Diffusion and consensus on weakly connected directed graphs

Let $G$ be a weakly connected directed graph with asymmetric graph Laplacian ${\cal L}$. Consensus and diffusion are dual dynamical processes defined on $G$ by $\dot x=-{\cal L}x$ for consensus and $\dot p=-p{\cal L}$ for diffusion. We consider both these processes as well their discrete time analogues. We define a basis of row vectors $\{\bar \gamma_i\}_{i=1}^k$ of the left null-space of ${\cal L}$ and a basis of column vectors $\{\gamma_i\}_{i=1}^k$ of the right null-space of ${\cal L}$ in terms of the partition of $G$ into strongly connected components. This allows for complete characterization of the asymptotic behavior of both diffusion and consensus --- discrete and continuous --- in terms of these eigenvectors. As an application of these ideas, we present a treatment of the pagerank algorithm that is dual to the usual one. We further show that the teleporting feature usually included in the algorithm is not strictly necessary. This is a complete and self-contained treatment of the asymptotics of consensus and diffusion on digraphs. Many of the ideas presented here can be found scattered in the literature, though mostly outside mainstream mathematics and not always with complete proofs. This paper seeks to remedy this by providing a compact and accessible survey.Comment: 19 pages, Survey Article, 1 figur

J- and Ks-band Galaxy Counts and Color Distributions in the AKARI North Ecliptic Pole Field

We present the J- and Ks-band galaxy counts and galaxy colors covering 750 square arcminutes in the deep AKARI North Ecliptic Pole (NEP) field, using the FLoridA Multi-object Imaging Near-ir Grism Observational Spectrometer (FLAMINGOS) on the Kitt Peak National Observatory (KPNO) 2.1m telescope. The limiting magnitudes with a signal-to-noise ratio of three in the deepest regions are 21.85 and 20.15 in the J- and Ks-bands respectively in the Vega magnitude system. The J- and Ks-band galaxy counts in the AKARI NEP field are broadly in good agreement with those of other results in the literature, however we find some indication of a change in the galaxy number count slope at J~19.5 and over the magnitude range 18.0 < Ks < 19.5. We interpret this feature as a change in the dominant population at these magnitudes because we also find an associated change in the B - Ks color distribution at these magnitudes where the number of blue samples in the magnitude range 18.5 < Ks < 19.5 is significantly larger than that of Ks < 17.5

A systematic review and meta-analysis on the effect of neoadjuvant chemotherapy on complications following immediate breast reconstruction

Background The impact of neoadjuvant chemotherapy (NACT) on surgical outcomes following immediate breast reconstruction (IBR) remains unclear. While it is generally considered safe practice to perform an IBR post NACT, reported complication rates in published data are highly variable with the majority of studies including fewer than 50 patients in the NACT and IBR arm. To evaluate this further, we conducted a systematic review and meta-analysis on the effect of NACT on autologous and implant based immediate breast reconstructions. We aimed to assess for differences in the post-operative course following IBR between patients who received NACT with those who did not. Methods PubMed, EMBASE, and Cochrane Library were searched from 1995 to Sept 2, 2020 to identify articles that assessed the impact of NACT on IBR. All included studies assessed outcomes following IBR. Only studies comparing reconstructed patients receiving NACT to a control group of women who did not receive NACT were included. Unadjusted relative risk of outcomes between patients who received or did not receive NACT were synthesized using a fixed-effect meta-analysis. The evidence was assessed using the Newcastle Ottawa Scale scores and GRADE. Primary effect measures were risk ratios (RRs) with 95% confidence intervals. Results A total 17 studies comprising 3249 patients were included in the meta-analyses. Overall, NACT did not increase the risk of complications after immediate breast reconstructions (risk ratio [RR]: 0.91, 95% CI 0.74 to 1.11, p = 0.34). There was a moderate, but not significant, increase in flap loss following NACT compared with controls (RR: 1.23, 95% CI 0.70 to 2.18, p = 0.47; I2 = 0%). Most notably, there was a statistically significant increase in implant/expander loss after NACT (RR: 1.54, 95% CI 1.04 to 2.29, p = 0.03; I2 = 34%). NACT was not shown to significantly increase the incidence of hematomas, seromas or wound complications, or result in a significant delay to commencing adjuvant therapy (RR: 1.59, 95% CI 0.66 to 3.87, p = 0.30). Conclusion Immediate breast reconstruction after NACT is a safe procedure with an acceptable post-operative complication profile. It may result in a slight increase in implant loss rates, but it does not delay commencing adjuvant therapy

Inelastic Quantum Transport

We solve a Schrodinger equation for inelastic quantum transport that retains full quantum coherence, in contrast to previous rate or Boltzmann equation approaches. The model Hamiltonian is the zero temperature 1d Holstein model for an electron coupled to optical phonons (polaron), in a strong electric field. The Hilbert space grows exponentially with electron position, forming a non-standard Bethe lattice. We calculate nonperturbatively the transport current, electron-phonon correlations, and quantum diffusion. This system is a toy model for the constantly branching ``wavefunction of the universe''.Comment: revtex, 13 pages, 4 figure

Local Electronic Structure of a Single Magnetic Impurity in a Superconductor

The electronic structure near a single classical magnetic impurity in a superconductor is determined using a fully self-consistent Koster-Slater algorithm. Localized excited states are found within the energy gap which are half electron and half hole. Within a jellium model we find the new result that the spatial structure of the positive-frequency (electron-like) spectral weight (or local density of states), can differ strongly from that of the negative frequency (hole-like) spectral weight. The effect of the impurity on the continuum states above the energy gap is calculated with good spectral resolution for the first time. This is also the first three-dimensional self-consistent calculation for a strong magnetic impurity potential.Comment: 13 pages, RevTex, change in heuristic picture, no change in numerical result

