Incompleteness of graph neural networks for points clouds in three dimensions

Graph neural networks (GNN) are very popular methods in machine learning and have been applied very successfully to the prediction of the properties of molecules and materials. First-order GNNs are well known to be incomplete, i.e., there exist graphs that are distinct but appear identical when seen through the lens of the GNN. More complicated schemes have thus been designed to increase their resolving power. Applications to molecules (and more generally, point clouds), however, add a geometric dimension to the problem. The most straightforward and prevalent approach to construct graph representation for molecules regards atoms as vertices in a graph and draws a bond between each pair of atoms within a chosen cutoff. Bonds can be decorated with the distance between atoms, and the resulting "distance graph NNs" (dGNN) have empirically demonstrated excellent resolving power and are widely used in chemical ML, with all known indistinguishable configurations being resolved in the fully-connected limit, which is equivalent to infinite or sufficiently large cutoff. Here we present a counterexample that proves that dGNNs are not complete even for the restricted case of fully-connected graphs induced by 3D atom clouds. We construct pairs of distinct point clouds whose associated graphs are, for any cutoff radius, equivalent based on a first-order Weisfeiler-Lehman test. This class of degenerate structures includes chemically-plausible configurations, both for isolated structures and for infinite structures that are periodic in 1, 2, and 3 dimensions. The existence of indistinguishable configurations sets an ultimate limit to the expressive power of some of the well-established GNN architectures for atomistic machine learning. Models that explicitly use angular or directional information in the description of atomic environments can resolve this class of degeneracies

Inverse Compton scattering in mildly relativistic plasma

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and calculated the Sunyaev-Zel'dovich effect in the cosmic background radiation. Our semi-analytic method is based on a separation of photon diffusion in frequency and real space. We use Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zel'dovich effect (not possible with the extended Kompaneets equation) and discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high temperature clusters ($k_B T_e \gtrsim 15$ keV) relativistic corrections based on a fifth order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zel'dovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the cross-over frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections, and should be taken into account for high-precision work, but are smaller than the typical kinematic effect from cluster radial velocities.Comment: LateX, 30 pages and 11 figures. Accepted for publication in the Astrophysical Journa

X-ray Spectral Signatures of the Photon Bubble Model for Ultraluminous X-ray Sources

The nature of ultraluminous X-ray sources in nearby galaxies is one of the major open questions in modern X-ray astrophysics. One possible explanation for these objects is an inhomogeneous, radiation dominated accretion disk around a $\sim 10 M_{\odot}$ black hole -- the so-called ``photon bubble'' model. While previous studies of this model have focused primarily on its radiation-hydrodynamics aspects, in this paper, we provide an analysis of its X-ray spectral (continuum and possible edge and line) characteristics. Compton reflection between high and low density regions in the disk may provide the key to distinguishing this model from others, such as accretion onto an intermediate mass black hole. We couple a Monte Carlo/Fokker-Planck radiation transport code with the XSTAR code for reflection to simulate the photon spectra produced in a photon bubble model for ULXs. We find that reflection components tend to be very weak and in most cases not observable, and make predictions for the shape of the high-energy Comptonizing spectra. In many cases the Comptonization dominates the spectra even down to $\sim$ a few keV. In one simulation, a \sim 9 \kev feature was found, which may be considered a signature of photon bubbles in ULXs; furthermore, we make predictions of high energy power-laws which may be observed by future instruments.Comment: Accepted for publication in the Astrophysical Journa

Evolution of the Low-Energy Photon Spectra in Gamma-Ray Bursts

We report evidence that the asymptotic low-energy power law slope alpha (below the spectral break) of BATSE gamma-ray burst photon spectra evolves with time rather than remaining constant. We find a high degree of positive correlation exists between the time-resolved spectral break energy E_pk and alpha. In samples of 18 "hard-to-soft" and 12 "tracking" pulses, evolution of alpha was found to correlate with that of the spectral break energy E_pk at the 99.7% and 98% confidence levels respectively. We also find that in the flux rise phase of "hard-to-soft" pulses, the mean value of alpha is often positive and in some bursts the maximum value of alpha is consistent with a value > +1. BATSE burst 3B 910927, for example, has a alpha_max equal to 1.6 +/- 0.3. These findings challenge GRB spectral models in which alpha must be negative of remain constant.Comment: 12 pages (including 6 figures), accepted to Ap

Monte-Carlo simulations of thermal/nonthermal radiation from a neutron-star magnetospheric accretion shell

We discuss the space-and-time-dependent Monte Carlo code we have developed to simulate the relativistic radiation output from compact astrophysical objects, coupled to a Fokker-Planck code to determine the self-consistent lepton populations. We have applied this code to model the emission from a magnetized neutron star accretion shell near the Alfven radius, reprocessing the radiation from the neutron sar surface. We explore the parameter space defined by the accretion rate, stellar surface field and the level of wave turbulence in the shell. Our results are relevant to the emission from atoll sources, soft-X-ray transient X-ray binaries containing weakly magnetized neutron stars, and to recently suggested models of accretion-powered emission from anomalous X-ray pulsars.Comment: 24 pages, including 7 figures; uses epsf.sty. final version, accepted for publication in ApJ. Extended introduction and discussio

