Non-reversible Gaussian processes for identifying latent dynamical structure in neural data

A common goal in the analysis of neural data is to compress large population recordings into sets of interpretable, low-dimensional latent trajectories. This problem can be approached using Gaussian process (GP)-based methods which provide uncertainty quantification and principled model selection. However, standard GP priors do not distinguish between underlying dynamical processes and other forms of temporal autocorrelation. Here, we propose a new family of “dynamical” priors over trajectories, in the form of GP covariance functions that express a property shared by most dynamical systems: temporal non-reversibility. Non-reversibility is a universal signature of autonomous dynamical systems whose state trajectories follow consistent flow fields, such that any observed trajectory could not occur in reverse. Our new multi-output GP kernels can be used as drop-in replacements for standard kernels in multivariate regression, but also in latent variable models such as Gaussian process factor analysis (GPFA). We therefore introduce GPFADS (Gaussian Process Factor Analysis with Dynamical Structure), which models single-trial neural population activity using low-dimensional, non-reversible latent processes. Unlike previously proposed non-reversible multi-output kernels, ours admits a Kronecker factorization enabling fast and memory-efficient learning and inference. We apply GPFADS to synthetic data and show that it correctly recovers ground truth phase portraits. GPFADS also provides a probabilistic generalization of jPCA, a method originally developed for identifying latent rotational dynamics in neural data. When applied to monkey M1 neural recordings, GPFADS discovers latent trajectories with strong dynamical structure in the form of rotations

HST/FOS Eclipse Observations of the Nova-like Cataclysmic Variable UX Ursae Majoris

[abridged abstract] We present and analyze Hubble Space Telescope observations of the eclipsing nova-like cataclysmic variable UX UMa obtained with the Faint Object Spectrograph. Two eclipses each were observed with the G160L grating (covering the ultraviolet waveband) in August of 1994 and with the PRISM (covering the near-ultraviolet to near-infrared) in November of the same year. The system was 50% brighter in November than in August, which, if due to a change in the accretion rate, indicates a fairly substantial increase in Mdot_acc by >~ 50%. Model disk spectra constructed as ensembles of stellar atmospheres provide poor descriptions of the observed post-eclipse spectra, despite the fact that UX UMa's light should be dominated by the disk at this time. Suitably scaled single temperature model stellar atmospheres with T_eff = 12,500-14,500 K actually provide a better match to both the ultraviolet and optical post-eclipse spectra. Evidently, great care must be taken in attempts to derive accretion rates from comparisons of disk models to observations. One way to reconcile disk models with the observed post-eclipse spectra is to postulate the presence of a significant amount of optically thin material in the system. Such an optically thin component might be associated with the transition region (``chromosphere'') between the disk photosphere and the fast wind from the system, whose presence has been suggested by Knigge & Drew (1997).Comment: 35 pages, including 12 figures; to appear in the ApJ (Vol. 499

56Ni dredge-up in the type IIp Supernova 1995V

We present contemporary infrared and optical spectra of the plateau type II SN 1995V in NGC 1087 covering four epochs, approximately 22 to 84 days after shock breakout. The data show, for the first time, the infrared spectroscopic evolution during the plateau phase of a typical type II event. In the optical region P Cygni lines of the Balmer series and of metals lines were identified. The infrared (IR) spectra were largely dominated by the continuum, but P Cygni Paschen lines and Brackett gamma lines were also clearly seen. The other prominent IR features are confined to wavelengths blueward of 11000 \AA and include Sr II 10327, Fe II 10547, C I 10695 and He I 10830 \AA. We demonstrate the presence of He I 10830 \AA on days 69 and 85. The presence of this line at such late times implies re-ionisation. A likely re-ionising mechanism is gamma-ray deposition following the radioactive decay of 56Ni. We examine this mechanism by constructing a spectral model for the He I 10830 \AA line based on explosion model s15s7b2f of Weaver & Woosley (1993). We find that this does not generate the observed line owing to the confinement of the 56Ni to the central zones of the ejecta. In order to reproduce the He I line, it was necessary to introduce additional upward mixing of the 56Ni, with 10^{-5} of the total nickel mass reaching above the helium photosphere. In addition, we argue that the He I line-formation region is likely to have been in the form of pure helium clumps in the hydrogen envelope.Comment: Accepted for publication in MNRAS, 32 pages including 11 figures (uses psfig.sty - included

Addendum: "The Dynamics of M15: Observations of the Velocity Dispersion Profile and Fokker-Planck Models" (ApJ, 481, 267 [1997])