Local Electronic Structure of Defects in Superconductors

The electronic structure near defects (such as impurities) in superconductors is explored using a new, fully self-consistent technique. This technique exploits the short-range nature of the impurity potential and the induced change in the superconducting order parameter to calculate features in the electronic structure down to the atomic scale with unprecedented spectral resolution. Magnetic and non-magnetic static impurity potentials are considered, as well as local alterations in the pairing interaction. Extensions to strong-coupling superconductors and superconductors with anisotropic order parameters are formulated.Comment: RevTex source, 20 pages including 22 figures in text with eps

The First Measurements of Galaxy Clustering from IRAC Data of the Spitzer First Look Survey

We present the first results of the angular auto-correlation function of the galaxies detected by the Infrared Array Camera (IRAC) instrument in the First Look Survey (FLS) of the Spitzer Space Telescope. We detect significant signals of galaxy clustering within the survey area. The angular auto-correlation function of the galaxies detected in each of the four IRAC instrument channels is consistent with a power-law form $w(\theta)=A\theta^{1-\gamma}$ out to \theta = 0.2\arcdeg, with the slope ranging from $\gamma = 1.5$ to 1.8. We estimate the correlation amplitudes $A$ to be $2.95 \times 10^{-3}$, $2.03 \times 10^{-3}$, $4.53 \times 10^{-3}$, and $2.34 \times 10^{-3}$ at \theta=1\arcdeg for galaxies detected in the IRAC 3.6$\mu$m, 4.5$\mu$m, 5.8$\mu$m, and 8.0$\mu$m instrument channels, respectively. We compare our measurements at 3.6$\mu$m with the previous K-band measurements, and discuss the implications of these results.Comment: Accepted for publication in the ApJ Supplements Spitzer Special Issue; 12 pages including 3 figures and 1 tabl

Evidence for a Massive Post-Starburst Galaxy at z ~ 6.5

We present results from a search for high-redshift J--band ``dropout'' galaxies in the portion of the GOODS southern field that is covered by extremely deep imaging from the Hubble Ultradeep Field (HUDF).Using observations at optical, near-infrared and mid-infrared wavelengths from the Hubble and Spitzer Space Telescopes and the ESO-VLT, we search for very massive galaxies at high redshifts and find one particularly remarkable candidate. Its spectral energy distribution is consistent with a galaxy at z ~ 6.5 and a stellar mass of 6x10e11 M(sun) (for a Salpeter IMF). We interpret a prominent photometric break between the near-infrared and Spitzer bandpasses as the 3646A Balmer discontinuity. The best-fitting models have low reddening and ages of several hundred Myr, placing the formation of the bulk of the stars at z > 9. Alternative models of dusty galaxies at z ~ 2.5 are possible but provide significantly poorer fits. The object is detected with Spitzer at 24 micron. This emission originats from an obscured active nucleus or star formation. We present optical and near-infrared spectroscopy which has, thus far, failed to detect any spectral features. This helps limit the solution in which the galaxy is a starburst or active galaxy at z ~ 2.5. If the high-redshift interpretation is correct, this object would be an example of a galaxy that formed by a process strongly resembling traditional models of monolithic collapse, in a way which a very large mass of stars formed within a remarkably short period of time, at very high redshift.Comment: Accepted for publication in Ap.J. 31 pages, 6 diagram

Advances in ab-initio theory of Multiferroics. Materials and mechanisms: modelling and understanding

Within the broad class of multiferroics (compounds showing a coexistence of magnetism and ferroelectricity), we focus on the subclass of "improper electronic ferroelectrics", i.e. correlated materials where electronic degrees of freedom (such as spin, charge or orbital) drive ferroelectricity. In particular, in spin-induced ferroelectrics, there is not only a {\em coexistence} of the two intriguing magnetic and dipolar orders; rather, there is such an intimate link that one drives the other, suggesting a giant magnetoelectric coupling. Via first-principles approaches based on density functional theory, we review the microscopic mechanisms at the basis of multiferroicity in several compounds, ranging from transition metal oxides to organic multiferroics (MFs) to organic-inorganic hybrids (i.e. metal-organic frameworks, MOFs)Comment: 22 pages, 9 figure

A Redshift z=5.4 Lyman alpha Emitting Galaxy with Linear Morphology in the GRAPES/UDF Field

We have discovered an extended Lyman alpha plume associated with a compact source at redshift 5.4 in slitless spectroscopic data from the Grism ACS Program for Extragalactic Science (GRAPES) project. The spatial extent of the emission is about 6 x 1.5 kpc (1 x 0.25 arcsec). Combining our grism data and the broadband images from the Hubble UltraDeep Field (UDF) images, we find a Lyman alpha line flux of 2e-17 erg/cm2/s and surface brightness 7e-17 erg/cm2/s/arcsec2. The UDF images show diffuse continuum emission associated with the Lyman alpha plume (hereafter UDF 5225), with three embedded knots. The morphology of UDF 5225 is highly suggestive of a galaxy in assembly. It is moreover possible that the prominent Lyman alpha emission from this object is due to an active nucleus, and that we are seeing the simultaneous growth through accretion of a galaxy and its central black hole. Followup observations at higher spectral resolution could test this hypothesis.Comment: 14 pages, accepted for publication in the Astrophysical Journa