The Cosmic Mach Number: Comparison from Observations, Numerical Simulations and Nonlinear Predictions

We calculate the cosmic Mach number M - the ratio of the bulk flow of the velocity field on scale R to the velocity dispersion within regions of scale R. M is effectively a measure of the ratio of large-scale to small-scale power and can be a useful tool to constrain the cosmological parameter space. Using a compilation of existing peculiar velocity surveys, we calculate M and compare it to that estimated from mock catalogues extracted from the LasDamas (a LCDM cosmology) numerical simulations. We find agreement with expectations for the LasDamas cosmology at ~ 1.5 sigma CL. We also show that our Mach estimates for the mocks are not biased by selection function effects. To achieve this, we extract dense and nearly-isotropic distributions using Gaussian selection functions with the same width as the characteristic depth of the real surveys, and show that the Mach numbers estimated from the mocks are very similar to the values based on Gaussian profiles of the corresponding widths. We discuss the importance of the survey window functions in estimating their effective depths. We investigate the nonlinear matter power spectrum interpolator PkANN as an alternative to numerical simulations, in the study of Mach number.Comment: 12 pages, 9 figures, 3 table

Approximate MAP Decoding on Tail-Biting Trellises

We propose two approximate algorithms for MAP decoding on tail-biting trellises. The algorithms work on a subset of nodes of the tail-biting trellis, judiciously selected. We report the results of simulations on an AWGN channel using the approximate algorithms on tail-biting trellises for the $(24,12)$ Extended Golay Code and a rate 1/2 convolutional code with memory 6.Comment: 5 pages, 2 figures, ISIT 200

Extramedullary Plasmacytoma of Soft Tissues and Gingiva

Extramedullary plasmacytoma (EMP) is a rare plasma cell neoplasm of soft tissue without bone marrow involvement or other systemic characteristics of multiple myeloma. It accounts for 3% of all plasma cell tumors. Multiple extramedullary plasmacytoma is defined when there is more than one extramedullary tumor of clonal plasma cells and such presentation has not been described earlier. We report such rare case of multiple extramedullary plasmacytoma involving multiple soft tissues in chest, abdomen, mandible, maxilla, and gingiva

ESR measurements of phosphorus dimers in isotopically enriched 28Si silicon

Dopants in silicon have been studied for many decades using optical and electron spin resonance (ESR) spectroscopy. Recently, new features have been observed in the spectra of dopants in isotopically enriched 28Si since the reduced inhomogeneous linewidth in this material improves spectral resolution. With this in mind, we measured ESR on exchange coupled phosphorus dimers in 28Si and report two results. First, a new fine structure is observed in the ESR spectrum arising from state mixing by the hyperfine coupling to the 31P nuclei, which is enhanced when the exchange energy is comparable to the Zeeman energy. This fine structure enables us to spectroscopically address two separate dimer sub-ensembles, the first with exchange (J) coupling ranging from 2 to 7 GHz and the second with J ranging from 6 to 60 GHz. Next, the average spin relaxation times, T1 and T2 of both dimer sub-ensembles were measured using pulsed ESR at 0.35 T. Both T1 and T2 for transitions between triplet states of the dimers were found to be identical to the relaxation times of isolated phosphorus donors in 28Si, with T2 = 4 ms at 1.7 K limited by spectral diffusion due to dipolar interactions with neighboring donor electron spins. This result, consistent with theoretical predictions, implies that an exchange coupling of 2 - 60 GHz does not limit the dimer T1 and T2 in bulk Si at the 10 ms timescale.Comment: 24 pages, 9 figure

Painting galaxies into dark matter halos using machine learning

We develop a machine learning (ML) framework to populate large dark matter-only simulations with baryonic galaxies. Our ML framework takes input halo properties including halo mass, environment, spin, and recent growth history, and outputs central galaxy and halo baryonic properties including stellar mass ($M_*$), star formation rate (SFR), metallicity ($Z$), neutral ($\rm HI$) and molecular ($\rm H_2$) hydrogen mass. We apply this to the MUFASA cosmological hydrodynamic simulation, and show that it recovers the mean trends of output quantities with halo mass highly accurately, including following the sharp drop in SFR and gas in quenched massive galaxies. However, the scatter around the mean relations is under-predicted. Examining galaxies individually, at $z=0$ the stellar mass and metallicity are accurately recovered ($\sigma\lesssim 0.2$~dex), but SFR and $\rm HI$ show larger scatter ($\sigma\gtrsim 0.3$~dex); these values improve somewhat at $z=1,2$. Remarkably, ML quantitatively recovers second parameter trends in galaxy properties, e.g. that galaxies with higher gas content and lower metallicity have higher SFR at a given $M_*$. Testing various ML algorithms, we find that none perform significantly better than the others, nor does ensembling improve performance, likely because none of the algorithms reproduce the large observed scatter around the mean properties. For the random forest algorithm, we find that halo mass and nearby ($\sim 200$~kpc) environment are the most important predictive variables followed by growth history, while halo spin and $\sim$Mpc scale environment are not important. Finally we study the impact of additionally inputting key baryonic properties $M_*$, SFR and $Z$, as would be available e.g. from an equilibrium model, and show that particularly providing the SFR enables $\rm HI$ to be recovered substantially more accurately.Comment: 15 pages, 10 figures, 1 table, accepted version from MNRA

Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems

We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a hybrid dynamical system, nearby executions generically contract superexponentially to a constant-dimensional subsystem. Under a non-degeneracy condition on the rank deficiency of the associated Poincare map, the contraction occurs in finite time regardless of the stability properties of the orbit. Hybrid transitions may be removed from the resulting subsystem via a topological quotient that admits a smooth structure to yield an equivalent smooth dynamical system. We demonstrate reduction of a high-dimensional underactuated mechanical model for terrestrial locomotion, assess structural stability of deadbeat controllers for rhythmic locomotion and manipulation, and derive a normal form for the stability basin of a hybrid oscillator. These applications illustrate the utility of our theoretical results for synthesis and analysis of feedback control laws for rhythmic hybrid behavior