytochemicals: Evidence for a novel synergic outcome

Wound-healing is a dynamic skin reparative process that results in a sequence of events, including inflammation, proliferation, and migration of different cell types as fibroblasts. Fibroblasts play a crucial role in repairing processes, from the late inflammatory phase until the fully final epithelization of the injured tissue. Within this context, identifying tools able to implement cell proliferation and migration could improve tissue regeneration. Recently, plants species from all over the world are coming out as novel tools for therapeutic applications thanks to their phytochemicals, which have antioxidant properties and can promote wound healing. In this paper, we aimed at investigating antioxidant activity of waste extracts from different medicinal plants, endemic of the Mediterranean area, on fibroblast proliferation and wound healing. We determined the amount of total phenols and anti-oxidant activity by ABTS assay. We then evaluated the cytotoxicity of the compounds and the proliferative capabilities of fibroblasts by scratch assay. Our results showed that waste extracts retain antioxidant and regenerative properties, inducing tissue re-establishment after environmental stress exposure. Taken together, our findings suggest that waste material could be used in the future also in combinations to stimulate wound healing processes and antioxidant responses in damaged skin