It has recently come to our attention that there are axis scale errors in three of the figures of Dull et al. (1997, hereafter D97). D97 presented Fokker-Planck models for the collapsed-core globular cluster M15 that include a dense, centrally concentrated population of neutron stars and massive white dwarfs, but do not include a central black hole. In this Addendum, we present corrected versions of Figures 9, 10, and 12, and an expanded version of Figure 6. This latter figure, which shows the full run of the velocity dispersion profile, indicates that the D97 model predictions are in good agreement with the moderately rising HST-STIS velocity dispersion profile for M15 reported by Gerssen et al. (2002, astro-ph/0209315). Thus, a central black hole is not required to fit the new STIS velocity measurements, provided that there is a sufficient population of neutron stars and massive white dwarfs. This conclusion is consistent with the findings of Gerssen et al. (2002, astro-ph/0210158), based on a reapplication of their Jeans equation analysis using the corrected mass-to-light profile (Figure 12) for the D97 models.Comment: 4 pages, 4 figures, submitted to Ap

Phase resolved spectroscopy and Kepler photometry of the ultracompact AM CVn binary SDSS J190817.07+394036.4

{\it Kepler} satellite photometry and phase-resolved spectroscopy of the ultracompact AM CVn type binary SDSS J190817.07+394036.4 are presented. The average spectra reveal a variety of weak metal lines of different species, including silicon, sulphur and magnesium as well as many lines of nitrogen, beside the strong absorption lines of neutral helium. The phase-folded spectra and the Doppler tomograms reveal an S-wave in emission in the core of the He I 4471 \AA\,absorption line at a period of $P_{\rm orb}=1085.7\pm2.8$\,sec identifying this as the orbital period of the system. The Si II, Mg II and the core of some He I lines show an S-wave in absorption with a phase offset of $170\pm15^\circ$ compared to the S-wave in emission. The N II, Si III and some helium lines do not show any phase variability at all. The spectroscopic orbital period is in excellent agreement with a period at $P_{\rm orb}=1085.108(9)$\,sec detected in the three year {\it Kepler} lightcurve. A Fourier analysis of the Q6 to Q17 short cadence data obtained by {\it Kepler} revealed a large number of frequencies above the noise level where the majority shows a large variability in frequency and amplitude. In an O-C analysis we measured a $\vert\dot{P}\vert\sim1.0\,$x$\,10^{-8}\,$s\,s$^{-1}$ for some of the strongest variations and set a limit for the orbital period to be $\vert\dot{P}\vert<10^{-10}$s\,s$^{-1}$. The shape of the phase folded lightcurve on the orbital period indicates the motion of the bright spot. Models of the system were constructed to see whether the phases of the radial velocity curves and the lightcurve variation can be combined to a coherent picture. However, from the measured phases neither the absorption nor the emission can be explained to originate in the bright spot.Comment: Accepted for publication in MNRAS, 15 pages, 14 figures, 5 table

GJ 900: A new hierarchical system with low-mass components

Speckle interferometric observations made with the 6 m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences in 2000 revealed the triple nature of the nearby ($\pi_{Hip}=51.80\pm1.74$ mas) low-mass young ($\approx200$ Myr) star GJ 900. The configuration of the triple system allowed it to be dynamically unstable. Differential photometry performed from 2000 through 2004 yielded $I$- and $K$-band absolute magnitudes and spectral types for the components to be $I_{A}$=6.66$\pm$0.08, $I_{B}$=9.15$\pm$0.11, $I_{C}$=10.08$\pm$0.26, $K_{A}$=4.84$\pm$0.08, $K_{B}$=6.76$\pm$0.20, $K_{C}$=7.39$\pm$0.31, $Sp_{A}$$\approx$K5--K7, $Sp_{B}$$\approx$M3--M4, $Sp_{C}$$\approx$M5--M6. The ``mass--luminosity'' relation is used to estimate the individual masses of the components: $\mathcal{M}_{A}$$\approx0.64\mathcal{M}_{\odot}$, $\mathcal{M}_{B}$$\approx0.21\mathcal{M}_{\odot}$, $\mathcal{M}_{C}$$\approx0.13\mathcal{M}_{\odot}$. From the observations of the components relative motion in the period 2000--2006, we conclude that GJ 900 is a hierarchical triple star with the possible orbital periods P$_{A-BC}$$\approx$80 yrs and P$_{BC}$$\approx$20 yrs. An analysis of the 2MASS images of the region around GJ 900 leads us to suggest that the system can include other very-low-mass components.Comment: 7 pages, 5 figure