FEATURES OF THE CLINICAL SIGNIFICANCE OF POLYMORPHIC VARIANTS OF ENOS AND AGTR2 GENES IN PATIENTS WITH CAD

Coronary heart disease (CHD) is a major cause of mortality. Morphological substrate of CHD in most cases is atherosclerosis, which is based on structural genes polymorphism eNOS and AGTR2. The aim of the study was to study the prevalence of eNOS and AGTR2 genes in patients with coronary artery disease and the association of these genes with coronary heart disease. The study involved 187 patients aged 36 to 86 years (62,2±11,2) with different forms of CHD: stable and unstable angina, myocardial infarction and 45 people without CHD. Determination of gene polymorphisms was performed by real-time PCR analyzer of nucleic acids IQ 5 Bio-Rad. Statistical analysis was performed using Statistica 10.0. The study revealed a significant difference between the incidence of homozygous AA allelic variant gene AGTR2 group of patients with myocardial infarction and the comparison group; polymorphic variant AA AGTR2 gene is associated with earlier onset of coronary artery disease; It found that carriers of the polymorphic variant gene GA AGTR2 beginning statistically CHD occurred significantly later than in carriers of alleles GG and AA; age CHD debut TT allele carriers of the eNOS gene is associated with an earlier onset of the disease and statistically significantly different from the age of first CHD in carriers of alleles of polymorphic variants of GG and GT; revealed a positive correlation between the polymorphic allele AGTR2 gene with the presence of arterial hypertension in patients with coronary artery disease; It determined that the T allele carriers of the polymorphic gene eNOS is associated more early onset of hypertension, found the association of the polymorphic allele gene AGTR2 the need to use higher doses of ACE inhibitor — perindopril

Orbital Comptonization in accretion disks around black holes

We have performed Monte Carlo simulations of Compton upscattering of low-energy photons in an accretion disk around a Schwarzschild black hole. The photons gain energy from the rotational motion of the electrons in the disk. The upscattering occurs near the black hole horizon, where the flow velocity of the electrons approaches the speed of light. We show that this type of bulk-flow Comptonization can produce power-law X-ray spectra similar to the ones observed in black-hole X-ray transients in the high/soft state, i.e., a soft bump dominating the spectrum below ~ 10 keV and a power-law tail with photon index in the range 2-3. In order to reproduce the observed hard to soft flux ratio the disk has to have vertical optical depth above ~ 3 at the last stable orbit. We conclude that the power-law component of the high/soft state of black-hole transients may be due to an intrinsically cool disk extending all the way to the hole, without a separate hot plasma component.Comment: 6 pages, 6 figure

Chandra Observations of Type Ia Supernovae: Upper Limits to the X-ray Flux of SN 2002bo, SN 2002ic, SN 2005gj, and SN 2005ke

We set sensitive upper limits to the X-ray emission of four Type Ia supernovae (SNe Ia) using the Chandra X-ray Observatory. SN 2002bo, a normal, although reddened, nearby SN Ia, was observed 9.3 days after explosion. For an absorbed, high temperature bremsstrahlung model the flux limits are 3.2E-16 ergs/cm^2/s (0.5-2 keV band) and 4.1E-15 ergs/cm^2/s (2-10 keV band). Using conservative model assumptions and a 10 km/s wind speed, we derive a mass loss rate of \dot{M} ~ 2E-5 M_\odot/yr, which is comparable to limits set by the non-detection of Halpha lines from other SNe Ia. Two other objects, SN 2002ic and SN 2005gj, observed 260 and 80 days after explosion, respectively, are the only SNe Ia showing evidence for circumstellar interaction. The SN 2002ic X-ray flux upper limits are ~4 times below predictions of the interaction model currently favored to explain the bright optical emission. To resolve this discrepancy we invoke the mixing of cool dense ejecta fragments into the forward shock region, which produces increased X-ray absorption. A modest amount of mixing allows us to accommodate the Chandra upper limit. SN 2005gj is less well studied at this time. Assuming the same circumstellar environment as for SN 2002i, the X-ray flux upper limits for SN 2005gj are ~4 times below the predictions, suggesting that mixing of cool ejecta into the forward shock has also occurred here. Our reanalysis of Swift and Chandra data on SN 2005ke does not confirm a previously reported X-ray detection. The host galaxies NGC 3190 (SN 2002bo) and NGC 1371 (SN 2005ke) each harbor a low luminosity (L_X ~ 3-4E40 ergs/s) active nucleus in addition to wide-spread diffuse soft X-ray emission.Comment: 16 pages, to appear in ApJ (20 Nov 2007