A Far-Ultraviolet Spectroscopic Survey of Luminous Cool Stars

FUSE ultraviolet spectra of 8 giant and supergiant stars reveal that high temperature (3 X 10^5 K) atmospheres are common in luminous cool stars and extend across the color-magnitude diagram from Alpha Car (F0 II) to the cool giant Alpha Tau (K5 III). Emission present in these spectra includes chromospheric H-Lyman Beta, Fe II, C I, and transition region lines of C III, O VI, Si III, Si IV. Emission lines of Fe XVIII and Fe XIX signaling temperatures of ~10^7 K and coronal material are found in the most active stars, Beta Cet and 31 Com. A short-term flux variation, perhaps a flare, was detected in Beta Cet during our observation. Stellar surface fluxes of the emission of C III and O VI are correlated and decrease rapidly towards the cooler stars, reminiscent of the decay of magnetically-heated atmospheres. Profiles of the C III (977A) lines suggest that mass outflow is underway at T~80,000 K, and the winds are warm. Indications of outflow at higher temperatures (3 X 10^5K) are revealed by O VI asymmetries and the line widths themselves. High temperature species are absent in the M-supergiant Alpha Ori. Narrow fluorescent lines of Fe II appear in the spectra of many giants and supergiants, apparently pumped by H Lyman Alpha, and formed in extended atmospheres. Instrumental characteristics that affect cool star spectra are discussed.Comment: Accept for publication in The Astrophysical Journal; 22 pages of text, 23 figures and 8 table

HST Observations of Chromospheres in Metal Deficient Field Giants

HST high resolution spectra of metal-deficient field giants more than double the stars in previous studies, span about 3 magnitudes on the red giant branch, and sample an abundance range [Fe/H]= -1 to -3. These stars, in spite of their age and low metallicity, possess chromospheric fluxes of Mg II (2800 Angstrom) that are within a factor of 4 of Population I stars, and give signs of a dependence on the metal abundance at the lowest metallicities. The Mg II k-line widths depend on luminosity and correlate with metallicity. Line profile asymmetries reveal outflows that occur at lower luminosities (M_V = -0.8) than detected in Ca K and H-alpha lines in metal-poor giants, suggesting mass outflow occurs over a larger span of the red giant branch than previously thought, and confirming that the Mg II lines are good wind diagnostics. These results do not support a magnetically dominated chromosphere, but appear more consistent with some sort of hydrodynamic, or acoustic heating of the outer atmospheres.Comment: 36 pages, 12 figures, 7 tables, and accepted for publication in The Astronomical Journa

Modeling Eclipses in the Classical Nova V Persei: The Role of the Accretion Disk Rim

Multicolor (BVRI) light curves of the eclipsing classical nova V Per are presented, and a total of twelve new eclipse timings are measured for the system. When combined with previous eclipse timings from the literature, these timings yield a revised ephemeris for the times of mid-eclipse given by HJD = 2,447,442.8260(1) + 0.107123474(3) E. The eclipse profiles are analyzed with a parameter-fitting model that assumes four sources of luminosity: a white dwarf primary star, a main-sequence secondary star, a flared accretion disk with a rim, and a bright spot at the intersection of the mass-transfer stream and the disk periphery. A matrix of model solutions are computed, covering an extensive range of plausible parameter values. The solution matrix is then explored to determine the optimum values for the fitting parameters and their associated errors. For models that treat the accretion disk as a flat structure without a rim, optimum fits require that the disk have a flat temperature profile. Although models with a truncated inner disk (R_in >> R_wd) result in a steeper temperature profile, steady-state models with a temperature profile characterized by T(r) \propto r^{-3/4} are found only for models with a significant disk rim. A comparison of the observed brightness and color at mid-eclipse with the photometric properties of the best-fitting model suggests that V Per lies at a distance of ~ 1 kpc.Comment: Accepted for publication in The Astrophysical Journal. Thirty-nine pages, including 9 figures. V2 - updated to include additional references and related discussion to previous work overlooked in the original version, and to correct a typo in the ephemeris given in the abstract. V3 - Minor typos corrected. The paper is scheduled for the 20 June 2006 issue of the ApJ. V4 - An error in equation (9) has been corrected. The results presented in the paper were not affected, as all computations were made using the correct formulation of this equatio